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Lana71 [14]
2 years ago
11

The rational function has a y-intercept of 7. What is the equation for this function?

Mathematics
1 answer:
Schach [20]2 years ago
0 0

Answer:

\large\boxed{f(x)=\dfrac{4}{x+2}+5}

Step-by-step explanation:

f(x)=\dfrac{a}{x-b}+c\\\\\text{We have}\\\text{(1) the vertical asymptote}\ x=-2.\ \text{Therefore}\ b=-2.\\\text{(2) the horizontal asymptote}\ y=5.\ \text{Therefore}\ c=5.\\\text{(3) the point (0, 7). Put the coordinates of the point to the equation}\\\text{of the function}\\y=\dfrac{a}{x-(-2)}+5\\\\7=\dfrac{a}{0+2}+5\qquad\text{subtract 5 from both sides}\\\\2=\dfrac{a}{2}\qquad\text{multiply both sides by 2}\\\\4=a\to a=4\\\\\text{Finally:}\\\\f(x)=\dfrac{4}{x+2}+5

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Vladimir79 [104]

Answer:

2005 points

Step-by-step explanation:

1. 35x50=750

2. 2 min. 45 sec.=(-165 sec.)

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6 0
2 years ago
Vector C has a magnitude of 22.2 m and points in the −y‑ direction. Vectors A and B both have positive y‑ components, and make a
natali 33 [55]

Answer:

The magnitude of A is 17.46 m and B is 1.50 m

Step-by-step explanation:

If the vector sum A+B+C =0, then the sum of the projection of the vector in axes x- is zero and the sum of the projection of the vector in the axes y- is also zero.

Ax+Bx+Cx = 0

Ay+By+Cy = 0

|Ax| = cos 41.9 * |A|

|Ay| = sin 41.9 * |A|

|Bx| = cos 28.2 * |B|

|By| = sin 28.2 * |B|

|Cx| = 0

|Cy| = 22.2

Ax+Bx+Cx = 0

|Ax|-|Bx|+0 =0

the vector Ax is in the positive direction of the x- axes and Bx in the negative direction and C do not have a component in the x- axes

cos 41.9 * |A| - cos 28.2 * |B| = 0 (I)

Ay+By+Cy = 0

|Ay|+|By|-|Cy|=0

the vector Ay and By are the positive direction of the y- axes and Cy in the negative direction

sin 41.9 * |A| + sin 28.2 * |B| - 22 =0 (II)

Now we have a system of 2 (I and II) equations and 2 variables (|A| and |B|)

cos 41.9 * |A| - cos 28.2 * |B| = 0

sin 41.9 * |A| + sin 28.2 * |B| = 22

cos 41.9 * |A| = cos 28.2 * |B|

|A| = cos 28.2 * |B| / cos 41.9

sin 41.9 * |A| + sin 28.2 * |B| = 22

sin 41.9 *  cos 28.2 * |B| / cos 41.9 + sin 28.2 * |B| = 22

tg 41.9 * cos 28.2 * |B| + sin 28.2 * |B| = 22

(tg 41.9 * cos 28.2 + sin 28.2) * |B| = 22

|B| = 22 / (tg 41.9 * cos 28.2 + sin 28.2)

|B| = 17.46

|A| = 1.50

3 0
1 year ago
Find the measure of angle BAC
Anon25 [30]
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7 0
2 years ago
Solve for -5x < 2 step by step
lutik1710 [3]

Answer:

x > -2/5

Step-by-step explanation:

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x > -2/5

Because we divided by a negative number, the sign has to change direction.

5 0
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Answer:

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Step-by-step explanation:

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2 years ago
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