please help!!!!!!!!!!!!!

Answer:

see explanation

Step-by-step explanation:

(a)

given y is inversely proportional to x³ then the equation relating them is

y = [tex]\frac{k}{x^3}[/tex] ← k is the constant of proportion

to find k use any of the ordered pairs from the table

using (1, 8 ) , then

8 = [tex]\frac{k}{1^3}[/tex] = [tex]\frac{k}{1}[/tex] ⇒ k = 8

y = [tex]\frac{8}{x^3}[/tex] ← equation of proportion

(b)

when y = 64 , then

64 = [tex]\frac{8}{x^3}[/tex] ( multiply both sides by x³ )

64x³ = 8 ( divide both sides by 64 )

x³ = [tex]\frac{8}{64}[/tex] = [tex]\frac{1}{8}[/tex] ( take cube root of both sides )

x = [tex]\sqrt[3]{\frac{1}{8} }[/tex] = [tex]\frac{1}{2}[/tex]

Given data:

Total packs 3x3 sticky notes: 24 packs

Cost of 24 packs: 28.99

Number of sticky notes in a pack: 100

With the information above, we can proceed to find the answers to the questions

Part A: What is the price for each pack?

Since 24 packs cost 28.99

Then 1 pack will cost =

Hence, a pack will cost $1.21

Part B: How much is every single sticky note?

Since each pack cost 1.21, and each pack has 100 sticky notes, then

each sticky note will cost

=> every single sticky note will cost $0.012

The length and the width of the rectangle are 14 and 15 meters, respectively

From the question, the statement is given as

Length and width are consecutive integers

Where

Area = 210 square feet

Represent the dimensions with x and y

Where Length = x and Width = y

And also, we have

y = x + 1

The area of a rectangle is

Area = Length x width

Mathematically, this can be represented as

Area = x * y

So, we have

x * y = 210

Substitute y = x + 1 in x * y = 210

x * (x + 1) = 210

Express 210 as 14 * 15

x * (x + 1) = 14 * 15

This means that

x = 14

Substitute x = 14 in y = x + 1

y = 14 + 1

Evaluate

y = 15

So, we have

x = 14 and y = 15

Hence, the length and the width are 14 and 15 meters

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The number of permutations possible to seat the 3 pairs of siblings in a way that one may not sit right next to their sibling and no child may sit directly in front of his or her sibling is 96.

A permutation cannot be formed with siblings in the same row.

As a result, each row should have siblings from various families.

Any of the six youngsters can take the first seat.

After deducting the kid who currently occupies the first seat and their sibling, the second seat can be filled by any of the four children.

permutation = 6 × 4

permutation = 6 × 4 × 2

Now, for the third row, there are only 3 children left to be seated.

Only 2 out of the remaining three can be seated in the first position.

Hence, the remaining possibility is 2.

permutation = 6 × 4 × 2 × 2

Similarly, the third row can only be filled with one possibility remaining of the 6 since it is not allowed to seat siblings right up front.

permutation = 6 × 4 × 2 × 2 × 1 × 1 = 96

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The opposite for each number is: ( -8, 8), (-1,1), (-17,17), (31,-31) and (11,-11).

Thus, you can conclude that the opposite number of a positive number is a negative number. And the opposite number of a negative number is a positive number.

The question gives the follow numbers

1. -8 8

2. -1 -11

3. -17 17

4. 31 -31

5. 11 1

The opposite for:

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Answer:

The rule is. the nth term  aₙ is given by

aₙ = n² + 1

Step-by-step explanation:

The following is the summary of n, aₙ

n            aₙ      In terms of n

1             2        1² + 1

2            5        2² + 1

3            10       3² + 1

4            17        4² + 1

5            26       5² + 1

6            37       6² + 1

So the nth term is given by
n² + 1

The distance between Ashely’s house and the public library is of 7.8 miles.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between these two points is given by the following rule:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the Cartesian plane, with the hypotenuse representing the distance between them.

In the context of this problem, the coordinates of her house and of the library are given as follows:

Hence the distance is calculated as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]D = \sqrt{(10 - 4)^2+(7 - 2)^2}[/tex]

D = sqrt(61)

D = 7.8 miles, as each unit on the plane represents one mile.

The problem states that each unit on the plane represents one mile and the image gives their position on the plane.

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Answer: 6

Step-by-step explanation:

m = -4 / 2 = -2 / 1 = -2

The profuct of the given expression (x-2)³ is (x³ - 6x² + 12x - 8).

So, (x-2)³:

Do, the product as follows:

Perfect cube root formula: (a - b)³ = a³ - 3a²b + 3ab² -b³

Simplify:

Therefore, the profuct of the given expression (x-2)³ is (x³ - 6x² + 12x - 8).

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3 equations that can be used to solve the given scenario are:

So, equations that can be used to solve the following scenario are:

Then,

Therefore, 3 equations can be used to solve the given scenario are:

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Answer:

a.) Let x be Kim's sister's age.  Kim's age would therefore be 2x.

b.) 2x + x = 36

c.) 2x + x = 36  

          3x = 36

             x = 12

d.) So Kim's sister (x) is 12.

e.) Since Kim's age is 2x, Kim is 24.

Step-by-step explanation:

See above.

Answer:

b= -1, -6

Step-by-step explanation:

divide by common factor

then use x=- b+- sqrt b^2-4ac/2a

separate the equations and solve them

Answer:
[tex]k - a + h[/tex]

Step-by-step explanation:

Hope this helps you! :))

Step-by-step explanation:

even though the line segment pieces of the horizontal and the inclined lines are of different lengths, but the ratio between the pieces of the same line must be the same.

in other words

x/27 = (32-18)/18 = 14/18 = 7/9

9x/27 = 7

x/3 = 7

x = 7×3 = 21

Explanation

we have a secant and a tangent

To solve the question, we will apply the intersecting secant and tangent theorem

So, for the question

we have

Therefore, the value of PB is 12

Answer:

The value of k is;

Explanation:

Given the equation:

To solve, let us subtract 8 from both sides;

then, we can then divide both sides by -3;

To solve further we need to take the logarithm of both sides;

finding the value of the log;

solving for k;

Therefore, the value of k is;

Using the concept of Application of Derivatives(A.O.D),we got 4.79 inches will be the square size for making the volume of candy box maximum.

A candy box is made from a piece of a cardboard that measures 43 × 23 inches.

Let squares of equal size will be cut out of each corner with the measure of x inches.  

Therefore, measures of each side of the candy box will become

Length = (43 - 2x)

Width   = (23 - 2x)

Height  = x

Now we have to calculate the value of x for which volume of the box should be maximum.

Volume (V) = Length×Width×Height

 =>V = (43 -2x)×(23 - 2x)×(x)

 =>V= [(43)×(23) - 46x - 86x + 4x²]×x

 =>V= [989 - 132x + 4x²]×x

 =>V= 4x³- 132x² + 989x

Now we find the derivative of V and equate it to 0

[tex]\frac{dV}{dx}[/tex]= [tex]12x^{2} -264x+989[/tex]=0

Now we get values of x by quadratic formula

x=(264±[tex]\sqrt{264^{2}-4.12.989 }[/tex] )/24

=>x=(264±[tex]\sqrt{69696-47472}[/tex])/24

=>x=(264+√22224)/24, and x=(264-√22224)/24

=>x=(264+149.07)/24 and x=(264-149.07)/24

=>x=17.212                  and x=4.79

Now we test it by second derivative test for the maximum volume.

[tex]\frac{d^{n}V }{dx}[/tex]=24x-264

For x = 17.212

[tex]\frac{d^{n}V }{dx}[/tex]=(24×17.212)-264=413.088-264=149.088

This value is > 0 so volume will be minimum.

For x = 4.79

[tex]\frac{d^{n}V }{dx}[/tex]=(24×4.79)-264= -149.04

-149.04 < 0, so volume of the box will be maximum.

Therefore, for x = 4.79 inches volume of the box will be maximum.

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(Complete Question) is

A candy box is made from a piece of cardboard that measures 43 by 23 inches. Squares of equal size will be cut out from  each corner. The sides will then be folded up so that to form a rectangular box. What size square should be cut from each corner so that to obtain maximum​ volume?

The height of the box is decreasing at a rate of 2/45 cm/sec.

The volume of a box remains constant at 1100m³ but the area of the base is increasing at a rate of 10 m²/sec.

Since the base of the box is a square, let the sides of the box be a, a, and h. The area of the base can be written as,

A = a²

Differentiate the above equation with respect to t.

dA/dt = 2a(da/dt)

Substitute 10 for dA/dt and 15 for a, to find the rate of change of side of base.

10 = 2(15)(da/dt)

da/dt = 1/3

The volume of the box can be written as,

V = (a)(a)(h) = a²h

Differentiate the above equation with respect to t.

0 = 2a(da/dt) + a² (dh/dt)

dh/dt = -2/a (da/dt)

Substitute 15 for a and 1/3 for da/dt in the above equation, to find the rate of change of height of the box.

dh/dt = -2/15 (1/3)

         = -2/45

Thus, the height of the box is decreasing at a rate of 2/45 cm/sec.

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Answer:0.0008994

Step-by-step explanation:

[tex]=-10x^4-4x^3+6x^2[/tex]

Answer: No.

Step-by-step explanation:

    To test this ordered pair, we plug it back into the equation given as (x, y), and then simplify to solve. If we end up with an equal equation, the answer is yes. If not, the answer is no.

y = 1/2x - 3

(1) = 1/2(-8) - 3

1 = -4 - 3

1 ≠ -7

           This ordered pair is not a solution.

Answer:

It means that you are done.

Step-by-step explanation:

When you are trying to find factors of a number or an algebraic expression, you must keep on factoring until you have all PRIME factors. PRIME factors cannot be further factored. So that means you are done factoring.

example: (a number)

6

factors: 2 and 3

2 and 3 are prime they can't be factored anymore so you have completely factored 6.

example: 20

factors: 4 and 5

5 is prime but 4 is not, so you can factor it more.

4 is 2×2

So 20 factored is 2×2×5

Or algebra example:

Factor x^4 - 81

factors: x^2 - 9 and x^2 + 9

x^2 + 9 cannot be factored more (prime) but x^2-9 can. Its x-3 and x+3.

To determine the percet of shoppers that use coupons, the manager interviews every shopper thay enters the greeting aisle and records wether they use or not coupons.

Since he does not take any measures, nor divide the shopers into groups or, for example, interviews one every k number of shoppers, the sampling method he used is the most simple and common one, named

"Simple random sample" or "random sample"

Explanation

To answer the question, we have to understand the different parts of an algebraic expression

An expression containing variables, numbers, and operation symbols is called an algebraic expression. is an example of an algebraic expression. Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.

We are given the algebraic expression:

For the given question

The difference means the result of subtracting one number from another or How much one number differs from another, so we have

Then

The coefficient is is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial, so we have

Also

A quotient is a number resulting from the division of one number by another, so we have

Finally,

A product is the result of multiplication or an expression that identifies factors to be multiplied.

Thus, we have

4.

The volume of a cube equals its side cubed. Since the side of the cube is 12ft long, then its volume is given by:

Then, the volume of the cube, is:

5.

The volume of the prism equals the product of each of its dimensions. Then:

Then, the volume of the rectangular prism, is:

Answer:

Rewrite using the commutative property of multiplication.

2

(

2

x

0

y

2

)

−

3

y

x

3

Anything raised to

0

is

1

.

2

(

2

⋅

1

y

2

)

−

3

y

x

3

Multiply

2

by

1

.

2

(

2

y

2

)

−

3

y

x

3

Rewrite the expression using the negative exponent rule

b

−

n

=

1

b

n

.

2

1

(

2

y

2

)

3

y

x

3

Simplify the denominator.

Tap for more steps...

2

1

8

y

6

y

x

3

Simplify terms.

x

3

4

y

5

Answer:

C

Step-by-step explanation:

1 we need you to provide the function for people to better understand how to answer.

2 Option c was the only one that made sense.

pls mark brainliest

A sale price for the bicycles that would allow this company to achieve a profit of $189,800 is: B. $230.

In order to determine the sale price for the bicycles that would make it possible for this company to achieve a profit of $189,800, we would simply evaluate the profit function by substituting the value of the profit as follows:

P(x) = −2x² + 920x + 84,000

189,800 = −2x² + 920x + 84,000

Re-arranging the profit function by collecting like terms, we have:

2x² + 920x + 189,800 - 84, 000 = 0

2x² - 920x + 105,800 = 0

Dividing both sides by 2, we have:

x² - 460x + 52,900 = 0

Next, we would solve the quadratic equation by using factorization method:

x² - 230x  -230x + 52,900 = 0

x(x - 230) + 230(x - 230) = 0

(x - 230)(x + 230) = 0

x = 230 or -230

Since the price cannot be negative, the required sale price for this company is equal to $230.

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Complete Question:

A bicycle company has designed and built a new model of sports bicycle. They have determined that the profit for the sale of the bicycles can be modeled by the function P(x) = −2x² + 920x + 84,000, where x is the price of each bicycle. Which of the following is a sale price for the bicycles that will allow the company to achieve a profit of $189,800?

A. $210

B. $230

C. $250

D. $270

The answer of the linear equation for Y=2x+5 is x = (y-5)/2.

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.  The standard form of a linear equation in one variable is of the form Ax + B = 0.  Now in this equation, x is a variable, A is a coefficient, and B is constant.

The given linear equation is,

Y=2x+5

Now, solve this linear equation for x

Take 5 to LHS it will change sign to -ve

y-5 = 2x

Next, take coefficient of x below to LHS

(y-5)/2 = x

Now, swap the sides

x = (y-5)/2

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