if line cd is perpendicular to line EF m angle ECH = (x+5) and m angle HCD = (3x-7) find each missing value x= ECH HCD GCF ECG GCD

Step-by-step explanation:

Given

Solving (a): The value of x

Since CD is perpendicular to EF, then the following relationship exists

Where ECD = 90° and DCF = 90°

Substitute values for ECH, HCD and ECD

Collect like terms

Divide both sides by 4

Solving (b): The value of ECH

Given that

Substitute 23 for x

Solving (c): The value of HCD

Given that

Substitute 23 for x

Solving (d): Solving GCF

GCF and ECH are opposites

Hence,

Solving (e): The value of ECG

Make ECG the subject of formula

Substitute 28 for ECH

Solving (f): The value of GCD

Recall that DCF = 90 and GCF = 28

Part A: 4a-3

Part B: (3a-5b) × (3a+5b)

Step-by-step explanation:

16a² - 24a + 9

(4a)² - 2(4a)(3) + 3²

(4a - 3)² = side²

side = 4a - 3

9a² - 25b²

(3a)² - (5b)²

(3a - 5b)(3a + 5b)