Select all expressions that are equivalent to 16x−12−24x+4. Show or explain your reasoning. 1. 16x - 12(1 + 2x) + 4

2. 40x - 16

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

4. -8(x+1)

the correct one is 1. 16x - 12(1 + 2x) + 4

Step-by-step explanation:

16x−12−24x+4 is equivalent to 8x-8

1.  16x - 12(1 + 2x) + 4 is equivalent to 8x-8

2.  40x-16 is equivalent to 8(5x−2)

3.  4 - 12 + (2x - 3x) is equivalent to −x−8

4.   -8(x+1) is equivalent to −8x−8

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°