If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the second equation is substituted into the first equation. 2x − 3y = −29 x + 4y = 13 (6 points) Select one: a. 2(4y + 13) − 3y = −29 b. 2(−4y + 13) − 3y = −29 c. 2x − 3(4y + 13) = −29 d. 2x − 3(−4y + 13) = −29

9514 1404 393

  3)  D

  4)  D

  5)  B

  6)  B

Step-by-step explanation:

3) A "Pythagorean triple" is a set of 3 integers that could be the sides of a right triangle. The only triangle shown with integer side lengths is choice D.

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5) The only triangle for which the square of the hypotenuse is the sum of the squares of the other two sides is choice D.

  11² +2² = (5√5)²

  121 + 4 = 125

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6) The lengths of sides of each right triangle are 2/3 of those of choice D in problem 4. That is, they are a 7-24-25 triangle, multiplied by 2. That means the height is 24·2 = 48, and the area is ...

  A = 1/2bh

  A = 1/2(28 m)(48 m) = 672 m² . . . . matches choice B

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7) The side lengths of a 30-60-90 triangle have the ratios 1 : √3 : 2. That is, the short leg is half the hypotenuse, a fact stated in A and D. Those true statements make it clear that statement B is false.