In the △pqr, pq = 39 in, pr = 17 in, and the altitude pn = 15 in. find qr. consider all cases.

  QR = 28 inches or 44 inches

Step-by-step explanation:

In right triangle QNP, the length of QN is given by the Pythagorean theorem as ...

  QP² = QN² +PN²

  QN = √(QP² -PN²) = √(1521 -225) = √1296 = 36

In right triangle RNP, the length of RN is similarly found:

  RN = √(RP² -PN²) = √(289 -225) = √64 = 8

So, we have N on line QR with QN = 36 and RN = 8.

If N is between Q and R, then ...

  QR = QN +NR = 36 +8 = 44

If R is between Q and N, then ...

  QR = QN -NR = 36 -8 = 28

The possible lengths of QR are 28 in and 44 in.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

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step-by-step explanation: