A rectangular gym has an area of 4x^2ft^2. The school decides to add a new
weight room. The total area of the gym and the weight room is (4x^2+480)ft^2.
What does the constant term represent in terms of this problem?

Answer:

x = -8

Step-by-step explanation:

-2x-2=14

We want to solve for x

Add 2 to each side

-2x-2+2 = 14+2

-2x=16

Divide each side by -2

-2x/-2 =16/-2

x = -8

Answer:

The standard deviation of the age is 6.16

Step-by-step explanation:

* Lets talk about the variance and the standard deviation

- The variance is the measure of how much values in a set of data are

 likely to differ from the mean value of the same data

- The steps to find the variance are:

1- Find the mean of the data  

2- Subtract the mean from each value and square the answer

3- Add all of these squared answer and divide the sum by the number

  of the values

- The answer of the step 3 is The variance (σ²)

- The standard deviation (σ) is the square root of the variance

* Now lets solve the problem

∵ The variance of the ages of the people who attended a rock

  concert is 38

∴ σ² = 38

∵ The standard deviation is the square root of the variance

∴ σ = √38 = 6.16

* The standard deviation of the age is 6.16

Answer:

[tex]\sigma=6.16[/tex]

Step-by-step explanation:

By definition, the variance V of a population is defined as:

[tex]V = \sigma^2[/tex]

Where [tex]\sigma[/tex] is the standard deviation

We know that [tex]V = 38[/tex], then we can solve the equation for the standard deviation [tex]\sigma[/tex]

[tex]38 = \sigma^2[/tex]

[tex]\sigma^2=38[/tex]

[tex]\sigma=\sqrt{38}[/tex]

[tex]\sigma=6.16[/tex]

Finally  the standard deviation is: [tex]\sigma=6.16[/tex]

Using Heron's formula where s = 9 ...... and a = b = c = the side lengths .....we have......

A = √[s(s -a)^3] = √[4*3^3] = √[4*27] = √[4*9*3] = √[36*3) = 9√3 sq. in.

Answer: [tex]\sqrt{32}\text{ mi}[/tex]

Step-by-step explanation:

The Pythagoras theorem of right triangle says that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

From the given figure , the hypotenuse of the right triangle = [tex]\sqrt{113}\text{ mi}[/tex]

Then According to Pythagoras theorem , we have

[tex](\sqrt{113})^2=x^2+(9)^2\\\\\Rightarrow\ x^2=113-81\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=\sqrt{32}\text{ mi}[/tex]

Answer:

F

Step-by-step explanation:

F

zero

Anytime you have zero as a possible answer, you have to consider it carefully. Part of the whole number system is 0. They go up from there. No fraction is a whole number. No decimal is a whole number except those that are equal to  a whole number.

The rest are all decimals so they are not whole numbers. Note I just noticed that the other numbers have periods after the choice. There are other whole numbers there if that is the case.

C D E and F are all whole numbers if that is a period after their choice letters.

[tex]y=\dfrac{k}{x}[/tex]

1.

[tex]12=\dfrac{k}{13}\\\\k=156[/tex]

2.

[tex]y=\dfrac{156}{x}[/tex]

3.

[tex]y=\dfrac{156}{44}=\dfrac{39}{11}[/tex]

Answer: -2,0 0,4

Step-by-step explanation:

let me know if you need help still UwU

Answer:

The function is positive from (-∞,-2) and (0,4).

Explanation:

To find the intervals where the function is positive, note where the line of the graph is above the x-axis.

As the functions goes toward negative infinity, the arrow of the graph is pointed up, so the function is positive starting from -∞ until x = -2, where it becomes negative.

The function once again goes above the x-axis at x = 0 and stays positive until x = 4. After this point, the function decreases forever, so (-∞,-2) and (0,4) are the only intervals where the function is positive.

Answer:

31 seats

Step-by-step explanation:

Let x be the smaller van, and y be the larger one.

We know that y = x + 14

We also know that 2x + y = 65

If we replace y by its value in the second equation we have:

2x + (x + 14) = 65, then we solve

2x + x + 14 = 65

3x + 14 = 65

3x = 51

x = 17

We now know the smaller van has 17 seats.

To find how many seats are in the big one, we take the first equation:

y = x + 14

y = 17 + 14

y = 31

Answer:

Step-by-step explanation:

its the first one in edge

The graph which shows a rate of change of 1/2 is the linear graph shown in the image attached below.

Rate of change = change in y / change in x.

The two points between -4 and 0 on the x-axis as shown in the diagram attached are, (-4, 1) and (0, 3). It is also a linear graph.

Rate of change = (3 - 1)/(0 -(-4)) = 2/4 = 1/2

The graph that shows a rate of change is the linear graph attached below.

Learn more about the rate of change on:

https://brainly.com/question/25184007

#SPJ5

Answer:

16x² + 56x + 49

Step-by-step explanation:

First, expand:

(4x + 7)² = (4x + 7)(4x + 7)

Follow the FOIL method. FOIL = First, Outside, Inside, Last.

(4x)(4x) = 16x²

(4x)(7) = 28x

(7)(4x) = 28x

(7)(7) = 49

16x² + 28x + 28x + 49

Combine like terms:

16x² + (28x + 28x) + 49

16x² + (56x) + 49

16x² + 56x + 49 is your answer.

~

Answer:

3 m^2 + 4m +7

Step-by-step explanation:

3x^24 + 4x^12 + 7

Let  m =x^12

m^2 = x^12 ^2 = x^24

Substitute this into the first equation

3 m^2 + 4m +7

Answer:

[tex]\large\boxed{y=4(x-3)^2+2\ \bold{vertex\ form}}\\\boxed{y=4x^2-24x+38\ \bold{standard\ form}}[/tex]

Step-by-step explanation:

The vertex form of a parabola:

[tex]y=a(x-h)^2+k[/tex]

(h, k) - vertex

We have the vertex at (3, 2) → h = 3 and k = 2.

Substitute:

[tex]y=a(x-3)^2+2[/tex]

The point (4, 6) is on athe parabola. Put the coordinates of this point to the equation:

[tex]6=a(4-3)^2+2[/tex]       subtract 2 from both sides

[tex]6-2=a(1)^2+2-2[/tex]

[tex]4=a\to a=4[/tex]

Finally:

[tex]y=4(x-3)^2+2[/tex]          vertex form

use (a - b)² = a² - 2ab + b²

[tex]y=4(x^2-6x+9)+2[/tex]          use the distributive property

[tex]y=4x^2-24x+36+2[/tex]

[tex]y=4x^2-24x+38[/tex]             standard form

Answer:

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

Step-by-step explanation:

Hopefully this helps :)

Answer:

The LCM of 8 and 9 is 72.

Step-by-step explanation:

Please mark brainliest and have a great day!

Final answer:

The volume of the core of the golf ball from Great Drive, with a diameter of 1.68 inches, is approximately 2.48 cubic inches. This is calculated using the formula for the volume of a sphere with the radius derived from the given diameter. The correct answer is 2.48 in³, which is option A.

Explanation:

The volume of a sphere is given by the formula V = (4/3) πr3, where π is pi (approximately 3.14159) and r is the sphere's radius. The diameter of the golf ball's core is given as 1.68 inches, so the radius is half of that, which is 0.84 inches. Plugging this into the formula gives us:

V = (4/3) π (0.84 inches)3 = (4/3) π (0.84 inches × 0.84 inches × 0.84 inches)

Doing the math, we find that:

V ≈ (4/3) π (0.592704 inches3) ≈ 2.48 in3

Therefore, the volume of the core of the ball rounded to the nearest hundredth is 2.48 cubic inches.

The correct answer is option A.

The y-intercept is where it crosses the y-axis. That means the x-coordinate is zero there. So this point represents how much it cost before any hours are applied. This is also known as the initial cost.

Answer:

l

Step-by-step explanation:

Answer: [tex]\frac{1}{(x+1)(x+y)}[/tex]

Step-by-step explanation:

Given the expression:

[tex](\frac{x-y}{x^2-1})(\frac{x-1}{x^2-y^2})[/tex]

The first step is to multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction. Then:

[tex]=\frac{(x-y)(x-1)}{(x^2-1)(x^2-y^2)}[/tex]

Since [tex](x^2-1)[/tex] and [tex](x^2-y^2)[/tex] are perfect squares, you can factorize them in the form:

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Then:

[tex]=\frac{(x-y)(x-1)}{(x+1)(x-1)(x+y)(x-y)}[/tex]

Simplifying, you get:

[tex]=\frac{1}{(x+1)(x+y)}[/tex]

The sum of all the angles of a triangle is 180 degrees. To solve for y you can make a formula of the sum of the angles equal to 180 like so...

y + y + 60 = 180

Now you must combine like terms. This means that first numbers with the same variables (y) must be combined...

y + y + 60 = 180

y + y = 2y

2y + 60 = 180

Now bring 60 to the left side by subtracting 60 to both sides (what you do on one side you must do to the other). Since 60 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

2y + 60 - 60 = 180 - 60

2y + 0 = 120

2y = 120

Next divide 2 to both sides to finish isolating y. Since 2 is being multiplied by y, division (the opposite of multiplication) will cancel 2 out (in this case it will make 2 one) from the left side and bring it over to the right side.

2y / 2 = 120 / 2

y = 60

C. 60

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

I just know it is 0.222222222222

Step-by-step explanation:

Answer:

± [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt{\frac{4}{9} }[/tex]

= [tex]\frac{\sqrt{4} }{\sqrt{9} }[/tex] = ± [tex]\frac{2}{3}[/tex]

Answer:

This question is not complete.

Step-by-step explanation:

Hi, The question is not complete but i think the question was this:

Which of the following is the correct factorization of the polynomial below?

x^3 - 12

A. (x + 3)(x - 4)

B. (x - 3)(x + 4)

C. (x + 3)(x^2 - 4x + 4)

D. The polynomial is irreducible.

in which case, the answer will be this:

D as this polynomial can't be reduced

Answer:

x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)

Step-by-step explanation:

Question is incomplete (options are missing);

However, I'll factorize the polynomial using identity

Given

x³ - 12

This can be factorized using the following identity

a³ - b³ = (a - b)(a² + ab + b²)

By comparison,

a³ = x³ and b³ = 12

a = x and b = ∛12

Replace a with x and b with ∛12 in the above equation

a³ - b³ = (a - b)(a² + ab + b²) becomes

x³ - 12 = (x - ∛12)(x² + x∛12 + ∛12²)

x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)

This is as far as it can be factorized

So, the factorization of x³ - 12 using identity is (x - ∛12)(x² + x∛12 + 12²/³)

Answer:

A and B are the solutions....

Step-by-step explanation:

7 and 12 are smaller than 17.

Answer:

A. [tex]x=7[/tex]

B. [tex]x=12[/tex]

Step-by-step explanation:

Check each option individually.

A. [tex]17>7[/tex] is true, so it is a correct choice.

B. [tex]17>12[/tex] is true, so it is a correct choice.

C. [tex]17>17[/tex] is false, so it is an incorrect choice.

Answer:

7.81 dollars

Step-by-step explanation:

20 which was given to

take away the cost of the bill of 12.19

which will give you how much change you will need to give back

For this case we must find the point that Harold used to arrive at the following equation:

[tex]y = 3 (x-7)[/tex]

Starting from the fact that the equation of the point-slope form of a line is given by:

[tex](y-y_ {1}) = m (x-x_ {1})[/tex]

If we compare the standard equation with Harold's, we see that the slope of the line is [tex]m = 3.[/tex]

In addition, it is observed that [tex]x_ {1} = 7[/tex]and [tex]y_ {1} = 0.[/tex]

Then, the correct option is: Harold used the point (7,0)

ANswer:

When Harold wrote his equation, the point was used (7,0).

Answer:

60 degrees-30 = 90

50'-40'= 10

40"-50"= 10

Please mark brainliest and have a great day!

Answer: i think C

Step-by-step explanation:

Answer:

A.) ∠3, ∠6, and∠7

If you have a protractor, that would help you alot :) but I hope this help you!

Answer:

A. ∠3, ∠6 and ∠7.

Step-by-step explanation:

Given,

r ║ s

Also, t is the common transversal of parallel lines r and s,

By the given diagram,

∠2 and ∠3 are vertical angles,

By vertically opposite angle theorem,

∠2 ≅ ∠3,

∠2 and ∠6 are corresponding angle,

By the corresponding angle theorem,

∠2 ≅ ∠6,

∠2 and ∠7 are alternate exterior angles,

By the alternate exterior angle theorem,

∠2 ≅ ∠7

Hence, Option 'A' is correct.

Answer: [tex]y=(x-1)^2-4[/tex]

Step-by-step explanation:

The vertex form of the equation of a parabola is:

[tex]y=a(x-h)^2+k[/tex]

Where (h,k) is the vertex.

To obtain this form, we need to complete the square:

Move the 3 to the other side of the equation:

[tex]y+3=x^2-2x[/tex]

Add this value to both sides of the equation: [tex](\frac{-2}{2})^2=1[/tex]

[tex]y+3+1=x^2-2x+1[/tex]

[tex]y+4=x^2-2x+1[/tex]

Then, rewriting:

 [tex]y+4=(x-1)^2[/tex]

Finally, we must solve for "y", getting the equation of the parabola in vertex form:

 [tex]y=(x-1)^2-4[/tex]

Answer:

4

Step-by-step explanation:

[tex]f(x)=-2x+3, 0<x<=4[/tex]

Answer:

4

Step-by-step explanation:

The domain is the inputs (or the x values)

We start at -6 (but do not include it) and end at +4 (we include it)

-6 < x ≤4

The value that is included is 4

Plug 14 in for a and 12 in for b like so...

14 + 7(12)

14 + 84

98

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex] y = 2 5 0 ( 0 . 8 9 ) ^ x [/tex]

Initial value: 250

Decay

Decay rate: 11%

[tex] y = 4 0 ( 1.11 ) ^ x [/tex]

Initial value: 40

Growth

Growth rate: 11%

Step-by-step explanation:

The function we have on the left of the table is:

[tex] y = 2 5 0 ( 0 . 8 9 ) ^ x [/tex]

Initial value (when x = 0): [tex] y = 2 5 0 ( 0 . 8 9 ) ^ 0 [/tex]

y = 250 (initial value)

Growth or Decay: 0.89 < 1 so decay

Decay rate: (1 - 0.89) * 100 = 11%

Function on right side:

[tex] y = 4 0 ( 1.11 ) ^ x [/tex]

Initial value (when x = 0): [tex] y = 4 0 ( 1 . 1 1 ) ^ 0 [/tex]

y = 40 (initial value)

Growth or decay: 1.11 > 1 so growth

Growth rate: (1.11 - 1) * 100 = 11%

i took the test 100%