Which expression shows 56x+40y−48z written as a product of the greatest common factor and one other factor?
​

A
8(7x+5y−6z)
B
8(7x+5y+6z)
C
8x(7+5y−6z)
D
4(14x+10y−12z)

To graph 2/5 on a number line, divide the number line into equal segments and locate the point that represents 2/5.

To graph 2/5 on a number line, divide the number line into equal segments and find the point that represents 2/5. Start by labeling the endpoints of the number line with the corresponding values. In this case, you can label 0 on the left and 1 on the right. Since the number line is divided into 5 equal segments, mark the points that correspond to 1/5, 2/5, 3/5, and 4/5 between 0 and 1. Then, locate the point that corresponds to 2/5 and mark it on the number line. Remember to place a dot to represent the point.

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Answer:

28 oz can is the better deal.

Step-by-step explanation:

In order to compare the two, we need to find the unit rate for each can. In this case, the unit rate will be in dollars per oz.

For the 28 oz can,

unit rate = $1.89 ÷ 28 = $0.675 / oz

For the 32 oz can

unit rate = $2.95 ÷ 32 = $0.922 / oz

comparing the unit rates, we can see that the unit rate for the 28 oz can is lower (i.e it costs less per oz for the 28 oz can compared to the 32 oz can)

Hence the 28 oz can is the better deal.

He has 20 quarters, 15 dimes and 10 pennies.

Step-by-step explanation:

Let,

Quarters = x

Dimes = y

Pennies = z

We know that,

A quarter is 25 cents, dime is 10 cents and penny is 1 cent.

Total amount = $6.60 = 6.60*100 = 660 cents

According to given statement;

25x+10y+z=660   Eqn 1

x=2z    Eqn 2

y=z+5   Eqn 3

Putting these values of x and y in Eqn 1

[tex]25(2z)+10(z+5)+z=660\\50z+10z+50+z=660\\61z=660-50\\61z=610\\[/tex]

Dividing both sides by 61;

[tex]\frac{61z}{61}=\frac{610}{61}\\z=10[/tex]

Putting z=10 in Eqn 2

[tex]x=2(10)\\x=20[/tex]

Putting z=10 in Eqn 3

[tex]y=10+5\\y=15[/tex]

He has 20 quarters, 15 dimes and 10 pennies.

Keywords: linear equations, substitution method

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Answer:

Step-by-step explanation:

1) 7x^2-5x+10x-8x=7x^2+5x-8x=7x^2-3x

2) -6a^3+5a^3+2a-a=-a^3+2a-a=-a^3+a

3) -4(x+5)-5(x-1)=-4x-20-5x+5=-9x-20+5=-9x-15

4) -a+5b-6a+5(a+1)=-7a+5b+5a+5=-2a+5b+5

5) 18x^4-3x^3-2x^3+x^2-10+6

=18x^4-5x^3+x^2-4

To simplify algebraic expressions, combine like terms, variables and exponents. We simplified five examples, using techniques such as distribution and combining like terms.

To simplify algebraic expressions, one has to combine like terms, which are terms with the same variables and exponents. Here, let's do that:

7x2 – 5x + 10x - 8x simplifies to 7x2 + 5x because -5x + 10x - 8x = 5x.

-6a3 + 5a3 + 2a? - a? simplifies to -a3 + a (assuming the '?' is meant to be a variable).

- 4(x + 5) – 5(x - 1) simplifies first by applying distribution (-4x -20 -5x +5) which then becomes -9x - 15.

-a + 5b - 6a + 5(a + 1) simplifies to -2a + 5b + 5 once you distribute and combine like terms.

18x4 - 3x3 - 2x3 + x2 - 10 + 6 simplifies to 18x4 - 5x3 + x2 - 4 since -3x3 and -2x3 add up to -5x3 and -10 and 6 adds up to -4.

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Answer: choice D

2x^5 - 6x^3 + 3x^2 - x

Explanation:

Polynomials in standard form always have the exponents decrease (ie go from largest to smallest) when we read from left to right. For choice D, the exponents from left to right are: 5, 3, 2, 1. This is decreasing order. The other answer choices do not have the exponents in decreasing order. The degree of the polynomial in choice D is a 5th degree polynomial since 5 is the largest exponent.

Answer:

y = 4x + 20

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 4, thus

y = 4x + c ← is the partial equation

To find c substitute (- 5, 0) into the partial equation

0 = - 20 + c ⇒ c = 0 + 20 = 20

y = 4x + 20 ← equation of line

The number of adults was 52 and number of children was 88.

Step-by-step explanation:

Cost for one adult = $8

Cost for one child = $5

People attended = 140

Amount raised = $856

Let,

x be the number of adult

y be the number of children

According to given statement;

x+y=140   Eqn 1

8x+5y=856   Eqn 2

Multiplying Eqn 1 by 8'

[tex]8(x+y=140)\\8x+8y=1120\ \ \ Eqn\ 3\\[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](8x+8y)-(8x+5y)=1120-856\\8x+8y-8x-5y=264\\3y=264[/tex]

Dividing both sides by 3

[tex]\frac{3y}{3}=\frac{264}{3}\\y=88[/tex]

Putting y=88 in Eqn 1;

[tex]x+88=140\\x=140-88\\x=52[/tex]

The number of adults was 52 and number of children was 88.

Keywords: linear equations, subtraction

Learn more about linear equations at:

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Answer:

An independent clause is a group of words that contains both a subject and a predicate. It expresses a complete thought and can stand alone as a sentence. It can also be joined to other dependent or independent clauses to make a more interesting and complex sentence.Step-by-step explanation:

Answer:

-42

Explanation:

(-6)(-7)(-1)

do (-6)(-7)

-negative sign and -negative sign= +positive sign

(-6)(-7)=42

(42)(-1)

+positive sign and -negative sign=-negative sign

answer:

-42

Answer:

D: None of these are true

Explanation:

If the points on the scatter plot seem to form a line that slants down from left to right, there is a negative relationship or negative correlation between the variables. If the points on the scatter plot seem to be scattered randomly, there is no relationship or no correlation between the variables

Answer: 15.5

Step-by-step explanation:

(10.5-7)+(4x3)

following PEDAS we do operations in parentheses first

10.5-7=3.5

4x3=12

we now have 3.5+12 as our intermediate expression

and 3.5+12 = 15.5

Answer:

15.5

Step-by-step explanation:

(10.5-7)+(4*3)

3.5+12

15.5

Answer:

x-intercept: (14/9,0)

y-intercept: (0,-2)

Step-by-step explanation:

9x-7y=14

For x-intercept:

Plug in 0 for y, then solve for x (the remaining variable)

For y-intercept:

Plug in 0 for x, then solve for y (the remaining variable)

Answer:

a. .3

b. .7

c. The car is fairly reliable because there is more people with no mechanical issues than there is people with mechanical issues

Step-by-step explanation:

Answer:

A. 3

B. .7

C. The car is fairly reliable, their is more people with no mechanical issues than their is people with mechanical issues

Step-by-step explanation:

The answer to your question is D, as 5 is being multiplied by c, and the term product refers to multiplication.

Answer:

its represented by my 20 inch pito

Answer:

(3,4)

Step-by-step explanation: I'm assuming you want to know the final point you end up at. The first part of our coordinate pair is our x value, so we want to reduce our x-value by 4 to go left 4 units, the second part is our y-value, we want to reduce it by 1 to go down 1 unit. So, our final coordinate pair is (7-4,5-1) or (3,4).

Answer:

k

Step-by-step explanation:

;

Answer:

Part A) The rate is [tex]\frac{12}{4}\ \frac{feet}{years}[/tex]

Part B) In 1 year the tree grows 3 feet

Step-by-step explanation:

Part A)  write the rate at which this tree grows as a fractions

we know that

To find out the rate at which the tree grows divide 1/4 foot by 1/12 year

so

[tex]\frac{(1/4)}{(1/12)}=\frac{12}{4}\ \frac{feet}{years}[/tex]

Part B) how many feet does the tree grow in 1 year?

we know that

The tree grows at rate of [tex]\frac{12}{4}\ \frac{feet}{years}[/tex]

Simplify

[tex]\frac{3}{1}\ \frac{feet}{year}[/tex]

That means ----> The tree grows 3 ft in 1 year

therefore

In 1 year the tree grows 3 feet

In the context of the question, the Y-intercept represents the cost of the tablet that Mio purchased before counting the ongoing costs per month for internet service.

In the context of this problem, the Y-intercept in the graph represents the cost of buying the tablet. Using the algebraic equation for a line, which is y = b + mx, the 'b' term is the Y-intercept. When x (in this case, the number of months) equals zero, y is the initial cost, which serves as our Y-intercept. This is the starting point on the Y-axis, and in the context of Mio's spending, this would be her initial expenditure which is the cost of the tablet itself.

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Answer:

x=6, y=9. (6, 9).

Step-by-step explanation:

-x+y=3

-4x+3y=3

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

-x=3-y

x=-3+y

x=y-3

---------

-4(y-3)+3y=3

-4y+12+3y=3

-y+12=3

-y=3-12

-y=-9

y=9

-x+9=3

-x=3-9

-x=-6

x=6

x=6, y=9.

Answer:

14 of these device have to fill and pour in order to add enough sugar.

Step-by-step explanation:

Given:

The recipe calls for 4 2/3 cups of sugar. The only measuring device which measures 1/3 cup.

Now, to get how many of this device have to fill and pour in order to add enough sugar.

First we convert the quantity in improper fraction from mixed :

[tex]4\frac{2}{3} = \frac{14}{3}[/tex]

According to question:

We divide 14/3 cups of sugar by 1/3 measuring cup to get quantity of device to be fill and pour:

[tex]\frac{14}{3} \div \frac{1}{3}[/tex]

[tex]\frac{14}{3}\times \frac{3}{1}[/tex]

Now, by evaluating we get:

[tex]14[/tex]

Therefore, 14 of these device have to fill and pour in order to add enough sugar.

Answer:

3.5 unit right and compressed by 3.5 units respectivleyy

Step-by-step explanation:

Answer:

0.2988

Step-by-step explanation:

To find the depth of the swimming pool, use the formula for the volume of a rectangular solid and substitute the given values to calculate the depth as 2.5 meters.

The depth of the Olympic-size swimming pool can be calculated using its volume, length, and width.

First, use the formula for the volume of a rectangular solid:

Volume = Length x Width x Depth

4000 = 80 x 20 x Depth

Depth = 4000 / (80 x 20) = 2.5 meters

Depth = 2.5 meters

Answer:

C) Solution set of{x|X<-3} n {xl x> 5) is an the empty set.

Step-by-step explanation:

Here, the solution set is given as : set of  {x| x < -3 } ∩   {x l x > 5)

Now, defining the each set , we get

{x| x < -3 }   = ( .... -6,-5,-4 ,-3)  = P

and the SET  {x l x > 5} = (5,6,7,........ )  = Q

Now, by taking the intersection of two sets,we get

P ∩ Q = NULL SET as they don not have any element in common.

⇒ {x| x < -3 } ∩   {x l x > 5} is an empty set

Hence, solution set of{x|X<-3} n {xl x> 5) is an the empty set.

To fit two identical cars in a 23-foot 6-inch wide garage with 3 feet 6 inches clearance on each side and between the cars, the cars must each be 6 feet 6 inches wide.

The subject matter of your question is a math problem involving subtraction and division. To find out how wide the cars can be, you first need to determine the total available space for the cars. The total width of the garage is 23 feet 6 inches. However, you need to leave room for clearance on either side of the cars and in between them. The clearance is a total of 3 feet 6 inches multiplied by 3 (one for each side and one for between the cars), which is 10 feet 6 inches. Subtract this from the total width of the garage, and you get 13 feet available for the cars. Since the cars are identical, you simply divide this by 2. Each car can be 6 feet 6 inches wide.

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Solve 2y + 3x = 7 and 4x + 3y = 15 by elimination, we get x = -9, y = 17. Multiply and subtract equations to eliminate y, then substitute the result to find x or y.

To solve the system of equations 2y + 3x = 7 and 4x + 3y = 15 using the elimination method, we aim to eliminate one variable to solve for the other. Here's a step-by-step explanation:

The solution for the system of equations is x = -9 and y = 17.

Answer:

$60

Step-by-step explanation:

Let the company's fixed charge be "x"

And let the the hourly rate be "h"

Firstly, 2 hours + fixed = $110, we can write:

2h + x = 110

Next, 3 hours + fixed = $150, we can write:

3h + x = 150

We multiply the first equation by "-1" to get:

-1 * [2h + x = 110] = -2h - x = -110

Now we add this equation to the 2nd:

3h + x = 150

-2h - x = -110

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

h = 40

Hence, the hourly rate is $40

So, it would cost 1.5 * 40 = $60 for 1.5 hours

Answer:

He made 16 groups which means 5 Students in each group

Step-by-step explanation:

Because 80 divided by 16 is 5 and 5 is a prime number

Answer:

x = 0 , y = 2

Step-by-step explanation:

Solve the following system:

{6 x - 5 y = -10 | (equation 1)

4 x + 3 y = 6 | (equation 2)

Subtract 2/3 × (equation 1) from equation 2:

{6 x - 5 y = -10 | (equation 1)

0 x+(19 y)/3 = 38/3 | (equation 2)

Multiply equation 2 by 3/19:

{6 x - 5 y = -10 | (equation 1)

0 x+y = 2 | (equation 2)

Add 5 × (equation 2) to equation 1:

{6 x+0 y = 0 | (equation 1)

0 x+y = 2 | (equation 2)

Divide equation 1 by 6:

{x+0 y = 0 | (equation 1)

0 x+y = 2 | (equation 2)

Collect results:

Answer: {x = 0 , y = 2