Factor the expression. 63a - 42b​

Answer:

Step-by-step explanation:

A(1.00) + S(0.50) = 500

A + S = 900

S = 900 - A

A(1.00) + (900 - A)(0.50) = 500

              A + 450 - 0.5A = 500

                               0.5A = 50

                                    A = 100 adults

                                     S = 900 - 100

                                     S = 800 students

No. of students tickets sold is 800 and no. of adult tickets sold is 100.

A linear equation has highest degree of 1 and it contains two variables generally x and y.

According to the given question At a school game, student tickets were 50 cents each and adult tickets were $1 each. If the total receipts from 900 tickets were $500.

Assuming no. of students to be x and no. of adults to be y.

∴ x + y = 900...(i)

And

0.5x + y = 500...(ii)

Subtracting eqn (i) and (ii) we get

0.5x = 400

x = 800.

So, 800 + y = 900

y = 100.

Therefore how many tickets are sold is same as the no. of students and adults which are 800 and 100 respectively.

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Answer:

15 ft.

Step-by-step explanation:

I will assume that either both objects are standing straight. We can use similar triangles.

We can see that the side 8 is similar to the side 20, since they are both shadows. Therefore, we can set up an equation:

[tex]\frac{6}{8} =\frac{x}{20}[/tex]

we can cross multiply and get:

8x=120

solve for x:

x=15

Therefore, the lamppost must be 15 feet tall (unless it fell down but we won't talk about that)

Answer:

Fred save about 3.15$ because is 20% off

Answer:

18000

Step-by-step explanation:

The number of meters in 18 kilometers is 18,000 meters(m)

x meters = 18 kilometers

x meters = 18 kilometers × 1000

x = 18,000 meters

Therefore, 18 kilometers is equivalent to 18,000 meters

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Answer:

5.2%

Step-by-step explanation:

Volume of cylinder= πr²h

In Container A,

D= 18ft, r=18/2=9ft, h=15ft

volume= 22/7 × 9² × 15

= 26730/7 cubic ft.

In Container B,

D=16ft, r= 16/2=8ft, h=18ft

volume= 22/7 × 8² × 18

= 25344/7 cubic ft.

percent of amount of water left in Container A= percent of container A that is full after pumping

Amount of water left in Container A,

26730/7 - 25344/7 = 1386/7

Therefore, % of container A that is full= 1386/7 ÷ 26730/7 × 100

(1386×7×100)/(7×26730)= 5.185

To the nearest tenth= 5.2%

Answer:

Step-by-step explanation:

We have no idea what time zone you are in so hope this gets there soon enough.

Do you mean "What fraction of a FULL spool of yarn did he use?" because he used 5/6 of the spool he had.

IF SO

Then

(5/7)(5/6) = 25/42

That's just under 60% of a full spool would be used to complete the same project again.

An increase in the ending inventory will cause the cost of food sold at the end of the year to appear lower that it really is.

The cost of goods ( example, food) is directly affected by the amount of inventory at the end of an account period.

If the ending Inventory increases and everything else remains the same, the cost of goods sold is calculated as follows;

cost of food sold = Benning inventory  +  purchases  - ending inventory

From the equation above, an increase in the ending inventory will cause the cost of food sold at the end of the year to appear lower that it really is.

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Answer: They are inverses of each other

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Explanation:

We'll need to compute h(f(x)) and f(h(x)) to see if we get x each time.

[tex]h(x) = 9x-4\\\\h(f(x)) = 9(f(x))-4\\\\h(f(x)) = 9\left(\frac{x+4}{9}\right)-4\\\\h(f(x)) = x+4-4\\\\h(f(x)) = x\\\\[/tex]

and,

[tex]f(x) = \frac{x+4}{9}\\\\f(h(x)) = \frac{h(x)+4}{9}\\\\f(h(x)) = \frac{9x-4+4}{9}\\\\f(h(x)) = \frac{9x}{9}\\\\f(h(x)) = x\\\\[/tex]

Both composite functions lead to x each time.

The equations h(f(x)) = x and f(h(x)) = x being true means each function is the inverse of the other.

Answer:

+ 1

Step-by-step explanation:

Given

x² + 2x

Using the method of completing the square

add ( half the coefficient of the x- term)² to x² + 2x

= x² + 2(1)x + 1²

= x² + 2x + 1

= (x + 1)² ← perfect square

Step-by-step explanation:

the function actually is

y = 40(x - 1) + 70 = 40x - 40 + 70 = 40x + 30

still, the slope (the factor of x) is 40.

that means y (the cost) increases by 40 for every additional hour (x increases by 1).

so, the rate of change (slope) is 40/1 = $40 per hour.

Answer:

The fraction 1/4 is a rational number.

It stands for the ratio between the integers 1 and 4.

Answer:

this is your answer

Step-by-step explanation:

this is your answer

[tex]\tan \left(-\dfrac{\pi}3\right)\\\\=-\tan \left(\dfrac{\pi}3\right)\\\\=-\sqrt 3[/tex]

The maximum possible number of people on the train is 183.

Given that a train has 11 train cars, and at least 11 passengers are in each train car, and no 3 neighboring train cars have more than 50 passengers altogether, to determine what is the maximum possible number of people on the train, the following calculation must be done:

Therefore, the maximum possible number of people on the train is 183.

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Answer:

189

Step-by-step explanation:

Set up 11 slots on a piece of paper, to simplify since each car must have 11 cars we will be alternating 28,11,11 in a repeated pattern thus getting us 28,11,11,28,11,11,28,11,11,28,11 when you add them up you get 189

Answer:

2x²+2x+8

Step-by-step explanation:

4x²-2x+10-2x²+4x-2

=4x²-2x²-2x+4x+10-2

=2x²+2x+8

Answer:

25

Step-by-step explanation:

10 + (b - a) · 5

10 + (7 - 4) · 5

10 + 3 · 5

10 + 15 = 25

Answer:

25

Step-by-step explanation:

If a = 4 and b = 7

First you gotta plug it in, so it'd become 10+(7-4)×5

Next we gotta use PEMDAS. So it would be 7-4 which would be 3, multiply that by 5 which would make 15, then add 10 for 25.

Answer:

i believe it would be likely

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

[tex](x-3)^2=5\implies \sqrt{(x-3)^2}=\sqrt{5}\implies (x-3)=\sqrt{5}\implies x = \sqrt{5}+3[/tex]

Answer:

The difference between their total amounts is .34 cents

also it didnt look like i was supposed to count a discount for charles so i didnt :)

Step-by-step explanation:

14.99 times .07 = 1.04

14.99 + 1.04 = 16.03

17.99 times .15 = 2.69

17.99 -2.69 = 15.30

15.30 times .7 = 1.07

15.30 + 1.07 = 16.37

16.37 - 16.03 = .34

Answer:

1) undefined

2) 0

Step-by-step explanation:

Slope formula:

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

Problem 1:

(x1, y1) = (-7, 8)

(x2, y2) = (-7, -6)

Plug those 2 points into the slope formula and solve:

[tex]m=\frac{-6-8}{-7--7}\\\\m=\frac{-14}{0}[/tex]

Here, you can't divide by 0, so this slope is undefined. An undefined slope would make a completely vertical line on a graph. In this case, the equation of the line would be just:

[tex]x=-7[/tex]

Problem 2:

(x1, y1) = (-9, -8)

(x2, y2) = (3, -8)

[tex]m=\frac{-8--8}{3--9}\\\\m=\frac{0}{12}\\\\m=0[/tex]

The slope is 0, and that would make a horizontal line on a graph. The equation would be:

[tex]y=-8[/tex]

You don't actually need to fully work out the slope that way. If you ever have 2 points with the same x-coordinate, the slope has to be undefined. If you ever have 2 points with the same y-coordinate, then the slope has to be 0, assuming it's linear of course. You can see that in the points given, the first 2 have the same x and the second 2 have the same y.

28.3

Step-by-step explanation:

the difference is the answer to a subtraction problem so we can plug in our numbers like this

25.6-(-2.7) which equals 28.3

a good thing to remember when subtracting negative numbers is that a positive and negative won't always make a negative like in this example

Answer:

He's right it's 28.3

Step-by-step explanation:

Check the picture below.

Answer:

..2

Step-by-step explanation:

The number of different dog families that you can create will be 3060.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

A canine sanctuary is offering 18 unique canines, yet you have space for just 4 of them.

Then the number of different dog families that you can create is given as,

¹⁸C₄ = (18!) / [(18 - 4)! x 4!]

¹⁸C₄ = (18 x 17 x 16 x 15 x 14!) / (14! x 4 x 3 x 2 x 1)

¹⁸C₄ = 6 x 17 x 2 x 15

¹⁸C₄ = 3060

The number of different dog families that you can create will be 3060.

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Answer:

2

Step-by-step explanation:

Write out all the factors for 14

Then write out the multiples of 7

Compare the numbers then find the greatest number in 14's factors that isn't in 7's multiples

Check the picture below.

Answer:

greater

Step-by-step explanation:

if you add them and do the multiplication it is greater

Answer:

It would be equal

Step-by-step explanation:

You first divide 5/5, which is equal to 1, multiply that by 2 to get 2.

After that, there is a 3/4 sitting around so you add 3/4 to 2.

Then you will see that both are equal.

Answer:

the integer is 5

Step-by-step explanation:

x^2+3(x+1)=43

x^2+3x+3=43

x^2+3x+(9/4)=43-3+(9/4)

(x+(3/2))^2=42 1/4

x+(3/2)=sqrt(42 1/4)

x+(3/2)=6 1/2

x=(6 1/2)-(3/2)

x=5

check:

5^2+3(6)=43

25+18=43

43=43

Answer:

5

Step-by-step explanation:

let positive integer be x

x² + 3(x+1)=43

x²+3x+3-43=0

x² + 3x - 40 = 0

x² + 8x - 5x - 40 = 0

x(x+8) - 5(x+8)=0

(x-5)(x+8)=0

x-5=0 or x+8=0

x=5. or x=-8

but the question says positive integer,

therefore, x=5

Answer:

850 divided by 7.5

Step-by-step explanation: