The length of a box is 1 cm more than its width. The height of the box is 8 cm greater than the width. The dimensions can be represented by x, x + 1, and x + 8. Multiply the dimensions and find the greatest common factor of the terms.

Answers

Answer 1

Answer:

The greatest common factor is x

Step-by-step explanation:

Dimensions: x,x+1,x+8

Multiplication of thee dimensions:

⇒ Product      =   [tex]x(x+1)(x+8)\\x(x^{2}+8x+1x+8)\\x(x^{2} +9x+8)\\x^{3} +9x^{2} +8x[/tex]

By factorization ,

[tex]x^{3} +9x^{2} +8x\\x(x^{3} +9x+8)[/tex]

Therefore, the greatest common factor of these terms are x

Answer 2
The greatest common factor (GCF) of a group of numbers has been the largest factor that each of the values shares in common.It refers to the largest number that could be divided evenly into two or smaller numbers.This component is a smaller number that divides evenly into the larger number.

Given Dimensions:

[tex]\to \bold{x, x+1,\ and\ x+8}[/tex]

Multiplying the three dimensions:

[tex]\to x(x+1)(x+8)\\\\\to x(x^2+ 8x+x+8)\\\\\to x(x^2+9x+8)\\\\\to x^3+9x^2+8x\\\\[/tex]

Therefore, the "greatest common factor" of the term is x.

Learn more:

Factor: brainly.com/question/18877132


Related Questions

Sylvia burns 6 calories per minute when she runs, How many calories does she burn when
she runs for 15 minutes?

Answers

Answer: 90 calories

15 x 6 = 90

How many minutes will it take a caterpillar to go seven feet if it travels 24 inches per minute? To travel seven feet, it will take the caterpillar a0 minutes.

Answers

Answer:

3 and and half minutes--> 7ft

Step-by-step explanation:

If it travels 24 inches aka 2ft per minute

then it has to travel 12 inches aka 1ft in 30secs

SO

3mins and 30secs to travel 7ft

24inches--- 2ft---- per minute

4ft--- 2 mins

6ft---- 3mins

7ft--- 3minutes and 30 seconds

There is a zombie outbreak in a city that infects 10 people right away. Each of the 10 zombies are able to infect 2 people every minute. How many people are infected in 8 minutes?

Answers

160 people infected in 8 min

Help with this find the image of (1 ,2) after a reflection about y=x followed by a reflection about y=-x

Answers

Answer: (-1, -2)

Step-by-step explanation:

so at first you have (1, 2)

then you were asked to reflect about y=x which is (x, y) = (y, -x)

(1, 2) = (2, -1)

then followed by y=-x which is (x, y) = (-y, -x)

(2, -1) = (-1, -2)

I hope this helps!

What is the relationship between the area of ABCD and the area of EFGH? Quadrilateral ABCD with side measures 18 for AB, 24 for BC; quadrilateral EFGH with side measures 6 for EF, x for FG The ratio of the area of ABCD to the area of EFGH is 1:9. The ratio of the area of ABCD to the area of EFGH is 3:1. The ratio of the area of ABCD to the area of EFGH is 1:3. The ratio of the area of ABCD to the area of EFGH is 9:1.

Answers

Answer:

The ratio of the area of ABCD to the area of EFGH is 9:1.

Step-by-step explanation:

Let us assume that the shapes are rectangles and they are similar. If the two shapes are similar then their sides are in the same proportion. Therefore the ratio of the sides are in the same proportion.

[tex]\frac{AB}{BC}=\frac{EF}{FG}\\ \\\frac{18}{24}=\frac{6}{x}\\\\18x=24*6\\ \\x=\frac{24*6}{18}=8[/tex]

The area of ABCD = AB × BC = 18 × 24 = 432

The area of EFGH = EF × FG = 6 × 8 = 48

The ratio of the area of ABCD to the area of EFGH = Area of ABCD / Area of EFGH = 432 / 48 = 9/1 = 9 : 1

Read the following statements. The sum of the angle measures of a triangle is 180°. Two angles of a triangle measure 40°and
60", so Juan concludes that the third angle measures 80°. What do you notice about the how the conclusions were made from
the statement above?

Answers

Answer:

what number must be added to sum of two angles that the sum of three angles become 180.

Since sum of two angles is 100 , 80 must be added to 100 to make it equal to 180.

Step-by-step explanation:

Given

sum of measure of angle of triangle = 180°

given two angles 40°and  60°

Let the third angle be x°

thus

40°+  60°+x° = 180°

100°+x° = 180°

x° =  180°- 100° =  80°

Thus, third angle measure 80°

She must have sum the first two known angles.

as given sum of three angles are 180

she must have assumed other angle to be x

then sum of all three angles must be 180

now to find third angle she subtracted sum of two known angles to find third angle.

other way can what number must be added to sum of two angles that the sum of three angles become 180.

Since sum of two angles is 100 , 80 must be added to 100 to make it equal to 180.

1)Sheyna drive to the lake and back. It took two hours less time to get there than it did to get back. The average speed on the trip there was 60 mph. The average speed on the way back was 36 mph. How many hours did the trip there take?

Answers

Answer:

8 hours

Step-by-step explanation:

Given:

Sheyna drives to the lake with average speed of 60 mph and

[tex]v_1 = 60\ mph[/tex]

Sheyna drives back from the lake with average speed of 36 mph

[tex]v_2 = 36\ mph[/tex]

It took 2 hours less time to get there than it did to get back.

Let [tex]t_1[/tex] be the time taken to drive to lake.

Let [tex]t_2[/tex] be the time taken to drive back from lake.

[tex]t_2-t_1 = 2[/tex] hrs ..... (1)

To find:

Total time taken = ?

[tex]t_1+t_2 = ?[/tex]

Solution:

Let D be the distance to lake.

Formula for time is given as:

[tex]Time =\dfrac{Distance}{Speed }[/tex]

[tex]t_1 = \dfrac{D}{60}\ hrs[/tex]

[tex]t_2 = \dfrac{D}{36}\ hrs[/tex]

Putting in equation (1):

[tex]\dfrac{D}{36}-\dfrac{D}{60} = 2\\\Rightarrow \dfrac{5D-3D}{180} = 2\\\Rightarrow \dfrac{2D}{180} = 2\\\Rightarrow D = 180\ miles[/tex]

So,

[tex]t_1 = \dfrac{180}{60}\ hrs = 3 \ hrs[/tex]

[tex]t_2 = \dfrac{180}{36}\ hrs = 5\ hrs[/tex]

So, the answer is:

[tex]t_1+t_2 = \bold{8\ hrs}[/tex]

Solve for b. 2/3 b + 5 = 20 - b

Answers

Answer:

b = 9

Step-by-step explanation:

Step 1: Add b on both sides (Addition Equality)

5/3b + 5 = 20

Step 2: Subtract 5 on both sides (Subtraction Equality)

5/3b = 15

Step 3: Divide both sides by 5/3 (Division Equality)

b = 9

solving polinomial(2x+8)(2x-1)​

Answers

Answer:

4x²+14x-8 ( multiplying)

x=-4 , x=1/2 ( find solution)

Step-by-step explanation:

(2x+8)(2x-1)​

start :

2x*2x=4x²

2x*-1 = -2x

8*2x=16x

8*-1=-8

add the results  : 4x²-2x+16x-8 = 4x²+14x-8

If you mean find the solution :

(2x+8)(2x-1)​=0

2x+8=0

x=-8/2=-4

OR 2x-1=0

then x=1/2

Answer:

=4x2+14x−8

Step-by-step explanation:

(2x+8)(2x−1)

=(2x+8)(2x+−1)

=(2x)(2x)+(2x)(−1)+(8)(2x)+(8)(−1)

=4x2−2x+16x−8

=4x2+14x−8

I hope this helps! :]

*PLEASE ANSWER, MAKE SURE YOU ANSWER CORRECTLY* What dimensions would you need to measure the volume of the following prism?

Answers

Answer:

base of the triangle, height of the triangle, height of the prism.

Step-by-step explanation:

The formula for calculating the volume of the right triangle prism above is given as [tex] base area * height of prism [/tex].

The base is a right triangle. Area of the right triangular base = ½*base*height of the triangle.

Therefore, the dimensions needed to find the volume of the prism are: "base of the triangle, height of the triangle, and height of the prism.

Answer:

The guy above me is correct its base of the triangle, height of the triangle, height of the prism

Step-by-step explanation:

I also got it correct on my quiz.

Find the domain for the rational function f of x equals quantity x plus 1 end quantity divided by quantity x minus 2 end quantity.

(−[infinity], 2) (2, [infinity])

(−[infinity], −2) (−2, [infinity])

(−[infinity], 1) (1, [infinity])

(−[infinity], −1) (−1, [infinity])

Answers

Answer:

[tex](- \infty, 2), (2, \infty)[/tex]

Step-by-step explanation:

Given the function:

[tex]f(x) = \dfrac{x+1}{x-2}[/tex]

To find:

Domain of the function.

Solution:

First of all, let us learn about definition of  domain of a function.

Domain of a function is the valid input values that can be provided to the function for which output is defined.

OR

Domain of a function [tex]f(x)[/tex] are the values of [tex]x[/tex] for which the output [tex]f(x)[/tex] is a valid value.

i.e. The function does not tend to [tex]\infty[/tex] or does not have [tex]\frac{0}0[/tex] form.

So, we will check for the values of [tex]x[/tex] for which [tex]f(x)[/tex] is not defined.

For value to tend to [tex]\infty[/tex], denominator will be 0.

[tex]x-2\neq 0 \\\Rightarrow x \neq 2[/tex]

So, the domain can not have x = 2

Any other value of x does not have any undefined value for the function [tex]f(x)[/tex].

Hence, the answer is:

[tex]\bold{(- \infty, 2), (2, \infty)}[/tex]     [2 is not included in the domain].


[tex]15 \times 94 - 89 \div 5[/tex]

Answers

1410-89/5
1410-17.8= 1392.2

Which statement is false? Question 4 options: All whole numbers are integers. All natural numbers are whole numbers. All real numbers are irrational numbers. All whole numbers are real numbers.

Answers

All real numbers are irrational numbers is false

Answer:

C

Step-by-step explanation:

Not all real numbers are irrational.

Is 7/12 rational or irrational

Answers

Answer:

7/12 is a rational

Step-by-step explanation:

because it is containing a quantity which are expressible


2(3x + 1) - (x - 5) = 42

Answers

Answer:

6x+2-1x+5=42

Step-by-step explanation:

Answer:

6x+2-x-5=42

Step-by-step explanation:

Give an actual answer please

Rhett decides to build a square room for his movie and music collection. If the area of the room is 4x2 + 28x + 49 square feet, what is the length of one side of the room?
(7x + 2) feet
(2x + 7) feet
(2x − 7) feet
(7x − 2) feet

Answers

Hello There!!

Your best answer choice will be is A.

(2x + 7) feet.

Because, All you have to do for this problem is factor the equation. I would be hard to explain on this so I recomment you watch a video on it. If you did not know how to factor, you could have muliplied each of the answers by themselves to determine the correct answer because it is a square.

Hope This Helps!!

Answer:

(2x+7)

Step-by-step explanation:

4x^2 + 28x + 49

This is a perfect square trimonial

a^2 + 2ab + b^2 =  (a+b)^2

(2x)^2 + 2 * 2x*7 + 7^2

( 2x+7)^2

Find the value of x.

Answers

Answer:

x = 20

Step-by-step explanation:

Intersecting Chords Theorem: ab = cd

Step 1: Label our variables

a = x

b = x - 11

c = x - 8

d = x - 5

Step 2: Plug into theorem

x(x - 11) = (x - 5)(x - 8)

Step 3: Solve for x

x² - 11x = x² - 8x - 5x + 40

x² - 11x = x² - 13x + 40

-11x = -13x + 40

2x = 40

x = 20

Answer: x=20

Step-by-step explanation:

[tex]ab=cd[/tex]

[tex]x(x - 11) = (x - 5)(x - 8)[/tex]

[tex]x^2 - 11x = x^2 - 13x + 40[/tex]

[tex]x^2 - 11x = x^2 - 8x - 5x + 40[/tex]

[tex]-11x = -13x + 40\\2x = 40\\x = 20[/tex]

Solve for x. 23x +2=15x+48x+6

Answers

Answer:

[tex]x = - \frac{1}{10} [/tex]

Step-by-step explanation:

23x +2 = 15x+48x+6

To solve for x group like terms

That's

Send the constants to the right side of the equation and those with variables to the left side

We have

23x - 15x - 48x = 6 - 2

Simplify

- 40x = 4

Divide both sides by -40

[tex] \frac{ - 40x}{ - 40} = \frac{4}{ - 40} [/tex]

We have the final answer as

[tex]x = - \frac{1}{10} [/tex]

Hope this helps you

If you simplify both sides, it shows that 23x+2=63x+6. If you cancel out the x, it shows that 2=40x+6. If you cancel out the numbers it shows that -4=40x. Divide all sides to show that -1/10=x.

What is the radical equivalent for 197^7/8?

Answers

Answer:

[tex]\sqrt[8]{197^{7} }[/tex]

Step-by-step explanation:

[tex]\sqrt[8]{197^{7} }[/tex]

PLEASE HELP!!!!!! URGENT!!!!!!!!! ALGEBRA! Hannah, Yu, and Becky went to buy groceries together. All three of them bought pasta, noodles, and split peas. Hannah bought 3 packs of pasta, 10 packs of noodles, and 2 packs of split peas. Yu bought 5 packs of pasta, 12 packs of noodles, and 1 pack of split peas. Becky bought 3 packs of pasta, 15 packs of noodles, and 2 packs of split peas. Hannah, Yu, and Becky spent $8.41, $9.42, and $9.66 respectively on these items. What are the costs of a pack of pasta, a pack of noodles, and a pack of split peas? A) Pasta: $0.69 per pack, Noodles: $0.25 per pack, Split peas: $0.99 per pack B) Pasta: $1.09 per pack, Noodles: $0.20 per pack, Split peas: $1.97 per pack C) Pasta: $0.99 per pack, Noodles: $0.25 per pack, Split peas: $1.47 per pack D) Pasta: $0.69 per pack, Noodles: $0.20 per pack, Split peas: $1.97 per pack

Answers

Answer: C

Step-by-step explanation:

The costs of a pack of pasta, a pack of noodles, and a pack of split peas are Pasta: $0.99 per pack, Noodles: $0.25 per pack, Split peas: $1.47 per pack

Solve.

-7(2z + 4) = 21

Answers

Answer:

-7/2

Step-by-step explanation:

cuz thats right

-14z - 28 = 21
-14z = 49
z = -7/2

A rectangular box with a square base contains 24 cubic feet. if the height of the box is 18 inches, how many feet are there in each side of the base?

Answers

Answer:

4

Step-by-step explanation:

V = Lwh

the volume (given) = 24 ft^3

the height (given) = 18" = 1.5'

24 = L*w*1.5

divide both sides by 1.5

16 = Lw

You need to find the number of feet in each side of the base

since the box has a square base

L = W

AND, found above, L*w = 16

so 4*4= 16

Answer - 4

Bill’s car gets 30 miles to the gallon. For every gallon of gas it consumes, his car runs 30 miles. Use this information to determine whether this relation is a function
write a equation for the number of miles Bill travels, y, in terms how much gas it uses, x.

Answers

Answer:

Step-by-step explanation:

No. of miles driven in 1 gallon = 30 miles.

since we have to distance traveled in miles.multiply LHS and RHS by x

No. of miles driven in 1*x gallon = 30*x miles.

No. of miles driven x gallons = 30*x = 30x miles

As given that

the number of miles Bill travels is represented by y

gas used is x

then

y = 30x

=> x = y/30

Thus, Bill's car uses y/30 gallon gas to travel Y miles.

Answer:

Part a: Bill’s car travels 30 miles per gallon of gas. If y represents the number of miles the car travels on x gallons of gas, the equation that represents this situation is y = 30x.

Part b:       gallons of gas (x) miles (y)

                                    1         30

                                    2        60

                                    3        90

Part c: There is no x-value that would lead to multiple y-values.

Part d: Yes, y = 30x is a function, because for every input, or x-value, there is only one output, or y-value.

Step-by-step explanation:

edmentum answers 100% correct

slopes of the line parallel and perpendicular to y=32x-1

Answers

Answer:

see below

Step-by-step explanation:

This is in slope intercept form

y = mx+ b  where m is the slope and b is the y intercept

32 is the slope

Parallel lines have the same slope so 32 would be the slope of  the parallel line

Perpendicular lines have slopes that multiply to -1

m*32 = -1

m = -1/32

The slope of the perpendicular line is -1/32

Question 5 of 10
Which type of unemployment is characterized by a worker looking for a job
when there is no reason that he or she should not find one?
A. Structural unemployment
B. Seasonal unemployment
C. Frictional unemployment
D. Periodic unemployment

Answers

I think the answer has to be C. Frictional unemployment

PLEASE HELP ASAP! If t is a real number, what is the maximum possible value of the expression -t^2 + 8t -4?

Answers

Answer:

12

Step-by-step explanation:

Hello, as the coefficient of the leading term is negative we know that the vertex of the parabola is a maximum. So we need to find the vertex.

This expression is maximum for

[tex]t=-\dfrac{b}{2a} \text{ where the parabola equation is}\\\\ax^2+bx+c=0[/tex]

So, here, it gives t = 8/2=4, and then, the maximum is

[tex]-4^2+8*4-4=-16+32-4=32-20=12[/tex]

So the answer is 12.

Thanks

If y varies directly as x and z, and Y=40 when x =5 andz = 4, find y when x=2 and z = 1



Pls answer it ASAP

Answers

Answer: When x=2 and z = 1, then the value of y =4.

Step-by-step explanation:

Given: y varies directly as x and z i.e. [tex]y\ \alpha \ xz[/tex]

[tex]y=k(xz)[/tex]      (i) , where k is the proportionality constant.

Put  Y=40 ,x =5 and z = 4, then we get

[tex]40=k(5\times4)\\\\\Rightarrow\ k=\dfrac{40}{20}\\\\\Rightarrow\ k=2[/tex]

Required equation: [tex]y=2(xz)[/tex]  [Put value of k in (i)]

Now put x=2 and z = 1, then we get

[tex]y=2(2\times1)=2(2)=4\\\\\Rightarrow\ y=4[/tex]

Hence, when x=2 and z = 1, then the value of y =4.

1. Find the slope of a line passing through points (0,0) and (4,5)
o 4/5
5/4
4/9
5/9
Option 5

Answers

Answer:

slope = [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (4, 5)

m = [tex]\frac{5-0}{4-0}[/tex] = [tex]\frac{5}{4}[/tex]

Answer:

The answer is 5/4

Step-by-step explanation:

Slope of a line is given by

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

where

m is the slope and

( x1 , y1) and (x2 , y2) are the points of the line

Slope of the line between the points

(0,0) and (4,5) is

[tex]m = \frac{5 - 0}{4 - 0} = \frac{5}{4} [/tex]

Hope this helps you

Find n. A. 5 B. 5√3 C. 10 D. 10√3/3

Answers

Answer:

Option A

Step-by-step explanation:

Using trigonometry ratios

tan∅= opp/adj

tan 30°=n/(5√3)

1/√3 = n/(5√3)

n = (5√3)/√3

n = 5

PLEASE - Select the correct answer.

Answers

Answer:

D

Step-by-step explanation:

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