Given f ( x ) = 1 x + 12 , find the average rate of change of f ( x ) on the interval [ 9 , 9 + h ] . your answer will be an expression involving h

The formula for y in terms of x is y = [tex]\frac{16}{25} x^{3}[/tex]

Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.

Given that,

Y is inversely proportional to a³ When a = 2, y = 10

A is directly proportional to x when x = 4, a = 20

If y is inversely proportional to a³

[tex]\frac{y}{x^{3} }[/tex]∝1

y = [tex]\frac{k}{a^{3} }[/tex], where k is the proportionality constant

Given, a=2, y=10, then 10 = [tex]\frac{k}{2^{3} }[/tex]

k = 10 × 2³

k = 80

Substituting k = 80 back into the formula;

y = [tex]\frac{80}{a^{3} }[/tex]............. 1

Similarly, if a is directly proportional to x, then a ∝ x i.e a = kx

If x=4, a=20 then;

20 = 4k

k = [tex]\frac{20}{4}[/tex]

k = 5

Substituting k = 5 back into the formula;

a = 5x ....... 2

Substitute equation 2 into 1;

y = [tex]\frac{80}{a^{3} }[/tex]

y = [tex]\frac{80}{5x^{3} }[/tex]

y = [tex]\frac{80}{125x^{3} }[/tex]

y = [tex]\frac{16}{25x^{3} }[/tex]

Therefore, the formula for y in terms of x is y = [tex]\frac{16}{25} x^{3}[/tex]

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Answer:

4 * 5 * 6 = 120  possible meals can we order.

Step-by-step explanation:

given that-

If you go to a restaurant and there are 4 choices for main dishes, 5 choices for sides, and 6 choices for drinks

4 * 5 * 6 = 120 combinations or Ways to Order

we can order the main dish in 4 different ways. Then, we can choices for sides in 5 different ways and the drinks in 6 different ways.

(The outcome of the selection of the first does not influence the second or third)

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Answer:

82 because 102.50/1.25=82

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Step-by-step explanation:

The unit rate of the graph is is inches per hour

A graph will hold as many information as the plotter will wish to give it. The information the graph has the more compicated wit will be

The graph plotted is a graph of snowfall in inches against time in hours. The input values of the graph is the time in hours while the snow fall in inches is the output values

The unit rate of graphs is gotten from the the units plotted against the other unit. Here it is inches against hours

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Check the picture below.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~7 - (-2)~~)^2 + (~~9 - 7~~)^2} \implies d=\sqrt{(7 +2)^2 + (9 -7)^2} \\\\\\ d=\sqrt{( 9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }[/tex]

Answer:

Step-by-step explanation: the answer is .75. your welcome

the answer is 3/4 or 0.75

Answer:

x = 1/2, y = 4

Step-by-step explanation:

2x + 3y = 13----------> 2x + 3y = 13

4x - y = -2------------> 12x - 3y = -6

-----------------

14x = 7

x = 1/2, y = 4

The given exponential function represents the growth in function with a percentage increase as 57.3%.

Given we have the exponential function as :

y=8800(1.573)ˣ

it is in the form of: y=k.aˣ

therefore, if a>2 then the function represents growth.

and if a<1 then the function represents decay.

now, x=1.573

1.573 > 1

so, the function represents change in growth.

therefore, 1.573 - 1

= 0.573

= 57.3%

hence the change in growth of the function is increased by 57.3%.

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Answer:

200.96 square inches

Step-by-step explanation:

it's asking for the area of a circle

we know that the radius is 8, so we can just plug it into the circle area formula which is

area = (pi) r^2

you plug in 8 for r (r stands for radius)

8^2 is 64

64 times pi is 200.96 (because pi=3.14)

Answer:

FM and GB

Step-by-step explanation:

the angles are corresponding meaning that the lines must be parallel

The function that represents the vertical stretch by a factor of 3 of f(x) is given as follows:

g(x) = 3x - 21.

Vertical stretches or compression to the graph of a function f(x) are applied by the multiplication of a constant a to the function, as follows:

g(x) = a x f(x).

Then the value of the constant determines if it is an stretch or a compression.

For this problem, we want a vertical stretch with a factor of 3, then the constant is given as follows:

a = 3.

Then the definition of function g(x) is given by:

g(x) = 3f(x)

g(x) = 3(x - 7)

g(x) = 3x - 21.

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Answer:

211a+9x

Step-by-step explanation:

first, calculate the exponents (the number times itself) of each number

9a +81a +121a+9x

the reason they are positive is that a negative times a negative equals a positive ex: -3 x -3 = 9

next, combine the coefficients

starting with the variable for a

9a+81a+121a= 211a

x has no other coefficients so it would remain 9x

so the simplified answer would be

211a+9x

The value of x in the triangle extended through W to X is 39.5°.

It should be noted that a triangle has a total angle of 180° and also has three sides. Based on the information given, the following can be deduced:

Angle 1 = 3x - 4.

Angle 2 = 6x + 6

Angle 3 = x + 20

Therefore, the value of x will be gotten by adding the values and equating to 180°. This will be:

3x - 4 + 6x + 6 + x + 20 = 180

4x + 22 = 180

Collect like terms

4x = 180 - 22

4x = 158°

Divide

x = 158/4

x = 39.5°

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Answer: 39.5°

Step-by-step explanation:

The sum of the expression 10,000 + 2,000 + 60 + 1 is 12061

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

10,000 + 2,000 + 60 + 1

The sum of the expression can be calculated using a calculator

So, we have

10,000 + 2,000 + 60 + 1 = 12061

Hence, the value of the sum 10,000 + 2,000 + 60 + 1 is 12061

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The total amount received at the end of 1 year will be 242000

The amount available in Austin's saving account: $100,000

Rate of interest = 142% per year

Simple interest: Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

The formula for simple interest is given:

Simple Interest = P*R*T/100

where P = principal amount invested

R = rate of interest per year

T = time in years for which the amount is invested

Substituting the values in the formula we get:

Simple interest = 100000*142*1/100

= 142000

Total amount after 1 year = Principal invested + Simple interest earned

= 100000 + 142000

= 242000

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Answer:

perimeter of triangle = a + b + c

perimeter = 3x-5+2x+19-x

                = 6x + 14

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Answer: P=2a + b which = A- 3x - 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

SOLUTION:

Step 1:

In this question, we have the following question:

A rock is dropped from a height of 10 feet. The height of the rock is modeled by the graph shown.

Part A



​​What is the height of the rock 0.5 seconds after being dropped? The height of the rock 0.5 seconds after being dropped is ........... feet

6 .

Step 2:

Part B



To the nearest tenth of a second, how many seconds after being dropped does the rock hit the ground?The rock hits the ground approximately ...............................seconds after being dropped.

0.8



For an equivalent expression for [tex]18^{-7}\\[/tex] * [tex]18^5\\[/tex] it is option 4 that is correct that means the equivalent expression can be seen as [tex]\frac{1}{18} ^{2}[/tex].

Expressions that can be considered are equivalent do the same thing even when they have distinct appearances. When we get to enter the same value(s) for the same variable, two algebraic expressions that are equivalent have the same value (s).

Calculating the equivalent expression,

[tex]18^{-7}\\[/tex] * [tex]18^5\\[/tex]

= [tex]18^{-7+5}[/tex]

=[tex]18^{-2}[/tex]

=  [tex]\frac{1}{18} ^{2}[/tex]

An expression that can be considered equivalent to another phrase but then differs in appearance is the one that has the same value or worth. In algebra, we can say 2(2x – 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.

When two expressions can be reduced to a single thread expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. You can also determine whether two expressions are equivalent.

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Answer:

2600 meters

Step-by-step explanation:

2.6x1000

The numerical value of x is 2 as segment AB equals segment BC.

A midpoint is simply a point that divides a line segment into two equal halves.

Given the data in the question;

Given that B is the midpoint of segment AC, this means that segment AB is equal to segment BC.

Hence

Segment AB = Segment BC

4x + 5 = 13

Solve for x

Subtract 5 from both sides

4x + 5 - 5 = 13 -5

4x = 8

Divide both sides by 4

4x/4 = 8/4

x = 8/4

x = 2

Therefore, the value of x is 2.

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There are 2 numbers between 7 and 5 and 3 numbers between 5 and 2

The value of m in the right triangle to the nearest tenth is 7.2 units.

The figure above is a right triangle.

The right triangles are similar.

Therefore, right triangle ABC is similar to right triangle BDC.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Therefore, let's find the value of m using the similar triangle principle,

m / 13 = 4 / m

cross multiply

m × m  = 13 × 4

m² = 52

square root both sides

√m² = √52

m = 7.21110255093

Therefore,

m = 7.2 units.

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[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-9)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-8)}}} \implies \cfrac{-4 +9}{3 +8} \implies \cfrac{ 5 }{ 11 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-9)}=\stackrel{m}{ \cfrac{ 5 }{ 11 }}(x-\stackrel{x_1}{(-8)}) \implies {\large \begin{array}{llll} y +9= \cfrac{ 5 }{ 11 } (x +8) \end{array}}[/tex]

Step-by-step explanation:

The answer is 8+2x . This is the correct answer .

The simplification of number 17/0 gives the undefined form.

For the given question;

The expression is 17/0

Let us say that 17/0 = x

Its means; 17 = x ×0

17 = 0

But , 17 ≠ 0

As, given expression 17/0 can not be defined by any number.

Thus, 17/0 is an undefined term.

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The expression represented by 50 added to half of a number, c is 50 + c/2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

50 added to half of a number, c

half of a number, c means divide c by 2

So, we have

50 added to half of a number, c  => 50 added to c/2

Added to means +

So, we have

50 added to half of a number, c  => 50 + c/2

Hence, the expression represented by the statement is  50 + c/2

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