In a paint factory, an old conveyer line has filled 40 barrels of paint, and is filling more at a rate of 1 barrel per minute. A worker just switched on a newer line that can fill 3 barrels per minute. In a little while, the two lines will have filled an equal number of barrels. How many barrels will each line have filled?
Write a system of equations, graph them, and type the solution.

Answer:

[tex]x = \frac{ - 3}{2} \: or \: \frac{1}{3} [/tex]

Step-by-step explanation:

[tex]7 {x}^{2} + 10x - 3 = {x}^{2} + 3x[/tex]

[tex] = > 7 {x}^{2} - {x}^{2} + 10x - 3x -3 = 0[/tex]

[tex] = > 6 {x}^{2} + 7x - 3 = 0[/tex]

[tex] = > 6 {x}^{2} + 9x - 2x - 3 = 0[/tex]

[tex] = > 3x(2x + 3) - 1(2x + 3) = 0[/tex]

[tex] = > (2x + 3)(3x - 1) = 0[/tex]

Here x will have 2 values.

1) [tex]2x + 3 = 0[/tex]

[tex] = > 2x = - 3[/tex]

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

2)[tex]3x - 1 = 0[/tex]

[tex] = > 3x = 1[/tex]

[tex] = > x = \frac{1}{3} [/tex]

Answer:

Brass + Brass = Woodwind

Brass + Woodwind = 150

Brass = 50, Woodwind = 100

Step-by-step explanation:

Hi there!

The two addition equations would be:

Brass + Brass = Woodwind

(As there are twice as many woodwind as brass)

AND

Brass + Woodwind = 150

(As there are 150 of those instruments in total)

These two equations fully describe this situation, and you can use them to solve the problem using substitution as well.

Since Woodwind = Brass + Brass, then:

Brass + Woodwind =150

Can also be written as:

Brass + (Brass+Brass) = 150

Now we can solve by combining all the like terms which gives us:

3*Brass = 150

Brass = 150/3

Brass = 50 meaning that Woodwind = 100, as 50+50=100.

Hope this helped!

Answer:

x= -3/2, -11/2 or -1.5

Answer:

Step-by-step explanation:

16^x=1/64

[tex](2^4)^x=64^{-1} =(2^6)^{-1}=2^{-6}\\2^{4x}=2^{-6}\\4x=-6\\x=-\frac{6}{4} =-\frac{3}{2}[/tex]

Answer:

The ribbon cost is $77

Step-by-step explanation:

Firstly, we need to get the 3rd side of the triangle

This represents the hypotenuse since we have 2 legs, we need the side connecting the legs

To get this, we use Pythagoras’ theorem

This states that the square of the hypotenuse equals the sum of the squares of the two other sides

Let the hypotenuse be marked x

Thus;

x^2 = 56^2 + 33^2

x^2 = 3136 + 1089

x^2 = 4225

x = square root of 4225

x = 65 feet

So the length of all the sides will be;

56 + 33 + 65 = 154 feet

So the cost of the ribbon will be;

154 feet. * 0.5

= $77

Answer:

30

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

drag  10 to the

Step-by-step explanation:

Answer:

In order from left to right (each slash will be one line on the number line.)

Step-by-step explanation:

-10   -9            -7           -5      -4                -2           0

/____/___/___/__/___/____/___/_____/__/___/

Answer:

The answer is the first one

Step-by-step explanation:

Answer:

The unit rate is 6.5mph or 6.5 miles per hour.

Step-by-step explanation:

22.75/3.5 = 6.5

Answer:

The formula f(t) will be:

[tex]\:f\left(t\right)=2150\left(0.962\right)^t[/tex]              

Step-by-step explanation:

We know that exponential decline in Maths can be termed as a consistent reduction of an amount by percentage over a certain period of time.

It can be expressed using the formula

[tex]f\left(t\right)=\:a\:\left(1-b\right)^t[/tex]

here

f(t) represents the final amount

a represents the original amount

b represents the decay factor

t represents the amount that has passed

Now, map our problem using the same concept formula

as

2150 members are at the beginning, so

a = 2150  

as the size of the population has been experiencing an annual decline of 3.8%. so

b = 3.8%= 0.038

so substituting b = 0.038 and a = 2150  

[tex]P=f\left(t\right)=\:a\:\left(1-b\right)^t[/tex]

[tex]\:f\left(t\right)=2150\left(1-0.038\right)^t[/tex]

[tex]\:f\left(t\right)=2150\left(0.962\right)^t[/tex]

Therefore, the formula f(t) will be:

[tex]\:f\left(t\right)=2150\left(0.962\right)^t[/tex]              

Answer:

$0.29 cents

Step-by-step explanation:

6.88/24 = 0.28666666666 about 0.29

Answer:

Step-by-step explanation:

3/4 / 1/2

i think u multiply the recipricol 3/4x2/1=6/4 or 3/2

Answer:

2x = y

Step-by-step explanation:

As you can see in the table, y = 2x, this is proven by the fact that if you divide any value in the y of the table by 2 you will get its corresponding x value, proving that 2x = y is the function that is used to represent this table's value.

Answer:

2x = y

Step-by-step explanation:

If x = 10

2x = y

2 * 10 = y

20 = y

We want to compare the graphs of the two given linear equations, we will find that they have the same y-intercept but opposite slopes.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here the two equations are:

So you can easily see that the two equations have the same y-intercept but opposite slopes.

So both of them pass through the point (0, 1) and both are lines, these are the similarities.

And the difference is that the slopes are just different.

If you want to learn more about linear equations you can read:

https://brainly.com/question/14323743

Answer:

A. 10 + 2

Step-by-step explanation:

288 ÷ 24 is shown below. 240 ÷ 24 = 10 288 – 240 = 48 48 ÷ 24 = 2

After obtaining the quotient of 288 ÷ 24 = 10,

Multiplying the divisor 24 by 10 = 240 and subtracting 240 from 288 to obtain the remainder = 48, the divisor is again used in 48 and the quotient obtained is added to the intula quotient value of 10 ; (10 + 2) and the process repeated

Answer:

Two triangles are similar if they meet one of the following criteria. : Two pairs of corresponding angles are equal. : Three pairs of corresponding sides are proportional. : Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.

Answer:

10 pounds will cost $17.50

Step-by-step explanation:

(5.25 / 3) * 10 = x

1.75 * 10 = x

17.50 = x

Answer:

10 pounds of apples will cost $17.50.

Step-by-step explanation:

First, we need to find the unit rate.

$5.25/3 = $1.75

Now we need to multiply $1.75 by 10 pounds.

$1.75 × 10 = $17.50

Answer:

The equation to determine the normal price of each cookie is

7(x - 0.75) = 2.80

The normal price of each cookie = $1.15

Step-by-step explanation:

Let us represent the normal price of a cookie as : x

We are told that:

Today each cookie costs \$0.75less than the normal price.

The price of a cookie today is

x - 0.75

Right now if you buy 7 of them it will only cost you \$2.80$

Hence:

7(x - 0.75) = 2.80

Solving for x

7x - 5.25 = 2.80

7x = 2.80 + 5.25

7x = 8.05

x = 8.05/7

x = $1.15

The normal price of each cookie = $1.15

Answer:

$ 1.15

Step-by-step explanation:

7(c-0.75) = 2.80 is the equation

$1.15 is the total for C

I did this khan before and this is correct

Hope this helps!

;)

Answer:

Yea i think it is the first one

Step-by-step explanation:

Answer:

a(n-1)+d

d=5

The anser is A

Answer:

Since x and y are directly related, the equation for their comparison will look like

kx = y

where k is your constant. They give you an instance in the problem where x = 27 and y = 81. Plug this into the above equation and solve for k.

kx = y

k (27) = 81

k = 3

So, the constant of variation is 3.

Answer: I think it is the last question

Step-by-step explanation:

Answer:

a° = 124°

Step-by-step explanation:

Angle E + 250° = 360 because they make a full angle

a° + 126° + E = 360°

a° = 360 - 126 - 110

a° = 124°

Answer:

a=125°

Step-by-step explanation:

The angle at E=360-250=110°

Draw a horizontal through E, parallel to AB and CD such that it divides angle E into two angles of 55° each. Produce line AB to M such that the 55° at E is alternate with it.

A and 55° are now supplementary angles therefore

a+55°=180°

a=180-55=125°

Answer:

Both are correct

Step-by-step explanation:

All the angles are equal, therefore causing the triangles to be similar.

Answer:

28:35, which in fraction form is 28/35, but simplified is 4/5 or 4:5

Step-by-step explanation:

Answer:

a) 10% off or $20 off

b) 25% off or $124.99 off

Step-by-step explanation:

In order to find the markdown on the shredder we simply need to divide the sale price by the original price. Once we have that we subtract that decimal from 1 and multiply by 100 to get the markdown percentage. We can also subtract the original price from the sales price to get the markdown dollar value.

179.99 / 199.99 = 0.899

(1 - 0.899) * 100 = 10%

199.99 - 179.99 = $20

Now, for the printer we are provided the markdown perentage so to find the markdown dollar value we need to divide the perentage by 100 to turn it into a decimal and multiply that decimal by the regular price of the printer. We can also subtract the markdown dollar value from the original price to get the sale price...

25% / 100 = 0.25

0.25 * 499.99 = 124.99

499.99 - 124.99 = $375

Answer:

y = 4

Step-by-step explanation:

21 = 3(y + 3), Distribute

21 = 3y + 9, Subtract 9 on both sides

12 = 3y, Divide 3 on both sides

4 = y