a cylinder with a diameter of 24 inches and a height of 8 inches has the same volume as a cone with a diameter of 12 inches. what is the height of the cone?

Answer:

The length of the rug is [tex]7\ ft[/tex]

The width of the rug is [tex]3\ ft[/tex]

Step-by-step explanation:

Let

x----> the length of the rug

y----> the width of the rug

we know that

The area of the rug is

[tex]A=xy[/tex]

[tex]A=21\ ft^{2}[/tex]

so

[tex]21=xy[/tex] -----> equation A

[tex]x=y+4[/tex] -----> equation B

substitute equation B in equation A and solve for y

[tex]21=(y+4)y[/tex]

[tex]y^{2}+4y-21=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]y=3\ ft[/tex]

see the attached figure

Find the value of x

[tex]x=3+4=7\ ft[/tex]

therefore

The length of the rug is [tex]7\ ft[/tex]

The width of the rug is [tex]3\ ft[/tex]

Answer: Option B.

Step-by-step explanation:

Given the system of inequalities:

[tex]y<x^2+6[/tex]

[tex]y>x^2-4[/tex]

The solution of the system of inequalities is the region between the parabolas. This region is: below the parabola [tex]y=x^2+6[/tex] and above the parabola [tex]y=x^2-4[/tex]

Then, if a point is a solution of the system, then it must be in the region between this parabolas.

You can observe in the figure attached that the point  that is in this region is the point (2,6), therefore, the answer is the option B.

-x=2-3x+3

add 3x to both sides

2x=2+3

combine like terms

2x=5

divide by 2

x= 5/2

Answer:

The answer is x = 5/2.

Step-by-step explanation:

Add the like terms which are 3 & 2.  Add like variables which would be 3x added to both sides then you get 2x = 5. Divide by 2 on both sides to get x = 5/2.

Answer:

a cylinder can model a log and a rectangular prism would model a board

Step-by-step explanation:

vocab

Answer:

a cylinder can model a log and a rectangular prism would model a board

Step-by-step explanation:

Answer:

E(m) = 12m

Step-by-step explanation:

Your earnings will be the amount of times you mow the lawn * $12 per job

so if m is the amount of times and 12 is the amount your Earnings(E) = 12m

45:15 =

15:5 =

3:1

Normally, the ratio would be 45:15, but you should simplify like shown above.

The book to magazine ratio of the numbers of books and magazines Manny read over the summer is 3:1.

The student's question pertains to finding the ratio of books Manny read over the summer to the magazines he read. Given that Manny read 45 books and 15 magazines, these numbers can be turned into a ratio by placing them over each other (books/magazines). Therefore, the book to magazine ratio would be 45:15. However, this ratio can be simplified by dividing both numbers by their greatest common divisor, which in this case is 15. When both numbers are divided by 15, the simplified book to magazine ratio is 3:1. Hence, for every 3 books Manny reads he also reads 1 magazine.

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Answer:

8 - 3 =5

5 is the range of the values given

Step-by-step explanation:

We are only given 2 values;

3 and 8

It seems more reasonable to compute the range of these values as a measure of spread.

The range of a data-set is simply the difference between the maximum and the minimum values.

In our case, the maximum is 8 while the minimum is 3. The range is thus;

8 - 3 = 5

Final answer:

The interquartile range (IQR) is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). If Q1 is 3 and Q3 is 8, the IQR is 5.

Explanation:

The interquartile range (IQR) is the range of the middle 50 percent of the data values, calculated by subtracting the first quartile (Q1) from the third quartile (Q3). If the student asks about the interquartile range between 3 and 8, it seems that they may be referring to the quartiles directly, which would be unusual since quartiles are typically values derived from the data set. However, if we assume that in this case, 3 represents Q1 and 8 represents Q3, then the IQR can be calculated simply as:

IQR = Q3 - Q1 = 8 - 3 = 5.

The IQR indicates the spread of the central half of a data set and is useful in identifying potential outliers and understanding the distribution of data.

Answer:

x=-1 should be your answer

Answer:

see explanation

Step-by-step explanation:

Given

y = x² + 2x + 1

To find the zeros let y = 0, that is

x² + 2x + 1 = 0 ← x² + 2x + 1 is a perfect square

(x + 1)² = 0

x + 1 = 0 ( subtract 1 from both sides )

x = - 1 with multiplicity 2 ← zero

This indicates that the graph has a minimum turning point at (- 1, 0)

Note from your table

the value for x = - 1 should be y = 0 ( not - 2 )

Answer:

1377 dollars

Step-by-step explanation:

the third option

because 1/3 is not equal to three

where as if we replace the x with one in all the other we would find that the equation is correct.

D and B because you at the picture

The correct answers are A, B, and C for the given function y = (2/3)x.

The slope of a line is defined as the gradient of the line.

The equation y = (2/3)x represents a line in the coordinate plane, where the x value of a point on the line is multiplied by the constant 2/3 to get the y value of that point.

A. The equation y = (2/3)x represents a proportional relationship because for every change in x by some unit, there is a corresponding change in y by 2/3 times that unit.

B. The unit rate of change of y with respect to x is 2/3. This means that for every unit increase in x, the value of y will increase by 2/3 times that unit.

C. The slope of the line is 2/3. The slope of a line gives you the rate of change of y with respect to x, and in this case, the slope is 2/3.

D. A change of three units in x results in a change of two units in y. Since the unit rate of change of y with respect to x is 2/3, a change of three units in x will result in a change of 2/3 × 3 = 2 units in y.

E. A change of three units in x results in a change of one unit in y is not true, because the unit rate of change of y with respect to x is 2/3, which is different from 1.

Therefore, the correct answers are A, B, and C.

Learn more about the Slope of the Line here:

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Answer:

Her monthly principal payment is D: $579.81 and monthly interest payment is 0.4375.

Step-by-step explanation:

Ok, in order to calculate the monthly principal and interest payment, we can use this relatively simple equation. The equation is:

[tex]M=P\frac{r(1+r)^{n} }{((1+r)^{n}-1) }[/tex]

Where variables represent the following:

M is your monthly payment.

P is your principal.

r is your monthly interest rate, calculated by dividing your annual interest rate by 12.

n is your number of payments (the number of months you will be paying the loan throughout the 30 years)

Then, in this case:

M=?

P=$105,000

5.25%=5.25/100=0.0525, then [tex]r=\frac{0.0525}{12} =0.004375[/tex]

[tex]n=12*30=360[/tex]

So, [tex]M=105,000\frac{0.004375(1+(0.004375))^{360} }{((1+(0.004375))^{360}-1)}[/tex] $

Solving this,

[tex]M=105,000\frac{0.004375(1.004375))^{360} }{((1.004375))^{360}-1)}[/tex] $

[tex]M=105,000\frac{0.004375(4.8141) }{((4.8141))-1)}[/tex] $

[tex]M=105,000\frac{0.02106 }{3.8142}[/tex] $

[tex]M=105,000(0.005522)/tex] $

[tex]M=579.81[/tex] $

Her monthly principal payment is $579.81.

Answer: $579.81 APEX

Answer:

$136.00

Step-by-step explanation:

100 + 12 +12 + 12

simple interest is only against the loan itself

compound interest is the loan plus interest . . .then that sum . . .again then that some

Term = 5x^2

h = variable

21 is a constant

I think ab is an expression or the product of two factors.

1 quarter = 25 cents

1 nickel = 5 cents

2 quarters = 25*2 = 50 cents

50 cents + 5 cents = 55 cents, or $0.55

2 quarters and one nickel is 55cents

Answer:

8 rabbits

22 chickens

Step-by-step explanation:

c = chickens

r = rabbits

heads - c + r = 30

legs - 2c + 4r = 76

We can now use these two equations to create one by isolating the variable (c) in the first equation.

c = 30 - r

2c + 4r = 76

2(30 - r) + 4r = 76

60 - 2r + 4r = 76

2r = 16

r = 8

Now we know that there are 8 rabbits, which means that there has to be 22 chickens in order to have 30 heads.

To solve the problem of finding the number of chickens and rabbits, we can use a system of equations.

To solve this problem, we can use a system of equations. Let's consider the number of chickens as 'c' and the number of rabbits as 'r'.

We know that there are a total of 30 heads, which means that c + r = 30.

We also know that there are a total of 76 legs, which means that 2c + 4r = 76.

We can solve this system of equations by substitution or elimination to find the values of c and r. From there, we can determine the number of chickens and rabbits that Jessie has.

Let's solve it using the elimination method: Multiply the first equation by 2 to match the coefficient of 'c' in the second equation. You will get 2c + 2r = 60. Subtract this equation from the second equation to eliminate 'c', and you will get 2r - 2r = 76 - 60. Simplifying, we have 0 = 16, which is not true.

There is no solution for this system of equations. Therefore, the problem may be set up incorrectly.

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Answer:

x = 12 is the excluded value

Step-by-step explanation:

An excluded value is the value/s of x that make the denominator of the rational function equal to zero as this would make the function undefined.

Equate the denominator to zero and solve for x

6x - 72 = 0 ⇒ 6x = 72 ⇒ x = 12 ← excluded value

Answer: x=12

Step-by-step explanation:

Answer:

D. Gabrielle is more justified in choosing not to get insurance

Step-by-step explanation:

Gabrielle is more justified in choosing not to get insurance because she is in good heath and haven't had the need to visit a doctor in a long time.

Chances are she'll be fine, at least until he health situation changes.

Juan on the other hand should find a way to afford the insurance, because of his failing health he can't predict his health costs in short term.  So, an insurance would be a great thing for him to have, it would at least give him some financial security because chances are his health costs would be higher than his premiums.

Answer:

8x+3

Step-by-step explanation:

Take 1/5 of 15x and 15

Then add 5x

8x+3 is the answer

Answer:

B. 5040

Step-by-step explanation:

We want to find the value of [tex]7![/tex].

We read [tex]7![/tex] as ''seven factorial''

By definition, [tex]n!=n(n-1)(n-2)...3\cdot2\cdot1[/tex]

We need to find the product of all the positive integers less than or equal to the given number.

This implies that:

[tex]7!=7\times 6\times 5\times 4\times 3\times 2\times 1[/tex]

[tex]7!=5040[/tex]

job a would be the biggest money maker job. $15 an hour working at most 15 hours = $225. $8 an hour working 34 hours = $272. You would make $47 more at job a

Answer:

You should choose Job A.

Step-by-step explanation:

I did the math.

2

You know that OA = 4 because the radius of the circle on the left is 4. So, subtract that from OP to find that AP = 5.

Finally, subtract BP, which is 3 because of the circle’s radius. You then find that AB = 2

Answer:

The answer is 2 i think.

Step-by-step explanation:

Answer:

C. 4s < 20

Step-by-step explanation:

One side measures s. The perimeter is the sum of the lengths of the 4 sides, so the perimeter is s + s + s + s. Since all side lengths are equal, the perimeter is simply 4s. The perimeter is less than 20 inches, so 4s must be less than 20.

The inequality is

C. 4s < 20

Answer:

The answer is C on Edge 2021

Step-by-step explanation:

C : 4s < 20

Hope this helps!

Answer:

1.25315*102

Step-by-step explanation:

The number 125.315 is already in standard form. This form, also known as scientific notation, simplifies the representation of large or small numbers. However, 125.315 doesn't need this kind of simplification.

The number 125.315 is already in standard form. In Mathematics, standard form, also known as scientific notation, refers to expressing a number as a number between 1 and 10 multiplied by a power of 10. The purpose is to simplify the representation of very large or very small numbers. For instance, 2000 would be written as 2 x 10^3 in scientific notation. However, 125.315 is not a large enough number that needs to be simplified in such a manner.

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Answer:

7500

Step-by-step explanation: 750 * 10

Answer:75 kilograms

You would have to divide 750 by 10 and you would get 75

Answer: Reflection

Step-by-step explanation:

Looking at this as a reference they reflect across the y-axis

The answer would be 5227. If you subtract what is in parenthesis first and then multiply it that should be your answer.

Answer:  [tex]5,227[/tex]

Step-by-step explanation:

Given the expression [tex]63*83-(6-4)[/tex] you can simplify it by applying these steps:

First, make the subtraction of the numbers that are inside of the parentheses:

 [tex]=63*83-(2)[/tex]

Apply multiplication of signs to eliminate the parentheses. Remember that:

[tex](-)(-)=+\\(+)(+)=+\\(-)(+)=-[/tex]

Then:

[tex]=63*83-2[/tex]

Now, make the multplication indicated:

[tex]=5,229-2[/tex]

Finally, subtract both numbers:

[tex]=5,227[/tex]

Answer:

if you are looking for a possible solution

x + 3y = 3

3 + 3(0) = 3

2x + y = 11

2(4) + 3 = 11

Step-by-step explanation:

In this the solution is y = -1 and x = 6.

Answer:

the answer is 3 i believe

Step-by-step explanation:

[tex]20 / 4[/tex]

Answer:

Step-by-step explanation:

The general form of a linear function is ax + b.

f(x) = ax + b

f(1) = a + b = -7

f(2) = 2a + b = -10

So using a system of equations we solve for 'a' and 'b'.

a + b = -7 | 2a + b = -10

We multiply the first one by -1.

-a - b = 7 | 2a + b = -10

And then we solve the system by elimination(by adding the equations):

a = -3

Solving for b: a + b = -7 <=> -3 +b = -7 => b = -4

So the general rule of the function is:

f(x) = -3x - 4