15. change the fraction w – 3 / w + 5 into an equivalent fraction with the denominator w^2 + w – 20.

a. w^2 + 7w – 12 / w^2 + w – 20.

b. w^2 – 7 – 12 / w^2 + w – 20

c. w^2 – 7w + 12 / w^2 + w – 20

d. w^2 + 7w + 12 / w^2 + w – 20

C.

Step-by-step explanation:

We have been given a fraction and we are asked to write the equivalent fraction of our given fraction with the denominator  .

First of all we will divide by to find the expression that we need to multiply with our given fraction to get the denominator

Let us factor out by splitting the middle term

Now we will multiply the numerator and denominator of by to find the equivalent fraction.

Therefore, option C is the correct choice.

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°