7. A vending machine only accepts dimes and quarters. There are 85 coins
in the machine with a total value of $16.75. How many of each coin are in
the machine?

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

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:

c

Step-by-step explanation:

The slope-intercept form is y=mx+b, where m is the slope and

b is the y-intercept.

y=mx+b

m=−3

b=0

y=-3x+0

The required y-intercept of the given y = -3 is (0, 0)

Slope-intercept form of the line:

If the line have m slope and b as y-intercept then the equation of the line will be y = mx + b

Here we have given that the equation of the line

y = -3x

Make this equation like general form of slope-intercept form

y = -3x + 0

Therefore comparing with general form we have

Slope m = -3

y-intercept = b = 0

The coordinate will be (0, 0)

Therefore the correct option is (c)

This is the conclusion to the answer.

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Answer:

Co-ordinates of point R is (26,2)

Step-by-step explanation:

Given point:

Endpoint S(8,4)

Mid-point M of segment RS (17,3)

Let endpoint [tex]R[/tex] have co-ordinates [tex](x_2,y_2)[/tex]

Using midpoint formula:

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are co-ordinates of the endpoint of the segment.

Plugging in values to find the midpoint of segment KN.

[tex]M=(\frac{8+x_2}{2},\frac{4+y_2}{2})[/tex]

We know [tex]M(17,3)[/tex]

So, we have

[tex](17,3)=(\frac{8+x_2}{2},\frac{4+y_2}{2})[/tex]

Solving for [tex]x_2[/tex]  

[tex]\frac{8+x_2}{2}=17[/tex]

Multiplying both sides by 2.

[tex]\frac{8+x_2}{2}\times 2=17\times 2[/tex]

[tex]8+x_2=34[/tex]

Subtracting both sides by 8.

[tex]8+x_2-8=34-8[/tex]

∴ [tex]x_2=26[/tex]

Solving for [tex]y_2[/tex]  

[tex]\frac{4+y_2}{2}=3[/tex]

Multiplying both sides by 2.

[tex]\frac{4+y_2}{2}\times 2=3\times 2[/tex]

[tex]4+y_2=6[/tex]

Subtracting both sides by 4.

[tex]4+y_2-4=6-4[/tex]

∴ [tex]y_2=2[/tex]

Thus co-ordinates of point R is (26,2)  (Answer)

Answer: Yes

Step-by-step explanation: Erica would be correct. 4x is called a term. When we see a variable next to a number which in this case is X, it's important to understand that this means multiplication.

We can also say that the expression 4x is a product of both 4 and X.

Final answer:

Erica is correct; the expression 4x is considered one term because it consists of a single element with a coefficient and a variable multiplied together.

Explanation:

Erica is correct in saying that the expression 4x has one term. In mathematics, a term is a single mathematical expression that may be a number, a variable, or numbers and variables multiplied together. The expression 4x consists of the number 4 and the variable x multiplied together, which forms a single term. It does not have any addition or subtraction signs that would separate it into multiple terms.

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:

(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).

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

Answer:

0.2988

Step-by-step explanation:

Answer:

its represented by my 20 inch pito

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:

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

Answer:

$5728

Step-by-step explanation:

$4000 is deposited into an account with 4.8% interest.

We assume that there are no withdrawals from the account.

Then we are asked the determine the amount will be there in the account after 9 years.

From the formula of simple interest, the final amount in the account after 9 years will be [tex]4000(1 + \frac{4.8 \times 9}{100}) = 5728[/tex] dollars. (Answer)

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:

[tex]\large\boxed{\sqrt{108}=6\sqrt3}[/tex]

Step-by-step explanation:

[tex]\sqrt{108}=\sqrt{4\cdot27}=\sqrt{4\cdot9\cdot3}\\\\\text{use}\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt4\cdot\sqrt9\cdot\sqrt3=2\cdot3\cdot\sqrt3=6\sqrt3\\==========================\\\\\sqrt{108}=\sqrt{36\cdot3}=\sqrt{36}\cdot\sqrt3=6\sqrt3\\\\==========================\\\\\begin{array}{c|c}108&2\\54&2\\27&3\\9&3\\3&3\\1\end{array}\qquad108=2^2\cdot3^2\cdot3\\\\\sqrt{108}=\sqrt{2^2\cdot3^2\cdot3}=\sqrt{2^2}\cdot\sqrt{3^2}\cdot\sqrt3\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=2\cdot3\cdot\sqrt3[/tex]

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:

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:

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

Answer:

3500

Step-by-step explanation:

I divided everything and I ended up just multiplying 70x50 which got me 3500. I'm sorry, but I don't know in what way to write the equation. I don't know if it's y=mx+b or some other way. all I was able to come up with was y=50x+70

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

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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You left out how much flour each pizza needs. Without that info no one can answer teh question.

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:

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:

Total number of Jelly beans in the sack = 72

Number of red beans = 36

Number of green beans = 12

Number of yellow beans = 12

Number of orange beans = 6

Number of black beans = 6

Step-by-step explanation:

Let total number of jelly beans be =[tex]x[/tex]

We are given fractions of different colors of beans. To find the exact number of beans we need to multiply the fraction with the total number of beans.

Fraction of total are red beans = [tex]\frac{1}{2}[/tex]

Number of red beans = [tex]\frac{1}{2}\times x= \frac{x}{2}[/tex]

Fraction of total are green beans = [tex]\frac{1}{6}[/tex]

Number of green beans = [tex]\frac{1}{6}\times x= \frac{x}{6}[/tex]

Fraction of total are yellow beans = [tex]\frac{1}{6}[/tex]

Number of yellow beans = [tex]\frac{1}{6}\times x= \frac{x}{6}[/tex]

Fraction of total are orange beans = [tex]\frac{1}{12}[/tex]

Number of orange beans = [tex]\frac{1}{12}\times x= \frac{x}{12}[/tex]

Number of black beans = 6

Total number of beans can be given as

[tex] \frac{x}{2}+\frac{x}{6}+\frac{x}{6}+\frac{x}{12}+6[/tex]

Since we assumed total number of beans to be [tex]x[/tex], so we have.

[tex] \frac{x}{2}+\frac{x}{6}+\frac{x}{6}+\frac{x}{12}+6=x[/tex]

Multiplying each term by 12 to remove fractions.

[tex] (12\times\frac{x}{2})+(12\times\frac{x}{6})+(12\times\frac{x}{6})+(12\times\frac{x}{12})+(12\times6)=12\times x[/tex]

[tex]6x+2x+2x+x+72=12x[/tex]

combining like terms.

[tex]11x+72=12x[/tex]

Subtracting both sides by [tex]11x[/tex]

[tex]11x+72-11x=12x=11x[/tex]

[tex]72=x[/tex]

∴ [tex]x=72[/tex]

Total number of Jelly beans in the sack = 72

Number of red beans = [tex]\frac{1}{2}\times 72= 36[/tex]

Number of green beans = [tex]\frac{1}{6}\times 72= 12[/tex]

Number of yellow beans = [tex]\frac{1}{6}\times 72= 12[/tex]

Number of orange beans = [tex]\frac{1}{12}\times 72= 6[/tex]

number of black beans = 6

Justin has 72 jelly beans in total. By dividing the total number accordingly, he has 36 red, 12 green, 12 yellow, 6 orange, and 6 black jelly beans.

Let's assume the total number of jelly beans Justin has is represented by the variable x. We know that half of them are red, so there are x/2 red jelly beans. Similarly, since 1/6 are green and another 1/6 are yellow, there are x/6 green jelly beans and x/6 yellow jelly beans. As for the orange jelly beans, they represent 1/12 of the total, which means Justin has x/12 orange jelly beans. We are given that there are 6 black jelly beans, which do not need to be divided into fractions. To find the total, x, we can write an equation considering all the portions mentioned and the known number of black jelly beans:

x/2 (red) + x/6 (green) + x/6 (yellow) + x/12 (orange) + 6 (black) = x

Finding a common denominator (12), we rewrite the equation:

6x/12 + 2x/12 + 2x/12 + x/12 + 6 = x

Combine like terms:

(6x + 2x + 2x + x)/12 + 6 = x

11x/12 + 6 = x

To solve for x, subtract 11x/12 from both sides:

6 = x - 11x/12

6 = x(12/12) - 11x/12

6 = (12x - 11x)/12

6 = x/12

Multiplying both sides by 12 gives us:

x = 72

So, Justin has a total of 72 jelly beans. Calculating the number for each color:

In conclusion, Justin has 36 red, 12 green, 12 yellow, 6 orange, and 6 black jelly beans, adding up to a total of 72 jelly beans.

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

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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.

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:

Total number of employees at Tia's toy store [tex]=9[/tex]

Step-by-step explanation:

To find the number of employees who worked on Tia's store .

We have to add the total number of values from the employee column.

As the question mentioned.

Each of the staff members have different number of hours of sleep on thanksgiving night.

So

The summation of the number of employees from the frequency table

[tex]=(1+0+4+2+1+1)=9[/tex]

So there are [tex]9[/tex] employees working on thanksgiving night in Tia's store.

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.