Express your answer as a polynomial in standard form.f(x) = x + 10g(x) = 2?= 2? + 2x – 7Find: (fog)(x)

Express Your Answer As A Polynomial In Standard Form.f(x) = X + 10g(x) = 2?= 2? + 2x 7Find: (fog)(x)

Answers

Answer 1

Given function f and g, we can write:

[tex](f\circ g)(x)=f(g(x))[/tex]

This means that we can just substitute g(x) into f to obtain the result. So let's do that:

[tex]\begin{gathered} (f\circ g)(x)=f(g(x))=g(x)+10=(x^2+2x-7)+10 \\ (f\circ g)(x)=x^2+2x-7+10 \\ (f\circ g)(x)=x^2+2x+3 \end{gathered}[/tex]

This already is in the standard form, so that is the answer.


Related Questions

Write an equationthe product of a number and 8, decreased by 3, is less than or equal to 9

Answers

The product ( multiplication) of a number (x) and 8, decreased (minus) by 3, is less or equal (

≤) to 9.

Inequality:

8x-3 ≤ 9

Find lateral surface area and volume of the solid object(Round to nearest whole number as needed)

Answers

[tex]\begin{gathered} \text{LSA}\approx312m^2 \\ V\approx794m^3 \end{gathered}[/tex]

1) Note that this solid, is a cross-sectioned cone. We can find the Lateral Surface Area, using this formula:

[tex]LSA=\pi\cdot s\cdot(R+r)_{}[/tex]

Where R, is the biggest radius, s for the slant height, r for the smallest radius.

2) So, plugging the measures into that we can write out:

[tex]\text{LSA}=\pi\cdot9.63(6.20+4.10)=311.61m^2\approx312m^2[/tex]

Note that we have rounded it off to the nearest whole. So now, let's find the volume of that solid:

[tex]V=\frac{\pi h}{3}(R^2+Rr+r^2)[/tex]

Plugging into that the given dimensions:

[tex]\begin{gathered} V=\frac{\pi h}{3}(R^2+Rr+r^2) \\ V=\frac{\pi\cdot9.4}{3}(6.2^2+6.2\cdot4.1+4.1^2) \\ V\approx794m^3 \end{gathered}[/tex]

Note the volume in cubic meters.

And that is the answer

This is an ACT (pre calculus) practice problem that I need help onBelow, I will list the answer options for this problem.A. 1B. -2C. 4D. The limit does not exist.

Answers

Notice that the function is discontinuous specifically in x=1; therefore,

[tex]\lim _{x\to1}f(x)\to\text{does not exist}[/tex]

However, we are being asked for the limit when we approach x=1 from the left.

And, according to the graph, that limit is:

[tex]\lim _{x\to1^-}f(x)=4[/tex]

The answer is 4, option C.

Select two ratios that are equivalent to 7: 10.Choose 2 answers

Answers

for an equivalent number you can multiply by the same number on each side of the expression

ex:

[tex]\frac{7\times3}{10\times3}=\frac{21}{30}[/tex]

and

[tex]\frac{7\times5}{10\times5}=\frac{35}{50}[/tex]

In politics, marketing, etc. we often want to estimate a percentage or proportion p . One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 34% with a margin of error of 1.6% . Describe the conclusion about p using an absolute value inequality.this is copy and pasted from my assignment

Answers

Given: The below

[tex]\begin{gathered} ME(Margin-of-error)=1.6\% \\ proportion(p)=34\% \end{gathered}[/tex]

To Determine: The conclusion about p using an absolute value inequality

Solution

Using the absolute inequality about p using an absolute value inequality below

[tex]|p-\hat{p}|\leq ME[/tex]

Substituting the given

[tex]\begin{gathered} p-E\leq p\leq p+E \\ 34\%-1.6\%\leq p\leq34\%+1.6\% \\ 32.4\%\leq p\leq35.6\% \end{gathered}[/tex]

Hence, p is most likely going to be between 32.4% and 35.6%

(32.4% ≤ p ≤ 35.6%)

Directed line segment DE has endpoints D(-4,-2) and E(1,8). Point F divides DE such that DF:FE is 3:2What are the coordinates of F?

Answers

The Solution.

The given points are

[tex]D(-4,-2)\text{ and E(1,8)}[/tex]

The formula is

[tex]\frac{mx_2+nx_1}{m+n}_{},\frac{my_2+ny_1}{m+n}[/tex]

In this case,

[tex]m=3,n=2[/tex]

Therefore,

[tex]\begin{gathered} (\frac{mx_2+nx_1}{m+n}_{},\frac{my_2+ny_1}{m+n}) \\ =(\frac{3(1)+_{}2(-4)_{}}{3+2}_{},\frac{3(8)_{}+2(-2)_{}}{3+2}) \\ \end{gathered}[/tex][tex]=(\frac{3-8}{5},\frac{24-4}{5})=(-\frac{5}{5},\frac{20}{5})[/tex][tex]=(-1,4)[/tex]

Hence, the correct answer is (-1, 4) (option 3)

Solve the right TriangleRound your answer to the nearest tenth

Answers

We have a right triangle, in order to find the missing sides we will use trigonometric functions

we will use the function tangent to find b

[tex]\tan (40)=\frac{b}{20}[/tex]

we need to isolate the b

[tex]\begin{gathered} b=\tan (40)\cdot20 \\ b=16.78 \end{gathered}[/tex]

b round to the nearest tenth is b=16.8

For c we will use the cosine

[tex]\cos (40)=\frac{20}{c}[/tex]

we need to isolate the c

[tex]c=\frac{20}{\cos (40)}=26.1[/tex]

round to the nearest tenth c=26.1

then to find angle A we need to remember that the sum of the interior angles of a triangle is 180°, so the equation to find A is

40+90+A=180

A=180-90-40

A=50°

Find the unit rate to determine the better buy:16 oz jar of peanut butter for $2.49 or 64 oz jar of peanut butter for $6.99Round to the nearest cent

Answers

Answer:

64 oz jar of peanut butter for $6.99

Explanation:

First, determine the unit rates for the two:

[tex]\begin{gathered} \text{16 oz jar of peanut butter for \$2}.49 \\ Unit\text{ Rate=}\frac{\text{\$}2.49}{16\text{ oz}} \\ \approx\$0.16\text{ per oz} \end{gathered}[/tex]

Similarly:

[tex]\begin{gathered} \text{64 oz jar of peanut butter for \$}6.99 \\ Unit\text{ Rate=}\frac{\text{\$}6.99}{64\text{ oz}} \\ \approx\$0.11\text{ per oz} \end{gathered}[/tex][tex]0.11<0.16[/tex]

Therefore, the better buy is a 64 oz jar of peanut butter for $6.99.

If 2/1 = 60°, find the measures of the other angles if the lines / and m are parallel.

Answers

We have a transversal with two parallel lines:

If ∠1 =60°

∠1 = ∠8 using the alternate exterior angles property.

Also

∠1 =∠4 and ∠8 = ∠5 using the corresponding angles ( they are vertical angles)

Now, ∠1 and ∠2 are supplementary angles, they together form a right line.

Supplementary angles are equal to 180°, then, we can deduce the next equation:

∠1 + ∠2 = 180°

Replacing ∠1 = 60°

60° + ∠2 = 180°

Solve for ∠2:

∠2 = 180° - 60°

∠2 = 120°

Then ∠2 = ∠7 using the alternate exterior angles property.

Also

∠7 = ∠6 and ∠2 = ∠3

So far we got:

∠1 = ∠4 = ∠5 = ∠8 = 60°

and

∠2 = ∠3 = ∠6 = ∠7 = 120°

Therefore, the correct answer is the third option.

Sarah blends coffee for tasti delight. She needs to prepare 110 pounds of blended coffee beans selling for $4.91 per pound. She plans to do this by blending g together a high quality bean coating $6.00 per pound and a cheaper bean at $3.00 per pound. To the nearest pound, find how much high quality coffee bean and how much cheaper coffee bean she should blend.

Answers

Let x = amount of high quality coffee bean

110 - x = amount of cheaper coffee bean

6x + 3(110 - x) = 4.91 * 110

open the parenthesis

6x + 330 - 3x = 540.1

6x - 3x + 330 = 540.1

3x + 330 = 540.1

subtract 330 from both-side of the equation

3x = 540.1 - 330

3x =210.1

Divide both-side of the equation by 3

x = 70.0

Therefore, amount of high quality coffee bean = 70 lbs

Amount of low quality coffee bean = 110 - x = 110 - 70 =40 lbs

I really need help with thisGraph y - 4 = -2(x-1)

Answers

We are given the following equation in the point-slope form.

[tex]y-4=-2(x-1)[/tex]

Recall that the general form of the equation in point-slope form is given by

[tex]y-y_1=m(x-x_1)[/tex]

Comparing the given equation with the point-slope form, we have

m = -2

Point = (1, 4)

Recall that the slope is given by

[tex]m=\frac{\text{rise}}{\text{run}}=\frac{-2}{1}[/tex]

Start at point (1, 4) then 2 units down and 1 unit to the right.

As you can see, we started at the point (1, 4) then sketched other points by going 2 units down and 1 unit to the right.

Write full solution.Find the domain and solve the following equation:log,(x-5)+log, (x+3) = 1

Answers

We have the following equation:

[tex]\log _,(x-5)+\log _,(x+3)=1[/tex]

First, we apply the apply the following rule:

[tex]\begin{gathered} \log _ab+\log _ac=\log _ab\cdot c \\ \log _,(x-5)+\log _,(x+3)=\log _,(x-5)\cdot(x+3) \\ \log _,(x-5)\cdot(x+3)=1 \\ \end{gathered}[/tex]

For any non null number, we have:

[tex]n^0=1[/tex]

Therefore, we have:

[tex]\begin{gathered} (x-5)\cdot(x+3)=0 \\ x_1=5 \\ x_2=-3 \end{gathered}[/tex]

Which city had the most days with a high less than 32 degrees F?

Answers

Answer

3. City B had the most days with a high less than 32 degrees F.

4. City B had the most days over 90 degrees F.

Explanation

Please check the annotated diagram of the given histogram below for better understanding.

Find the circumference of the circle to the nearest tenth. Use 3.14 for p. The length from the center of the circle is 17in2849.4 in.53.4 in.907.5 in.106.8 in.

Answers

106.8 in (option D)

Explanation:

In the absence of a diagram:

Since the length from the center of the circle is 17in, this means it is the radius.

As radius is from the center to the circumference.

Circumference of a circle = 2πr

π = 3.14

r = 17 in

[tex]\text{Circumference = 2}\times3.14\times17[/tex][tex]\text{Circumference of the circle = 106.76 in}[/tex]

To the nearest tenth, the circumfernce of the circle is 106.8 in (option D)

Can somebody please help me with 2. B? Algebra 2.

Answers

2.b

y= 3 (x-1)^2

It has been Stretched by 3 ,and translated 1 unit to the right

suppose 160 geology students measure the mass of an ore sample. due to the human error and limitations in the reliability of the balance not all the readings are equal the result are found to closely approximate a normal curve with the mean 85 g and the standard deviation 1 g . use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings more than 85 g

Answers

Empirical rule formula:

- 68% of data falls between 1 standard deviation about mean (34% on left side and 34% on right side)

- 95% of data falls between 2 standard deviations about mean (47.5% on left side and 47.5% on right side)

- 99.7% of data falls within 3 standard deviations from the mean.(49.85% on left side and 49.85% on right side).

According to the simmetry of the normal curve and the empirical rule, 49.85 % of students reported a value greater than 85 g. It implies 80 geology students reported a value greater than 85 g.

How many hours is the water level increasing? ___ hours(Write a whole number)

Answers

Answer:

[tex]25[/tex]

Explanation:

Here, we want to know the number of hours for which the water level is increasing

We can get this from the given plot

We had an increase, then it became constant, followed by a decrease and then being constant again

There was an increase from 0 to 3000 gallons within 25 hours

Thus, we can say the water level increased for 25 hours

. Suppose Calvin Cordozar Broadus, Jr. (aka Snoop Doggy Dogg) is considering moving his family toManhattan. His real estate agent has managed to locate a penthouse apartment that overlooks Central Park for $2.4million. He will have $2.1 million from the sale of his current home as a down payment. Snoop would like to finance theremainder of the cost and his banker has presented two options: a 30-year fixed-rate mortgage at 8% or a 20-year fixedrate mortgage at 7.5%.6. How much will Snoop have to finance?7. Determine the monthly mortgage payment for the 30-year loan. (round to the hundredths places)8. Determine the monthly mortgage payment for the 20-year loan. (round to the hundredths places)9. Which loan is more economical in the long run?10. How much is saved in interest by choosing the more economical mortgage? (round to the hundredths places)

Answers

Solution

Question 6)

The price of the Penthouse is $2.4 million

Down Payment is $2.1 Million

So the amount that must be financed is $2.4 million - $2.1 million

= $0.3 million or $300,000

Question 7)

A mortgage is loan one takes to buy a house or other property. To determine the monthly loan payment (P) one uses the formula

[tex]P\text{ = }\frac{\frac{r}{m}A}{1\text{ - }(1\text{ + }(\frac{r}{m})-mt)}[/tex]

Where A is the loan amount, m is the number of payments per year, t is the number of years, and r is the interest rate of the loan.

To evaluate two mortgages in terms of economics it is advised to calculate the interest outgo on each of them and compare.

Monthly Payments (P) for the loan can be found using the formula

[tex]P=\frac{\frac{r}{m}\text{A}}{\text{1{\text{{\text{-\lparen}}}}1+{\text{{\text{\lparen}}}}}\frac{r}{m})^{-mt})}[/tex]

Where A is the loan amount, m is the number of payments per year, t is the number of years, and r is the interest rate.

For a 30-year loan at 8%:

Given data

A = $300,000

r = 8%

t = 30

m = 12

[tex]\begin{gathered} P=\frac{\frac{8}{12}\text{ }\times\text{ \$300,000}}{1\text{ - }(1\text{ + }(\frac{8}{12})^{-12\times30})} \\ =\text{ \$ 2 , 201.29 } \end{gathered}[/tex]

The monthly loan payment for a 30-year loan at 8% would be $2,201.29

Question 8)

For a 20-year loan at 7.5%:

[tex]P\text{ = }\frac{\frac{r}{m}\times\text{ A}}{1\text{ - }(\text{ 1 + }(\frac{r}{m})(-mt))}[/tex]

Given data

A = $300,000

r = 7.5%

t = 20

m = 12

Substitute the values in the equation.

[tex]\begin{gathered} \text{P = }\frac{\frac{7.5}{12}\times300000}{1\text{ - }(1\text{ + }(\frac{7.5}{12})(-12\times20)} \\ =\text{ \$ 2 , 416.78 } \end{gathered}[/tex]

The monthly loan payment for a 20-year loan at 7.5% = $2,416.78

Question 9)

30 years loan

Find the number of months in 30 years by multiplying 30 by 12

Number of months in 30 years = 30 x 12 = 360 months

Next, calculate the interest payment.

[tex]\begin{gathered} \text{Interest payment = \$2201.29}\times\text{ 360 - \$300,000} \\ Interest\text{ payment = \$492464.40} \end{gathered}[/tex]

20 years loan

Find the number of months in 20 years by multiplying 20 by 12

Number of months in 20 years = 20 x 12 = 240 months

Next, calculate the interest payment.

[tex]\begin{gathered} Interest\text{ payment = \$2416.78 }\times\text{ 240 - \$300000} \\ Interest\text{payment=}\operatorname{\$}580,027.2\text{-}\operatorname{\$}\text{\times300,000} \\ Interest\text{payment=}\operatorname{\$}280,027.20 \end{gathered}[/tex]

20 years mortgage is more economical to choose because you will pay less interest.

Question 10)

To find the money saved in the interest, you will subtract the interest paid in 20 years from the interest paid in 30 years.

Interest saved = $492464.4 - $280027.2

Interest saved = $212,437.20

Simplify with positive exponents: $$\left(\frac{\left(-5y^3z^4\right)^2\left(yz^5\right)^{-2}}{\left(10y^4z\right)^3\left(y^3z^2\right)^{-1}}\right)$$

Answers

We have the expression:

[tex]\mleft(\frac{\left(-5y^3z^4\right)^2\left(yz^5\right)^{-2}}{\left(10y^4z\right)^3\left(y^3z^2\right)^{-1}}\mright)[/tex]

And we have to simplify it.

To do that, it is useful to see how many variables are in the expression and how they are placed. In this case, there are 2 variables (y and z) that are factors with different exponents and are within parenthesis that have their own exponents.

Then, we start by rearranging the factors and applying the exponents so there are no more parenthesis.

After that we will group each variable and simplify the exponents.

The steps to do this are:

[tex]\begin{gathered} \mleft(\frac{\left(-5y^3z^4\right)^2\left(yz^5\right)^{-2}}{\left(10y^4z\right)^3\left(y^3z^2\right)^{-1}}\mright) \\ \frac{(-5)^2\cdot y^{3\cdot2}\cdot z^{4\cdot2}\cdot y^{-2}\cdot z^{5\cdot(-2)}}{10^3\cdot y^{4\cdot3}\cdot z^3\cdot y^{3\cdot(-1)}\cdot z^{2\cdot(-1)}} \\ \frac{25\cdot y^6\cdot z^8\cdot y^{-2}\cdot z^{-10}}{1000\cdot y^{12}\cdot z^3\cdot y^{-3}\cdot z^{-2}} \end{gathered}[/tex]

We can now group the similar variables as:

[tex]\begin{gathered} (\frac{25}{1000})\cdot(\frac{y^6\cdot y^{-2}}{y^{12}\cdot y^{-3}})\cdot(\frac{z^8\cdot z^{-10}}{z^3\cdot z^{-2}}) \\ \frac{1}{40}\cdot y^{6+(-2)-12-(-3)}\cdot z^{8+(-10)-3-(-2)} \\ \frac{1}{40}\cdot y^{-5}\cdot z^{-3} \\ \frac{1}{40y^5z^3} \end{gathered}[/tex]

In this last part, we apply the product of a power rule, where we have a product of numbers with the same base. If that is the case, we can add the exponents:

[tex]x^b\cdot x^c=x^{b+c}[/tex]

In the case of a quotient, we can apply the rule but the exponent in the denominator is substracted instead of added.

Answer:

The simplified expression is: 1/(40y^5z^3).

[tex]\frac{1}{40y^5z^3}[/tex]

The Lone Star Shipping Company charges $14 plus $2 a pound to ship an overnight package. Discount Shipping Company charges $20 plus $1.50 a pound to ship an overnight package. For what weight is the charge the same for the two companies?Required to answer. Multi Line Text.

Answers

[tex]\begin{gathered} \text{Lone star:} \\ C_1=2P+14 \\ \text{Discount company:} \\ C_2=1.50P\text{ +20} \\ \text{where C is the cost and P the pounds} \end{gathered}[/tex][tex]\begin{gathered} \text{Now, the charge is the same when:} \\ C_1=C_2 \\ \text{this implies that} \\ 2P+14=1.50P+20 \\ \text{hence} \\ 2P-1.50P=20-14 \\ 0.5P=6 \\ P=\frac{6}{0.5} \\ P=12 \\ \text{HENCE, THE SAME CHARGE OCUrrs when P=12 pounds} \end{gathered}[/tex]

z is jointly proportional to x ^ 3 and y ^ 2. If z = 28 whenx x = 5 and y = 4 find x = 6 and y = 5 (Round off your answer to the nearest hundredth)

Answers

We know that z is proportional to x^3 and y^2.

We can express this with a proportionality constant k as:

[tex]z=k\cdot x^3\cdot y^2[/tex]

We know that when x = 5 and y = 4, z = 28.

We can use this to find the value of k as:

[tex]\begin{gathered} z=kx^3y^2 \\ 28=k(5)^3(4)^2 \\ 28=k*125*16 \\ k=\frac{28}{125*16} \\ k=\frac{28}{2000} \\ k=0.014 \end{gathered}[/tex]

We can know calculate z for x = 6 and y =5:

[tex]\begin{gathered} z=0.014x^3y^2 \\ z=0.014*6^3*5^2 \\ z=0.014*216*25 \\ z=75.6 \end{gathered}[/tex]

Answer: 75.6

For the following terms name the operation using a) words and b) symbols13. Sum 14. Quotient

Answers

The symbol of the sum is +

The symbol to calculate the quotient is / or ÷

Example: 7 + 5 = 12

6 ÷ 2 = 3

Where 12 is the sum of 12 and 5 and 3 is the quotient of 6 divided by 2.

Answer: Sum: +

Quotient: ÷

I need to see if I got my # 4 answer right

Answers

The ratio of green to yellow rattles sold is 2 : 7

Total number of rattles sold = 108

Number of green rattles sold :

(Total rattles / sum of ratio) × green ratio

(108 / (2 + 7)) × 2

(108 / 9) × 2 = 12 × 2 = 24 rattles

Number of Yellow rattles sold :

(Total rattles / sum of ratio) × yellow ratio

(108 / (2 + 7)) × 7

(108 / 9) × 7 = 12 × 7 = 84 rattles

First try was incorrect 2 The area of the trapezoid below is 20 mm . Find the height. Round to the nearest tenth if the answer is in decimal form. 6 mm h 5 mm 4 mm

Answers

[tex]\begin{gathered} \text{Area =}\frac{(4+6)}{2}\cdot h \\ \text{Area =20mm}^2 \\ 20=\frac{(4+6)}{2}\cdot h \\ 20=5\cdot h \\ h=\frac{20}{5} \\ h=4\operatorname{mm} \\ \text{the height is 4mm} \end{gathered}[/tex]

Recommendations Language arts Science Mund the slope from two points a and the slope of the line that passes through (10, 5) and (7,4). Simplify your answer and write it as a proper fraction, improper fraction, or in Noring ready yet These can help

Answers

To find the slope of the line that passes through (10, 5) and (7,4)

we will use the formula:

[tex]\text{slope =}\frac{y_2-y_1}{x_2-x_1}[/tex]

x₁= 10 y₁=5 x₂=7 y₂=4

[tex]\text{slope}=\frac{4-5}{7-10}[/tex]

Evaluate:

[tex]\text{slope}=\frac{-1}{-3}[/tex][tex]\text{slope}=\frac{1}{3}[/tex]

Suppose a sample of 1453 tankers is drawn. Of these ships 989 did not have spills. Using the data estimate the proportion of all tankers that had spills. Answer your answer as a fraction or a decimal number rounded to three decimal places.

Answers

We have the following situation:

• We have a sample of 1453, n = 1453.

• Of these ships, 989 did not have spills.

And from this, we need to estimate the proportion of oil tankers that had spills.

To find it, we can proceed as follows:

1. We need to find the sample proportion of ships that had spills. These ships are:

[tex]\begin{gathered} 989\text{ ships did not have spills from 1453.} \\ \text{ Then the ships that have spills are:} \\ 1453-989=464 \end{gathered}[/tex]

2. Then the sample proportion is given by:

[tex]\begin{gathered} \hat{p}=\frac{464}{1453}=0.319339298004 \\ \\ \text{ If we round this value to a decimal number rounded to three decimal places: } \\ \\ \hat{p}=0.319 \end{gathered}[/tex]

Therefore, in summary, the proportion of oil tankers that had spills is (as a fraction or decimal with three places):

[tex]\begin{gathered} \hat{p}=\frac{464}{1453} \\ \\ \hat{p}=0.319 \end{gathered}[/tex]

Solve.Consuela used this recipe to make breakfast trail mix. She filled each bag with 4 cups of the mix. How many bags did she fill?

Answers

First, we add all the cups.

[tex]12+9+7=28[/tex]

So, the mix is equivalent to 28 cups. If she uses 4 cups for each bag, we have

[tex]\frac{28}{4}=7[/tex]Hence, she filled 7 bags in total.

Given the function f(x) = x^2 - 7x + 8 determine the average rate of change of the function over the interval -1 ≤ x ≤ 7

Answers

Answer

-1

Step-by-step explanation

The average rate of change of function f(x) over the interval a ≤ x ≤ b is calculated as follows:

[tex]avg\text{ rate of change }=\frac{f(b)-f(a)}{b-a}[/tex]

where f(b) and f(a) are the function f(x) evaluated at x = b and x = a respectively.

In this case, the function is:

[tex]f(x)=x^2-7x+8[/tex]

And the interval is -1 ≤ x ≤ 7. Evaluating f(x) at x = 7 and x = -1:

[tex]\begin{gathered} f(7)=7^2-7\cdot7+8 \\ f(7)=49-49+8 \\ f(7)=8 \\ f(-1)=(-1)^2-7\cdot(-1)+8 \\ f(-1)=1+7+8 \\ f(-1)=16 \end{gathered}[/tex]

Then, the average rate of change of this function is:

[tex]\begin{gathered} avg\text{ rate of change }=\frac{f(7)-f(-1)}{7-(-1)} \\ avg\text{ rate of change}=\frac{8-16}{7+1} \\ avg\text{ rate of change}=-1 \end{gathered}[/tex]

Out of 350 students. 3 15 went on the class field trip. What percent of the students did not go on the class field trip?

Answers

In total we have 350 students

315 went on the class field trip

In order to know how many students did not go on the class field trip

350-315=35

if

350--- 100%

35 --- x

where x is the percentage of students did not go on the class field trip

[tex]x=\frac{35\times100}{350}=\frac{3500}{350}=10[/tex]

the percentage of students did not go on the class field trip is 10%

What is the eighth term of the arithmetic sequence defined as: A(n) = 21+ 2(n-1)?
39
37
35
32

Answers

The eighth term of the arithmetic sequence defined as A(n) = 21+ 2(n-1) is 35.

What is meant by arithmetic sequence?An arithmetic sequence is a set of numbers that are ordered and have a common difference between each consecutive term. In the arithmetic sequence 3, 9, 15, 21, 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence. An arithmetic sequence is a set of numbers that follow a specific pattern. It is an arithmetic sequence if you take any number in the sequence and subtract it from the previous one, and the result is always the same or constant.

Let the function be A(n) = 21 + 2(n - 1)

then the value of n be 8

an = 21 + 2(n - 1)

= 21 + 2(8 - 1)

Simplifying the above equation,

= 21 + 2 × 7

= 21 + 14

= 35

Hence,  The eighth term of the arithmetic sequence defined as: A(n) = 21+ 2(n-1) is 35

To learn more about arithmetic sequence, refer to:

https://brainly.com/question/6561461

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Sasha wrote four statements about the graph shown. She wrotetwo incorrect statements. Identify the two statements and writethe correct description or label.a. Since a > 0, the graph opens upward.b. Since lal > 1, the shape of the parabola is widerthan the quadratic parent function.c. The vertex of the parabola is (0, 0).d. The axis of symmetry is the line y = 0.TotSign Write the sum using sigma notation: 123 +4+***+122= sum l ^ A B where 8 A marine biologist is using an underwater drone to study a delicatecoral reef. The linear equation 20y 30x = -900 gives the drone'selevation, y, in meters from the surface of the water after x seconds.Graph the equation. What are the slope and y-intercept of the line?What part of the graph represents this situation? 1) For the following pairs equations explain why the equations are equivalent (or not) -11(x-2)=8 x-2=8+11 2)For the following pairs of equations explain why the equations are equivalent. (Or Not!) -3(2x+9)=12 2x+9=-4 Question 8 of 10 Multiply (x - 2)(3x + 4) using the distributive property. Select the answer choice showing the correct distribution. A. (x-2)(3x) + (x-2)(4) B. (X)(3x + 4) + (x - 2) C. (x-2)(3x) + (3x)(4) D. (X)(3x) + 4(x) + 3x + 4 SUBMIT For csc 330:a) state value of the ratio exactlyb) find one equivalent expressionc) draw a diagram to illustarte. f(x) = 5x2 + 2x 3What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. Find the value of 9y+1 given that -2y-1=5.Simplify your answer as much as possible. 2. 205 randomly selected students from a certain community college were asked a question "Withwhom do you find it easier to make friends? Possible responses were 'opposite sex', 'samesex''no difference'. The students were also categorized as male or female. The followingtable records the data collected.Opposite Sex Same Sex No Difference TotalFemale 582070 148Male 241340 77Total 8233110 225a) What is the probability that a randomly selected student would say that it is easier to makefriends with the same sex or male?b. What proportion of female students answered that it is easier to make friends with the samesex?c. What probability that a male student said it easier to make friends with opposite sex? Which expression best estimates 6O 7-2 6-18-3 3-2NEATRY10:DAITEELKATEER EEN ANDER HEAADEMPIRENTE] PAR MEpar spenna#] [3]5\y\x{] =>DEEEN TOEGERHENDEROgeJENTERE3 - 10 How do you find the common difference of an arithmetic sequence? Ex. 28,18,8,-2 A sphere and a cylinder each have the same radius. The cylinder has a height that is triple the radius. Which figure has a greater volume, the cylinder or the sphere? 9x +7x simplify the expression ABC is a triangle for which < ABC = 90, AB= 10cm and BC=15cm, Find Ac? how do I solve this? What is the least common multiple of 62 +39 - 21 and 6x +54x+84? O 6x +54x+84 6x +93x +63 62 +52x + 111x 42 O 12x + 102x + 114 - 84 Find a dishes between an order pairs (-2 -1) and (-5,-4) round your solution to the nearest 10th, if necessary. simplify (2^x-6)(^x-2) 1.Given the polynomial12x5 + 3xy 3 - 15x' + 2x8+ 101.Put the polynomial in standard form.2. What is the leading coefficient?3. What is the constant?4. What is the degree of the polynomial? Balance the equation by placing appropriate coefficients in front of each reactant and product Question 9 (3 points)y = -x3 + 2x + 3d: {-2, 1,2} r: {3Blank 1:Blank 2:IBlank 3: