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2 years ago

Find the value of r so that the line through (8,r) and (4,5) has a slope of -4

Mathematics

1 answer:

Ratling [72]2 years ago

7 0

Answer:

r = - 11

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to - 4

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (4, 5) and (x₂, y₂ ) = (8, r)

m = $\frac{r-5}{8-4}$ = $\frac{r-5}{4}$ = - 4 ( multiply both sides by 4 )

r - 5 = - 16 ( add 5 to both sides )

r = - 11

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fenix001 [56]

10: 3
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3 years ago

Can someone show me how to factor this please?

Alex_Xolod [135]

Answer:

$\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}$

Step-by-step explanation:

We want to solve the equation:

$2\sin ^2 \theta + 3\sin \theta + 1 = 0$

In the interval [0, 2π).

Notice that this is in quadratic form. Namely, by letting u = sin(θ), we acquire:

$\displaystyle 2u^2 + 3u + 1 = 0$

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$\displaystyle (2u+1)(u+1) = 0$

By the Zero Product Property:

$\displaystyle 2u + 1 = 0\text{ or } u + 1 = 0$

Solve for each case:

$\displaystyle u = -\frac{1}{2} \text{ or } u = -1$

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$\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}$

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3 years ago

Identify the missing number.<br> X^4 • X^? = X^5

MArishka [77]

Answer:

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Step-by-step explanation:

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3 years ago

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masya89 [10]

Answer:

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2 years ago

I need to get this done

Allushta [10]

Answer:

x = 17 and y = 8

Step-by-step explanation:

Since (6x + 3) and (8x - 31) are alternate interior angles, they are congruent.

Therefore, you can set them equal to each other and solve for x.

8x - 31 = 6x + 3

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Divide both sides by two

x = 17

Since (5y + 35) and (6x + 3) are consecutive interior angles, they add up to 180. Plug in 17 for x.

(5y + 35) + (6(17) + 3) = 180

Add like terms

5y + 140 = 180

5y = 40

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7 0

3 years ago