if f(x)=3x-1 and g(x)= x+2, find (f-g)(x)​

The monthly payment for the loan of $1500 with $92.81 interest over 9 months is $176.98.

To calculate the monthly payment for a $1500 loan with $92.81 in interest over 9 months, we must first find the total amount to be paid back, which includes both the principal and the interest. The total repayment amount will be $1500 (the original loan) plus $92.81 (the interest), making the total amount $1592.81.

We can then divide this total amount by the number of months the loan will be held to find the monthly payment:

Monthly Payment = Total Repayment Amount ÷ Total Months

Monthly Payment = $1592.81 ÷ 9

Monthly Payment = $176.98

Therefore, the student needs to pay $176.98 every month to pay off the loan in 9 months.

Answer:

OF course!Dividing by 100 just means move the decimal two places to the left, so the answer is 9.652

Step-by-step explanation:

Answer:

=9.852

Step-by-step explanation:

985.2/100

=9.852

Answer:

2/3 of a year is 8 months.

Step-by-step explanation:

Since there is 12 months in a year, divide 12 by 3.

12÷3= 4

Now, multiply 4 by 2.

4×2= 8

This gives you the answer of 8 months.

Answer: 8 months

Step-by-step explanation: multiply denominator and numerator by 4 so it can be equivalent to 12 months.

Number of adult tickets = 75

Number of student tickets = 175

Solution:

Let x represents the number of adult tickets and

y represents the number of student tickets.

Total number of tickets sold = 250

⇒ x + y = 250 – – – – (1)

Cost of adult ticket = $15

Cost of student ticket = $5

Total cost of collection = $2000

15x + 5y = 2000 – – – – (2)

Multiply equation (1) by 5

⇒ (1) × 5  5x + 5y = 1250 – – – – (3)

Subtract equation (3) from equation (2), we get

15x + 5y – 5x – 5y = 2000 – 1250

⇒ 10x = 750

⇒ x = 75

Substitute x = 75 in equation (1), we get

⇒ 75 + y = 250

⇒ y = 250 – 75

⇒ y = 175

Number of adult tickets = 75

Number of student tickets = 175

Test corner points for maximum revenue. The optimal solution is 250 adult tickets and 0 student tickets, yielding $3750.

To solve this problem, let's set up the equations based on the given information:

1. The total number of tickets sold cannot exceed 250:

[tex]\[ x + y \leq 250 \][/tex]

2. The total revenue must be at least $2000:

[tex]\[ 15x + 5y \geq 2000 \][/tex]

Now, let's solve this system of inequalities step by step:

Step 1: Graph the constraints:

Let's graph the lines corresponding to the equations:

x + y = 250 and  15x + 5y = 2000

Step 2: Find the feasible region:

The feasible region is the area that satisfies all the given constraints. In this case, it will be the region below or on the lines ( x + y = 250 ) and ( 15x + 5y = 2000 ), and within the boundaries of the axes.

Step 3: Identify the corner points:

The corner points of the feasible region are the points where the lines intersect or touch the boundary lines.

Step 4: Test the corner points:

Substitute the coordinates of each corner point into the objective function (the total revenue) to find which one yields the maximum revenue.

Let's start with the calculations:

1. **Graph the constraints:**

We'll need to find the intercepts of each line and draw them on the graph.

For ( x + y = 250 ):

When ( x = 0 ), ( y = 250 )

When ( y = 0 ), ( x = 250 )

For ( 15x + 5y = 2000 ):

When ( x = 0 ), ( y = 400 )

When ( y = 0 ),[tex]x = \frac{2000}{15} = \frac{400}{3} \)[/tex]

Now, let's plot these points and draw the lines.

2. **Find the feasible region:**

Shade the region below or on the lines ( x + y = 250 ) and ( 15x + 5y = 2000 ), and within the boundaries of the axes.

3. **Identify the corner points:**

The corner points of the feasible region are the points where the lines intersect or touch the boundary lines.

4. **Test the corner points:**

Substitute the coordinates of each corner point into the objective function ( R = 15x + 5y ) to find which one yields the maximum revenue.

Let's calculate the corner points:

Corner Point 1: (0, 0)

[ R = 15(0) + 5(0) = 0 ]

Corner Point 2: (250, 0)

[ R = 15(250) + 5(0) = 3750 ]

Corner Point 3: (0, 400)

[ R = 15(0) + 5(400) = 2000 ]

Now, let's compare the revenues:

- Corner Point 1: $0

- Corner Point 2: $3750

- Corner Point 3: $2000

The maximum revenue is $3750, which occurs at the corner point (250, 0).

Therefore, to maximize revenue while satisfying the given constraints, the Arlington Drama Club should sell 250 adult tickets and 0 student tickets.

To simplify a fraction by division you must have common factors between the denominator and the neominator to divide (or cancel) them

Answer: r = 12.1cm, d = 24.2cm, Area = 460.0cm²

Step-by-step explanation:

From the formula,

Circumference of a circle = πd or 2πr.

To find the radius, we have to equate 76 cm to πd or 2πr and make r or d the subject of the formula. Now

76 = 2πr, don't forget that

π = 22/7 or 3.142

Now make r the subject of the formula

r = 76/2π

= 76/2 x 3.142

= 76/6.284

= 12.1 cm

d = 2r

= 2 x 12.1

= 24.2cm.

Area of the circle is πr²

= 3.142 x (12.1)²

= 3.142 x 146.41

= 460.0 cm²

This is pretty much half the volume of a rectangular prism, so we multiply 4.8*2.5*3.4 to get 40.8 mm^3

Then we take half of that to get 20.4 mm^3

Hope that helped you to understand!

Answer:

The missing terms are - 3x and - 6x.

Step-by-step explanation:

The table represents the factorization of x2 – 9x + 18. It is partially completed.

So, the unknown term in the first row and second column will be the product of -3 and x i.e. -3x.

And the unknown term in the second row and first column will be the product of -6 and x i.e. -6x.

Therefore, the missing terms are - 3x and - 6x. (Answer)

The two terms that are missing in the diagram are –3x and –6x

The two missing term can be obtained as follow:

Thus, the two missing term are –3x and –6x

The missing term can be obtained by doing a partial factorisation of the expression. This can be obtained as follow:

x² – 9x + 18

x² – 9x + 18

x² – 3x – 6x + 18

Thus, the missing terms are –3x and –6x

Complete question:

See attached photo

Learn more about factorisation:

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Answer:

x=-5, y=-2. (-5, -2).

Step-by-step explanation:

-8x-3y=46

-8x+9y=22

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

3(-8x-3y)=3(46)

-8x+9y=22

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

-24x-9y=138

-8x+9y=22

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

-32x=160

x=160/-32

x=-5

-8(-5)-3y=46

40-3y=46

3y=40-46

3y=-6

y=-6/3

y=-2

Answer:

(-5, -2)

Step-by-step explanation:

You can find the solution to the system by either doing substitution or elimination. Since it is already it standard form, the easier way that I am showing you is elimination.

- 8x - 3y = 46                             First you subtract! not add because you must

- 8x + 9y = 22​                           cancel 8 them out.

---- 6y=24

       6     6

y=-2

to find x, just plug into either equation!

Answer:

exact form is 5/12

decimal form is 0.416666

Step-by-step explanation:

Equivalent fractions are fractions that have the same value or proportion. To find an equivalent fraction to a given fraction, you multiply or divide both the numerator and the denominator by the same number. Therefore, 10/24 and 15/36 are equivalent fractions to 5/12.

To find an equivalent fraction to 5/12, you simply multiply or divide both the numerator (the top number) and the denominator (the bottom number) by the same non-zero number. An equivalent fraction will have a different numerator and denominator, but it will represent the same value or proportion. For example, if we multiply both the numerator and the denominator of 5/12 by 2, we get 10/24. Therefore, 10/24 is an equivalent fraction to 5/12.

Similarly, if we multiply 5 (the numerator) and 12 (the denominator) by 3, we get the equivalent fraction 15/36.

So, 5/12 = 10/24 = 15/36 in terms of value or proportion.

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The break even point for this book store is 10

Solution:

Given that, book store cost $80 a day to keep open, and it spends $15 for each book that it sells

Cost to open the book store = $ 80

The formula for solving the break even point (BEP) is:

[tex]BEP = \frac{\text{Fixed cost}}{\text{Selling price - variable cost}}[/tex]

Fixed Cost is the cost that remains constant whether the services provided or products sold increases or decreases

Variable Cost is the cost that varies or differs in proportion to the products or services produced, whether they increased or decreased

In this problem,

Fixed cost = $ 80

Selling price = $ 23

Variable cost = $ 15

Therefore,

[tex]BEP = \frac{80}{23-15}\\\\BEP = \frac{80}{8}\\\\BEP = 10[/tex]

Thus break even point for this book store is 10

In order for the bookstore to continue its business, it should sell at least 10 books to meet its $80 cost

Answer:p=10

Step-by-step explanation:

The total length of the three longest bulletin boards when placed side by side would be 180 inches.

To calculate the total length of the three longest bulletin boards when placed side by side, we first need to determine the average length of a bulletin board and then multiply it by three.

The length of bulletin boards can vary widely depending on their purpose, but let's assume a standard size commonly found in schools or offices.

A typical bulletin board might measure around 4 feet (48 inches) in length.

However, some bulletin boards can be longer, reaching up to 6 or 8 feet.

Let's take a conservative estimate of 5 feet (60 inches) for our calculations.

So, if we have three bulletin boards each measuring 5 feet (60 inches) in length, the total length when placed side by side would be:

Total length = Length of one bulletin board × Number of bulletin boards

Total length = 60 inches × 3

Total length = 180 inches

Therefore, the total length of the three longest bulletin boards when placed side by side would be 180 inches.

Answer:

F(3) = 2 * 3 - 1, which is 6 - 1 equaling 5.

Step-by-step explanation:

3 times 2 is six since you have to follow PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction). Multiplication is before Subtraction, and that is why we multiply 2 and 3 first, since 3 replaces the variable x. After multiplying 2 and 3 to get 6, subtract by 1 to get 5.

Answer: 5

Answer:

x = - 2

Step-by-step explanation:

– 2(– 3х + 4) + 3x — 3 = — 29

6x - 8 + 3x - 3 = - 29

9x = - 29 + 8 + 3

9x = - 18

x = - 18 : 9

x = - 2

Answer:

x = -2

Step-by-step explanation:

– 2(– 3х + 4) + 3x — 3 = — 29 multiply -2 with inside the parenthesis remember negative sign multiplied by negative sign is positive

6x - 8 + 3x - 3 = - 29 add the like terms

9x - 11 = -29

9x = -29 + 11

9x = -18

x = -2

Answer:

If Ty can make 7 signs in 2 hours that means in 4 hours he could double that output to make 14 signs. Harrison, on the other hand, makes 15 signs every 4 hours. Therefore, by default - Harrison makes 1 more sign every 4 hours than Ty. Harrison has the greater rate. You have to figure out how many signs Ty can make in 4 hours, by multiplying 2 x 7 = 14. Hope that helps.

Step-by-step explanation:

Answer:

  -$85

Step-by-step explanation:

The charge will be $25 + ($10/h)(6 h) = $25 +60 = $85.

Jeffrey's savings will decrease by $85, so the net change is -$85.

Answer:

The new principal after the first payment is $ 1,380.65

Step-by-step explanation:

1. We calculate the amount of interest to pay in the first payment, this way:

Interest = Amount of loan * (interest rate/months in a year)

Replacing with the real values we know:

Interest = 1,500 * (0.1/12)

Interest = 1500 * 0.0083 = $ 12.50

2. Now we subtract the Interest from the monthly payment, as follows:

Payment to principal = 131.85 - 12.50

Payment to principal = $ 119.35

3. Finally we subtract that 1st payment to principal from the initial principal to get the new principal, this way:

New Principal = 1,500 - 119.35

New Principal = $ 1,380.65

The new principal after the first payment is $ 1,380.65

Answer:

35/12

Step-by-step explanation:

1 1/2+1 5/12

=3/2+17/12

=3*6+17*1/12

=18+17/12

=35/12

Tom read a total of 11/12 of the two books combined by reading 1/2 of the first book and 5/12 of the second book, after finding a common denominator to add the fractions.

To calculate the total fraction of the two books that Tom has read, we need to add the fractions of each book he has read together. Tom read 1/2 of the first book and 5/12 of the second book.

To add these fractions, they need to have a common denominator. The lowest common denominator between 2 and 12 is 12.

Therefore, we convert 1/2 into 6/12 so that both fractions have the same denominator.

Now, the fractions to be added are 6/12 (from the first book) and 5/12 (from the second book).

Adding these fractions, we get:

6/12 + 5/12 = 11/12

So, Tom has read a total of 11/12 of the two books combined. This method of finding a common denominator and then adding the numerators is an effective strategy to add fractions with different denominators, providing a clear, step-by-step approach to solving such problems in mathematics.

Multiply the top equation by 6 and and the bottom equation by –5 and then add the equations is the correct answer.

Solution:

Given system of equations:

8x + 5y = –7 – – – – (1)

–7x + 6y = –4 – – – – (2)

Multiply top equation by 6 and and bottom equation by –5

(1) × 6 ⇒ 48x + 30y = –42

(2) × –5 ⇒ 35x – 30y = 20

Now add these two equations, we get

(48x + 30y) + (35x – 30y) = –42 + 20

48x + 35x + 30y  – 30y = –42 + 20

83x = –20

The variable y is eliminated.

Therefore Multiply the top equation by 6 and and the bottom equation by –5 and then add the equations is the correct answer.

Answer:

Multiply the top equation by −5, then add the equations.

Step-by-step explanation:

Did it on Khan Academy

Answer:

C: Graph A is a linear function and Graph B is also a function but a low and high constant rate

Answer:

Area = [tex]\frac{5}{12}[/tex] x²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here b = [tex]\frac{5}{6}[/tex] x and h = x, thus

A = [tex]\frac{1}{2}[/tex] × [tex]\frac{5}{6}[/tex] x × x = [tex]\frac{5}{12}[/tex] x²

Answer:

  5·7

Step-by-step explanation:

From your knowledge of multiplication tables, you know that ...

  5×7 = 35

Both 5 and 7 are prime numbers, so that is the prime factorization.

Answer:

15/2

Step-by-step explanation:

y varies directly as x can be written as:

y & x

y = Kx

K = y/x

But from the question, we were told that:

y = 10

X = 20

K = y/x

K = 10/20

K = 1/2

The formula for the expression is:

y = Kx

y = 1/2 x

Now let us solve for y, when:

x = 15

y = 1/2 x

y = 1/2 x 15

y = 15/2

Final answer:

To find the value of y when x = 15, we first determined the constant of proportionality (k) using the given y and x values, which was found to be 0.5. We then plugged x = 15 into the direct variation formula y = kx, resulting in y = 7.5.

Explanation:

If y varies directly with x and y = 10 when x = 20, then we can write this direct variation as y = kx, where k is the constant of proportionality. To find k, we substitute the known values of x and y and solve for k:
10 = k × 20
k = 10 / 20
k = 0.5
With k found, we can now determine what y is when x = 15:

y = k × x
y = 0.5 × 15
y = 7.5

Percentage change in perimeter is 100%.

Step-by-step explanation:

Calculate perimeter of R1 = 2 (length + breadth) = 2 (5 + 3)  = 16 ft

Calculate perimeter of R2 = 2 (10 + 6) = 32 ft

= (32 - 16/16) [tex]\times[/tex] 100 = 100%

Answer:

This is a function and there is no value of x for which we will get two or more different values of y.

Step-by-step explanation:

A relation contains the points (-5,-10), (-2,-4), (-1,-2), (4,8), and (5,10).

So, if we want to model the equation that includes those points then we will get the equation of a straight line passing through the origin {Since the rate of change of y with respect to x is uniform.

The equation is y = 2x

Now, this is a function and there is no value of x for which we will get two or more different values of y. (Answer)

Answer:

Step-by-step explanation:

There is no answer because this is a formula

We need an equation — something that equals something else

Assuming you mean

[tex]8x^2 + 25y = 0\\25y = -8x^2\\y = -\frac{8}{25}x^2[/tex]

Answer:

x=1

Step-by-step explanation:

1-2x=-3x+2

-1=-x

1=x

Answer:

8

Step-by-step explanation:

plus 6 plus 3 look iam just trying to cheat I got stuff to do

Answer: 47

Step-by-step explanation:

Just add 27 and 20 then you get f

Just use inverse operations