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miskamm [114]
3 years ago
8

Find the Mid point of (-5,-9) (-7,-4)

Mathematics
1 answer:
lyudmila [28]3 years ago
8 0

Answer: ( -6 , -6.5 )

Step-by-step explanation:

The formula for calculating Mid - point is given by

M = (\frac{x_{1}+x_{2}}{2} , \frac{y_{1}+y_{2}}{2} )

x_{1} = -5

x_{2} = -7

y_{1} = -9

y_{2} = -4

substituting into the formula , we have

M = \frac{-5-7}{2} , \frac{-9-4}{2}

M = \frac{-12}{2} , \frac{-13}{2}

Therefore : mid point = ( -6 , -6.5 )

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Given f(x)=x3 and g(x)= 1-5x2, fine (fog)(x) and it’s Domain
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Answer:

Option B. f(g(x)) = (1-5x ^ 2) ^ 3  all real numbers

Step-by-step explanation:

We have

f(x) = x ^ 3 and g(x) = 1-5x ^ 2

They ask us to find

(fog)(x) and it's Domain

To solve this problem we must introduce the function g(x) within the function f(x)

That is, we must do f(g(x)).

So, we have:

f(x) = x ^ 3

g(x) = 1-5x ^ 2

Then:

f(g(x)) = (1-5x ^ 2) ^ 3

The domain of the function f(g(x)) is the range of the function g(x) = 1-5x ^ 2.

Since the domain and range of g(x) are all real numbers then the domain of f(g(x)) are all real numbers

Therefore the correct answer is the option b: f(g(x)) = (1-5x ^ 2) ^ 3

And his domain is all real.

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The third term of an arithmetic sequence is equal to 9 and the sum of the first 8 term is 42. Find the first term and the common
zloy xaker [14]

Answer:

The first term is 14

The common difference is -2.5

Step-by-step explanation:

we know that

The rule to calculate the an term in an arithmetic sequence is

a_n=a_1+d(n-1)

where

d is the common difference

a_1 is the first term

we have that

The third term of an arithmetic sequence is equal to 9

so

a_3=9

n=3

substitute

9=a_1+d(3-1)

9=a_1+2d ----> equation A

The rule to find the sum of the the first n terms of the arithmetic sequence is equal to

S=\frac{n}{2} [2a_1+(n-1)d]

we have

The sum of the first 8 term is 42

so

S=42

n=8

substitute

42=\frac{8}{2} [2a_1+(8-1)d]

42=4[2a_1+7d]

10.5=2a_1+7d ----> equation B

Solve the system of equations

9=a_1+2d ----> equation A

10.5=2a_1+7d ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

the solution is (14,-2.5)

see the attached figure

therefore

a_1=14\\d=-2.5

The first term is 14

The common difference is -2.5

8 0
3 years ago
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