A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $80 million after 4 years, as shown in the graph:

There is a graph of a line with Years on the x axis and Profits in millions on the y axis that passes through 1, negative 100 and 4, 80.

Which equation most closely represents the line depicted in the graph?

a. f(x) = 60x − 160
b. f(x) = −60x + 160
c. f(x) = −80x + 4
d. f(x) = 80x − 4

Answer:  c.60   is correct

Step-by-step explanation:

Answer:

2m + 3n + 11

Step-by-step explanation:

You cannot combine the m and the n terms, but you can combine 5 and 6

It will take 22 years for the account value to reach $7500 with an annual interest rate of 9% per year.

According to the question,

We have the following information:

2500 dollars is placed in an account with an annual interest rate of 9%.

We know that following formula is used to find simple interest:

Simple interest = principal*rate*time/100

Now, the simple interest on any amount will be equal to the total amount after interest minus the principal amount:

7500-2500

5000

So, we have the following expression:

(2500*9*t)/100 = 5000

Now, using cross multiplication method:

t = (5000*100)/(2500*9)

t = 200/9 years

t = 22.2 years

Now, the nearest year will be 22 years.

Hence, it will take 22 years for the account value to reach $7500 with an annual interest rate of 9% per year.

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Answer: 66%

Step-by-step explanation: To convert a fraction to a percentage, divide the top number by the bottom number. For example, [tex]\frac{1}{4}[/tex] is 25% because if divide them, (1÷4=0.25) then we get 25%. So, for this problem, we solve 2÷3, which equals 0.66, or 66%.

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The expression for the amount when Kendra earns $11.60 per hour working at the movie theater is 11.60h.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Based on the information illustrated, let the number of hours be h.

Since Kendra earns $11.60 per hour working at the movie theater. The expression will be:

= Amount earned per hour × Number of hours

= 11.60 × h

= 11.60h

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Kendra earns $11.60 per hour working at the movie theater. How much will she earn for h hours?

The equation x² - 6x = 72 has a solution between 4 and 5

Use a trial and improvement method to find this solution.

There are a number of "improvement" techniques that can be used to improve an estimate of a solution to a polynomial. Some of them use the polynomial itself to form the iterator function.

Iterator

There are a number of ways we can solve the given equation for x. Often, at least one of these will converge when used for improving the estimated value of x.

 x₁ = ([tex]x^{2}[/tex] -72)/6 . . . . . . . add 6x-72, divide by 6

 x₂ = 72/(x^2 -6) . . . . . . . factor out x and divide by its coefficient

 x₃ = ∛(72 +6x) . . . . . . . add 6x and take the cube root

The first two of these iterators tend to diverge. For x = 4.5, they give ...

 x₁ = (4.5³ -72)/6 = 3.1875

 x₂ = 72/(4.5² -6) = 5.0526

Both of these stray out of the given interval of [4, 5].

However, the third one tends to converge, so can give us a useful approximation in one iteration:

 x₃ = ∛(72 +6×4.5) ≈ ∛99 ≈ 4.6261

Second iteration

Applying this again, we get ...

 x ≈ ∛(72 +6·4.6261) ≈ 4.6378

The approximate root to 1 decimal place is 4.6.

Additional comment

One of the quickest converging iterators is that provided by Newton's method. For finding the solution to f(x) = 0, it uses ...

 x₁ = x -f(x)/f'(x) . . . . . . . where f'(x) is the first derivative

For this problem, we can define ...

 f(x) = [tex]x^{2}[/tex] -6x -72   ⇒   f'(x) = 3x^2 -6

 x₁ = x -([tex]x^{2}[/tex] -6x -72)/(3x^2 -6) = (3[tex]x^{2}[/tex] -6x -[tex]x^{2}[/tex] +6x +72)/(3x^2 -6)

 x₁ = (2[tex]x^{2}[/tex] +72)/(3x^2 -6)

Then for x = 4.5, the "improved" solution is ...

 x₁ = (2(4.5³) +72)/(3(4.5²) -6)) = 254.25/54.75 = 339/73 ≈ 4.6438

A second iteration gives ...

 x ≈ 4.639026 . . . . accurate to 5 decimal places

Hence with this iterator, the number of accurate decimal places tends to double with each iteration.

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Answer:

Step-by-step explanation:

The original rectangle has dimensions of 70 x 35.

Therefore, we can find its perimeter and area with the standard formulas.

A = 70 * 35

= 2450 square units

P = 2(70) + 2(35)

= 210 units

The new rectangle is dilated by a 1/5 factor, so both dimensions will be one fifth the size of the original. When you have a scale factor that is 1 over some number, you can find the new measurement by dividing by that denominator.

Therefore, new rectangle's dimensions are:

70 ÷ 5 = 14

35 ÷ 5 = 7

Now, find area and perimeter of the new rectangle.

A = 14 * 7

= 98 square units

P = 2(14) + 2(7)

= 42 units

Answer:

Yes, All the three recipes use a proportional amount of flour.

Step-by-step explanation:

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

There are three different recipes to make cookies for different amount of flour.

Recipe 1 =  3 dozen cookies and 4.5 cups of flour

Recipe 2 =  4 dozen cookies and 6 cups of flour

Recipe 3 = 5 dozen cookies and 7.5 cups of flour

Now,

To check that all the recipes in proportion, we check the amount of flour for 1 dozen cookies.

For recipes 1;

The amount of flour = 4.5 / 3

                              = 1.5

For recipe 2;

The amount of flour = 6 / 4

                              = 1.5

For recipe 3;

The amount of flour = 7.5 / 5

                              = 1.5

Clearly, All are the same amount to make 1 dozen of cookies.

So, The all recipes are in proportions.

Therefore, All the three recipes use a proportional amount of flour.

The pounds of tomatoes Kent have now is 1.78 pound.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given that Keny had 2.43 pounds of tomatoes he sold 0.4 pound to Maria and 0.25 pound to Lara for their lunches.

The total pounds of tomatoes = 2.43

The pounds of tomatoes Kent have now;

2.43 - 0.4 - 0.25

= 1.78

Therefore, the pounds of tomatoes Kent have now is 1.78 pound.

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The number of coins that are in Jacob's collection is 50

information from the problem

Jacob has a coin collection

He keeps 5 of the coins in his box, which is 10% of the collection

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

10%

= 10 percent

= 10 / 100

= 0.1

The factor 0.1 of the total number of coin is 5

let the total number be x

0.1 * x = 5

0.1x = 5

x = 5 / 0.1

x = 50

The total number of coins is 50

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The expression when factored out is 8(4s + 5)

From the question, we have the following expression that can be used in our computation:

32s + 40

The terms of the above expression are:

32s and 40

And the factor of 32 and 40 is

Factor = 8

So, we divide 32s and 40 by 8

The results of these divisions are

32s/8 = 4s

40/8 = 5

So, we have the following results

32s + 40 = 8(4s + 5)

Hence, the factored expression is 8(4s + 5)

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Answer:

2,500

Step-by-step explanation:

40 × 7 × 9

=2,500d dollars

The person has to deposit $1948.05 per year.

what is compound interest?

Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.

In the given question, to find the value to be added per year we will use the formula.

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

Here A = 50,000

r (rate of interest) = 6 % or 0.06.

n = 1

t = 16

P = value deposit per year

On substituting the values,

[tex]P= \frac{50000 \times 0.06} {(1 +0.06)^{16} - 1}[/tex]

P =   3000 / 2.54- 1

 = $1948.05 .

Therefore, person has to deposit $1948.05 per year.

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The number of three-letter sequences that can be made from the word "COMBINATORICS" where no 2 letters can be the same is 720 ways

The question is asking of permutation

arranging the letters without repeating a word gives

COMBINATORICS ⇒ COMBINATRS

The newly arranged word gives 10 letters and arranging 10 letters by taking 3 at a time is 10P₃

The required permutation is 10P₃

10P₃

= 10! / (10 - 3)!

= 10! / 7!

= 720

= 720 ways

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Answer:

this is very easy, just do:

45(0.62/1)

and you get 27.9 miles

tada!

45 kilometers is equivalent to 27.9 miles.

Given that we need to convert 45 kilometers to miles.

We have given that,

1 kilometer = 0.62 miles)

To convert 45 kilometers to miles, we can use the conversion factor of 1 kilometer = 0.62 miles.

We multiply the given distance in kilometers by this conversion factor to obtain the equivalent distance in miles.

Step 1: Multiply 45 kilometers by 0.62 miles/kilometer:

45 km x 0.62 miles/kilometer = 27.9 miles

Therefore, 45 kilometers is equivalent to 27.9 miles.

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The zeros of the given function are -2, and 1 in the represented graph.

A function's zeros are the values of x when f(x) equals 0. As a result, its name. This indicates that when f(x) = 0, x is a function zero. When the graph crosses through x = a and is considered to be the function's zero. As a result, (a, 0) is a function zero.

The graph is given in the question,

According to the shown graph, the function in the given graph has located at the x-axis of the plane, which is the location or coordinates from where the line crosses which are -2, and 1.

Therefore, the zeros of the given function are -2, and 1 in the represented graph.

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Answer: 3.84 , 3 41/50 , 3.789 , 3

The total cost for Zap Electric Company and Bolt Electric Company are y = 0.06r + 6.55 and y = 0.12r + 2.83

An equation is an expression that shows the relationship between two or more numbers and variables.

Let r represent the number of kilowatt hours you use in one month, and let y represent the total cost of your electric service.

The Zap Electric Company charges $0.06 per kilowatt hour plus a $6.55 monthly service fee. Hence:

y = 0.06r + 6.55

The Bolt Electric Company charges $0. 12 per kilowatt hour plus a $2.83 monthly service fee. Hence:

y = 0.12r + 2.83

The cost is y = 0.06r + 6.55 and y = 0.12r + 2.83

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The Graph of x ≥ 3 is attach below

The definition of a linear inequality

The inequality symbol is used to compare two mathematical expressions in what are referred to as linear inequalities. The expression could be both numerical and algebraic, or it could just be one.

What does a linear inequality in mathematics look like?

What Is an Example of Linear Inequality? An example is the linear inequality x - 5 > 3x - 10. The LHS is obviously greater than the RHS because the greater than symbol is being used in this inequality. After being resolved, the inequality appears as follows: 2x 5 x (5/2).

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Answer:

[tex](x^2+7)(x^2-5)[/tex]

Answer:

false

Step-by-step explanation:

Credit Unions are not-for-profit financial service cooperatives

The equation -27v - 54v²-36v³ cannot be solved as it doesn't have a factor

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

There are 3 main types of equation

1. Slope-intercept : y = mx + c

                              where m is the slope and b is the y-intercept

2. Point-slope : [tex](y - y_{1} ) = m (x - x_{1} )[/tex]

                          Where m is the slope and [tex](x_{1},y_{1})[/tex] is a point on the line

3. Standard : Ax + By = C

                     where A, Band C are constants

Factorizing the equation we get

-3v(9 + 18v + 12v²)

= -9v(4v² +6v +3)

(4v² +6v +3) as this equation doesn't have a factor it is difficult to solve

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The value of x : 56

What is Angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

Given,

∠A = (2x - 6)°

∠B = 74°

Since, we have to find the value of x

we have to find it by Linear equation

∠A + ∠B = 180°

Substituting the values we have

(2x - 6)° + 74° = 180°

2x - 6 + 74 = 180

2x + 68 = 180

2x = 180 - 68

2x = 112

x = 112/2

x = 56

The value of  ∠A = 56 - 6 = 60°

Hence, The value of x = 56

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Answer:

n = -45

Step-by-step explanation:

2/3n + 4 = -26

subtract 4 from both sides:

2/3n + 4 - 4 = -26 - 4

2/3n = -30

divide both sides by 2/3:

(2/3n)/(2/3) = (-30)/(2/3)

n = -45

Answer:

n=-45

Step-by-step explanation:

2/3n+4=-26

        -4.  -4

2/3n=-30

/2/3.    /2/3

n=-30/1 *3/2

n=-90/2

n=-45

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The simplified form of the expression [tex]\frac{6}{7}c-\frac{5}{9}d-\frac{1}{2}c+\frac{1}{3}d[/tex] is [tex]\frac{5}{14}c-\frac{2}{9}d[/tex]

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

Therefore, let's simplify the expression as follows:

To simplify an expression means to write an equivalent expression which contains no similar terms.

his means that we will rewrite the expression with the fewest terms possible.

Hence,

[tex]\frac{6}{7}c-\frac{5}{9}d-\frac{1}{2}c+\frac{1}{3}d[/tex]

combine like terms

[tex]\frac{6}{7}c-\frac{1}{2}c-\frac{5}{9}d+\frac{1}{3}d[/tex]

Do the arithmetic

[tex]\frac{12c-7c}{14}+\frac{-5d+3d}{9}[/tex]

[tex]\frac{5}{14}c-\frac{2}{9}d[/tex]

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Base of the Sail is 12 feet and Height of the Sail is 5 feet

What is Right Angle Triangle?

A right triangle or right-angled triangle, or more technically an orthogonal triangle, historically known as a rectangled triangle, is a triangle with one right angle (that is, a 90-degree angle) and two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.

Solution:

Accroding to the Question,

Let, Base = x and Height = y

x = 7 + y

Using the Pythagorous Theorem

[tex]Base^{2} + Perpendicular^{2} = Hypotenuse^{2}[/tex]

[tex]x^{2} + y^{2} = 13^{2}[/tex]

Using the above mentioned relation

49 + y^2 + 14y + y^2 = 169

2y^2 + 14y - 120 = 0

Discriminant = 34

y = 5, -12

The length of a sail can not be neegative, therefore y = 5

From the equation 1, x = 12

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Answer: 4[tex]\frac{n}{4}[/tex]

Step-by-step explanation: