A home improvement store advertises 60 square feet of flooring cost $287.00, which includes $107.00 installation fee. Solve for how much each square foot costs.

We can write k(x) as the composition of g(x) and f(x).

k(x) = g(f(x))

A composition of two functions means that we need to evaluate one function in the other one.

Here we have the functions:

f(x)=  x²

g(x) = √(x - 1)

h(x) = 2x + 3

And we know that:

k(x) = √(x² - 1)

So we have a square root, then we need to evaluate g(x), and the argument is a square, then we need to evaluate in f(x), the composition is:

k(x) = g(f(x))

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To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:

b. (2x)^2 - (5)^2

Using the difference of squares formula, we can factor it as follows:

(2x + 5)(2x - 5)

Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.

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The diameter of the washing machine which is equivalent to the wavelength using the graph above would be = 2.5in.

To calculate the diameter of the washing machine drum, the formula that should be used is given below as follows;

V = fλ

where

V = displacement/time

F = 1/T

But;

Displacement = 10 in

Time = 2 seconds

V = 10/2 = 5 in/s

F = 1/2 = 0.5

λ = 5/0.5 = 2.5in

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Step-by-step explanation:

Initial velocity ,u= 14 m/s

a =_g

= 9.8 m/s

velocity at highest point,v=30 m/ s

=2as=v sqare _u square

=s= 35.99 m

Answer:

14.975÷9.5=1.57631578947

The quadratic equation that describes the function is  

f(x) = x² + 4x + 1

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is the table that describes the quadratic function h(x) as follows -

{x}                h{x}

−3               −2

−2               −3

−1                −2

0                  1

1                   6

2                  13

3                  22

The quadratic equation is of the form given -

y = ax² + bx + c

For the point (0, 1), we can write -

1 = c                                                      ..... Eq{1}

For the point (1, 6), we can write -

6 = a + b + 1

a + b = 5                                               ...... Eq{2}

For the point (2, 13), we can write -

13 = 4a + 2b + 1

4a + 2b = 12                                               ...... Eq{3}

From Eq{2}, we can write -

a = 5 - b

So, the equation 3 can be written as -

4(5 - b) + 2b = 12

20 - 4b + 2b = 12

20 - 2b = 12

2b = 8

b = 4                                    ...... Eq{4}

then

a = 1                                ...... Eq{5}

So, we can write the quadratic equation as -

f(x) = x² + 4x + 1

Therefore, the quadratic equation that describes the function is  

f(x) = x² + 4x + 1

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The length of h is obtained as follows:

h = 714.2 cm.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

\(\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}\)

The relation for this problem is given as follows:

sin(98º)/910 = sin(51º)/h

Hence the length of h is obtained with cross multiplication as follows:

h = 910 x sin(51º)/sin(98º)

h = 714.2.

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Answer:

3 and one third

Step-by-step explanation:

(3 1/3)

Answer:

---------------------

Formula for area of a rectangle with dimensions l and w is:

Substitute 10 for l and 4 for w:

The residual value of the graph is 5.89

The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y

Given that, The equation of the least-squares regression line is

ŷ = 3.6 + 0.113x, where ŷ is the diagonal and x is the area of the rectangle.

We need to find the residual of the equation,

Residual = actual y value − predicted y value,

Therefore,

The equation is ;

ŷ = 3.6 + 0.113x

Let the diagonal be 4.472 in²

Finding for x,

y = 3.6 + 0.113(4.472)

y = 4.10

In the table, the value of y for the x = 4.472 in is 10, but here we get 4.10

Therefore, the residual value = 10-4.10 = 5.89

Hence, the residual value of the graph is 5.89

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Mr. Lloyd could use his credit card to buy the TV. Therefore, option  A is the correct answer.

Using a credit card to make a purchase requires that the buyer have a credit limit that is large enough to cover the amount of the purchase. Mr. Lloyd does not have enough money in his bank account to pay for the television, so he would not be able to use a credit card to make the purchase.

Options B, C, and D are all viable options for Mr. Lloyd. He could save up money and pay cash for the television at a later date, or he could use his debit card to make the purchase when he has enough money in his bank account. He could also save money and use his debit card at a later date when he has enough money in his bank account.

Therefore, option  A is the correct answer.

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Mr. Lloyd wants to buy a new television, but he does not have enough money in his bank account to pay for one. Which of these is NOT an option for Mr. Lloyd?

A) He can use his credit card to buy the television now.

B) He can save money and pay cash for the television at a later date.

C) He can use his debit card to buy the television now.

D) He can save money and use his debit card to buy the television at a later date.

The constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

A proportional relationship is a mathematical equation that expresses two variables that are in proportion to one another. In this type of relationship, if one variable is multiplied by a certain constant factor, then the other variable will be multiplied by the same constant factor. For example, if the cost of 3 books is $15, then the cost of 6 books will be $30. In this case, the number of books and the cost of the books are in proportion to one another.

The constant of proportionality is the constant factor by which the two variables are multiplied to obtain each other. In other words, it is the ratio between the two variables that remain constant in a proportional relationship. It can be represented by the letter k, and is calculated by dividing one variable by the other.

To find the constant of proportionality from a graph, we need to look at the slope of the line. The slope is the ratio between the change in the y-values and the change in the x-values, which is also known as the rise over run. If the graph shows a proportional relationship, then the slope will remain constant throughout the graph.

For example, if the graph shows the relationship between the number of hours worked and the amount of money earned, and the slope is 10, then the constant of proportionality is 10. This means that for every hour worked, the person earns $10. The equation for this proportional relationship can be written as y = 10x, where y represents the amount of money earned and x represents the number of hours worked.

In conclusion, the constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

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Answer:

Step-by-step explanation:

let, the length is z

thus the ratio will be 5z : 4z

perimeter = 2 (a + b)

360 = 2 ( 5z + 4z )

180 = 9z

z = 20 cm

length = 100 cm and width = 80cm

area = length * width

area = 100*80

area = 8000cm²

Answer:

You need to multiple

Step-by-step explanation:

We can use trigonometric relations or Pythagorean's theorem, we will see that x = 8ft.

We can see that x is the hypotenuse of the triangle, and we know the length of one leg and the angle between them, then we can use the cosine trigonometric relation:

cos(60°) = 4ft/x

solving for x:

x = 4ft/cos(60°) = 8ft

Other way to find x is first find the other side and then use the pyhtagorean theorem, to get the other side y we need:

tan(60°) = y/4ft

y = 4ft*tan(60°)

Then using Pythagorean's theorem we get:

x = √( (4ft)² + (4ft*tan(60°))²)

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Answer:

780

Step-by-step explanation:

15*52=780

Answer:

Ayo its Jose is the only one who was trying to get me to do the thank you usa for the support of the joy luck club the story is about a mother that lost every thing in China and whent to America to start a new life but she make her daughter do something that she don't want to be ninja in and she is not sending her

Answer: 420

Step-by-step explanation:

60 apples per day times 7 days in a week = 420

Answer:

33.3% decrease (to 3sf)

Step-by-step explanation:

Percentage decrease = \(\frac{24-16}{24}\) × 100%

                                    = \(\frac{8}{24}\) × 100%

                                    = \(\frac{1}{3}\) × 100%

                                    = 33.3% (to 3sf)

Answer:

Yea i definitly just lost brain cells

Step-by-step explanation:

Answer:

appt

Step-by-step explanation:

The stock closest to its Purchase price is ABC Toys, with a change of $3.

To determine which stock is closest to its purchase price, we need to compare the changes in stock value to their initial purchase prices. However, we do not have information about the initial purchase prices of each stock.

One way to approach this problem is to calculate the absolute value of the change in stock value for each stock and then compare those values. The stock with the smallest absolute value of change will be closest to its purchase price.

Using this method, we get:

ABC Toys: |–$3| = $3

Golden Grains: |+$4| = $4

Fast Cars: |–$8| = $8

XYZ Clothing: |+$1| = $1

Therefore, the stock closest to its purchase price is ABC Toys, with a change of $3.

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Based solely on financial considerations, Vim Cola should be discontinued.

We have,

Differential analysis to determine whether Vim Cola should be continued or discontinued:

Differential Analysis:

Continue vs. Discontinue Vim Cola table is given below.

The differential analysis shows that if Vim Cola is continued (Alternative 1), the company will have sales of $235,000, a cost of goods sold of $111,000, and operating expenses of $143,000.

This will result in a gross profit of $124,000 and an operating loss of $19,000.

If Vim Cola is discontinued (Alternative 2), the company will have no sales or cost of goods sold related to Vim Cola, but will still have $25,000 of fixed operating expenses.

This will result in an operating loss of $25,000.

The difference between the two alternatives is an operating income(loss) of ($6,000).

Since the difference is negative, discontinuing Vim Cola would result in a better financial outcome for the company.

Therefore,

Based solely on financial considerations, Vim Cola should be discontinued.

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Here's a differential analysis for Lavonia Beverage Inc. to decide whether Vim Cola should be continued or discontinued:

Differential Analysis

Alternative 1: Continue Vim Cola

Alternative 2: Discontinue Vim Cola

Sales revenue $235,000 $0

Cost of goods sold:

Variable costs (111,000) 0

Fixed factory overhead costs (16,650) 0

Total cost of goods sold (127,650) 0

Gross profit $107,350 $0

Operating expenses:

Variable expenses (114,400) (28,800)

Fixed expenses (28,600) 0

Total operating expenses (143,000) (28,800)

Operating income (loss) $(35,650) $(28,800)

The analysis shows that if Lavonia Beverage Inc. continues to sell Vim Cola, it will generate sales revenue of $235,000 and incur total variable costs of $111,000.

Additionally, 15% of the cost of goods sold, or $16,650, is fixed factory overhead costs. Total cost of goods sold for Vim Cola is $127,650 ($111,000 + $16,650).

On the other hand, if Vim Cola is discontinued, the company will lose the sales revenue of $235,000 but will also save on the variable and fixed costs associated with the product.

Variable operating expenses are estimated to be 20% of total operating expenses, or $28,800. Fixed operating expenses associated with Vim Cola are estimated to be 20% of total fixed operating expenses, or $28,600.

Thus, based on the analysis, it appears that Vim Cola is generating a loss of $35,650 if it continues to be sold, while discontinued it would result in a loss of $28,800. Therefore, it may be advisable to discontinue Vim Cola.

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The inequality graphed on the number line can be written as:

-3 ≤ x < 2

Here we can see an inequality graphed on a number line, we can see that we start with a closed circle at x = -3

A closed circle means that x = -3 is a solution.

And we can see that it ends with an open circle at x = 2, the open circle means that the point is not a solution.

Then the inequality thati is shown in the number line is written as:

-3 ≤ x < 2

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Answer:

2x - 12 = y

Step-by-step explanation:

→ Add y to both sides

2x = 12 + y

→ Minus 12 from both sides

2x - 12 = y

Answer:

35

Step-by-step explanation:

because the straight line is 180 so if you add 35+55=90 and 90+90=180

Answer:

35°

Step-by-step explanation:

What I did was look at ∠ABC and know that collinear is a straight line, and that a straight line is equal to 180°. Then I saw that ∠ABD was a right angle or 90° and that ∠BCE was equal to 55°, so I added those 2 together and got 145°. then I subtracted that from the 180°. because that is what a straight line equals and I got 35°. So, I would say ∠DBE is equal to 35°.

Answer:

1/3.  To reduce a fraction, divide both the numerator and denominator by the GCF.

Let x sweatshirts were produced at the factory.

The number of defective shirts is 15.

Equate 3% of x to 15, to obtain the value of x.

So 500 sweatshirts were produced at the factory.

Use the remainder theorem: we can decompose the given polynomial in terms of quotient and remainder polynomials \(q(x)\) and \(r(x)\), respectively, such that

\(x^4 - 5x^3 + x^2 - 10x - 5 = (x + 3) q(x) + r(x)\)

Then letting x = -3 makes the quotient term vanish, and we're left with a remainder of

\(r(-3) = (-3)^4 - 5\times(-3)^4 + (-3)^2 - 10\times(-3) - 5 = \boxed{250}\)