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3 years ago

EASY POINTS! NO LINKS!!

Mathematics

2 answers:

leonid [27]3 years ago

8 0

D.

Step-by - step- explanation

Have a great day hope this helped :)

Talja [164]3 years ago

4 0

The answer is D :)))))))))

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Given the function () = $

elena-s [515]

The inverse of the function f(x) = 1/3x^2 - 3x + 5 is f-1(x) = 9/2 + √[3(x + 7/4)], the sum of the arithmetic series is 1078 and the common ratio of the sequence is 2

<h3>The inverse of the function?</h3>

The function is given as:

f(x) = 1/3x^2 - 3x + 5

Next, we rewrite the function as in vertex form

Using a graphing calculator, the vertex form of the function f(x) = 1/3x^2 - 3x + 5 is

f(x) = 1/3(x - 9/2)^2 - 7/4

Express f(x) as y

y = 1/3(x - 9/2)^2 - 7/4

Swap x and y

x = 1/3(y - 9/2)^2 - 7/4

Add 7/4 to both sides

1/3(y - 9/2)^2 = x + 7/4

Multiply through by 3

(y - 9/2)^2 = 3(x + 7/4)

Take the square root of both sides

y - 9/2 = √[3(x + 7/4)]

Add 9/2 to both sides

y = 9/2 + √[3(x + 7/4)]

Rewrite as an inverse function

f-1(x) = 9/2 + √[3(x + 7/4)]

<h3>Sum of arithmetic series</h3>

Here, we have:

5 + 18 + 31 + 44 + ... 161

Calculate the number of terms using:

L = a + (n -1)d

So, we have:

161 = 5 + (n - 1) * 13

This gives

(n - 1) * 13 = 156

Divide by 13

n - 1 = 12

Add 1

n = 13

The sum is then calculated as:

Sn = n/2 * [a + L]

This gives

Sn =13/2 * (5 + 161)

Evaluate

Sn = 1078

Hence, the sum of the arithmetic series is 1078

<h3>The common ratio of the sequence</h3>

Here, we have:

T11 = 32 * T6

The nth term of a geometric sequence is

Tn = ar^(n-1)

This gives

ar^10 = 32 * ar^5

Divide by ar^5

r^5 = 32

Take the fifth root

r = 2

Hence, the common ratio of the sequence is 2

Read more about sequence at:

brainly.com/question/7882626

#SPJ1

6 0

1 year ago

Please help! Thank you!

djyliett [7]

Answer:

Step-by-step explanation:

4 0

2 years ago

Mara's family is driving to her grandmothers' house. The family travels 239.4 miles between the hours of 9:10 a.M. To 1:40 p.M.

anzhelika [568]

Answer:

53.2 mph

Step-by-step explanation:

Mara's family travels 239.4 miles between the hours of 9:10 a.m. to 1:40 p.m.

1:40 p.m. is 13:40.

Thus, they traveled for

13 hours 40 minutes - 9 hours 10 minutes = 4 hours 30 minutes

that is $4\frac{1}{2}=4.5$ hours.

Use formula:

$D=r\cdot t,$

where

D = distance

r = rate

t = time.

In your case,

D = 239.4 miles

t = 4.5 hours

Hence,

$239.4=4.5r\\ \\r=\dfrac{239.4}{4.5}=53.2\ mph$

5 0

2 years ago

Read 2 more answers

Rashawn read 25 pages of his book each day until he finished the book. His book was 400 pages long.

Anna71 [15]

I think it's the second one.

7 0

3 years ago

Read 2 more answers

Cole spent a total of 523.46 on holiday gifts for his friends and family. If he bought gifts for eleven people,about how much di

Vlada [557]

Answer:

Cole spend 47.587 on buying gifts for each person.

Step-by-step explanation:

Given:

Total money spend on gifts = 523.46

Number of people gifts were bought for = 11

We need to find how much he spend on each person.

Solution:

To find how much he spend on each person we will divide total money spend on gifts with number of people gifts were bought for.

framing in equation form we get;

Spending on each person = $\frac{523.46}{11} = 47.587$

Hence Cole spend 47.587 on buying gifts for each person.

6 0

3 years ago