If
f
(
x
)
=
x
6
+
3
x
−
1
f(x)=x
6
+3x−1, then what is the remainder when
f
(
x
)
f(x) is divided by
x
+
1
x+1?

The volume of a sphere with a radius of 3 inches is [tex]\(36 \pi\)[/tex] cubic inches. Therefore, the correct option is [tex]\(36 \pi\)[/tex] cubic inches.

The volume V of a sphere with radius r is given by the formula:

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

Given that the radius r is 3 inches, we can substitute this value into the formula:

[tex]\[ V = \frac{4}{3} \pi (3)^3 \]\[ V = \frac{4}{3} \pi (27) \]\[ V = \frac{4}{3} \times 27 \times \pi \]\[ V = 36 \pi \][/tex]

So, the volume of the sphere is [tex]\( 36 \pi \)[/tex] cubic inches.

Therefore, the correct option is: [tex]\( 36 \pi \)[/tex] cubic inches.

Complete Question:

The radius of a sphere is 3 inches. Which represents the volume of the sphere?

[tex]$12 \pi$[/tex] cubic inches

[tex]$36 \pi$[/tex] cubic inches

[tex]$64 \pi$[/tex] cubic inches

[tex]$81 \pi$[/tex] cubic inches

Answer:

[tex]x=-50[/tex]

Step-by-step explanation:

we have

[tex]\frac{x}{5} =-10[/tex]

Solve for x

That means ----> isolate the variable x

Multiply by 5 both sides to remove the fraction

[tex]\frac{x}{5}(5) =-10(5)[/tex]

Simplify

[tex]x=-50[/tex]

Answer:

1.509909034 x10 ^36

Step-by-step explanation:

10 plus 18 is 28

Then you would multiply 28 by 25 numbers of itself.

Answer:

Step-by-step explanation:

14 strikes out of 70 attempts.....what percent were strikes ?

14/70 = 0.2

to turn a decimal to a percent, either multiply by 100 or move the decimal point 2 spaces to the right.

0.2 * 100 = 20% <==== strikes

Answer:

20%

Step-by-step explanation:

Step-by-step explanation:

firstly there is hole in the ozone

secondly i believe it is because of the axis of the earth and that the raidiation to coming to the equator not the poles

Answer:

The cost for full day car rental will be $100.

Step-by-step explanation:

A bike shop charges x dollars to rent a bike for half a day. It charges (x + 40) dollars to rent a bike for a full day.

On that day the shop made a total of $600 from the bike rentals. If there were 5 half day and 3 full day rental, then we can write

5x + 3(x + 40) = 600

⇒ 8x = 600 - 120

⇒ 8x = 480

⇒ x = $60

Therefore, the cost for full day car rental will be $(x + 40) = $100. (Answer)

Answer:

5 3.00 for 4 is 1.50 each so add 3.00 +1.50 is 4.50

Answer:

the zeros as  x = 5 or x = -6 . SO the correct option is Option B.

Step-by-step explanation:

i) the zeros of any expression of f(x) is found by equating f(x) to zero and then solving for x.

ii) therefore to find the zeros ( or roots) of the given expression we can write f(x) = [tex]x^{2} + x - 30 = 0[/tex]

iii) therefore [tex]x^{2} + x - 30 = 0[/tex]   ⇒  [tex]x^{2} + 6x - 5x - 30 = 0[/tex]  .... from visual observation

 therefore we can write [tex]x( x + 6) -5(x + 6) = 0[/tex]    ⇒ [tex](x - 5)(x + 6) = 0[/tex]

 therefore either x - 5 = 0, or, x + 6 = 0 if the above equation is to be true.

iv) therefore solving for x we get the zeros as  x = 5 or x = -6. So the correct option is Option B.

Answer:

Therefore the zeros of

[tex]f(x)=x^{2}+x-30[/tex]

are

[tex]x=-6\ and\ x= 5[/tex]

Step-by-step explanation:

Given:

[tex]f(x)=x^{2}+x-30[/tex]

To Find:

Zeros of the  function.

Solution:

Zeros of Polynomial or function:

Zeros of the polynomial means while substituting the value of X in the polynomial you will get the value of the polynomial or function equals to Zero.

Hence to find a value of zeros , the value of function should be zero.

Therefore,

f(x) =0

[tex]x^{2}+x-30=0[/tex]

To find the value of 'x' we need to factorize the above quadratic equation.

First is to remove the factor of -30 such that  when you add the factors you should get one.

-30 = 6 × -5

6 - 5 = 1

Hence by splitting the middle term we get

[tex]x^{2}+6x-5x-30=0\\x(x+6)-5(x+6)=0\\(x+6)(x-5)=0\\x+6=0\ or\ x-5=0\\x=-6\ or\ x=5[/tex]

Therefore the zeros of

[tex]f(x)=x^{2}+x-30[/tex]

are

[tex]x=-6\ and\ x= 5[/tex]

Option A and Option B are correct answers.

Step-by-step explanation:

Option a: Diego's teacher writes a test worth 100 points. There are 6 more multiple choice questions than short answer questions.

Reason:

Let x denote the multiple choice questions.

Let y denote the short answer questions.

It is given that there are 6 more multiple choice questions than short answer questions and writing it as equations,

[tex]y=x+6[/tex]

Also, given that Diego's teacher writes a test worth 100 points and writing it as equations,

[tex]x+y=100[/tex]

Option b: Lin and her younger cousin measure their heights. They notice that Lin is 6 inches taller, and their heights add up to exactly 100 inches.

Reason:

Lin is represented by the variable y.

Her younger cousin is represented by the variable x.

It is given that Lin is 6 inches taller and writing it as equation, we get,

[tex]y=x+6[/tex]

Also, given that their heights add up to exactly 100 inches and thus, writing it as equation, we get,

[tex]x+y=100[/tex]

Thus, Option a and Option b represent the same system of equations. Hence, both story can be represented by the system of equations.

The story that can be represented with the system of equations is story B.

Description of simultaneous equations

Simultaneous equations are a set of two or more equations that have to be solved together in order to determine the needed values.

If Lin is 6 inches taller than her cousin, if Lin's height is represented with y and her cousin's height is represented with x, then the equation is: y = x + 6. If the sum of their ages is 100, this can be represented with: x + y = 100.

To learn more about simultaneous equations, please check: https://brainly.com/question/25875552

Answer:

Step-by-step explanation:

$3307.50

Answer:

river c is 2850 and river d is2650

Step-by-step explanation:

Answer:

Step-by-step explanation:

I would look at it by taking the 100 off of the 5500. Leaving you with 5400 you would then Divide that by two since there is two rivers being described. So River d is 2700 miles long and then river c is 2800. Hope it helps :)

first you should find the hourly rate so you take 34 and divide it by 4 to get 8.5 which will be the hourly rate

then you take 8.5 and multiply it by 10 to get how much she'll earn for 10 hours of working

the answer for how much will she earn in 10 hours is $85.

Final answer:

To determine if a triangle can be formed given three side lengths, apply the triangle inequality theorem by comparing the sum of any two sides to the length of the remaining side. Option B and option D would give triangles.

Explanation:

To determine if a triangle can be formed given the measures of three sides, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Let's examine each given set of side lengths:

A. 2cm, 4cm, 8cm: In this case, 2cm + 4cm = 6cm, which is less than 8cm. So, a triangle cannot be formed with these side lengths.

B. 3cm, 4cm, 6cm: Here, 3cm + 4cm = 7cm, which is greater than 6cm. The sum of any two sides is always greater than the third side, so a triangle can be formed with these side lengths.

C. 4cm, 5cm, 10cm: In this case, 4cm + 5cm = 9cm, which is less than 10cm. So, a triangle cannot be formed with these side lengths.

D. 5cm, 6cm, 12cm: Here, 5cm + 6cm = 11cm, which is greater than 12cm. The sum of any two sides is always greater than the third side, so a triangle can be formed with these side lengths.

Therefore, option B (3cm, 4cm, 6cm) and option D (5cm, 6cm, 12cm) would give triangles.

Answer:

1540

Step-by-step explanation:

Add 718 and 822! Thanks

To find out how many people saw the play altogether, add the number of people who went on Friday and Saturday. The total number of people who saw the play is 1540.

To find out how many people saw the play altogether, we need to add the number of people who went on Friday and the number of people who went on Saturday.

On Friday, 718 people went to the school play. On Saturday, 822 people went.

To find the total number of people who saw the play, we add 718 and 822:

Total number of people = 718 + 822 = 1540

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Final answer:

After using 4 1/4 yards out of 5 3/4 yards of cloth to make curtains, 1 1/2 yards of cloth remain.

Explanation:

You are provided with 5 3/4 yards of cloth and you use 4 1/4 yards for making curtains. To find out how much cloth remains, you need to subtract the amount used from the total amount provided. You perform the subtraction by converting the mixed numbers to improper fractions or by subtracting the whole numbers and fractions separately.

First, subtract whole numbers:

Next, subtract the fractions:

Combine the whole number and the fraction for the final answer:

The fifth term of the geometric sequence is 640, so the correct option is D.

Here we have a geometric sequence, such that the terms are given by:

[tex]A_n = 40*(-2)^{(n-1)}[/tex]

To get the 5-th term, we just need to replace n by 5 on the above rule, so we can write:

[tex]A_5 = 40*(-2)^{(5-1)} = 40*(-2)^4 = 640[/tex]

Then the value of the 5-th term is 640, which means that the correct option is D.

If you want to learn more about geometric sequences:

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800/85 = 9.411764705882353‬ inches

ans = 9.411764705882353‬ inches

Answer:

9.41 inches to the nearest hundredth.

Step-by-step explanation:

By proportion it is 800 / 85

= 9.41 inches.

Answer:

one solution

Step-by-step explanation:

the numbers aren't the same, the variables don't repeat

Answer:

y = - [tex]\frac{2}{3}[/tex] x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Rearrange 2x + 3y = 6 into this form

Subtract 2x from both sides

3y = - 2x + 6 ( divide all 3 terms by 3 )

y = - [tex]\frac{2}{3}[/tex] x + 2 ← in slope- intercept form

Answer:

c

Step-by-step explanation:

c

y = 5x + 4 is the equation of the line whose slope is 5 and y intercept is (0,4)

Solution:

Given that we have to write the equation of the line whose slope is 5 and y intercept is (0,4)

The equation of line in slope intercept form is given as:

y = mx + c -------- eqn 1

Where, "m" is the slope of line and "c" is the y - intercept

Given that,

Slope = m = 5

Also, y intercept is (0,4)

Therefore, c = 4

Substitute c = 4 and m = 5 in eqn 1 to get equation of line

y = 5x + 4

Thus the equation of line is found

Answer:

133%

Step-by-step explanation:

24/18=4/3=1.33...=133%

Answer:

75%

Step-by-step explanation:

because it = 18/24 or 75%

Answer:

Step-by-step explanation:

y = -x + 1

2y = -2x + 2......reduce by divide everything by 2 and u get y = -x + 1

same line......infinite solutions....CONSISTENT and  DEPENDENT

Final answer:

The system of equations represented by y = -x + 1 and 2y = -2x + 2 is both consistent and dependent, as the equations are essentially the same, representing the same line with infinitely many solutions.

Explanation:

To determine whether the system of equations is consistent and independent, consistent and dependent, or inconsistent, we need to assess if they have one unique solution, infinitely many solutions, or no solutions at all. The two equations given are y = -x + 1 and 2y = -2x + 2.

Consistency: To see if the equations are consistent, they must at least have one solution. By looking at the second equation, we can simplify it by dividing every term by 2, yielding y = -x + 1, which is identical to the first equation. This implies that both equations actually represent the same line.

Dependence: Given that both equations are the same, they have an infinite number of solutions where the two lines would intersect if they were different. Since they are the same line, the system is considered dependent.

Therefore, the system of equations is both consistent and dependent, as both equations are the same, representing the same line and thus having infinitely many solutions.

The value of k is 8

Solution:

Given that,  points (9, 9) and (10, k) fall on a line with a slope of -1

To find: value of "k"

The slope of a line with points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given as:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Here given that,

slope = m = -1

[tex](x_1, y_1) = (9, 9)\\\\(x_2, y_2) = (10, k)[/tex]

Substitute the values in formula, and solve to get value of k

[tex]m = \frac{k-9}{10-9}\\\\-1 = \frac{k-9}{10-9}\\\\-1 = \frac{k-9}{1}\\\\k-9 = -1\\\\k = -1+9\\\\k = 8[/tex]

Thus the value of k is 8

Answer: 75%

Step-by-step explanation:

Height given :

69, 62, 73, 67, 63, 65, 73, 71, 70, 66, 59, 75

The total number of height given = 12

The height less than 73 are 69 , 62, 67 ,63 , 65 , 71 , 70 , 66 , 59

The total number of heights less than 73 = 9

Therefore : the percentage of these students who are shorter than 73 inches = total number of students shorter than 73/ total number of height x 100

= 9/12 x 100

= 75%

About 75% of the students are shorter than 73 inches. This was determined by counting the number of students shorter than 73 inches (9 students) and dividing by the total number of students (12 students), then multiplying by 100%

To calculate the percentage of students shorter than 73 inches, you first need to count how many students are shorter than 73 inches. From the given data, the heights of the students shorter than 73 inches are 69, 62, 67, 63, 65, 71, 70, 66, and 59. Thus, there are 9 students out of 12 who are shorter than 73 inches.

Now, to get the percentage, you divide the number of shorter students by the total number of students, and then multiply the result by 100. This is how it looks: (9/12)*100% = 75%. Thus, 75% of these students are shorter than 73 inches.

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Answer:

distributive property

Dist. can be identified by x(y+z)

Answer:

Unpaid balance = $ 250.22

Finance charge = $ 3.13

New balance = $ 348.60

Step-by-step explanation:

Calculate the unpaid balance, finance charge, and new balance using the unpaid balance method.Note: interest rate is given as a monthly rate.

Previous balance = $410.22

Payments/credits = $160.00

subtract 410-160 to get unpaid balance

Unpaid balance = $ 250.22

Monthly rate = 1.25%

multiply 250 by monthly rate (decimal) .0125 to get finance charge

Finance charge = $ 3.13

New purchases = $95.25

add unpaid balance and finance charge and new purchases to get new balance

New balance = $ 348.60

Final answer:

To calculate the unpaid balance, finance charge, and new balance using the unpaid balance method, subtract the payments/credits from the previous balance, add the finance charge, add the new purchases, and calculate the new balance.

Explanation:

To calculate the unpaid balance, finance charge, and new balance using the unpaid balance method, follow these steps:

Start with the previous balance.

Subtract the payments/credits.

Add the finance charge.

Add the new purchases.

Calculate the new balance.

For example, with a previous balance of $410.22, payments/credits of $160.00, and new purchases of $95.25, the equation would be: unpaid balance = previous balance - payments/credits = $410.22 - $160.00 = $250.22. The finance charge would then be calculated by multiplying the unpaid balance by the monthly interest rate. Finally, the new balance would be the unpaid balance plus the finance charge and new purchases.