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3 years ago

F(x) = 4x^2 + 5x + 3; g(x) = 5x - 7, find g(f(x)).

Mathematics

1 answer:

andrezito [222]3 years ago

5 0

$g(f(x))=5(4x^2+5x+3)-7=20x^2+25x+15-7=20x^2+25x+8$

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Svetlanka [38]

Answer:

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3 years ago

Use identities to find the values of the sine and cosine functions for the following angle measure.

puteri [66]

Using the cosine double angle formula,

$\cos 2\theta=2\cos^2 \theta-1=\frac{12}{13}\\\\2\cos^{2} \theta=\frac{25}{13}\\\\\cos^{2} \theta=\frac{25}{26}\\\\\boxed{\cos \theta=\frac{5}{\sqrt{26}}}$

(Note I took the positive case since $\theta$ terminates in the first quadrant)

Using the Pythagorean identity,

$\sin^2 \theta+\cos^2 \theta=1\\\\\sin^2 \theta+\frac{25}{26}=1\\\\sin^2 \theta=\frac{1}{26}\\\\\boxed{\sin \theta=\frac{1}{\sqrt{26}}}$

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1 year ago

How do you graph -3.5 and -1.5 on the number line?

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find where -3.5 and -1.5 would be on a number line from -5 to 5

Step-by-step explanation:

-5 -4 -3 -2 -1 0 1 2 3 4 5

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3 years ago

Find the quotient. Write the remainder as a decimal.<br> 72)99=

tekilochka [14]

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Step-by-step explanation:

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3 0

3 years ago

triangle is placed in a semicircle with a radius of 8cm, as shown below. Find the area of the shaded region. Use the value 3.14

zhuklara [117]

Answer:

Area of shaded region is $36.48 \ cm^2$ .

Step-by-step explanation:

We have drawn the diagram for your reference.

Given:

radius = 8 cm

Diameter is 2 times radius.

Diameter = $2\times 8 =16 \ cm$

We need to find the Area of shaded region.

Solution:

First we will find the Area of Semicircle.

Now we know that Area of semicircle is half times π times square of radius.

framing in equation for we get;

Area of Semicircle = $\frac{1}{2} \times \pi \times r^2 = \frac{1}{2} \times \pi \times 8^2=100.48\ cm^2$

Now we will find the Area of Triangle.

Now base diameter of the semicircle and height is radius of the circle.

We know that Area of triangle is half times base times height.

framing in equation form we get;

Area of triangle = $\frac{1}{2} \times 16 \times 8 = 64 \ cm^2$

Now Area of the shaded region can be calculated by subtracting Area of triangle from Area of semicircle.

framing in equation form we get;

Area of the shaded region = $100.48 - 64 = 36.48 \ cm^2$

Hence Area of shaded region is $36.48 \ cm^2$ .

6 0

3 years ago