Given:
Given: BC = EF AC = EG AB = 10 BC = 3 Prove FG = 10Given: BC = EF
AC = EG
AB = 10
BC = 3
Prove FG = 10
[LIST]
[*]AC = AB + BC (Segment Addition Postulate)
[*]AB = 10, BC = 3 (Given)
[*]AC = 10 + 3 (Substitution Property of Equality)
[*]AC = 13 (Simplify)
[*]AC = EG, BC = EF (Given)
[*]EG = 13, EF = 3 (Segment Equivalence)
[*]EG = EF + FG (Segment Addition Postulate)
[*]13 = 3 + FG (Substitution Property of Equality)
[*]FG = 10 (Subtraction Property)
[/LIST]
Hans rented a truck for one day. There was a base fee of 16.95, and there was an additional charge oHans rented a truck for one day. There was a base fee of 16.95, and there was an additional charge of 76 cents for each mile driven. Hans had to pay 152.99 when he returned the truck. For how many miles did he drive the truck?
Set up the equation where x is the amount of miles he drove:
0.76x + 16.95 = 152.99
[URL='http://www.mathcelebrity.com/1unk.php?num=0.76x%2B16.95%3D152.99&pl=Solve']Plug this equation into our calculator[/URL]:
x = 179 miles
If Ef = 3x,Fg = 2x,and EG = 5If Ef = 3x,Fg = 2x,and EG = 5
By segment addition, we have:
EF + FG = EG
3x + 2x = 5
To solve for x, we t[URL='https://www.mathcelebrity.com/1unk.php?num=3x%2B2x%3D5&pl=Solve']ype this equation into our math engine [/URL]and we get:
x = 1
So EF = 3(1) = [B]3[/B]
FG = 2(1) = [B]2[/B]
If EF = 7x , FG = 3x , and EG = 10 , what is EF?If EF = 7x , FG = 3x , and EG = 10 , what is EF?
By segment addition:
EF + FG = EG
7x + 3x = 10
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=7x%2B3x%3D10&pl=Solve']type it in our search engine[/URL] and we get:
x = 1
Evaluating EF = 7x with x = 1, we get:
EF = 7 * 1
EF = [B]7[/B]
If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG?If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG?
By segment addition, we know that:
EF + FG = EG
Substituting in our values for the 3 segments, we get:
9x - 17 + 17x - 14 = 20x + 17
Group like terms and simplify:
(9 + 17)x + (-17 - 14) = 20x - 17
26x - 31 = 20x - 17
Solve for [I]x[/I] in the equation 26x - 31 = 20x - 17
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 26x and 20x. To do that, we subtract 20x from both sides
26x - 31 - 20x = 20x - 17 - 20x
[SIZE=5][B]Step 2: Cancel 20x on the right side:[/B][/SIZE]
6x - 31 = -17
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants -31 and -17. To do that, we add 31 to both sides
6x - 31 + 31 = -17 + 31
[SIZE=5][B]Step 4: Cancel 31 on the left side:[/B][/SIZE]
6x = 14
[SIZE=5][B]Step 5: Divide each side of the equation by 6[/B][/SIZE]
6x/6 = 14/6
x = [B]2.3333333333333[/B]
If FG = 9, GH = 4x, and FH = 7x, what is GH?If FG = 9, GH = 4x, and FH = 7x, what is GH?
By segment addition, we have:
FG + GH = FH
Substituting in the values given, we have:
9 + 4x = 7x
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%2B4x%3D7x&pl=Solve']type it in our math engine[/URL] and we get:
x = 3
The question asks for GH, so with x = 3, we have:
GH = 4(3)
GH = [B]12[/B]
If FG=11, GH=x-2, and FH=3x-11, what is FHIf FG=11, GH=x-2, and FH=3x-11, what is FH
By segment addition, we have:
FG + GH = FH
11 + x - 2 = 3x - 11
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=11%2Bx-2%3D3x-11&pl=Solve']type it in or math engine[/URL] and we get:
x = 10
FH = 3x - 11. So we substitute x = 10 into this:
FH = 3(10) - 11
FH = 30 - 11
FH = [B]19[/B]
If QR = 16, RS = 4x − 17, and QS = x + 20, what is RS?If QR = 16, RS = 4x − 17, and QS = x + 20, what is RS?
From the segment addition rule, we have:
QR + RS = QS
Plugging our values in for each of these segments, we get:
16 + 4x - 17 = x + 20
To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2B4x-17%3Dx%2B20&pl=Solve']we type it in our search engine[/URL] and we get:
x = 7
Take x = 7 and substitute it into RS:
RS = 4x - 17
RS = 4(7) - 17
RS = 28 - 17
RS = [B]11[/B]
if you buy 50 bales of hay at $3.56 each, and then buy an additional 234 bales at $3.33 each, how muif you buy 50 bales of hay at $3.56 each, and then buy an additional 234 bales at $3.33 each, how much do you pay for the entire lot of 284 bales?
Since cost = price * quantity, we have:
Total lot cost = price(1) of hay * bales(1) of hay + price(2) of hay * bales(2) of hay
Total lot cost = 3.56 * 50 + 3.33 * 24
Total lot cost = 178 + 79.92
Total lot cost = [B]257.92[/B]
In 2013, a local Dairy Queen had $502,000 in sales. In 2014, that same locations sales were up an adIn 2013, a local Dairy Queen had $502,000 in sales. In 2014, that same locations sales were up an additional 43%. What was this Dairy Queens total sales in 2014?
2014 Sales = 2013 Sales * 1.43
2014 Sales = 502,000 * 1.43
2014 Sales = [B]717,860[/B]
Isabel will run less than 36 minutes today. So far, she has run 22 minutes. What are the possible nuIsabel will run less than 36 minutes today. So far, she has run 22 minutes. What are the possible numbers of additional minutes she will run?
Set up our inequality. If she ran 22 minutes, we need to find an expression to find out the remaining minutes
x + 22 < 36
Subtract 22 from each side:
x < 14
Remember, she cannot run negative minutes, so our lower bound is 0, so we have:
[B]0 < x < 14
[/B]
It takes 3 city snowplows 14 hours to clear 500 miles of road. If the city wants the 500 miles of roIt takes 3 city snowplows 14 hours to clear 500 miles of road. If the city wants the 500 miles of road to be cleared in 6 hours, how many additional snowplows must they buy?
Set up unit rate per plow:
14 hours * 3 plows = 42 hours for one plow to clear 500 miles of road
Calculate the amount of plows we need:
42 hours / 6 hours = 7 plows
Additional plows = New plows - original plows:
Additional plows = 7 - 3
Additional plows = [B]4[/B]
It takes a crew of 4 painters 12 hours one house. If they wanted to paint the house in 8 hours, howIt takes a crew of 4 painters 12 hours one house. If they wanted to paint the house in 8 hours, how many additional painters must they hire?
It takes one painter 4 * 12 hours = 48 hours to paint the house.
Now we calculate the unit rate:
48 hours / 8 hours = 6 painters
6 painters - 4 original painters = [B]2 additional painters[/B]
Jessica has 16 pairs of shoes. She buys 2 additional pair of shoes every month. What is the slope inJessica has 16 pairs of shoes. She buys 2 additional pair of shoes every month. What is the slope in this situation?
Set up a graph where months is on the x-axis and number of shoes Jessica owns is on the y-axis.
[LIST=1]
[*]Month 1 = (1, 18)
[*]Month 2 = (2, 20)
[*]Month 3 = (3, 22)
[*]Month 4 = (4, 24)
[/LIST]
You can see for every 1 unit move in x, we get a 2 unit move in y.
Pick any of these 2 points, and [URL='https://www.mathcelebrity.com/slope.php?xone=3&yone=22&slope=+2%2F5&xtwo=4&ytwo=24&pl=You+entered+2+points']use our slope calculator[/URL] to get:
Slope = [B]2[/B]
Joe is paid a 4% commission on all his sales in addition to a $500 per month salary. In May, his salJoe is paid a 4% commission on all his sales in addition to a $500 per month salary. In May, his sales were $100,235. How much money did he earn in May?
[U]The commission and salary formula is:[/U]
Earnings = Salary + Commission Percent * Sales
Plugging in our numbers with 4% as 0.04, we get:
Earnings = 500 + 0.04 * 100235
Earnings = 500 + 4009.40
Earnings = [B]4,509.40[/B]
Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages andJulia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and .10 cents for additional texts. How many texts did she send out?
Let m be the number of messages. We have a cost function of:
C(m) = 9 + 0.1(m - 600)
We are given C(m) = 18.20
18.20 = 9 + 0.1(m - 600)
18.20 = 9 + 0.1m - 60
Combine like terms:
18.20 = 0.1m - 51
Add 51 to each side
0.1m = 69.20
Divide each side by 0.1
[B]m = 692[/B]
Julio has $150. Each week, he saves an additional $10. Write a function f(x) that models the total aJulio has $150. Each week, he saves an additional $10. Write a function f(x) that models the total amount of money Julio has after x weeks
f(x) = Savings per week * number of weeks + starting amount
f(x) = [B]10x + 150[/B]
kira will spend less than 27 on gifts. so far, she has spent 12$. what are the possible additional akira will spend less than 27 on gifts. so far, she has spent 12$. what are the possible additional amounts she will spend?
The key word in this problem is [I]less than[/I]. So we know this is an inequality.
Let s be Kira's possible spend. We have:
s + 12 < 27
To solve for s in this inequality, we subtract 12 from each side:
s + 12 - 12 < 27 - 12
Cancel the 12's on the left side, and we get:
[B]s < 15
[/B]
[I]The summary here is Kira can spend anything up to [U]but not including[/U] 15[/I]
KL=4, and JK=9 Find JLKL=4, and JK=9 Find JL
Using segment addition, we know that:
JL = JK + KL
JL = 9 + 4
JL = [B]13[/B]
Last month, a parking lot had 23 spaces in each of its rows. Recently, the lost was expanded, and 4Last month, a parking lot had 23 spaces in each of its rows. Recently, the lost was expanded, and 4 spaces were added to each row. If the lot has 8 rows, how many spaces are there now?
23 spaces + 4 additional spaces = 27 spaces
27 spaces * 8 rows = [B]216 spaces[/B]
LogarithmsFree Logarithms Calculator - Using the formula Log ab = e, this calculates the 3 pieces of a logarithm equation:
1) Base (b)
2) Exponent
3) Log Result
In addition, it converts
* Expand logarithmic expressions
M is the midpoint of AB. Prove AB = 2AMM is the midpoint of AB. Prove AB = 2AM
M is the midpoint of AB (Given)
AM = MB (Definition of Congruent Segments)
AM + MB = AB (Segment Addition Postulate)
AM + AM = AB (Substitution Property of Equality)
2AM = AB (Distributive property)
[MEDIA=youtube]8BNo_4kvBzw[/MEDIA]
Maria called her sister long distance on Wednesday. The first 5 minutes cost $3, and each minute aftMaria called her sister long distance on Wednesday. The first 5 minutes cost $3, and each minute after that cost $0.25. How much did it cost if they talked for 15 minutes?
First 5 minutes: $3
If they talked 15 minutes, the additional charge past 5 minutes is:
0.25 * (15 - 5)
0.25 * 10 minutes = $2.5
We add this to the first 5 minutes:
$3 + $2.5 = [B]$5.50[/B]
Maria is saving money to buy a bike that cost 133$. She has 42$ and will save an additional 7 each wMaria is saving money to buy a bike that cost 133$. She has 42$ and will save an additional 7 each week.
Set up an equation with w as the number of weeks. We want to find w such that:
7w + 42 = 133
[URL='https://www.mathcelebrity.com/1unk.php?num=7w%2B42%3D133&pl=Solve']Typing this equation into our search engine[/URL], we get:
w = [B]13[/B]
Mary spent a total of $291.94 for a party. She spent $200.29 on food, plus an additional $30.55 forMary spent a total of $291.94 for a party. She spent $200.29 on food, plus an additional $30.55 for each hour of the party. How long was the party?
First, figure out the remaining cost after food:
291.94 -200.29 = 91.65
91.65 / 30.55 per hour = 3 hours
Mr. Crimmins bought 15 apples and 15 oranges. Each apple cost $1.00, each orange cost $1.50. How mucMr. Crimmins bought 15 apples and 15 oranges. Each apple cost $1.00, each orange cost $1.50. How much more did he spend on oranges than apples?
[U]Calculate apple spend:[/U]
Apple Spend = Apple Cost * Number of Apples
Apple Spend = $1.00 * 15
Apple Spend =[B] [/B]$15
[B][/B]
[U]Calculate apple spend:[/U]
Orange Spend = Orange Cost * Number of Oranges
Orange Spend = $1.50 * 15
Orange Spend = $22.50
[B][/B]
[U]Calculate the additional amount spent on oranges over apples:[/U]
Additional Orange Spend = Orange Spend - Apple Spend
Additional Orange Spend = $22.50 - $15.00
Additional Orange Spend = [B]$7.50[/B]
Multiple Fractions (Addition or Ordering)Free Multiple Fractions (Addition or Ordering) Calculator - This adds 3 or more fractions or arranges a list of fractions from lowest to highest and highest to lowest (ordering fractions or sorting fractions)
Name the property shown. 6 + 5 + 84 = 84 + 5 + 6Name the property shown. 6 + 5 + 84 = 84 + 5 + 6
[B]
Commutative property of addition[/B]
Natalie made a deal with a farmer. She agreed to work for an entire year and in return, the farmer wNatalie made a deal with a farmer. She agreed to work for an entire year and in return, the farmer would give her $10,200 plus a prize pig.
After working for 5 months, Natalie decided to quit. The farmer determined that 5 months of work was equal to $3375 plus the pig. How much money was the pig worth?
The value of a year's work is $10,200 plus a pig of unknown value. The farmer took away $6825 because Natalie worked 5 months. If Natalie worked 7 more months, she would have been paid the additional $6825.
6825/7 months work = $975 per month
A full year's work is $975 * 12 = $11,700
Pig value = Full years work - payout
Pig value = 11,700 - 10,200
Pig value = [B]1,500[/B]
Number BondsFree Number Bonds Calculator - Adds or subtracts 2 numbers and using grouping by 10 or 100. Also called number bonds or addition facts. Multiplies two numbers using tape diagrams.
Oscar makes a large purchase at Home Depot and plans to rent one of its trucks to take his suppliesOscar makes a large purchase at Home Depot and plans to rent one of its trucks to take his supplies home. The most he wants to spend on the truck is $56.00. If Home Depot charges $17.00 for the first 75 minutes and $5.00 for each additional 15 min, for how long can Oscar keep the truck and remain within his budget?
Set up the cost equation C(m) where m is the number of minutes for rental:
C(m) = 17 * min(m, 75) + max(0, 5(m - 75))
If Oscar uses the first 75 minutes, he spends $17. So he's left with:
$56 - $17 = $38
$38 / $5 = 7 Remainder 3
We remove the remainder 3, since it's not a full 15 minute block. So Oscar can rent the truck for:
7 * 15 minute blocks = [B]105 minutes[/B]
Percent MathFree Percent Math Calculator - Simplifies expressions involving numbers and percents with respect to addition and subtraction
Pete ate 1/2 a pizza, Carol ate 1/3, and Joe ate 1/4. How much pizza was eaten?Pete ate 1/2 a pizza, Carol ate 1/3, and Joe ate 1/4. How much pizza was eaten?
Total pizza eaten is:
1/2 + 1/3 + 1/4
We need a common denominator. List out factors:
2: 1, 2, 4, 6, 8, 10, 12
3: 1, 3, 6, 9, 12
4: 1, 4, 8, 12
12 is our least common multiple:
1/2 = 6/12
1/3 = 4/12
1/4 = 3/12
So our addition becomes:
(6 + 4 + 3)/12 = 13/12 of a pizza
PQ=3.7 and PR=14.1 what is QRPQ=3.7 and PR=14.1 what is QR
QR = PR - PQ by segment addition
QR = 14.1 - 3.7
QR = [B]10.4[/B]
Prove the sum of any two rational numbers is rationalTake two integers, r and s.
We can write r as a/b for integers a and b since a rational number can be written as a quotient of integers
We can write s as c/d for integers c and d since a rational number can be written as a quotient of integers
Add r and s:
r + s = a/b + c/d
With a common denominator bd, we have:
r + s = (ad + bc)/bd
Because a, b, c, and d are integers, ad + bc is an integer since rational numbers are closed under addition and multiplication.
Since b and d are non-zero integers, bd is a non-zero integer.
Since we have the quotient of 2 integers, r + s is a rational number.
[MEDIA=youtube]0ugZSICt_bQ[/MEDIA]
Puzzle MasterFree Puzzle Master Calculator - A link to our friends: Puzzle Master has a large and unique collection of brain teasers; puzzles for sale. In addition they also carry chess,mechanical banks, puzzle books, magic trick books, boomerangs, etc.
Pythagorean TheoremFree Pythagorean Theorem Calculator - Figures out based on user entry the missing side or missing hypotenuse of a right triangle. In addition, the calculator shows the proof of the Pythagorean Theorem and then determines by numerical evaluation if the 2 sides and hypotenuse you entered are a right triangle using the Pythagorean Theorem
Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR?Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR?
From segment addition, we know that:
PQ + QR = PR
Plugging our given numbers in, we get:
2.7 + QR = 6.1
Subtract 2.7 from each side, and we get:
2.7 - 2.7 + QR = 6.1 - 2.7
Cancelling the 2.7 on the left side, we get:
QR = [B]3.4[/B]
Rafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every cRafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every copy of Math is Fun he sells. Let p represent his total pay (in dollars), and let c represent the number of copies of Math is Fun he sells. Write an equation relating to . Then use this equation to find his total pay if he sells 22 copies of Math is Fun.
We want a sales function p where c is the number of copies of Math is Fun
p = Price per sale * c + Base Salary
[B]p = 40c + 1900
[/B]
Now, we want to know Total pay if c = 22
p = 40(22) + 1900
p = 880 + 1900
p = [B]2780[/B]
Rita has spent $16 so far on gifts. The additional amount she will spend will be less than $14. WhatRita has spent $16 so far on gifts. The additional amount she will spend will be less than $14. What are the possible total amounts she will spend?
Rita will spend at least another cent on other gifts above the $16 she spent so far, but no more than $14. Also, the problem says less than 14. 16 + 14 is 30, so that is the top end of her spending.
Let's say her remaining spending is s. Set up the inequality for possible spending values.
[B]16 < s < 30[/B]
Ruth has already jarred 3 liters of jam and will jar an additional 1 liter of jam everyday. How muchRuth has already jarred 3 liters of jam and will jar an additional 1 liter of jam everyday. How much jam did Ruth jar if she spent 7 days making jam?
7 days at 1 liter = 7 x 1 = 7.
Add that 7 to our original 3 and we have, 7 + 3 = 10 liters of jam.
She ordered 6 large pizzas. Luckily, she had a coupon for 3 off each pizza. If the bill came to 38.9She ordered 6 large pizzas. Luckily, she had a coupon for 3 off each pizza. If the bill came to 38.94, what was the price for a large pizza?
[U]Determine additional amount the pizzas would have cost without the coupon[/U]
6 pizzas * 3 per pizza = 18
[U]Add 18 to our discount price of 38.94[/U]
Full price for 6 large pizzas = 38.94 + 18
Full price for 6 large pizzas = 56.94
Let x = full price per pizza before the discount. Set up our equation:
6x = 56.94
Divide each side by 6
[B]x = $9.49[/B]
Signed Integer OperationsFree Signed Integer Operations Calculator - This performs a string of signed integer operations, either all addition and subtraction, or all multiplication and division.
Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cSoda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point.
Calculate the revenue function R(c) where s is the number of sodas sold:
R(s) = Sale Price * number of units sold
R(s) = 50s
Calculate the cost function C(s) where s is the number of sodas sold:
C(s) = Variable Cost * s + Fixed Cost
C(s) = 0.25s + 900
Our break-even point is found by setting R(s) = C(s):
0.25s + 900 = 50s
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B900%3D50s&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]18.09[/B]
Survival RatesFree Survival Rates Calculator - Given a set of times and survival population counts, the calculator will determine the following:
Survival Population lx
Mortality Population dx
Survival Probability px
Mortality Probability qx
In addition, the calculator will determine the probability of survival from tx to tx + n
The charge to rent a trailer is $30 for up to 2 hours plus $9 per additional hour or portion of anThe charge to rent a trailer is $30 for up to 2 hours plus $9 per additional hour or portion of an hour. Find the cost to rent a trailer for 2.4 hours, 3 hours, and 8.5 hours.
Set up the cost function C(h), where h is the number of hours to rent the trailer. We have, for any hours greater than 2:
C(h) = 30 + 9(h - 2)
Simplified, we have:
C(h) = 9h - 18 + 30
C(h) = 9h + 12
The question asks for C(2.4), C(3), and C(8.5)
[U]Find C(2.4)[/U]
C(2.4) = 9(2.4) + 12
C(2.4) = 21.6 + 12
C(2.4) = [B]33.6
[/B]
[U]Find C(3)[/U]
C(3) = 9(3) + 12
C(3) = 27 + 12
C(2.4) = [B][B]39[/B][/B]
[U]Find C(8.5)[/U]
C(8.5) = 9(8.5) + 12
C(8.5) = 76.5 + 12
C(8.5) = [B]88.5[/B]
The cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is theThe cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the total cost to park for 5 hours?
Set up our equation where C is cost and h is the number of hours used to park
C = 1.5h + 2.25
With h = 5, we have:
C = 1.5(5) + 2.25
C = 7.5 + 2.25
C = 9.75
The cost of a taxi ride is $1.2 for the first mile and $0.85 for each additional mile or part thereoThe cost of a taxi ride is $1.2 for the first mile and $0.85 for each additional mile or part thereof. Find the maximum distance we can ride if we have $20.75.
We set up the cost function C(m) where m is the number of miles:
C(m) = Cost per mile after first mile * m + Cost of first mile
C(m) = 0.8(m - 1) + 1.2
C(m) = 0.8m - 0.8 + 1.2
C(m) = 0.8m - 0.4
We want to know m when C(m) = 20.75
0.8m - 0.4 = 20.75
[URL='https://www.mathcelebrity.com/1unk.php?num=0.8m-0.4%3D20.75&pl=Solve']Typing this equation into our math engine[/URL], we get:
m = 26.4375
The maximum distance we can ride in full miles is [B]26 miles[/B]
The cost of renting a rototiller is $19.50 for the first hour and $7.95 for each additional hour. HoThe cost of renting a rototiller is $19.50 for the first hour and $7.95 for each additional hour. How long can a person have the rototiller if the cost must be less than $95?
Setup the inequality:
$19.50 + $7.95x < $95
Subtract 19.50 from both sides:
7.95x < 75.50
Divide each side of the inequality by 7.95 to isolate x
x < 9.5
The next lowest integer is 9. So we take 9 + the first hour of renting to get [B]10 total hours[/B].
Check our work:
$7.95 * 9.5 + $19.50
$71.55 + $19.50 = $91.05
The first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The secoThe first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The second plan had a $21 monthly fee and charges an additional $.10 for each minute of calls. For how many minutes of calls will the cost of the two plans be equal?
Set up the cost equation C(m) for the first plan, where m is the amount of minutes you use
C(m) = 0.14m + 14
Set up the cost equation C(m) for the second plan, where m is the amount of minutes you use
C(m) = 0.10m + 21
Set them equal to each other:
0.14m + 14 = 0.10m + 21
[URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B14%3D0.10m%2B21&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = [B]175[/B]
The next number in the series 2,5,11,20,32,47, isThe next number in the series 2,5,11,20,32,47, is
[LIST]
[*]2 + 3 = 5
[*]5 + 6 = 11
[*]11 + 9 = 20
[*]20 + 12 = 32
[*]32 + 15 = 47
[/LIST]
Notice the addition pattern:
3, 6, 9, 12, 15
This means our next term is:
47 + (15 + 3)
47 + 18
[B]65
[MEDIA=youtube]mAj3tqXUbZs[/MEDIA][/B]
The volleyball team and the wrestling team at Clarksville High School are having a joint car wash tThe volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past, and they are making $2 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take?
Set up the earnings equation for the volleyball team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 4w + 81
Set up the earnings equation for the wrestling team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 2w + 85
If the raised the same amount in total, set both earnings equations equal to each other:
4w + 81 = 2w + 85
Solve for [I]w[/I] in the equation 4w + 81 = 2w + 85
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides
4w + 81 - 2w = 2w + 85 - 2w
[SIZE=5][B]Step 2: Cancel 2w on the right side:[/B][/SIZE]
2w + 81 = 85
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 81 and 85. To do that, we subtract 81 from both sides
2w + 81 - 81 = 85 - 81
[SIZE=5][B]Step 4: Cancel 81 on the left side:[/B][/SIZE]
2w = 4
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2w/2 = 4/2
w = [B]2 <-- How many cars it will take
[/B]
To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2:
E = 4(2) + 81
E = 8 + 81
E = [B]89 <-- Total Earnings[/B]
There are 50 pairs of pants. One-half of the pants are black. One-fifth of the pants are tan. How maThere are 50 pairs of pants. One-half of the pants are black. One-fifth of the pants are tan. How many pairs of pants are not black or tan.
First, determine what fraction of pants are black and tan:
1/2 + 1/5
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F2&frac2=1%2F5&pl=Add']fraction addition calculator[/URL], we get 7/10.
So the rest of the pants are 1 - 7/10.
1 can be written as 10/10.
So we have 10/10 - 7/10 = 3/10
3/10 * 50 = 150/10 = [B]15[/B]
Three people went to lunch and bought a large meal which they all split. The total cost, including tThree people went to lunch and bought a large meal which they all split. The total cost, including tip, was $30. Each person paid $10 to the waitress and started to leave the restaurant. As they left, the waitress came running up to them with five dollars saying that she made a mistake and that the meal and tip should have cost only $25.
The waitress then gave each person one dollar, but didn't know how to split the remaining two dollars. They told her to keep the extra two dollars as an additional tip.
When the people started talking about what had just happened, they started getting confused. They had each paid $10 for the meal and received one dollar back, so they each really paid $9 for the meal for a total of $27. Add the two dollars of extra tip and the total is $29. Where did the extra one dollar go?
[B]The missing dollar is not really missing. The cost of the meal is really $27. The $25 plus the extra two dollar tip was given to the waitress -- $27
What we have is the cost ($27) plus the refund ($3) = $30.
The $30 that was originally paid is accounted for as follows:
Restaurant + regular waitress tip: $25
Three people: $3 (refund)
Waitress: $2 (extra tip)
$25 + $3 + $2 = $30[/B]
To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional poTo ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional pound. To ship a package with FedEx, the cost will be $5 for the first pound and $0.30 for each additional pound. How many pounds will it take for UPS and FedEx to cost the same? If you needed to ship a package that weighs 8 lbs, which shipping company would you choose and how much would you pay?
[U]UPS: Set up the cost function C(p) where p is the number of pounds:[/U]
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.2(p - 1) + 7
[U]FedEx: Set up the cost function C(p) where p is the number of pounds:[/U]
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.3(p - 1) + 5
[U]When will the costs equal each other? Set the cost functions equal to each other:[/U]
0.2(p - 1) + 7 = 0.3(p - 1) + 5
0.2p - 0.2 + 7 = 0.3p - 0.3 + 5
0.2p + 6.8 = 0.3p + 4.7
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B6.8%3D0.3p%2B4.7&pl=Solve']type it in our search engine[/URL] and we get:
p = [B]21
So at 21 pounds, both UPS and FedEx costs are equal
[/B]
Now, find out which shipping company has a better rate at 8 pounds:
[U]UPS:[/U]
C(8) = 0.2(8 - 1) + 7
C(8) = 0.2(7) + 7
C(8) = 1.4 + 7
C(8) = 8.4
[U]FedEx:[/U]
C(8) = 0.3(8 - 1) + 5
C(8) = 0.3(7) + 5
C(8) = 2.1 + 5
C(8) = [B]7.1[/B]
[B]Therefore, FedEx is the better cost at 8 pounds since the cost is lower[/B]
[B][/B]
True False EquationsFree True False Equations Calculator - Determines if a set of addition and subtraction of numbers on each side of an equation are equivalent.
Also known as true or false equations
Tyrese’s sister is 41 inches tall. A ride at the amusement park states that riders must be at leastTyrese’s sister is 41 inches tall. A ride at the amusement park states that riders must be at least 52 inches tall to ride. Which statements describe how much taller Tyrese’s sister must be to ride?
Let h be the required additional height.
The phrase [I]at least[/I] means an inequality, using the >= sign, so we have:
h + 41 >= 52
If we want another way to express this, we [URL='https://www.mathcelebrity.com/1unk.php?num=h%2B41%3E%3D52&pl=Solve']type this inequality into our math engine[/URL] and we get:
[B]h >= 11[/B]
VectorsFree Vectors Calculator - Given 2 vectors A and B, this calculates:
* Length (magnitude) of A = ||A||
* Length (magnitude) of B = ||B||
* Sum of A and B = A + B (addition)
* Difference of A and B = A - B (subtraction)
* Dot Product of vectors A and B = A x B
A ÷ B (division)
* Distance between A and B = AB
* Angle between A and B = θ
* Unit Vector U of A.
* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).
* Cauchy-Schwarz Inequality
* The orthogonal projection of A on to B, projBA and and the vector component of A orthogonal to B → A - projBA
Also calculates the horizontal component and vertical component of a 2-D vector.
Whitney has already baked 2 cakes, and she can bake 1 cake with each additional stick of butter sheWhitney has already baked 2 cakes, and she can bake 1 cake with each additional stick of butter she buys. Write an equation that shows the relationship between the number of additional sticks of butter s and the number of cakes c.
[LIST]
[*]Let c, the number of cakes, be represented by f(s) where s are the number of sticks of butter.
[*]We already have 2 cakes to start, and each additional stick of butter gets us one more cake.
[/LIST]
f(s) = 1s + 2
Simplify, since 1s is just s
[B]f(s) = s + 2[/B]
writing and solving equationsMy daughter is having issues with a math problem for her homework. she tells me that I am doing it wrong but I am getting the correct answer... Can you please look at it and see if i am correct?
The problem is:
A painter charges $15.35 per hour, plus an additional amount for supplies. If he made $141.73 on a job where he worked 4 hours, how much did the supplies cost?
I have the equation as: $15.35 * 4 = $141.73 - x ... I got the answer of $80.33 for supplies
She is telling me that the teacher is wanting her to do the PEMDAS backwards but that is not working out for her and I am not understanding that at all. Any suggestions would help out
Thanks,
Tina
You are baking muffins for your class. There are 17 total students in your class and you have bakedYou are baking muffins for your class. There are 17 total students in your class and you have baked 5 muffins. Write and solve an equation to find the additional number x of muffins you need to bake in order to have 2 muffins for each student. Write your equation so that the units on each side of the equation are muffins per student.
2 muffins per student = 17*2 = 34 muffins.
We have an equation with a given 5 muffins, how much do we need (x) to get to 34 muffins (2 per student):
x + 5 = 34
To solve for x, we type this equation into our search engine and we get:
x = [B]29[/B]
You are baking muffins for your class. There are 17 total students in your class and you have bakedYou are baking muffins for your class. There are 17 total students in your class and you have baked 5 muffins. Write and solve an equation to find the additional number x of muffins you need to bake in order to have 2 muffins for each student. Write your equation so that the units on each side of the equation are muffins per student.
[U]Calculate total muffins:[/U]
Total muffins = 2 muffins per student * 17 students
Total muffins = 34
[U]Set up the equation using x for muffins:[/U]
[B]x + 5 = 34
[/B]
[U]To Solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B5%3D34&pl=Solve']type it in our search engine[/URL] and we get:[/U]
x = [B]29
[/B]
You are parking your car in a garage. The first hour is free but every additional hour is 2 dollars.You are parking your car in a garage. The first hour is free but every additional hour is 2 dollars. You parked for 3.25 hours. What is the cost?
[U]Calculate the number of paid hours:[/U]
Paid Hours = Total Hours - 1 (since first hour is free)
Paid Hours = 3.25 - 1
Paid Hours = 2.25
[U]Calculate the total cost:[/U]
Total Cost = Hourly Rate * Paid Hours
Total Cost = 2 * 2.25
Paid Hours = [B]$4.50[/B]
You started this year with $491 saved and you continue to save an additional $11 per month. Write anYou started this year with $491 saved and you continue to save an additional $11 per month. Write an algebraic expression to represent the total amount of money saved after m months.
Set up a savings function for m months
[B]S(m) = 491 + 11m[/B]
You work for a remote manufacturing plant and have been asked to provide some data about the cost ofYou work for a remote manufacturing plant and have been asked to provide some data about the cost of specific amounts of remote each remote, r, costs $3 to make, in addition to $2000 for labor. Write an expression to represent the total cost of manufacturing a remote. Then, use the expression to answer the following question. What is the cost of producing 2000 remote controls?
We've got 2 questions here.
Question 1: We want the cost function C(r) where r is the number of remotes:
C(r) = Variable Cost per unit * r units + Fixed Cost (labor)
[B]C(r) = 3r + 2000
[/B]
Question 2: What is the cost of producing 2000 remote controls.
In this case, r = 2000, so we want C(2000)
C(2000) = 3(2000) + 2000
C(2000) = 6000 + 2000
C(2000) = [B]$8000[/B]