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2 years ago

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The endpoints of a line segment are located at (–4, 7) and (6, –3). What is the length of the line segment? Round to the nearest

tenth.

1 answer:

Marrrta [24]2 years ago

7 0

Answer:

-14.1

Step-by-step explanation:

well I dont feel like explaining just go there

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Write the equation for the hyperbola with foci (–12, 6), (6, 6) and vertices (–10, 6), (4, 6).

fomenos

Answer:

$\frac{(x--3)^2}{49} -\frac{(y-6)^2}{32}=1$

Step-by-step explanation:

The standard equation of a horizontal hyperbola with center (h,k) is

$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$

The given hyperbola has vertices at (–10, 6) and (4, 6).

The length of its major axis is $2a=|4--10|$ .

$\implies 2a=|14|$

$\implies 2a=14$

$\implies a=7$

The center is the midpoint of the vertices (–10, 6) and (4, 6).

The center is $(\frac{-10+4}{2},\frac{6+6}{2}=(-3,6)$

We need to use the relation $a^2+b^2=c^2$ to find $b^2$ .

The c-value is the distance from the center (-3,6) to one of the foci (6,6)

$c=|6--3|=9$

$\implies 7^2+b^2=9^2$

$\implies b^2=9^2-7^2$

$\implies b^2=81-49$

$\implies b^2=32$

We substitute these values into the standard equation of the hyperbola to obtain:

$\frac{(x--3)^2}{7^2} - \frac{(y-6)^2}{32}=1$

$\frac{(x+3)^2}{49} -\frac{(y-6)^2}{32}=1$

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2 years ago

PLEASE HELP!! Which equation matches the table of values?

RoseWind [281]

The equation that represents the table of values is $y=(\frac{1}{4})^x$

Step-by-step explanation:

We need to find the equation that matches the table of values.

x y

0 | 1

1 | 1/4

2 | 1/16

3 | 1/64

So, when x =0 y=1 and when x=1, y=1/4

if $y=(\frac{1}{4})^x$

then putting x=0 we get y=1

x=1, we get y=1/4

x=2, we get y=1/16

x=3, we get y=1/64

So, the equation that represents the table of values is $y=(\frac{1}{4})^x$

Kindly check your options, as option D should be $y=(\frac{1}{4})^x$

Keywords: Solving Equations

Learn more about Solving Equations at:

#learnwithBrainly

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2 years ago

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How many vertices does the<br> pyramid have?

Westkost [7]

Answer:

5 vertices

Step-by-step explanation:

At base = 4 vertices

On top = 1 vertex

Total = 5 vertices

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