The surface area of the cushion in square inches

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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Answer:

There were 60 audience members at the seminar.

Step-by-step explanation:

Let's assume that the total number of audience members at the seminar is "x".

From the given information, we know that:

2/5 of the audience were students, so the number of students was (2/5)x

3/10 of the audience were retirees, so the number of retirees was (3/10)x

The rest were professionals, so the number of professionals was x - (2/5)x - (3/10)x = (1/10)x

We also know that there were 18 more students than professionals, so:

(2/5)x - (1/10)x = 18

Multiplying both sides by 10, we get:

4x - x = 180

Simplifying, we get:

3x = 180

x = 60

Therefore, there were 60 audience members at the seminar.

Answer:

csc θ = 13/12

Step-by-step explanation:

cos θ = 12/13

Formula: cos θ = 1/cscθ

Its just the reciprocal.

solve:

1/csc θ = 12/13

csc θ = 13/12

Answer:

\(\textsf{a)} \quad \text{cosec}\:\theta=\dfrac{13}{12}\)

Step-by-step explanation:

Given cosine trigonometric identity:

\(\boxed{\cos\theta=\dfrac{12}{13}}\)

To find the value of cosec θ, use the trigonometric identity:

\(\boxed{\text{cosec}\; \theta=\dfrac{1}{\cos\theta}}\)

Substitute the given value of cos θ into the cosec θ identity:

\(\implies \text{cosec}\:\theta=\dfrac{1}{\frac{12}{13}}\)

\(\implies \text{cosec}\:\theta=1 \div \dfrac{12}{13}\)

\(\implies \text{cosec}\:\theta=1 \times \dfrac{13}{12}\)

\(\implies \text{cosec}\:\theta=\dfrac{13}{12}\)

Therefore, the value of cosec θ is:

\(\boxed{\text{cosec}\:\theta=\dfrac{13}{12}}\)

Answer:

(7, 24, 25 ) and (11, 60, 61 )

Step-by-step explanation:

To obtain the Pythagorean triplets for a given value n

n , \(\frac{n^2-1}{2}\) , \(\frac{n^2+1}{2}\)

(a) for n = 7 , then

\(\frac{7^2-1}{2}\) = \(\frac{48}{2}\) = 24 , \(\frac{7^2+1}{2}\) = \(\frac{50}{2}\) = 25

Triplet = (7, 24, 25 )

(b) for n = 11

\(\frac{11^2-1}{2}\) = \(\frac{120}{2}\) = 60 , \(\frac{11^2+1}{2}\) = \(\frac{122}{2}\) = 61

Triplet = (11, 60, 61 )

Step-by-step explanation:

The last one.

-5 is notht included but 6 is.

Answer:

-5

Step-by-step explanation:

(i^2) = -1 so -1 -1 + 3x = 3x - 2. If x = i^2 = -1, then 3x = -3. -3 - 2 = -5

Step-by-step explanation:

Since we have three sides and trying to find an angle, use Law of Cosines

\(c = \sqrt{ {a}^{2} + {b}^{2} - 2ab \times \cos(d) } \)

where c is

Solving for the angle d.

\( \cos {}^{ -1 } (( \frac{ {c}^{2} - {b}^{2} - {a}^{2} }{ - 2ab} ) = d\)

where d is in degrees

The angle d is the opposite of the side c.

It does not matter what a and b is(they can be either 4 or 5)

let

c=7

a=4

b=5

\( \cos {}^{ - 1} ( \frac{ - 1}{5} ) = d\)

This angle must be within 0 and 180

We get

\(d = 101.54\)

Answer:

(5 + 16)=7 + (4 x 7)

Step by step - explanation:

Solve:

Add the numbers

(5 + 16)= 21.

(4 x 7) = 28 + 7 = 35.

So the result is 21 = 35.

Hope that helps. x

Answer:

Step-by-step explanation:

(5+16)=7+(4.7)

(21)=7+(4.7)

21=7+(4.7)

21=7+(28)

21=7+28

21=35

Answer: 21=35

Answer:478.85 in2

Step-by-step explanation:

Just divide LOL

A boutique owner needs to sell $1,200 in clothing each week. This week, she is within $125 of her goal. The variable in the equation is

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem.

Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

In the context of the problem, the boutique owner wants to make $1,200 in clothing each week. This amount in made by the number of items sold as this is added to get to the amount the boutique owner is targeting

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Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

Answer:

Below

Step-by-step explanation:

FALSE.... polygons have straight sides and angles.

6.5 / 12 = x / 24

x = 6.5 × 24 / 12

x = 6.5 × 2

x = 13

Answer:

Step-by-step explanation:

x/y=x/y

6.5/12=x/24

do cross multiplication

12x=24*6.5

x=156/12

x=13

Answer: b = 2z^2 (y^2 + 2z^2)  (y^4 - 2y z^2 + 4z^4)

Step-by-step explanation: you have to factor using the sum of the cubes formula a^3 + b^3 = (a + b) ( a^2 - ab + b^2)

From the constraint, we have

\(x+y+z=9 \implies z = 9-x-y\)

so that \(s\) depends only on \(x,y\).

\(s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy\)

Find the critical points of \(g\).

\(\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9\)

\(\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0\)

Using the given constraint again, we have the condition

\(x+y+z = 2x+y \implies x=z\)

so that

\(x = 9 - x - y \implies y = 9 - 2x\)

and \(s\) depends only on \(x\).

\(s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2\)

Find the critical points of \(h\).

\(\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3\)

It follows that \(y = 9-2\cdot3 = 3\) and \(z=3\), so the only critical point of \(s\) is at (3, 3, 3).

Differentiate \(h\) again and check the sign of the second derivative at the critical point.

\(\dfrac{d^2h}{dx^2} = -6 < 0\)

for all \(x\), which indicates a maximum.

We find that

\(\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)\)

The second derivative at the critical point exists

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\) for all x, which suggests a maximum.

Given, the constraint, we have

x + y + z = 9

⇒ z = 9 - x - y

Let s depend only on x, y.

s = g(x, y)

= xy + y(9 - x - y) + x(9 - x - y)

= 9y - y² + 9x - x² - xy

To estimate the critical points of g.

\($&\frac{\partial g}{\partial x}\) = 9 - 2x - y = 0

\($&\frac{\partial g}{\partial y}\) = 9 - 2y - x = 0

Utilizing the given constraint again,

x + y + z = 2x + y

⇒ x = z

x = 9 - x - y  

⇒ y = 9 - 2x, and s depends only on x.

s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²

To estimate the critical points of h.

\($\frac{d h}{d x}=18-6 x=0\)

⇒ x = 3

It pursues that y = 9 - 2 \(*\) 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).

Differentiate h again and review the sign of the second derivative at the critical point.

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\)

for all x, which suggests a maximum.

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Answer:

Min: 1

Q1: 2
Median: 7
Q3: 9
Max: 11.5

Step-by-step explanation:

The five bars of the box plot correspond (from left-to-right) to the numbers in the five-number summary.

The first bar represents the minimum, which in this case is 1.

The second bar represents the first quartile (Q1), which in this case is 2.

The third bar represents the median, which in this case is 7.

The fourth bar represents the third quartile (Q3), which in this case is 9.

And the fifth bar represents the maximum, which in this case is 11.5.

Answer:

Min: 1

Q1: 2

Median: 7

Q3: 9

Max: 11.5

Step-by-step explanation:

I hope it helps:)

Answer:

Step-by-step explanation:

Solution is the points below the line y = 2x - 2

Correct option is:

Answer:

B. below; y = 2x − 2

Step-by-step explanation:

i got it right on Time4learning

Answer: 80,304

Step-by-step explanation:

You are correct because in 8,304, the 8 is 8,000, and in 80,304, the 8 is 80,000.

8,000 x 10 = 80,000 so there you go. Also, the answer can be any 5 digit number with 8 as the ten thousands place(examples. 89,192, 83,026, 80,000)

Quick question, how long is Joseph saving for? If it's 1 money of saving, he can spend $1,775 and if he saves for 1 year he can spend up to 21300.

Answer:

Step-by-step explanation:

1.) round 14.25 to 14 or 14.3

2.) round 5.102 to 5

3.) Multiply 5 and 14= 70

4.) 71.5 would be if you multiplied 5 and 14.3.

The spherical coordinates of the given rectangular coordinates are (10, 0, 60).

The cartesian coordinate or rectangular coordinates describes the location of a point in space using an ordered triple where each coordinate represents a distance. The spherical coordinate system describes the location of a point in space using an ordered triple where coordinate describes one distance and two angles. In the spherical coordinate system, a point is represented by the ordered triple (ρ, θ, φ).

The equations which are used to convert from rectangular coordinates to spherical coordinates are:

ρ^2=x^2+y^2+z^2

tan⁡〖θ= y/x〗

φ=arccos⁡〖z/√(x^2+y^2+z^2 )〗

The given rectangular coordinates are (5√3, 0, 5). Hence,

ρ^2=〖(5√3)〗^2+0^2+5^2 ≈ 100

ρ ≈ √100 ≈ 10

tan⁡〖θ= 0/(5√3)=0〗

θ=  tan^(-1)⁡0=0

φ=arccos⁡〖5/√(〖(5√3)〗^2+0^2+5^2 )〗= arccos 5/10=arccos⁡0.5 ≈ 60

Note:  The question is incomplete. The complete question probably is: Convert from rectangular to spherical coordinates. (Use symbolic notation and fractions where needed. Give your answer as a point's coordinates in the form (*,*,*). (5√3, 0, 5)

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Answer:

option D

Step-by-step explanation:

Angle ADF and Angle FDE

ADF+ FDE

Answer:

D

Step-by-step explanation:

To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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Step-by-step explanation:

Factors of 256: 1, 2, 4, 8, 16, 32, 64, 128 and 256.

Hope it will help :)❤

Here the answer hope this helps:

factors of 256 are.... 1, 2, 4, 8, 16, 32, 64, 128 and 256.

Step-by-step explanation:

hope this helps

Answer:

m= 0

Step-by-step explanation:

6=m+6

6−6=m+6−6

m=0

brainliest would be appreciated. have a great day :)

Answer:

E

Step-by-step explanation:

its the only one that make sense

Answer: 16

Step-by-step explanation:

To get from 3 to 12, you multiply by 4

To get from 5 to 20, you multiply by 4

So you just multiply 4 by 4 to get x

Answer:

x = 16

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{x}{4}\) = \(\frac{20}{5}\) = 4 ( multiply both sides by 4 to clear the fraction )

x = 16

Step-by-step explanation:

I hope this answer is helpful ):

Answer:

=344

Step-by-step explanation:

(43)(8)

=344