The car salesman earns $850 per week plus 20% commission for each car the salesman sells. The salesman sold a used car for $2000 last week, which represents the amount of money the salesman took home? Show Work!
(A) $850.00
(B) $860.00
(C) $1,250.00
(D) $2,850.00

Answer:

The coordinates are x = -1 and y = -2.

Step-by-step explanation:

Given:

Equations are 2x-4y=6 and 3x+y=-5.

Now, to find the coordinates.

[tex]2x-4y=6[/tex]...........(1)

[tex]3x+y=-5[/tex]...........(2)

So, first we solve the equation 1 to get the value of [tex]x[/tex].

[tex]2x-4y=6[/tex]

Subtracting both sides by [tex]-4y[/tex] we get:

[tex]2x=6+4y[/tex]

Dividing both sides by 2 we get:

[tex]x=3+2y[/tex]

Now, we put the value of [tex]x[/tex] in equation 2 to get [tex]y[/tex].

[tex]3x+y=-5[/tex]

[tex]3(3+2y)+y=-5[/tex]

[tex]9+6y+y=-5[/tex]

[tex]9+7y=-5[/tex]

On solving the whole equation we get :

[tex]y=-2[/tex]

And, now putting the value of [tex]y[/tex] in equation (1) we get [tex]x[/tex]:

[tex]2x-4y=6[/tex]

[tex]2x-4(-2)=6[/tex]

[tex]2x+8=6[/tex]

[tex]2x=6-8[/tex]

[tex]2x=-2[/tex]

on solving we get:

[tex]x=-1[/tex]

Therefore, the coordinates are x=-1 and y=-2.

Answer:

Part 11) The table represent a direct variation. The equation is [tex]y=18x[/tex]

Part 12) The table represent a direct variation. The equation is [tex]y=0.4x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Part 11)

For x=0.5, y=9

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=9/0.5=18[/tex]

For x=3, y=54

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=54/3=18[/tex]

For x=-2, y=-36

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=-36/-2=18[/tex]

For x=1, y=18

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=18/1=18[/tex]

For x=-8, y=-144

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=-144/-8=18[/tex]

The values of k is the same for each ordered pair

therefore

The table represent a direct variation

The linear equation is

[tex]y=18x[/tex]

Part 12)

For x=-5, y=-2

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=-2/-5=2/5=0.40[/tex]

For x=3, y=1.2

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=1.2/3=0.40[/tex]

For x=-2, y=-0.8

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=-0.8/-2=0.4[/tex]

For x=10, y=4

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=4/10=0.4[/tex]

For x=20, y=8

Find the value of k

[tex]k=y/x[/tex] -----> [tex]k=8/20=0.4[/tex]

The values of k is the same for each ordered pair

therefore

The table represent a direct variation

The linear equation is

[tex]y=0.4x[/tex]

Answer: B

Step-by-step explanation: The equation of the line in Slope-intercept form is:

Where "m" is the slope of the line and "b" is the intersection of the line with the y-axis.

For the graph of the line, you can identify that:

And for, you can identify that:

Therefore, you can observe that the slope does not change, but now the line cuts the y-axis at . In other words, it was moved from to (3 units on the y-axis)

Then, it is the graph of translated 3 units upward, which means that the graph of g(x) is 3 units above the graph of f(x).

The graph of g is 3 units above the graph of f(x), the correct option is A.

The graph is a mathematical representation of the relation between two objects.

It helps in determining the function that fits best for the data obtained.

A function is a mathematical statement that defines a relationship between a dependent and an independent variable.

A function always has a defined range and domain, domain is all the value a function can have as input and range is all the value that a function can give as output.

The function f(x) = 2x

g(x) = 2x+3

Both functions are a straight line, an equation of a straight line is given by y =mx +c, m is the slope of the line and c is the y intercept.

In the function f(x), the slope is 2 and the intercept is 0

In the function g(x), the slope is 2 and the intercept is 3.

As the intercept is 3, the g(x) is 3 units above the graph f(x).

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Answer:

Step-by-step explanation:

[tex]x^2-3x=28\qquad\text{subtract 28 from both sides}\\\\x^2-3x-28=0\\\\x^2+4x-7x-28=0\qquad\text{distribute}\\\\x(x+4)-7(x+4)=0\\\\(x+4)(x-7)=0\iff x+4=0\ \vee\ x-7=0\\\\x+4=0\qquad\text{subtract 4 from both sides}\\\boxed{x=-4}\\\\x-7=0\qquad\text{add 7 to both sides}\\\boxed{x=7}[/tex]

Answer:

x = -4 or x = 7

Answer:

he can only buy 5

Step-by-step explanation:

7x5=35

he has 2 bucks left

Answer:

5

Step-by-step explanation:

5 times 7 is 35.  5 times 8 is 40 which is 3 dollars more than he has therefore he can only buy 5.

Answer:

6,9!

Step-by-step explanation:

Goodluck on your I-Ready!

To find the ordered pair with an x-value of 6, we need to look at the pattern for x and find the corresponding value for y. Using the pattern provided, the ordered pair would be (6, 18).

The problem states that Sonya is making a pattern of values for x and a pattern of values for y. We are asked to find the ordered pair that continues the patterns and has an x-value of 6.

To solve this, we need to look at the pattern for the x-values and find the corresponding value for y. Once we have the y-value, we can form the ordered pair (x, y) with x = 6.

For example, let's say the pattern for x is: 1, 2, 3, 4, 5

And the pattern for y is: 3, 6, 9, 12, 15

In this case, we can see that for x = 6, the corresponding y-value would be 18. So the ordered pair would be (6, 18).

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Do:

3x6

(3)(6)

6+6+6

Do not:

(3)-(6)

3/6

3+6

Answer:

16a^4

Step-by-step explanation:

You do 4a^2*4a^2= 16a^4 because area of square is length times width and we know that that length and width in a square is equal.

4*4= 16

a^2*a^2= a^4 (because when you multiply powers with the same base like a in this case, you add the powers up. So in this example it would be 2+2= 4)

Put them together to give you 16a^4

Final answer:

The area of a square with a side length of 4a² is A = 16a⁴, showcasing the area's proportionality to the fourth power of side length a.

Explanation:

The expression for the area of a square with a side length of 4a squared is found by squaring the side length. Since the side of the square is 4a², the area A is given by:

A = (4a²) × (4a²) = 16a⁴

The simplified expression for the area is 16a to the fourth power, which indicates that the area is proportional to the fourth power of the side length a.

The transformations are needed to transform the graph of f(x) to the graph of g(x) are:

vertical translation 1 unit up ⇒ 2nd answer

horizontal translation 5 units left ⇒ 4th answer

Step-by-step explanation:

Let us revise the translation:

∵ f(x) = 8x

∵ g(x) = (8x + 5) + 1

- From the notes above translation to the left h units added x by h

∵ 8x is added by 5

∴ f(x) translated 5 units to the left

- From the notes above translation up k units added f(x) by k

∵ f(x) is added by 1

∴ f(x) translated 1 unit up

The transformations are needed to transform the graph of f(x) to the graph of g(x) are:

vertical translation 1 unit up

horizontal translation 5 units left

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the answers are

horizontal translation 5 units left

vertical translation 1 unit up

I failed lol :((

Answer:

b. y = 27x

Step-by-step explanation:

When you talk about "per" it means multiplication, and 27 is being multiplied by (x) gallons of gas.

It cost $5 for his brother's ticket.

Step-by-step explanation:

Let,

Micheal's ticket price= x

His brother ticket price = y

According to given statement;

x+y=12    Eqn 1

y = x-2    Eqn 2

Putting value of y from Eqn 2 in Eqn 1

[tex]x+(x-2)=12\\x+x-2=12\\2x=12+2\\2x=14\\[/tex]

Dividing both sides by 2;

[tex]\frac{2x}{2}=\frac{14}{2}\\x=7[/tex]

Putting x=7 in Eqn 2

[tex]y=7-2\\y=5[/tex]

It cost $5 for his brother's ticket.

Keywords: linear equation, substitution method

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Answer:

see the explanation

Step-by-step explanation:

we know that

An isosceles triangle has two equal sides

step 1

Find the coordinates of point X (midpoint of segment AC)

we have

A(0,2a), C(2a,0)

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

substitute the values

[tex]X(\frac{0+2a}{2},\frac{2a+0}{2})[/tex]

[tex]X(a,a)[/tex]

step 2

Find the length side AX

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

A(0,2a), X(a,a)

substitute

[tex]AX=\sqrt{(a-2a)^{2}+(a-0)^{2}}[/tex]

[tex]AX=\sqrt{(-a)^{2}+(a)^{2}}[/tex]

[tex]AX=a\sqrt{2}\ units[/tex]

step 3

Find the length side BX

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

B(0,0), X(a,a)

substitute

[tex]BX=\sqrt{(a-0)^{2}+(a-0)^{2}}[/tex]

[tex]BX=\sqrt{(a)^{2}+(a)^{2}}[/tex]

[tex]BX=a\sqrt{2}\ units[/tex]

step 4

Compare the length side AX and BX

[tex]AX=a\sqrt{2}\ units[/tex]

[tex]BX=a\sqrt{2}\ units[/tex]

[tex]AX=BX[/tex]

so

The triangle AXB has two equal sides

therefore

Triangle AXB is an isosceles triangle

Answer:

Soooooooooooooo

Step-by-step explanation:

Okay.... Let me look up how to do this

The equation of the line that is parallel to y = -5x + 6 and passes through the point (-4, -1) in slope intercept form is y = -5x -21

Given that line passes through the point (-4, -1) and parallel to y = -5x + 6

We have to find the equation of line

Let us first calculate the slope of line having equation as y = -5x + 6

The slope intercept form of line is given as:

y = mx + c ---- eqn 1

where "m" is the slope of line and "c" is the y-intercept

Comparing the given equation of line y = -5x + 6 with slope intercept form y = mx + c,

we get the slope of line "m" = -5

We know that slope of two given parallel lines are always equal

Hence the slope of line which is parallel to line with equation y = -5x + 6 is also -5

Now we have to find the equation of line passing through point (-4, -1) with slope -5

Substitute (x, y) = (-4, -1) and m = -5 in eqn 1 to find "c" intercept

-1 = -5(-4) + c

-1 = 20 + c

c = -21

Substitute c = -21 and m = -5 in eqn 1 to get the equation of line

y = -5x + (-21)

y = -5x -21

Thus the equation of required line is found out as y = -5x -21

Bar graphs are effective for illustrating and comparing quantitative categories like size, quantity, rates, and distances. The bars can represent different entities and their height indicates a numerical or percentage value. This visual comparison aids in identifying data patterns, trends and relationships.

Bar graphs are a useful form of data representation in mathematics, especially when needing to illustrate and compare quantitative categories such as size, quantity, rates, and distances. In these graphs, just as it shows in Figure A7 and Figure A8, the bars can denote different categories like countries or years, and the height of the bars on the vertical axis signifies a numerical or a percentage value. The strength of bar graphs lies in their ability to provide a visual comparison, making it easier to spot patterns, trends, and the relationships between data.

Other types of graphs, such as line graphs and pie charts, have their unique uses, too. A line graph is best for showing the relationship over time between two variables, like the unemployment rate. Pie charts demonstrate how something is divided into parts, such as how a group of people or a sum of money is distributed.

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15 students will not be able to ride on bus for the field trip.

Step-by-step explanation:

No. of seats in one bus = 22 seats

1 seat is for 2 students, therefore, one bus can sit students;

No. of students in one bus = 22*2 = 44 seats

Total buses = 5

One bus can have 44 students, 5 buses can have;

5 buses = 44*5 = 220 students

Total students = 235

As the buses can have 220 students;

Students left = Total students - No. of students in 5 buses

[tex]Students\ left=235-220=15\ students[/tex]

15 students will not be able to ride on bus for the field trip.

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Final answer:

There are 15 seventh-grade students who will not be able to ride on a bus for the field trip, as the total bus seating capacity is for 220 students and there are 235 students going on the trip.

Explanation:

The subject of this question is Mathematics, specifically a problem involving division and subtraction to determine the number of students who will not have a seat on the buses. To solve this, we need to calculate the total seating capacity of all buses and then find the difference between the number of students and the total seating capacity.

Each bus has 22 seats and each seat can accommodate 2 students, so each bus can carry 22 x 2 = 44 students. There are 5 buses, so the total seating capacity is 5 x 44 = 220 students.

There are 235 seventh-grade students going on the field trip. To find out how many will not be able to ride the bus, we subtract the total seating capacity from the number of students: 235 - 220 = 15 students will not be able to ride on a bus for the field trip.

The standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

is y = x² - 3x + 2 ⇒ 3rd answer

Step-by-step explanation:

The standard form of a parabola is y = ax² + bx + c, where a, b , c are constant

To find a , b , c

∵ The standard form of a parabola is y = ax² + bx + c

∵ The parabola passes through points (2 , 0) , (3 , 2) , (4 , 6)

- Substitute the coordinates of each point in the equation

Point (2 , 0)

∵ x = 2 and y = 0

∴ 0 = a(2)² + b(2) + c

∴ 0 = 4a + 2b + c

- Switch the two sides

∴ 4a + 2b + c = 0 ⇒ (1)

Point (3 , 2)

∵ x = 3 and 2 = 0

∴ 2 = a(3)² + b(3) + c

∴ 2 = 9a + 3b + c

- Switch the two sides

∴ 9a + 3b + c = 2 ⇒ (2)

Point (4 , 6)

∵ x = 4 and y = 6

∴ 6 = a(4)² + b(4) + c

∴ 6 = 16a + 4b + c

- Switch the two sides

∴ 16a + 4b + c = 6 ⇒ (3)

Subtract equation (1) from equations (2) and (3)

∴ 5a + b = 2 ⇒ (4)

∴ 12a + 2b = 6 ⇒ (5)

- Multiply equation (4) by -2 to eliminate b

∴ -10a - 2b = -4 ⇒ (6)

- Add equations (5) and (6)

∴ 2a = 2

- Divide both sides by 2

∴ a = 1

Substitute the value of a in equation (4) to find b

∵ 5(1) + b = 2

∴ 5 + b = 2

- Subtract 5 from both sides

∴ b = -3

Substitute the value of a and b in equation (1) to find c

∵ 4(1) + 2(-3) + c = 0

∴ 4 - 6 + c = 0

- Add like terms

∴ -2 + c = 0

- Add 2 to both sides

∴ c = 2

Substitute the values of a , b , c in the standard form above

∵ y = ax² + bx + c

∵ a = 1 , b = -3 , c = 2

∴ y = (1)x² + (-3)x + (2)

∴ y = x² - 3x + 2

The standard form of a parabola with points through (2, 0) (3, 2)

(4, 6) is y = x² - 3x + 2

There is another solution you can substitute the x-coordinate of each point in each answer to find the corresponding value of y, if the value of y gives the same value of the y-coordinate of the point for the three points then this answer is the standard form of the parabola

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Answer:

C. y = x^2 - 3x + 2

Step-by-step explanation:

(4,6)

6 = 4² - 3(4) + 2

6 = 16 - 12 + 2

6 = 6

2 = 2

(3,2)

2 = 3² - 3(3) + 2

2 = 9 - 9 + 2

2 = 2

(2,0)

0 = 2² - 3(2) + 2

0 = 4 - 6 + 2

0 = 0

Answer:

y = 8

Step-by-step explanation:

8 + 24 = 32

32/4 = 8

Answer:

Step-by-step explanation:

y+24/4=8

y+24=8*4

y+24=32

y=32-24

y=8

Answer:

C) The probability that Jacob gets a mule deer is 1/7.

Step-by-step explanation:

Let us assume the number of mule deer in the woods  = m

So, the number of whitetail deer  = 6 x ( Number of mule deer) = 6 (m) = 6 m

Also, the total number of deer = Mule deer + whitetail deer

                                                    =  m + 6 m = 7 m

Let E: Event of Picking a mule deer in the woods.

[tex]\textrm{P(E)}  = \frac{\textrm{Number of favorable observations}}{\textrm{ Total number of observations }}[/tex]

So, here [tex]\textrm{P(Picking a mule deer )}  = \frac{\textrm{Number of Mule deers in the woods}}{\textrm{ Total number of deer }}  = \frac{m}{7m}  = \frac{1}{7}[/tex]

or, P(E) = 1/7

Hence, the  probability that Jacob gets a mule deer is 1/7.

Answer:

C) The probability that Jacob gets a mule deer is 1/7.

Step-by-step explanation:

Let us assume the number of mule deer in the woods  = m

So, the number of whitetail deer  = 6 x ( Number of mule deer) = 6 (m) = 6 m

Also, the total number of deer = Mule deer + whitetail deer

                                                   =  m + 6 m = 7 m

Let E: Event of Picking a mule deer in the woods.

So, here

or, P(E) = 1/7

Hence, the  probability that Jacob gets a mule deer is 1/7.

Step-by-step explanation:

cotx=t

t^2-6t-5=0

t=cotx=1or5

Answer:

C = [tex]$ \frac{1}{10} $[/tex]

D = [tex]$ \frac{1}{10^2} $[/tex]

Step-by-step explanation:

78.09 = 7 [tex]$ \times A + 8 \times B + 0 \times C + 9 \times D $[/tex]

78.09 = 7 [tex]$ \times 10^1 + 8 \times 10^0 + 0 \times \frac{1}{10} + 9 \times \frac{1}{10^2}[/tex]

⇒ C = [tex]$ \frac{1}{10} $[/tex]

   D = [tex]$ \frac{1}{10^2} $[/tex]

Hence, the answer.

Answer:

Explanation:

The figure contains a table with the monthly payment on a a $100 loan in function of the number of months (term in months) and the annual percent rates (8.00%, 10.00%, 12.00%, 14.00%).

You find the monthly payment on an $100 loan for the terms of the installment loan obtained by Corey Griffin, in the cell resulting from the intersection of the row for 18 months and the column for the rate of 8.00%. That is 5.91.

The meaning of that value is that it must repaid $5.91 monthly, per each $100 of loan.

Hence, for the $1,000, you compute the monthly payment in this way:

Now, to find the finance charge, compute the total payments and subtract the amount of the loan:

Thus, the finance charge is $63.80 (option A).

The distance between those two points is 41 and in decimal form to the nearest tenth, that's 6.4

Explanation:

Use the distance formula: √(x2 - x1)² + (y2 - y1)²

Then we plug in our x's and y's:

√(4 - (-1))² + ((-1) - 3)²

Then you simplify:

√(5)² + (-4)²   = √25 + 16

√41 (And if you need to, you can put this into decimal form.)

Answer:

6.4

Step-by-step explanation:

Use the distance formula and then fill in points for the variables.

Answer:

(cosx + 2)(cosx - 1)

Step-by-step explanation:

Using the trigonometric identity

cos²x + sin²x = 1 ⇒ sin²x = 1 - cos²x

Given

cosx - sin²x - 1

= cosx - (1 - cos²x) - 1

= cosx - 1 + cos²x - 1

= cos²x + cosx - 2

= (cosx + 2)(cosx - 1) ← in factored form

1. The rate of change is -1 and the initial value is 1.

2. The graph represents Ava’s travel plans is graph (I).

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

1. We have the coordinates as C(3, -2) and D(-2, 3).

So, the rate of change of linear function is

= 3 - (-2) / (-2 -3)

= 3+ 2 / (-5)

= 5/ (-5)

= -1.

and, the initial values is where the independent variable is zero which is (1, 0).

2. The graph represented for Ava journey is (A).

This, is because the speed of Ava car and speed of taxi is equal which is shown in graph 1 clearly.

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1. The rate of change is -1 and the initial value is 1 (Option B). 2. The graph represents Ava’s travel plans is: option A (Graph 1).

The rate of change for a linear function is given by the slope of the line. The slope (m) can be calculated using the formula:

m = change in y / change in x

In this case, using the given points C (3, -2) and D (-2, 3):

[tex]\[ m = \frac{{3 - (-2)}}{{(-2) - 3}} = \frac{{5}}{{-5}} = -1 \][/tex]

So, the rate of change is -1.

The initial value of a linear function is the y-intercept, which is the y-coordinate when x = 0. Substituting (x, y) = (-2, 3) and m = -1 into y = mx + b, find b (initial value):

3 = -1(-2) + b

3 = 2 + b

3 - 2= b

b = 1.

Therefore, the correct answer is:

B. The rate of change is -1, and the initial value is 1.

2. The graph depicting Ava's journey is labeled as (A) because it clearly illustrates that Ava's car and the taxi have the same speed, as shown in Graph 1.

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Answer:

The length of VW is [tex]25\ m[/tex]

Step-by-step explanation:

we know that

The perimeter of triangle TVW is equal to

[tex]P=VW+TV+TW[/tex]

we have

[tex]P=74\ m[/tex]

so

[tex]74=VW+TV+TW[/tex] -----> equation A

[tex]VW=TV+3[/tex] ----> equation B

[tex]TW=(VW+TV)-20[/tex] ----> equation C

substitute equation B in equation C

[tex]TW=(TV+3+TV)-20[/tex]

[tex]TW=2TV-17[/tex] ----> equation D

substitute equation B and equation D in equation A

[tex]74=(TV+3)+TV+(2TV-17)[/tex]

solve for TV

[tex]74=4TV-14[/tex]

[tex]4TV=74+14[/tex]

[tex]4TV=88[/tex]

[tex]TV=22\ m[/tex]

Find the value of VW

[tex]VW=TV+3[/tex] -----> [tex]VW=22+3=25\ m[/tex]

Find the value of TW

[tex]TW=2TV-17[/tex] -----> [tex]TW=2(22)-17=27\ m[/tex]

984 members of club would be in favor of used-gear sale based on results of survey.

Step-by-step explanation:

Number of people surveyed = 72

People in favor of sale = 63

Percentage of people in favor = [tex]\frac{People\ in\ favor\ of\ sale}{No.\ of\ people\ surveyed}*100[/tex]

Percentage of people in favor = [tex]\frac{63}{72}*100 = \frac{6300}{72}\\[/tex]

Percentage of people in favor = 87.5%

It means that 87.5% members of club will be in favor of sale.

Total members of club = 1125

Total members in favor = 87.5% of total members

[tex]Total\ members\ in\ favor=\frac{87.5}{100}*1125 = \frac{98437.5}{100}\\Total\ members\ in\ favor=984.3[/tex]

Rounding off to nearest whole number

Total members in favor = 984

984 members of club would be in favor of used-gear sale based on results of survey.

Keywords: percentage, division

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Answer:

n = -2

Step-by-step explanation:

Distribute first.

-32 - 32n = 8n + 48

Subtract 8n.

-32 - 40n = 48

Add 32

-40n = 80

n = -2

Answer: download Photomath is the best!! The answer is n=-2

Step-by-step explanation:

Answer:

width is 12 feet. Length is 32 feet.

Step-by-step explanation:

Answer:

Length= 52 Width= 44

Step-by-step explanation: