Beth filled 24 jars with paint if each jar holds 1 pint of paint how many gallons of paint did beth use

Answer:

A = 8 and B = 6

Step-by-step explanation:

Since (B = A - 2), we can substitute (A - 2) in for the "B" variable in the first equation to isolate "A".

(A - 5)² + (B - 3)² = 18                                 ----->  Original equation

(A - 5)² + ((A - 2) - 3)² = 18                         ----->  Plug in B = A - 2

(A - 5)² + (A - 5)² = 18                                ----->  Subtract

(A² - 10A + 25) + (A² - 10A + 25) = 18       ----->  Expand parentheses

2A² - 20A + 50 = 18                                 ------>  Add like terms

2A² - 20A + 32 = 0                                   ----->   Subtract 18 from both sides

2(A² - 10A + 16) = 0                                   -----> Remove common factor

2(A - 2)(A - 8) = 0                                      -----> Factor within parentheses

A = 2                                                         -----> Find A - 2 = 0

A = 8                                                        -----> Find A - 8 = 0

Since "A" gave two possible values, we need to plug them into both equations to see which value gives reasonable "B" values.

When A = 2:

B = A - 2                           -----> Original equation

B = 2 - 2                           -----> Plug in A = 2

B = 0                               -----> Subtract

(A - 5)² + (B - 3)² = 18       -----> Original equation

(2 - 5)² + (B - 3)² = 18       ------>  Plug in A = 2

(-3)² + (B - 3)² = 18           -----> Subtract within first parentheses

9 + (B - 3)² = 18               -----> Square value within first parentheses

(B - 3)² = 9                      ----->  Subtract 9 from both sides

B - 3 = 3                          ----->  Take square root of both sides

B = 6                               ----->  Add 3 to both sides

When A = 8:

B = A - 2                         -----> Original equation

B = 8 - 2                         -----> Plug in A = 8

B = 6                             -----> Subtract

(A - 5)² + (B - 3)² = 18       -----> Original equation

(8 - 5)² + (B - 3)² = 18       ------>  Plug in A = 8

(3)² + (B - 3)² = 18            -----> Subtract within first parentheses

9 + (B - 3)² = 18               -----> Square value within first parentheses

(B - 3)² = 9                      ----->  Subtract 9 from both sides

B - 3 = 3                          ----->  Take square root of both sides

B = 6                               ----->  Add 3 to both sides

As you can see, when A = 2, there are two possible values of "B" depending on the equation. However, when A = 8, both equations give a "B" value of B = 6. Therefore, A = 8 and B = 6 are the answers.

Answer:

  -8

Step-by-step explanation:

Put the given values where the corresponding variables are, and do the arithmetic.

__

  f(x) = 12 -3x

  f(5) = 12 -3(5) = -3

__

  j(x) = x² +4x -1 = (x +4)x -1

  j(-2) = (-2 +4)(-2) -1 = 2(-2) -1 = -5

__

  f(5) +j(-2) = -3 +(-5) = -8

The equation of the line that passes through the points (7, 450) and (14, 401) is y + 7x = 499

The equation of a line  can be represented as follows:

y - y₁ = m(x - x₁)

where

Therefore, (7, 450)(14, 401)

m = 401 - 450 / 14 - 7 = -49 / 7 = -7

Therefore, using (7, 450)

y - 450 = -7(x - 7)

y - 450 = -7x + 49

y + 7x = 49 + 450

y + 7x = 499

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The solution of the equation √x+2 + 4 = 6 is x = 2 and it is not an extraneous solution

The solution of the equation can be found as follows;

√x+2 + 4 = 6

subtract 4 from both sides

√x+2 + 4 - 4 = 6 - 4

√x+2  = 2

square both sides

(√x+2)² = 2²

x + 2 = 4

x= 4 - 2

x = 2

Therefore the solution is x = 2 and it is not a extraneous solution.

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Answer:

It should move three places to the left :3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

-3 log₂ (-n + 10) = -16+7

-3 log₂ (-n + 10) = -9

log₂ (-n + 10) = -9/-3

log₂ (-n + 10) = 3

-n + 10 = 2^3

-n + 10 = 8

n=2

Answer:

y=14; x=72

Step-by-step explanation:

y=(21×2)/3; x=(48×21)/14

Answer:

Solution: (-1, 1) and (10/3, 16/3) are Intercepts.

Step-by-step explanation:

Set the equations equal to themselves and solve for x and y.

Hope this helps! :)

Answer & step-by-step explanation:

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign. As you can clearly see here, there is no equal sign connecting anything here, thus, it is an expression.

Because for it to be called an equation you need to have the equal symbol (=) comparing two epressions.

Example of expression:

 2x - 4y + 14

Example of equation:

   -3y - 2 = -2x - 8

⇔ -3y = -2x + 6

⇔ -y = -[tex]\frac{2}{3}[/tex]x + 2

⇔ y = [tex]\frac{2}{3}[/tex]x - 2

The amount of co2 that Harry's vehicle would release to the atmosphere in a year is 12,000 pounds.

The first step is to determine the gallons of gasoline that the car would need in a year: 15,000 / 25 = 600 gallons

The second step is to determine the total emissions when the car uses 600 gallons: 600 x 20 = 12,000 pounds

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Answer:

[tex]y^{5}\times y^{3}=y^8[/tex]

Step-by-step explanation:

exponent property :

[tex]\left( a\right)^{n} \times \left( a\right)^{m} =\left( a\right)^{n+m}[/tex]

………………………………………

[tex]\Longrightarrow y^{5}\times y^{3}=y^{5+3}=y^8[/tex]

Answer:

To begin to answer this question, you will want to determine the equation for the volume of a rectangular prism. In this case, the equation is length times width times height or:

V = l * w * h

In the question, you are given several pieces of information that you can then plug into the equation. For example, you know the volume is 21,904 ft3 because they tell you that directly. You also know that the pool is 8 feet deep. I consider the depth to be the same as the height. With that information, you now have the equation:

21,904 ft3 = l * w * (8ft)

You are also told that the length is 2 times the width. Written as an equation, you would say that

l = 2w

Now, you can substitute that 2w for l to get the equation:

21,904 ft3 = (2w) * w * 8ft

We know that when you multiply a variable times itself, you get a squared variable, so 2w * w = 2w2 and that

21,904 ft3 = 2w2 * 8ft

Now, you can solve the equation to find w. At this point, it is easiest to drop the units of feet on the numbers to do the math. As long as all your numbers are in the same units (i.e. feet), you are good to go. Start by dividing each side by 8 to get

2738 = 2w2

Then divide both sides by 2 to get

1369 = w2

Finally, for this portion, take the square root of 1369 to get

w = 37 feet.

But you're not done yet. You know the width, and you know that l = 2w. Plug the value for w (37) into this equation to get the length, which is 74 feet.

The final answer is that the width of the pool is 37 feet and the length is 74 feet.

You can check your answer by plugging the length, width, and height (depth) into the equation for volume to see if you get 21,904ft3.

If you take 8 ft x 37 ft x 74 ft, you get 21,904 ft3 and you know that you answer is correct.

Step-by-step explanation:

Answer:

0.182

Step-by-step explanation:

2 / 11 = 0.181818...repeating

0.1818 round up since the 4th number 8 > 5

Answer:

0.182

Step-by-step explanation:

:)

The best estimate of the percentage of apples picked at the orchard in October that is damaged will be 6%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol 'percent' is used to symbolize it.

An apple orchard's workers pick 12,500 apples in the month of October.

A sample of 500 of these apples shows that 30 of them are damaged.

Then the best estimate of the percentage of apples picked at the orchard in October that is damaged will be

P = 30/500 x 100

P = 6%

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Answer:

y = 2x – 10

Step-by-step explanation:

ΔY divided by ΔX

= 5-7/0-4

= 2/1 = 2 (simplified)

plug in 2 into; 0=2(5)+b

= -10=b

so we have: y=2x-10

To solve this problem, we have to understand and establish some basic mathematical facts on a cone.

The answer to this question are option b and c only.

This is a solid figure that has the base of a circle and the top is made up round triangle.

The formula of volume of a cone is given as

[tex]v = \frac{1}{3}\pi r^2 h[/tex]

where;

In the given question, the first fact given is if the radius doubles the diameter and that false.

[tex]diameter = 2 * radius[/tex]

If we have the value of the the radius, we can calculated the base area using area of a circle

[tex]area = \pi r^2[/tex]

The volume of a cone is actually one-third the volume of a cylinder

we can only calculate the volume of the cone is we have the value of the height of the cone.

The answer to this question are option b and c only.

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Answer:

B, C, D, E

Step-by-step explanation:

Got it wrong the first time.

Answer:

17.2

Step-by-step explanation:

23 ⇒ Below 5, round down

20  ⇒ Add to decimal

17. 23 ⇒ 17.2 / 17.20

Answer:

6.75$

Step-by-step explanation:

because 15% of 45$ is 6.75$

Step-by-step explanation:

the photo should explain

Step-by-step explanation:

there are 13 out of 52 diamond cards.

and there are 26 out of 52 black cards.

so, for the first card to be diamond the probability is

13/52 = 1/4 = 0.25

but now, he does not put the card back.

he pulls the second card out of 51 possible cards.

the desired cases are still 26.

so, the probability to pull a black card as the second card under the restriction that the first card was a diamond is

26/51 = 0.509803922...

the probability for that combined event is then

1/4 × 26/51 = 26/204 = 13/102 = 0.12745098...

so, c. is the right answer.

Answer:

12

Step-by-step explanation:

This a Venn Diagram.....the shaded overlapping area is common to both sets.... it must be a multiple of 3   AND a multiple of  4

12    would work....Right?

Answer:

B.  12.

Step-by-step explanation:

The numbers that will go into the shaded area are those who are divisible by 3 and 4.

12  = (3*4)is the only one in the list.

In this question, we are presented with two triangles are required to find he missing sides in them. the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively

In the first triangle, we need to use trigonometric ratio to find the missing side in the triangle

Data;

To find the adjacent side, we need to use cosine rule on this problem.

[tex]cos\theta = \frac{adjacent}{hypothenuse} \\cos45 = \frac{x}{8\sqrt{2} } \\x = 8[/tex]

The adjacent side is equal to 8 units

In the second triangle, we also need to use trigonometric ratio, but let's write down our data

We can use both cosine and sine rule here or use one and use Pythagoras's theorem to find the other side.

[tex]cos \theta = \frac{adjacent}{hypothenuse} \\cos 30 = \frac{x}{10} \\x = 8.660[/tex]

The adjacent side is equal to 8.660, let's find the opposite side using sine rule

[tex]sin\theta = \frac{opposite}{hypothenuse} \\sin 30 = \frac{y}{10} \\y = 5[/tex]

And lastly, the value of the other angle is

[tex]90 + 30 + z = 180\\z = 180 - 120\\\\z = 60[/tex]

From the calculations above, the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively

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An estimate of the percentage of defective items in the population if 5 of 200 items were defective is 2.5%.

The percentage of a defective item out of a total item can be calculated as follows:

% defective item = no of defective item/total no of items × 100

According to this question, in a random sample of 200 items, 5 items were defective.

% defective item = 5/200 × 100

% defective item = 2.5%

Therefore, an estimate of the percentage of defective items in the population if 5 of 200 items were defective is 2.5%.

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Answer:

The answer is D. Hope this helps :)

Answer:

5/8

Step-by-step explanation:

There are 8 sections, and 4 sections that are 1, and 1 pink section. So adding these up, we get 5/8.

Hope this helped! :)

Answer: 9 cups

Step-by-step explanation: 8 multiply it by 9 .