Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.

Third-degree, with zeros of −3, −1, and 4, and a y-intercept of −13.

If h(x)=(fog)(x) then h'(3) = 12.

Given:

Let f and g be differentiable functions such that f(3)=5,g(3)=7,f'(3) = 13, g'(3) = 6,f'(7) = 2 and g'(7) = 0

h(x)=(fog)(x)

h(x) = f(g(x))

h'(x) = f'(g(x)) * g'(x)

h'(3) = f'(g(3) * g'(3)

= f'(7) * 6

= 2*6

= 12

Therefore If h(x)=(fog)(x) then h'(3) = 12.

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Answer:

Step-by-step explanation:Your calculations indicate that you will need 20.8 cubic yards of concrete for a slab floor. Which of the following quantities would be the best amount to order accounting for waste

Answer:

alternate interior angles theorem

Step-by-step explanation:

alternate interior angles theorem states that, if 2 parallel lines and a transversal form alternate interior angles, then, said angles are congruent.

Answer:

D

Step-by-step explanation:

First, we should find the equations of the two lines. The red line is just horizontal, and represents y = 4 while the blue line intersects the y-axis at -4 and every time it goes right one, it goes up 4, so it has a slope of four(also it looks kinda steep, so it cannot have a slope of 1/4). This means the equation is y = 4x - 4.

Notice the red line is dashed, that means the inequality is either less than or greater than. Also, the shaded part is below the vertical line, enclosing all the values of y less than 4, so the first inequality would be y < 4.

The blue line is solid, so it is either greater than or equal to or less than or equal to. To find out which one, we check to se where the point (0, 0) fits in:

y ? 4x - 4

0 ? 0 - 4

0 ? -4

Only a greater than or equal to sign would fit in: 0 ≥ -4

This means the answer is:

y < 4

y ≥ 4x - 4

which is option D

Answer:

Step-by-step explanation:

1)

The equation of a straight line:

y = k·x + b

x = 0

b = y = - 4

k = (y - y₀) / (x - x₀) = ( 4 - (-4)) / (2 - 0) =  8 / 2 = 4

y = 4·x - 4

2)

The equation of a straight line:

y = 4

3)

Shaded area:

y ≤ 4

y ≥ 4x - 4

Right answer:

D.

y ≤ 4

y ≥ 4x - 4

Answer:

.06

Step-by-step explanation:

6 hundredths

We want to write this as a decimal.

Writing decimals

This means write 6/100

There are two zeros so we need two numbers.

06/100

Then there are two numbers before the decimal.

We can write 06 before the decimal.

.06

6 hundredths can be written as 0.06 as a decimal.

What is fraction?

All fractions consist of a numerator and a denominator, separated by horizontal bars called fraction bars.

The denominator indicates the number of parts into which the whole is divided. Placed at the bottom of the break below the break bar. The

counter indicates how many sections of the fraction are displayed or selected. Placed at the top of the break above the break bar.

A common fraction is a numeral which represents a rational number. That same number can also be represented as a decimal, a percent, or with a negative exponent.

6 hundredths means that when you divide "something" into a hundred equal parts, 6 hundredths are six of the newly divided parts.

When you divide 6 by hundreds, you get 6 hundredths as a decimal, which is 0.06.

Therefore, 6 hundredths can be written as 0.06 as a decimal.

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Answer:

900

Step-by-step explanation:

300/12=25

75*12=900

Answer:

x = 40

Step-by-step explanation:

for m and n to be parallel then

2x and 80 are alternate angles and congruent , so

2x = 80 ( divide both sides by 2 )

x = 40

Step-by-step explanation:

if there is nothing missing, we have

x + 25/-8 = -6

in order to compare or add or subtract fractions, we need to bring them all to the same denominator (bottom part).

remember, integer numbers are fractions too. like here

-6 = -6/1

25/-8 = -25/8

so, how can we bring -6/1 to .../8 ?

by multiplying 1 by 8.

but we cannot multiply only the denominator by 8. otherwise we would suddenly have

-6/8

and is -6/8 = -6/1 ? no, certainly not.

to keep the original value of the fraction we have to do the same multiplication also with the numerator (top part).

so, we actually do

-6/1 × 8/8 = -48/8

with this little trick we have now .../8 to operate with, and our transformed fraction has still the same value

-6/1 = -48/8 indeed.

so, we have

x + -25/8 = -48/8

x - 25/8 = -48/8

x = -48/8 + 25/8 = -23/8

The average rate of change between year 1 and year 10 is given as follows:

4.3 thousand cars a year.

The average rate of change of a function is obtained by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In this problem, the function is presented as follows:

C(x) = 0.15x³ - 3.28x² + 23.75x - 2.1.

The interval is:

[1,10], hence a = 1, b = 10.

At x = 1, the numeric value is found replacing each instance of x by 1, hence:

C(1) = 0.15(1)³ - 3.28(1)² + 23.75(1) - 2.1 = 18.52 thousand cars.

At x = 10, the numeric value is found replacing each instance of x by 10, hence:

C(10) = 0.15(10)³ - 3.28(10)² + 23.75(10) - 2.1 = 57.4 thousand cars.

Then the average rate of change is obtained as follows:

r = (57.4 - 18.52)/(10 - 1) = 4.3 thousand cars a year.

The problem is given by the image shown at the end of the answer.

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Answer:

     [tex]y=2x-5[/tex]

Step-by-step explanation:

We want to find a linear function [tex]f(x)[/tex] with the values

[tex]f(0)=-5\\f(1)=-3[/tex]

These mean that when x is 0, y is -5, and when x is 1, y is -3.

This means that we want to find the equation of a line that goes through the ordered pairs below:

[tex](0,-5)\\(1,-3)\\[/tex]

Let's find the slope between the two ordered pairs. The slope is the rise over the run. The rise is the change in y-values.

[tex]-3--5=-3+5=2[/tex]

The change in y-values is 2.

The run is the change in x values.

[tex]1-0=1[/tex]

The change in x-values is 1.

The slope is the rise divided by the run, so:

[tex]slope=\frac{2}{1}=2[/tex]

Now that we know the slope, let's find the y-intercept! This is when x equals 0. Luckily, that number is already given! We know that when x equals 0, y equals -5!

[tex]intercept=-5[/tex]

Now that we have the slope and intercept, we can plug these numbers into slope-intercept form!

[tex]y=2x-5[/tex]

Check the picture below.

Answer:

40;100

step by step explanation:

The fraction that illustrates the decrease in sales is 15.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, August 1/3 and this was 2/5 more than what was sold earlier. Therefore the decrease will be:

= 2/5 - 1/3

= 6/15 - 5/15

= 1/5

The fraction is 1/15.

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Answer:

f ≤ - [tex]\frac{19}{3}[/tex]

Step-by-step explanation:

8 - (- 4f - 3 ) ≤ - f - 8 + 2f ← distribute parenthesis on left side by - 1

8 + 4f + 3 ≤ f - 8

4f + 11 ≤ f - 8 ( subtract f from both sides )

3f + 11 = - 8 ( subtract 11 from both sides )

3f ≤ - 19 ( divide both sides by 3 )

f ≤ - [tex]\frac{19}{3}[/tex]

Step-by-step explanation:

area of circle = πr²

internal radii - 3 cm = r1

external radii - 10 cm = r2

internal + external radii = πr1² + πr2²

= 22/7×3² + 22/7×10²

= 28.28 + 314.28

= 342.56 cm²

Answer: The answer to that would be 3.

Step-by-step explanation: So 5 / 1  2/3 = 3

Sorry my handwriting is so sloppy! Hope it helps!

Answer:

Step-by-step explanation:

so use the properties of powers, recall that powers like [tex]x^{2^{2} }[/tex] is the same as [tex]x^{2} *x^{2}[/tex] which can also be written as  [tex]x^{2*2}[/tex] = [tex]x^{4}[/tex].

I want to make this clearer.

[tex]x^{3^{3} }[/tex] = [tex]x^{3}[/tex]  * [tex]x^{3}[/tex] * [tex]x^{3}[/tex]  = [tex]x^{3*3*3}[/tex] =[tex]x^{27}[/tex]

I'm not sure if that's making it clearer or not.

so for your question  of  [tex](8x^{6}) ^{2/3}[/tex]  we can rewrite it to look like the above multiplication of powers

[tex]8x^{6*(2/3)}[/tex]

[tex]\frac{6}{1}[/tex] * [tex]\frac{2}{3}[/tex] = [tex]\frac{12}{3}[/tex]  = 4

[tex]8x^{4}[/tex]

The first step in simplifying is to apply that outer exponent of [tex]\frac{2}{3}[/tex] to each factor inside the parentheses.

      [tex]\left(8\cdot x^6\right)^{2/3} = \left(8\right)^{2/3} \cdot \left(x^6\right)^{2/3}[/tex]

Now using the concept that [tex](a)^{m/n} = \sqrt[m]{a^n}[/tex] for positive real numbers a and integers m and n, we can evaluate the first part:

       [tex](8)^{2/3} = \sqrt[3]{8^2} = \sqrt[3]{64} =4[/tex]

For the second part, we use the power-to-a-power rule, that says [tex](a^m)^n = a^{m\cdot n}[/tex]:

    [tex]\left(x^6\right)^{2/3} = x^{6\cdot \frac{2}{3}} = x^4[/tex]

Putting that all together, we have

    [tex]\left(8 x^6\right)^{2/3} = \left(8\right)^{2/3} \cdot \left(x^6\right)^{2/3} = 4x^4[/tex]

Answer:

2/5 is greater than 3/8, so 25 2/5 is greater

Step-by-step explanation:

Find the least common denominator or LCM of the two denominators:

LCM of 5 and 8 is 40

Next, find the equivalent fraction of both fractional numbers with denominator 40

For the 1st fraction, since 5 × 8 = 40,

2/5

=

2 × 8

5 × 8

=

16/40

Likewise, for the 2nd fraction, since 8 × 5 = 40,

3/8

=

3 × 5

8 × 5

=

15/40

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

16/40 > 15/ 40 or 2/5 > 3/8

Answer:

Of the homeowners, half have either a dog or a cat.

Step-by-step explanation:

Since 2/3 of all homeowners have a pet, and 3/4 of those have dogs or cats, we simply need to multiply 2/3 and 3/4 to see what fraction of all homeowners have a dog or a cat.

2/3 x 3/4 = 6/12

6/12 = 1/2

We can double check this. If there are 60 homeowners, and 2/3 have a pet, that would mean that 40 of those homeowners have a pet.

If 3/4 of the 40 homeowners have either a dog or a cat, that would equate to 30 homeowners having either a dog or a cat.

Since 30 is half of 60, this would mean that 1/2 of the 60 homeowners have a dog or cat!

Hope this answer helped you!

The required equation model is y =  -(4.4/1009)x + 16, its slope is -(4.4/1009), and the y-intercept of the line of fit is 16.

The given table shows the amounts of storage left y 7 (in gigabytes) on a music-playing device when there are x songs on MTR the device.

As per the given table, take two points (0, 16) and (1009, 11.6)

The required equation will be as:

y - 16 = [(11.6 - 16)/(1009-0)](x-0)

y - 16 = -(4.4/1009)x

y =  -(4.4/1009)x + 16

The above equation models the amount of storage left as a function of the number of songs.

Here slope is -(4.4/1009), and y-intercept is 16

Therefore, the required equation model is y =  -(4.4/1009)x + 16, its slope is -(4.4/1009), and the y-intercept of the line of fit is 16.

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Answer:

[tex]28t^4u^5v^9[/tex]

Step-by-step explanation:

I will answer this a few different ways depending on whether there are supposed to be exponents in the question.

As written

As written, the product is:

[tex](7tuv7)(4t3u4v2)[/tex]

All of the coefficients can be multiplied together. This is what that looks like:

[tex]4704tuvtuv[/tex]

Now, each variable multiplied by itself gets the exponent of 2.

[tex]4707t^2u^2v^2[/tex]

Assuming exponents and coefficients

Assuming exponents, the product is:

[tex](7tuv^7)(4t^3u^4v^2)[/tex]

Again, the coefficients can be multiplied, and the like variables written next to each other:

[tex]28tt^3uu^4v^7v^2[/tex]

When multiplying like terms with exponents, add the exponents. Variables without an exponent have an exponent of 1.

[tex]28t^4u^5v^9[/tex]

If the promissory note stated that there was a balloon payment at the end. The sum of all but the last monthly payment is: $56,525, $57,000.

Total payment = $475 × [(10 years × 12 months) -1]

Total payment = $475 × 119 payment

Total payment = $56,525

Total payment = $475 × [(10 years × 12 months) ]

Total payment = $475 × 120 payment

Total payment = $57,000

Therefore the monthly payment is; $56,525, $57,000.

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The average difference or mean in game scores across six games is 5.67

The mean is the average of a data set. The mode is the most common number in a data set. The median is the middle of the set of numbers. The mean is the average or the most common value in a collection of numbers. the mean is one of the measures of b, apart from the mode and median. Mean is nothing but the average of the given set of a data.

To solve this problem, we have to write the wins and loss separate and then find the mean.

Wins = 8 points, 7 points, 20 points, 9 points

Loss = 8 points, 2 points

The sum of win points = 8 + 7 + 20 + 9 = 44 points

The sum of lost points = 8 + 2 = 10 points

The mean difference = (win - loss)/ total number of games

The mean difference = ( 44 - 10) / 6

The mean difference = 34 / 6 =5.67

The mean difference in the game scores over six games is 5.67 points

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Answer:

-23

Step-by-step explanation:

h(x) = -2x - 5

Let x = 9

h(9) = -2*9 - 5

h(9) = -18 - 5

        = -23

Answer:

h(9) = -23

Step-by-step explanation:

Given explanation,

→ h(x) = -2x - 5

Then the value when h(x) = 9 is,

→ h(x) = -2x - 5

→ h(9) = -2(9) - 5

→ h(9) = -18 - 5

→ h(9) = -23

Hence, the value of h(9) is -23.

Answer:

The length is 12

The area is 72[tex]cm^{2}[/tex]

Step-by-step explanation:

3x + 7 = 5x -17  Subtract 3x from both sides

7 = 2x -17  Add 17 to both sdies

24 = 2x  Divide both sides by 2

12 = x

Area = length times witdth

Area = 6(12) = 72

Answer:

Step-by-step explanation:

part a):

6(3x+7)=6(5x-17)

part b):

18x+42=30x-102

42+102=30x-12x

144=12x

x=144/12

x=12

area = l x b

area = 6x{5(12)-17}

=6x(60-17)

=6x43

area=258cm2

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of f(g(x)) is 6x³ + 4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

3x + 4 = 5 is an equation.

2x + 4x = 4 is an equation.

We have,

The function f(x) represents the amount of money Barrett earns per gallon of ice cream, where x is the number of gallons of ice cream he makes.

The function g(x) represents the number of gallons of ice cream Barrett makes per hour, where x is the number of hours he works.

f(x) = 2x² + 4

g(x) = √(3x³)

Now,

f(g(x)):

= f(√(3x³))

= 2{√(3x³)}² + 4

= 2(3x³) + 4

= 6x³ + 4

Thus,

The value of f(g(x)) is 6x³ + 4.

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For every 50 y, there is 1 hour

A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.

The value of [tex]x_{11}[/tex] is 8

The value of [tex]x_{21}[/tex] is -1

A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.

We have,

[tex]\left[\begin{array}{ccc}3&-8\\1&1\\\end{array}\right] X=\left[\begin{array}{ccc}32\\7\\\end{array}\right][/tex]    _____(1)

Now,

[tex]X = \left[\begin{array}{ccc}x_{11}\\x_{21}\\\end{array}\right][/tex]  ________(2)

Multiplication of matrix.

From (1) and (2) we get,

[tex]3x_{11} - 8x_{21}[/tex] = 32 ____(a)

[tex]x_{11} + x_{21}[/tex] = 7 ______(b)

From (b) we get,

[tex]x_{11}[/tex] = 7 - [tex]x_{21}[/tex] ______(3)

Substitute (3) in (a)

Now,

3 (7 - [tex]x_{21}[/tex]) - 8[tex]x_{21}[/tex] = 32

21 - 3[tex]x_{21}[/tex] - 8[tex]x{21}[/tex] = 32

-11[tex]x_{21}[/tex] = 32 - 21

[tex]x_{21}[/tex] = -1

Now,

[tex]x_{11}[/tex] = 7 - (-1) = 7 + 1 = 8

Thus,

The value of [tex]x_{11}[/tex] is 8

The value of [tex]x_{21}[/tex] is -1

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The rate of change of the volume of the sphere is 100,530.96 mm^3/s

How to calculate rate of change of the volume of the sphere?

Given,

radius = r = 80 / 2 = 40 mm

rate of change radius = [tex]\frac{dr}{dt}[/tex] = 5 mm/s

Formula to calculate volume of the sphere is

[tex]V = \frac{4}{3}\pi r^{3}[/tex]

Differentiating the volume formula and we get new formula to calculate rate of change of the volume.

[tex]\frac{dV}{dt} = \frac{4}{3}\pi 3r^{2}\frac{dr}{dt}[/tex]

Simplify to

[tex]\frac{dV}{dt} = 4\pi r^{2}\frac{dr}{dt}[/tex]

Now, we put the given value to formula and calculate it

[tex]\frac{dV}{dt} = 4\pi (40)^{2}(5)[/tex]

[tex]\frac{dV}{dt} = 100,530.96[/tex] mm^3/s

Thus, the rate of change of the volume of the sphere is 100,530.96 mm^3/s

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