Question

Can someone please help me on these two?

Answer 1

Guided Practice 4: QR = 7.12

Guided Practice 5: x = 15

Explanation:

Guided Practice 4:

Given that:

PR =
`13 (3)/(4) ft = 13.75 ft`

PQ =
`6(5)/(8) ft = 6.63ft`

QR = ?

PQ + QR = PR

6.63 + QR = 13.75

Subtract 6.63 from both sides of the equation to solve for QR:

6.63 - 6.63 + QR = 13.75 - 6.63

QR = 7.12

Check if QR is valid:

PQ + QR = PR

6.63 + 7.12 = 13.75

13.75 = 13.75 (true statement).

Guided Practice 5:

Given that:

AC = 4x - 12

AB = x

BC = 2x + 3

AB + BC = AC

x + (2x + 3) = 4x - 12

Combine like terms:

3x + 3 = 4x - 12

Add 12 on both sides of the equation:

3x + 3 + 12 = 4x - 12 + 12

3x + 15 = 4x

Subtract 3x from both sides of the equation:

3x - 3x + 15 = 4x - 3x

15 = x

Check if AB = x is valid by plugging in 15 to x values in the equation:

AB + BC = AC

15 + 2(15) + 3 = 4(15) - 12

15 + 30 + 3 = 60 - 12

48 = 48 (True statement)