Given f(x) = 2x + 5 and g(x) = 3x + 6

1 answer:

3 0

• f(x) = 2x + 5

• g(x) = 3x + 6

To evaluate f(g(x)), replace x with g(x) in the equation of f:

f(g(x)) = 2 · g(x) + 5

f(g(x)) = 2 · (3x + 6) + 5

f(g(x)) = 2 · 3x + 2 · 6 + 5

f(g(x)) = 6x + 12 + 5

f(g(x)) = 6x + 17

Therefore,

f(g(8)) = 6 · 8 + 17

f(g(8)) = 48 + 17

f(g(8)) = 65 <———— this is the answer.

I hope this helps! =)

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SOLUTION

Consider the property, opposite angle of a cyclic quadrilateral are supplementary

hence

$\angle NMP+\angle NOP=180^0$

Recall that

$\begin{gathered} \angle NMP=\angle M=(8x-24)^0 \\ \text{and } \\ \angle NOP=\angle O=(4x)^0 \end{gathered}$

Hnece, we have that

$\begin{gathered} \angle M+\angle O=180^0(opposite\text{ angles of a cyclic quadrilateral)} \\ (8x-24)^0+4x^0=180^0 \end{gathered}$

Then

$\begin{gathered} 8x-24+4x=180 \\ 8x+4x-24=180 \\ 12x-24=180 \\ \text{Add 24 t o both sides } \\ 12x-24+24=180+24 \\ 12x=204 \\ \text{divide both sides by 12} \\ \frac{12x}{12}=\frac{204}{12} \\ \text{Then} \\ x=17 \end{gathered}$

Hence

x=17

Since

$\begin{gathered} \angle NOP=(4x)^0 \\ \text{substitute the value of x, we have } \\ \angle NOP=4\times17=68^0 \\ \text{Hence } \\ \angle NOP=68^0 \end{gathered}$

Therefore

The measure of angle NOP is 68⁰

Answer; 68⁰ (The fourth Option )

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1 year ago

Find the value of y for which line a is parallel to line b.

alexdok [17]

Y+38°= 180 beacuse if a and b are parallel they are co interior angles. This means that they will at to 180.

y=180-38= 142°

Answer: 142°

Drew out some hopefully helpful pictures below. Hope they help! let me know if you still have any questions!