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3 years ago

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An animal shelter spends $3.00 per day to care for each bird and $8.50 per day to care for each cat. Kayla noticed that the shel

ter spent $123.00 caring for birds and cats on Tuesday. Kayla found a record showing that there were a total of 30 birds and cats on Tuesday. How many birds were at the shelter on Tuesday?

2 answers:

Lady bird [3.3K]3 years ago

8 0

$123 = ($3b + $8.50c)

b + c = 30

b = 24 birds ($72)
c = 6 cats ($51)

51+72=123

There were 24 birds at the shelter on Tuesday.

Irina-Kira [14]3 years ago

5 0

Thirty birds were at the shelter on Tuesday

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Alexus [3.1K]

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Which pair of funtions is not a pair of inverse functions? please help!!

antiseptic1488 [7]

Answer:

$f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Step-by-step explanation:

we know that

To find the inverse of a function, exchange variables x for y and y for x. Then clear the y-variable to get the inverse function.

we will proceed to verify each case to determine the solution of the problem

<u>case A)</u> $f(x)=\frac{x+1}{6} , g(x)=6x-1$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y+1}{6}$

Isolate the variable y

$6x=y+1$

$y=6x-1$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=6x-1$

therefore

f(x) and g(x) are inverse functions

<u>case B)</u> $f(x)=\frac{x-4}{19} , g(x)=19x+4$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y-4}{19}$

Isolate the variable y

$19x=y-4$

$y=19x+4$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=19x+4$

therefore

f(x) and g(x) are inverse functions

<u>case C)</u> $f(x)=x^{5}, g(x)=\sqrt[5]{x}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=y^{5}$

Isolate the variable y

fifth root both members

$y=\sqrt[5]{x}$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=\sqrt[5]{x}$

therefore

f(x) and g(x) are inverse functions

<u>case D)</u> $f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y}{y+20}$

Isolate the variable y

$x(y+20)=y$

$xy+20x=y$

$y-xy=20x$

$y(1-x)=20x$

$y=20x/(1-x)$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=20x/(1-x)$

$\frac{20x}{1-x}\neq \frac{20x}{x-1}$

therefore

f(x) and g(x) is not a pair of inverse functions

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3 years ago

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Given the function g(x) = x2 + 10x + 20, determine the average rate of change of

Dmitrij [34]

A function assigns the values. The average rate of change for the given function g(x) is 1.

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

The average rate of change of a function is given by the formula,

Average rate of change, = [f(b)-f(a)]/(b-a), [a,b]

Where a is the lower limit and b is the upper limit.

Given the upper limit for the function is 0, therefore, the value of a is 0, similarly, the value of b is -9. Thus,

a = 0

g(a) = 0²+10(0)+20 = 20

b = -9

g(b) = (-9)²+10(-9)+20 = 11

The average rate of change for the function g(x), can be written as,

$\text{Average rate of change}= \dfrac{g(-9)-g(0)}{-9-0}=\dfrac{11-20}{-9} = 1$

Hence, the average rate of change for the given function g(x) is 1.

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2 years ago

zavuch27 [327]

Answer:

<A = 133degrees

Step-by-step explanation:

Find the diagram attached

Using the theorem that "the sum of opposite angle of a cyclic quadilateral is 180 degrees, hence;

m<A + m<C = 180

4x+5 + x + 15 = 180

4x+x+5+15 = 180

5x+20 = 180

5x = 180 - 20

5x = 160

x = 160/5

x = 32degrees

Get the measure of angle A

<A = 4x+5

<A = 4(32)+5

<A = 128+5

<A = 133degrees

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3 years ago