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valina [46]
3 years ago
10

PLEASE ANYONE I NEED YOUR HELP. For the points A(-2, 10) and B(-4,6). Find each of the following.

Mathematics
2 answers:
Rashid [163]3 years ago
8 0

Answer:

a. _ √20 , about 4.472136

b - (-3, 8)

c- Slope of 2

Step-by-step explanation:

Calculator

almond37 [142]3 years ago
5 0

Answer:

a. AB=2\sqrt{5}

b. (-3,8)

c. 2

Step-by-step explanation:

You have the points:

A(-2,10)

where i will call: x_{1}=-2 and y_{1}=10

B(-4,6)

where i will call: x_{2}=-4 and y_{2}=6

for our calculations we are going to need the distance in x between the points (\Delta x )and the distance in y between the points (\Delta y):

\Delta x =|x_{2}-x_{1}|=|-4-(-2)|=|-4+2|=|-2|=2\\\Delta y =|y_{2}-y_{1}|=|6-10|=|-4|=4

a. To find AB (the distance between point A and point B) you need The Pythagorean Theorem:

(AB)^2=(\Delta x)^2+(\Delta y)^2\\(AB)^2=(2)^2+(4)^2\\(AB)^2=4+16\\\\AB=\sqrt{20}\\ AB=2\sqrt{5}

b. to find the coordinates of the midpoint we average the x-coordinates and the y coordinates

x_{mid}=\frac{x_{1}+x_{2}}{2} =\frac{-2-4}{2}=\frac{-6}{2} =-3\\y_{mid}=\frac{y_{1}+y_{2}}{2} =\frac{10+6}{2}=\frac{16}{2} =8\\

so the midpoint (x_{mid},y_{mid}) is at: (-3,8)

c. For the slope we use the slope formula:

slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{6-10}{-4-(-2)}=\frac{-4}{-2}=2

The slope is equal to 2.

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Which equation represents an exponential function that passes through the point (2, 80)?
Lena [83]

The function f(x) = 5(x)⁴, and f(x) = 5(4)ˣ represents the function that passes through the point (2, 80) option second and fourth are correct.

<h3>What is an exponential function?</h3>

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent \rm y = a^x

where a is a constant and a>1

We have; an exponential function that passes through the point (2, 80).

f(x) = 4(x)⁵

Plug (2, 80) in the abovew function:

f(2) = 4(2)⁵ = 128 (false)

f(x) = 5(x)⁴

Plug (2, 80) in the abovew function:

f(2) = 5(2)⁴ = 80 (true)

f(x) = 4(5)ˣ

f(2) = 4(5)² = 100 (false)

f(x) = 5(4)ˣ

f(2) = 5(4)² = 80 (true)

Thus, the function f(x) = 5(x)⁴, and f(x) = 5(4)ˣ represents the function that passes through the point (2, 80) option second and fourth are correct.

Learn more about the exponential function here:

brainly.com/question/11487261

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