Simplify completely quantity 12 x plus 36 over quantity x squared minus 4 x minus 21 and find the restrictions on the variable.

a.) 12 over quantity x minus 7, x ≠ 7
b.) 12 over quantity x minus 7, x ≠ 7, x ≠ −3
c.) quantity x plus 3 over quantity x minus 7, x ≠ 7
d.)quantity x plus 3 over quantity x minus 7, x ≠ 7, x ≠ −3

Answer:

The number is 8.

Step-by-step explanation:

4(x+(-3))-4=2x

4(x-3)-4=2x

4x-12-4=2x

4x-2x-16=0

2x-16=0

2x=0+16

2x=16

x=16/2

x=8

Answer:

125 cubic inches

Step-by-step explanation:

The formula for the volume of a cube is:

[tex]V=a^3[/tex],

Where V is volume and a is edge length. Let's substitute the edge length of 5 from the problem into this formula.

[tex]V=5^3[/tex]

Now we can simplify. I will rewrite 5 cubed as 5*5*5 for simplicity.

[tex]V=5*5*5[/tex]

[tex]V=125[/tex]

So we have our volume, 125, but what does this mean? We have to figure out the units. Recall that our original unit was inches, thus the final answer is in inches. However, 125 inches does not make much sense, as we are dealing with volume, and not a line or distance. 125 cubic inches is the answer we are looking for, as cubic inches is the unit for volume deriving from inches.

The volume of a block of cheese is 125 in³.

It is a polygon having six faces.

The volume of a cube is side³.

We have,

Side length = 5 in

Now,

The volume of a block of cheese.

= Side³

= 5³
= 125 in³.

Thus,

125 in³ is the volume of a block of cheese.

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Answer:

The answer would be $3.60

Step-by-step explanation:

50% of $12 is $6. Take 40% off of that and you get $3.60.

Answer:

The answer is 2.40

Step-by-step explanation: That is the answer because 50 percent into 12 is 6 and 40 percent into 6 is 2.4 = 2.40

No. Because -2 has two outputs. To be a function  each input have to  have one output. I.E

2,3  4,5  6,7  8,9 are functions.

Answer:

3 packs of plates; 5 packs of cups

Step-by-step explanation:

First we have to find the least common multiple of the two. (factor tree, birthday cake) (Strategies not shown) You should get 180.

Next we have to see how many times each number goes into 180.

60 times 3 is 180 plates. 36 times 5 is 180.

That's your answer. Hope this helps!

Answer:

The value of  [tex]\frac{f}{g} (x)[/tex] is [tex]\dfrac{4x + 1}{x^{2} -5 }[/tex]

Step-by-step explanation:

Given as :

f(x) = 4 x + 1

g(x) = x² - 5

Let the value of [tex]\frac{f}{g} (x)[/tex] = A

So, According to question

[tex]\frac{f}{g} (x)[/tex]  = [tex]\dfrac{f(x)}{g(x)}[/tex]

Or, A = [tex]\dfrac{4x + 1}{x^{2} -5 }[/tex]

So, The value of  [tex]\frac{f}{g} (x)[/tex] = A =  [tex]\dfrac{4x + 1}{x^{2} -5 }[/tex]

Hence, The value of  [tex]\frac{f}{g} (x)[/tex] is [tex]\dfrac{4x + 1}{x^{2} -5 }[/tex] Answer

To calculate the composite function (f ∙ g)(-1) for the functions f(x) = x² + 3 and g(x) = 4x - 3, we first find g(-1) which is -7, and then calculate f(-7) which results in 52.

To find the composite function (f ∙ g)(x), we first apply the function g to x, and then apply the function f to the result of g(x). In this case, first find g(-1) and then apply f to that result.

Initialize with g(-1), which is 4(-1) - 3. Simplifying that, we get -4 - 3, which equals -7.

Now, take the result of g(-1), which is -7, and input it into f(x) to get f(g(-1)). Thus, f(-7) = (-7)² + 3. Calculating this gives us 49 + 3, which equals 52. Therefore, (f ∙ g)(-1) = 52.

Answer: 1/6 of a pound.

Step-by-step explanation: Divide 2/3 pounds by 4 people. To do this, multiply  2/3 by 4's reciprocal, which is 1/4. The reciprocal of a number is basically the reverse form of that number. 4 as a fraction is 4/1. The reciprocal of that would be 1/4. Hopefully you understand.

2/3 times 1/4 is 2/12. Simplify by dividing 2/12 by 2 and 12's greatest common factor: 2. 2 divided by 2 is 1; 12 divided by 2 is 6. Your final answer is 1/6.

The graph that shows the solution set for the inequality -5/2x -3<2 is a number line with an open circle at -2 and an arrow pointing to the left.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

To graph the solution set for the inequality -5/2x -3<2, you first need to solve the inequality for x.

-5x -6 < 4

-5x < 4 + 6

-5x < 10

x < -2

The graph of the solution set for the inequality x < -2 is a number line with an open circle at -2 and an arrow pointing to the left. The open circle indicates that -2 is not included in the solution set, and the arrow pointing to the left indicates that all values to the right of -2 are included in the solution set.

Hence, the correct answer would be an option (C).

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Answer: The three consecutive numbers are 23, 24 and 25, and 25 Is obviously the largest.

Step-by-step explanation:

Answer: 23 , 24 , 25

Step-by-step explanation:

Consecutive numbers are numbers that follow each other in order.

Let the first number be x , the second number be x + 1 and the third number number be x + 2.

From the first statement :

Their sum implies :

x + x +1 + x + 2 = 72

3x + 3 = 72

Subtract 3 from both sides of the equation:

3x + 3 - 3 = 72 - 3

3x = 69

Divide through by 3

3x/3 = 69/3

Therefore :

x = 23

Therefore :

The numbers are

23 , 24 and 25

Answer:

--9x^3+12x^2-x-2

Step-by-step explanation:

(2-3x)(3x^2-2x-1)

6x^2-4x-2-9x^3+6x^2+3x

-9x^3+6x^2+6x^2+3x-4x-2

-9x^3+12x^2-x-2

Answer:

[tex]10[/tex]

Step-by-step explanation:

Combinations : When there are total [tex]n[/tex] choices and you have to choose [tex]k[/tex]of them (in any order)

                 The possible ways [tex]= \ ^n{c_{k}} = \frac{n!}{k!(n-k)!}[/tex]

Here total chances [tex]=5[/tex]

and we have to choose [tex]2[/tex]of them.

Possible ways[tex]=\ ^5{c_{2}}[/tex]

                             [tex]=&\frac{5!}{2!(5-2)!} = \frac{5!}{3! 2!} \\\\=&\frac{5 \times 4\times 3!}{3! 2!} = \frac{5 \times 4}{2} = 10[/tex]

Answer:

Cost per ounce = $0.07 (7 cents per ounce)

Step-by-step explanation:

Each container is 7.8 ounces and there are 24 of them in a case.

Total weight in ounce of the case is:

7.8 * 24 = 187.2 ounces

It costs $12.99 for the case, which contains 187.2 ounces. We find the cost per ounce of yogurt by dividing the total cost by total ounces in the case.

12.99/187.2 = 0.0693

Rounded to nearest cent (2 decimal places), that would be:

Cost per ounce = $0.07 (7 cents per ounce)

The unit price of the Greek yogurt is $0.07 per ounce.

To calculate the unit price, we need to divide the total cost of the case by the total number of ounces in the case.

First, we determine the total number of ounces in the case by multiplying the number of containers by the ounces per container:

[tex]\[ 24 \text{ containers} \times 7.8 \text{ ounces per container} = 187.2 \text{ ounces} \][/tex]

Next, we divide the total cost of the case by the total number of ounces to find the cost per ounce:

[tex]\[ \frac{\$12.99}{187.2 \text{ ounces}} \approx \$0.0693 \text{ per ounce} \][/tex]

Finally, we round this to the nearest cent, which gives us:

[tex]\[ \$0.0693 \text{ per ounce} \approx \$0.07 \text{ per ounce} \][/tex]

Therefore, the unit price of the Greek yogurt, rounded to the nearest cent, is $0.07 per ounce.

The expected value of an insurance policy for the company is calculated by subtracting the expected costs (probability of accident * average payout) from the premium paid by the customer. In this case, the insurance company can expect to retain $185.20 from the annual premium after estimated payouts.

The subject of this question falls under the category of Mathematics, specifically in the field of probability and expected value. The expected value of an insurance policy is calculated as the product of the probability of an event (an accident in this case) and the corresponding payout, subtracted from the cost or premium of the policy. Here the insurance company estimates a 2.4% likelihood of an accident, which is a probability of 0.024, and the average payout being $2700.

First, determine the expected payout by the insurance company, which is computed by multiplying the probability of the event by the payout: 0.024 * $2700 = $64.80.

Then subtract this from the premium to calculate the company's expected value: $250 - $64.80 = $185.20.

This means, on average, the insurance company can expect to retain $185.20 from the annual premium after accounting for the estimated payouts from accidents.

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The expected value of this insurance policy for the company is approximately -$185.20.

Given information:

Likelihood of having an accident: 2.4% (expressed as a decimal, so (p = 0.024))

Average insurance payout: $2700

Annual premium charged: $250

The expected value ((E)) can be calculated as follows:

[tex][ E = (p \cdot \text{{Payout}}) - \text{{Premium}} ][/tex]

Substitute the given values: [ E = (0.024 x  2700) - 250 ]

Calculating: [ E = 64.8 - 250 = -185.2 ]

The expected value of this insurance policy for the company is approximately -$185.20.

Interpretation:

A negative expected value means that, on average, the insurance company is expected to lose money per policy sold.

In this case, the company charges a premium of $250 but expects to pay out an average of $2700 per accident. Therefore, the expected loss is $185.20 per policy.

Answer:

[tex]A=61.8\ units^2[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The area of triangle ABC applying the law of sines is equal to

[tex]A=\frac{1}{2}(AC)(BC)sin(C)[/tex]

substitute the given values

[tex]A=\frac{1}{2}(10)(13)sin(72^o)[/tex]

[tex]A=61.8\ units^2[/tex]

Answer:

c) 61.8 square units

Step-by-step explanation:

just took the test

Answer:

It’s incomplete

Step-by-step explanation:

Answer:

Part A:  An = 6 + 3( n - 1 )

Part B:  36

explanation:

We us the explicit rule 6 + 3( n - 1 ) to find out the he found in the 11th week

6 + 3( n - 1 )

6 + 3( 11 - 1 )

6 + 3( 10 )

6 + 30

36

Hope it helps!

Answer:

The quantity after t years 40 [tex](0.65)^{\textrm t}[/tex] millions tons

Step-by-step explanation:

Given as :

The rate of decrease of carbon dioxide each other = 35%

The quantity of carbon dioxide emitted this year = 40 million tons

Let the quantity of carbon dioxide emitted after t year = A millions tons

Now, According to question

The quantity of carbon dioxide emitted after t year = The quantity of carbon dioxide emitted this year × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, A millions tons = 40 millions tons × [tex](1-\dfrac{\textrm 35}{100})^{\textrm t}[/tex]

Or, A millions tons = 40 millions tons × [tex](\dfrac{100-35}{100})^{\textrm t}[/tex]

Or, A millions tons = 40 millions tons × [tex](\dfrac{65}{100})^{\textrm t}[/tex]

Or, A millions tons = 40 millions tons × [tex](0.65)^{\textrm t}[/tex]

So,The quantity after t years = A = 40  [tex](0.65)^{\textrm t}[/tex] millions tons

Hence The quantity after t years 40 [tex](0.65)^{\textrm t}[/tex] millions tons    Answer

Answer:

Y = 8 + 6X is correct answer.

Step-by-step explanation:

Let y be the total lenght of tree and x is number of years that has past after tree plantation.

So the total lenght of tree after x years can be presented with the help of equation given below.

 Y = 8 + 6X

* This equation show that there is direct relationshop between number of years and total height of tree.

For example after 3 years the height of three will be

Y = 8 + 6(3) = 26 inches

She would make $573.5 in a work if she sold $4,700 worth of merchandise

Step-by-step explanation:

The given is:

We need to find how much she would make in a work week

∵ Mae Ling earns a weekly salary of $315

∵ She earns a 5.5% commission on sales

∵ She sold by $4,700 in that week

- Add $315 to the product of 5.5% and $4,700

∴ She made = 315 + (5.5% × 4,700)

∵ 5.5% = 5.5 ÷ 100 = 0.055

∴ She made = 315 + (0.055 × 4,700)

∴ She made = 315 + 258.5

∴ She made = 573.5

She would make $573.5 in a work if she sold $4,700 worth of merchandise

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Answer:

dimeonsion 1 should be 3x13 dimension 2 should be 6x10 dimension 2 is what chris should choose

Step-by-step explanation:

ik this is from prodigy lol

Chris should create a rectangular rose garden with dimensions 8 meters in length and 8 meters in width to use all 32 meters of garden fencing.

To begin, let's assume the rectangular garden has a length (L) and a width (W). Since the garden is enclosed by fencing on all sides, the perimeter of the garden would be equal to the total length of the fencing, which is 32 meters.

Perimeter = 2L + 2W

Since we know the perimeter is 32 meters, we can set up the equation:

32 = 2L + 2W

To maximize the area of the garden, Chris needs to find the dimensions that will yield the largest possible area for a given perimeter. The area (A) of a rectangle can be calculated using the formula:

Area = L * W

Since we know the perimeter is 32 meters:

2L + 2W = 32

Solving for L:

2L = 32 - 2W

L = 16 - W

Now, substitute this value of L into the area equation:

Area = L * W

Area = (16 - W) * W

Expand the equation:

Area = 16W - W²

Now, this equation represents the area of the rectangular rose garden in terms of its width (W). To find the value of W that maximizes the area, we can take the derivative of the area equation with respect to W and set it equal to zero:

d(Area)/dW = 16 - 2W = 0

Solving for W:

2W = 16

W = 8 meters

Now that we have the width (W), we can find the length (L) using the previously derived equation:

L = 16 - W

L = 16 - 8

L = 8 meters

Therefore, to create a rectangular rose garden with 32 meters of fencing that utilizes all the available fencing, Chris should make the length and width of the garden 8 meters each.

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Answer:

10

Step-by-step explanation:

okay so if he has 2 dogs and he feeds each dog 250 grams twice a day

if he buys a 10 kilo bag, how many days will it last?

so first off, convert the 250 grams into kilos. which is 0.25

0.25 × 4 = 1 kilo

4 is the amount of times he feeds the dogs.

so in reality, it should take 10 days.

The number of days will the bag last is 10 days.

Given that,

Based on the above information, the calculation is as follows:

Here first we have to convert the 250 grams into kilos so it should be 0.25

And, there is no of times the dog feed is 4

So, it should be 1 kilo

And, there is the purchase of 10 kilos

Therefore, we can conclude that The number of days will the bag last is 10 days.

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Based on the number of square and round tiles, the probability of selecting two blue tiles and two white tiles is d. 1/40.

The probability of Jeremy's selection can be found as:

= (Probability of picking round white tile x Probability of picking square white tile) + (Probability of picking round blue tile x Probability of picking square blue tile)

Solving gives:

= (2 / 36 x 9 / 60) + (6 / 36 x 6 / 60)

= 0.025

= 1 / 40

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According to the figure, I can safely assume that the 10 cm line and 15 cm line are parallel.

Thus, there are two similar triangles, one with the 10 cm bottom and 15 cm bottom, where one triangle is larger by a factor of 15/10 = 3/2

We know that the 8 cm line segment and y both join to create the side of the large triangle.

8cm + y = the side of the large triangle

Multiplying 8cm by 3/2 gives us 12, since we know the large triangle is 3/2 times larger than the smaller one.

8 + y = 12

y = 4 cm

Finding x is going to be a bit different. We know that the 6 cm line and x form the side of the larger triangle, which we know is 3/2 times larger than x.

x + 6cm = ?

The side of the larger triangle is 3/2x, thus

x + 6 = 3/2 x

Subtract both sides by x

6 = 1/2 x

Multiply both sides by 2

12 cm = x

Thus, y = 4 and x = 12.

Let me know if you need any clarifications, thanks!

Henry spent [tex]5\frac{1}{4}[/tex] hours on yard work.

Step-by-step explanation:

Given,

Time spent on cutting the grass = [tex]1\frac{1}{2}=\frac{3}{2}\ hours[/tex]

Time spent on pulling weeds = [tex]1\frac{3}{4}=\frac{7}{4}\ hours[/tex]

Time spent on sweeping and bagging = 2 hours

Total time spent = Time spent on cutting + Time spent on pulling + Time spent on sweeping

Total time spent = [tex]\frac{3}{2}+\frac{7}{4}+2[/tex]

Taking LCM

Total time spent = [tex]\frac{6+7+8}{4}=\frac{21}{4}[/tex]

Total time spent = [tex]5\frac{1}{4}[/tex] hours

Henry spent [tex]5\frac{1}{4}[/tex] hours on yard work.

Keywords: fraction, addition

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Answer:

Step-by-step explanation:

y = 4.5x

Explanation:

9 ÷ 2 = 4.5

18 ÷ 4 = 4.5

27 ÷ 6 = 4.5

Answer:

[tex]\$ 199[/tex]

Step-by-step explanation:

Given: Maria spent $2388 for natural gas, last year.

Maria chooses to use balance billing process to pay this year´s gas bill.

Balance billing is a billing practice, where provider bill you the difference between total cost and allowed amount. It can be paid partially or monthly. It generally in practice for medical billing as healthcare bill are generated for difference between total cost and amount which is paid through insurance.

Now, lets find out monthly bill paid by Maria.

We know there are 12 months in a year.

∴ Monthly payment= [tex]\frac{\$ 2388}{12} = \$ 199[/tex]

∴Maria will pay $199 monthly as her gas bill this year.

Maria's monthly payment for natural gas this year using balance billing will be $199.

Step 1

Balance billing is a method where a utility company estimates the annual energy usage and divides it into equal monthly payments. To find Maria's monthly payment for natural gas this year, we divide the total amount she spent last year by 12 months.

Total amount spent last year = $2,388

Step 2

Monthly payment this year = Total amount spent last year / 12 months

[tex]\[ \text{Monthly payment} = \frac{2388}{12} = 199 \][/tex]

Maria's monthly payment for natural gas this year, using balance billing, will be $199, calculated by dividing the total amount she spent last year by 12 months.

Answer:

x = 2y + 6

Step-by-step explanation:

2x - 4y = 12

2x = 4y + 12

x = 2y + 6

To solve for 'X' in the equation 2x - 4y = 12, isolate 'X' by adding 4y to both sides, resulting in the equation 2x = 4y + 12. Further, divide the entire equation by 2 to get X = 2y + 6. The final value of 'X' would depend on the value of 'Y'.

To solve for X in the equation 2x - 4y = 12, we can proceed in the following manner:

Isolate X on one side of equation. In order to do this, we add 4y to both sides of the equation, thus changing the equation to 2x = 4y + 12.

Now, to solve for X, we need to divide the entire equation by 2. Therefore, the final equation is ready: X = 2y + 6.

Thereby, you have now solved for 'X' in the equation. Kindly note that as there is a 'y' variable involved as well, the final value of 'X' would depend on the value of 'Y'.

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Answer:

11+6i

Step-by-step explanation:

(3+4i)+(8+2i)=11+6i

Answer:

4

Step-by-step explanation:

Answer:

2*2 is 4 id4

Step-by-step explanation: