sat math

  1. math_celebrity

    The length of a rectangle is increased by 50% and the width is decreased by 50%. How does the area of the rectangle change?

    A = lw If we increased l by 50%, it would be 1.5l If we decreased w by 50%, it would be 0.5l A = (1.5l)(0.5w) = 0.75lw lw - 0.75lw = 0.25lw or 25% lower
  2. math_celebrity

    If 2^x + 2^x + 2^x + 2^x = 2^16, what is the value of x?

    If 2^x + 2^x + 2^x + 2^x = 2^16, what is the value of x? Add up the left side, we get: 4(2^x) = 2^16 But 4 = 2^2, so we have: 2^2(2^x) = 2^16 Using our exponent rule, we have: 2^(x + 2) = 2^16 x + 2 = 16 Subtract 2 from each side, we get: x = 14
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