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3 years ago

Solve the system by graphing. {-2x=2y-4, 2x-y=-5

Mathematics

1 answer:

Phantasy [73]3 years ago

5 0

x=(2y-4)/-2

x=-y+2

2(-y+2)-y=-5

-2y+4-y=-5

-3y+4=-5

-3y=-9

y=3

x=-y+2

x=-3+2

x=-1

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Estimate the slope of the tangent line of the function y(t)=\sqrt{(3t+1} at the point t=2.

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Answer: 0.567

Step-by-step explanation:

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3 years ago

Simplify the expression by factoring, showing the steps in your work.

alexdok [17]

Given:

$$\frac{12 x^{2}+31 x+7}{16 x^{2}+8 x+1}$

To find:

The simplified expression by factoring.

Solution:

Let us factor the numerator:

$12 x^{2}+31 x+7$

31x can be written as 3x + 28x.

$=\left(12 x^{2}+3 x\right)+(28 x+7)$

Take 3x common in 1st two terms and 7 common in next two terms.

$=3 x(4 x+1)+7(4 x+1)$

Make sure the remaining terms in the both brackets must be same.

Now, take out common factor (4x + 1).

$=(4 x+1)(3 x+7)$

In the same way, factorize the denominator:

$16 x^{2}+8 x+1$

8x can be written as 4x + 4x.

$=(16 x^{2}+4 x)+(4x+1)$

Take 4x common in 1st two terms and 1 common in next two terms.

$=4x(4 x+1)+1(4x+1)$

Make sure the remaining terms in the both brackets must be same.

Now, take out common factor (4x + 1).

$=(4x+1)(4x+1)$

Substitute the terms we found for numerator and denominator:

$$\frac{12 x^{2}+31 x+7}{16 x^{2}+8 x+1}=\frac{(4 x+1)(3 x+7)}{(4 x+1)(4 x+1)}$

Cancel the common factors.

$$=\frac{3 x+7}{4 x+1}$

The simplified expression is $\frac{3 x+7}{4 x+1}$ .

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3 years ago

Read 2 more answers

What is the value of x?

marshall27 [118]

Answer:

x=12

Step-by-step explanation:

Intersecting Chords Formula:

(segment piece) x (segment piece) = (segment piece) x (segment piece)

10 * x = ( 3+x) *8

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Subtract 8x

10x-8x = 24+8x-8x

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Divide by 2

2x/2 =24/2

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