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3 years ago

Find the inverse of the function.

Mathematics

2 answers:

yKpoI14uk [10]3 years ago

3 0

1/2 y +6 = x
y=2 (x-6)
= 2x-12
f^-1 (x)= 2x-12

Igoryamba3 years ago

3 0

Hello :
f(x) = 1/2 x +6
find : x
1/2x = f(x) -6
x = 2f(x) -12
the inverse is : f^-1 (x) = 2x-12

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How many different five-member teams can be made from a group of 17 people?

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Answer:

3, with 2 people left over

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2 years ago

7x2 - 5x+3<br> + 2x2 + 7x-8

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3 years ago

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A baseball player throws a ball from second base to home plate. How far does the player throw the ball?

Fynjy0 [20]

Answer:

The player throws 127.3 ft from second base to home plate.

Step-by-step explanation:

Given:

Distance from home to first base = 90 ft

Distance from first base to second base = 90 ft

We need to find the distance from second base to home.

Solution:

Now we can assume the complete scenario to be formed as a right angled triangle with two sides given and to find the third side.

Now by using Pythagoras theorem which states that;

Square of the hypotenuse side is equal to sum of squares of other two sides.

framing in equation form we get;

distance from second base to home = $\sqrt{90^2+90^2}= 127.27 \ ft$

Rounding to nearest tent we get;

distance from second base to home = 127.3 ft

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6 0

2 years ago

A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

Sveta_85 [38]

Answer:

$\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

$\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s$

where B stands for Base area

and P for Base Parimeter

$\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s$

now we need our algebraic skills to figure out s

simplify parentheses:

$\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144$

reduce fraction:

$\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144$

simplify multiplication:

$\displaystyle \: 16s + 64 = 144$

cancel 64 from both sides;

$\displaystyle \: 16s = 80$

divide both sides by 16:

$\displaystyle \: \therefore \: s = 5$

now we'll use Pythagoras theorem to figure out height

according to the theorem

$\displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2}$

substitute the value of l and s:

$\displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2}$

simplify parentheses:

$\displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2}$

simplify squares:

$\displaystyle \: {h}^{2} + 16 = 25$

cancel 16 from both sides:

$\displaystyle \: {h}^{2} = 9$

square root both sides:

$\displaystyle \: \therefore \: {h}^{} = 3$

recall the formula of a square pyramid

$\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h$

where A stands for Base area (l²)

substitute the value of h and l:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3$

simplify multiplication:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3$

reduce fraction:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}$

hence,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

8 0

2 years ago

Please help thank you

Allushta [10]

The average rate of change of credit card is $ 401.79 /year.

<h3>What is Average Rate?</h3>

A single rate that is a weighted average of the different rates that are applicable to property in various locations.
An average is a single number calculated as the average of a set of numbers, typically calculated as the sum of the numbers divided by the total number of numbers in the set (the arithmetic mean).

<u>Solution</u>

The difference of credit card debt between the year 2006 and 1992 = 8900 - 3275 = $5625

The difference of years between the year 2006 and 1992 = 2006 - 1992 = 14

average rate of change of credit card debt with respect to time = $\frac{difference of credit card debt}{difference of years}$

average rate = $\frac{5625}{14}$ = $ 401.79 / year

know more about average numerical brainly.com/question/18296887

#SPJ4

6 0

1 year ago