4.) Mr. Souders purchased a car priced at $9800. He paid $500 down and
agreed to a monthly payment of $250 per month for 48 months.
Including the down payment, what is the total cost of the car?
Please show your work.

$698.94

Step-by-step explanation:

M = P [r (1 + r) ∧n / ( (1 + r) ∧n) - 1) ]

P = the principal loan amount = $150,000

Annual percentage rate = 3.8%

r = monthly interest rate = 0.038 / 12 = 0.003166

Term in years = 30

n = number of payments over the loan’s lifetime monthly = 30 * 12 = 360

M = the total monthly mortgage payment

Using the formula,

M = 150,000 [0.003166 (1 + 0.003166)∧360 / ((1 + 0.003166)∧360) - 1]

M = 150,000 [(0.003166 * 3.120394) / (3.120394 - 1)]

M = 150,000 [0.009880 / 2.120394‬]

M = 150,000 * 0.004660 = $699 (rounded up value)

As per mortgage calculator we get the exact value

M = $698.94

Answer:

none

Step-by-step explanation:

you cant multiply or divide to make them equivalent

Answer: True

Step-by-step explanation: Just took the test

A system of equations is simply a collection of multiple equations that are either consistent, inconsistent, dependent or independent.

The system of equations is given as:

Next, we plot the graph of both equations (see attachment)

From the attached graph, the solution to the system of equation is (2/3,2/3)

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Answer: your welcome :)

Step-by-step explanation:

Answer:

It takes 1.68 hours to catch up to them.

Step-by-step explanation:

The speed of robber = 71 mph

The  speed of police =  78 mph

The police  start 10 minutes  later

by that time robber would have travelled

[tex]distance = \frac{speed}{time}[/tex]

10 minutes  =0.166667 hours

then the distance  =  11.8 mph

Let them meet at distance x from the bank.

time taken by police to reach x , time =[tex]\frac{ x}{78}[/tex]----------------------(1)

time taken by robber in the same time = [tex]\frac{x-11.8}{71}[/tex]---------------(2)

Equating (1) and (2)

[tex]\frac{x}{78} =\frac{ x-11.8}{71}[/tex]

[tex]71 x = 78(x - 11.8)[/tex]

71x =78x - 920.4

920.4 = 78x - 71x

920.4 = 7x

x = 131.48

The distance where they catch up with the robber from the bank is 131.48 miles

speed of police = 78 mph

distance =  131.48  miles

time they catch up = [tex]\frac{131.48}{78}[/tex]

= 1.68 hours

Step-by-step explanation:

[tex]Area \: of \: triangle = \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 3.2 \times 9.6 \\ = 1.6 \times 9.6 \\ = 15.36 \: {cm}^{2} \\ [/tex]

Answer:

[tex]\frac{145}{24}\approx 6[/tex]***

Answers may vary depending on the person reading the graph.

It is hard to tell what they think crosses nicely.

For example, I decided that the graph crossed nicely at the following points:

[tex](0,3)[/tex]

[tex](2,8)[/tex]

[tex](6,5)[/tex]

Step-by-step explanation:

I see that the graph crosses at [tex](0,3)[/tex],[tex](2,8)[/tex], and [tex](6,5)[/tex].

The equation [tex]y=ax^2+bx+c[/tex] tells us the [tex]y[/tex]-intercept is [tex]c[/tex] since when [tex]x=0[/tex] we have [tex]y=a(0)^2+b(0)+c=0+0+c=c[/tex].

The [tex]y[/tex]-intercept for our graph is [tex]3[/tex]. Therefore, [tex]c=3[/tex].

So far we have the equation:

[tex]y=ax^2+bx+3[/tex].

Let's enter the other points creating a system of linear equations to solve:

[tex]8=a(2)^2+b(2)+3[/tex]

[tex]5=a(6)^2+b(6)+3[/tex]

Let's simplify:

[tex]8=4a+2b+3[/tex]

[tex]5=36a+6b+3[/tex]

Let's subtract 3 on both sides:

[tex]5=4a+2b[/tex]

[tex]2=36a+6b[/tex]

I choose to solve the system by elimination.

Let's multiply the top equation by -3:

[tex]-15=-12a-6b[/tex]

[tex]2=36a+6b[/tex]

Now adding the equations results in:

[tex]-13=24a[/tex]

Divide both sides by 24:

[tex]\frac{-13}{24}=a[/tex]

Now using one of the equations we can find [tex]b[/tex]:

[tex]5=4a+2b[/tex] with [tex]a=\frac{-13}{24}[/tex]

[tex]5=4\frac{-13}{24}+2b[/tex]

[tex]5=\frac{-13}{6}+2b[/tex]

Add 13/6 on both sides:

[tex]5+\frac{13}{6}=2b[/tex]

[tex]\frac{30+13}{6}=2b[/tex]

[tex]\frac{43}{6}=2b[/tex]

Divide both sides by 2:

[tex]\frac{43}{2(6)}=b[/tex]

[tex]\frac{43}{12}=b[/tex]

So we have the equation:

[tex]y=\frac{-13}{24}x^2+\frac{43}{12}+3[/tex]

Let's evaluate [tex]a+b+c[/tex] now:

[tex]\frac{-13}{24}+\frac{43}{12}+3[/tex]

[tex]\frac{-13+86+72}{24}[/tex]

[tex]\frac{73+72}{24}[/tex]

[tex]\frac{145}{24}[/tex]

Answer:

Value of x is 34

Step-by-step explanation:

The figure is a quadrilateral;

Angles given are; 2x°, 88°,108° and (3x - 6)°

We already know that the interior angles of a quadrilateral add up to 360°

Therefore, to get the value of x;

2x° + 88° + 108° + (3x - 6)° = 360

5x° + 190° = 360°

5x° = 170°

 x = 34°

Thus, the value of x is 34

Answer:

88

Step-by-step explanation:

44 / 0.5 = 44*2 = 88

Answer:

Step-by-step explanation:

0.5 is the same as 5/10 which reduces to 1/2. Half of 44 is 22! The answer is 22!

The only option that is a graph of the function y = x² is: Second Graph

The general formula for a quadratic function is:

y = ax² + bx + c

Where a ≠ 0

We are given the quadratic function as:

y = x²

When x = -2, we have:

y = (-2)² = 4

When x = -1, we have:

y = (-1)² = 1

When x = 0, we have:

y = (0)² = 0

When x = 1, we have:

y = (1)² = 1

When x = 2, we have:

y = (2)² = 4

Looking at the graphs, the only one with these coordinate values is Graph 2

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Answer:

x           y

0          -7

1            -9

2            -5

3            5

Step-by-step explanation:

The give function is [tex]y=3x^2-5x-7[/tex]

Assuming the domain is :{0,1,2,3} then we substitute these values into the function and solve for the range.

When x=0, [tex]y=3(0)^2-5(0)-7=-7[/tex]

When x=1, [tex]y=3(1)^2-5(1)-7=-9[/tex]

When x=2, [tex]y=3(2)^2-5(2)-7=-5[/tex]

When x=3, [tex]y=3(3)^2-5(3)-7=5[/tex]

The table then becomes:

x           y

0          -7

1            -9

2            -5

3            5

Answer:

Sides/diagonals are congruent

Step-by-step explanation:

If the distance formula is used to determine the type of quadrilateral, then we are interested in knowing whether the opposite sides are congruent or adjacent sides are congruent.

We can also use the length of diagonals to determine which type of quadrilateral.

For instance the square has all sides equal.

The diagonals of the rectangle are congruent.

Product of 4.21 and 1.31 gives 5.5

Product of 3.21 and 1.72 gives 5.5

Solution:

Given that,

We have to find two decimals that gives a product close to 5.5

So, when the two decimals are added, the product must be close to 5.5

Let us consider the following two decimals

4.21 and 1.31

Let us multiply 4.21 and 1.31 and check if their product is close to 5.5

[tex]4.21 \times 1.31 = 5.5151 \approx 5.5[/tex]

Thus, product of 4.21 and 1.31 gives a product close to 5.5

Similarly, consider two decimals 3.21 and 1.72

Let us multiply 3.21 and 1.72 and check if their product is close to 5.5

[tex]3.21 \times 1.72 = 5.5212 \approx 5.5[/tex]

Thus product of 3.21 and 1.72 gives 5.5

Answer:

  The point from which measurements are made. The point where all coordinate values are zero.

Step-by-step explanation:

In the Newtonian/Euclidean universe, the laws of geometry and physics are the same everywhere. Hence, in order to tell one place from another, we define a point of origin from which all coordinates are measured. Then, every point in space can be named in terms of its coordinates relative to the origin.

Answer:

Step-by-step explanation:

3) divide by 3

18,6,2.....

4) 6 is subtracted

48,42,36.....

5) multiplied by 3

81, 243,729.....

6) multiplied by 2

32, 64 , 128......

7) 6 is subtracted

70,64,58,........

8) 12 is added

60,72,84,.......

9) divide by 2

32, 16, 8 ......

10) 5 is added

28,33,38.....

11)  13 is added

63, 76, 89,.......

12) 8 is subtracted

51, 43, 35,..........

Answer:

Graph the line using the slope and y-intercept, or two points.

Slope:  

2

y-intercept:  0 x  y 0 0 1 2

Step-by-step explanation:

Using the order of operations (PEMDAS), the expression 5 + 3 × (5 - 2) 2 evaluates to 32.

The expression to be evaluated is 5 + 3 × (5 - 2) 2. In mathematics you should always follow the order of operations, often remembered by the acronym PEMDAS which stands for: Parentheses, Exponents (i.e. Powers and Square Roots, etc.), Multiplication and Division, Addition and Subtraction. So in this case you should first evaluate the expression inside the parentheses (5 - 2), which equals 3. Then, 3 is squared to get 9 and is multiplied by 3 to get 27. Finally we add 5 to get a final answer of 32.

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Answer:

A

Step-by-step explanation:

count the lines on the bottom and top

The dimensions of the rectangle shown on the coordinate plane are : The base is 5 units and the height is 4 units.

A coordinate plane is a two-dimensional plane or region formed by the intersection of two number lines.

One number line is horizontal and called the x-axis, and the other number line is vertical and called the y-axis.

The point where they meet is called the origin. Points on a coordinate plane can be located by using numbers on the x-axis and the y-axis.

Given that a rectangle shown on the coordinate plane, we need to find the dimensions of the same,

So, if we see the figure we are going to have that, the base is of 5 units, (no matter if the base is -5 we will consider it as 5 units)

And the height is about 4 units.

Hence, the dimensions of the rectangle shown on the coordinate plane are : The base is 5 units and the height is 4 units.

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Answer:

look at the picture shown

The graph in option A (refer attachment) represents the relationship between the amount of time Joe walks and the distance he walks

Step-by-step explanation:

Given scenario is "Joe walks over on a treadmill at constant rate"

The equation which describes the relationship between' t' the time he walks in hours and ;d' the distance he walks in miles

                             d = 4 t

Now, we have to find the graph which indicates correctly about the relationship between the amount of time Joe walks and the distance he walks. Refer attachment to find the graph.

According to the given equation,

when t = 1 s so 'd' would would be 4 miles

when t = 2 s so 'd' would would be 8 miles

The above shows the plotting points in graph (t,d) = (1,4) (2,8). Hence, concluded that graph in option A (refer attachment) would be the right answer.

Because, others are not satisfying the equation d = 4 t

graph in option B shows the plotted points (t,d) = (4,1) (8,2)

graph in option C shows the plotted points (t,d) = (4,4) (8,8)

graph in option D shows the plotted points (t,d) = (4,4) (4,8)

Answer:

See explanation

Step-by-step explanation:

William is thinking of a number n.

Then

two times his number = 2n

five less than two times his number = 2n - 5

The result is between negative three and fifteen, so

[tex]-3\le 2n-5\le 15[/tex]

Solve this compound inequality. First, add 5:

[tex]-3+5\le 2n-5+5\le 15+5\\ \\2\le 2n\le 20[/tex]

Divide it by 2:

[tex]1\le n\le 10[/tex]

William's number is between 1 and 10

The compound inequality representing the range of numbers that William might be thinking of is 1 ≤ n ≤ 10.

We have,

Let's assume the number William is thinking of is "n."

According to the first clue, "five less than two times his number is between negative three and fifteen."

We can represent this using a compound inequality as follows:

-3 ≤ 2n - 5 ≤ 15

Explanation:

"two times his number" is represented as "2n."

"five less than two times his number" is "2n - 5."

So, the compound inequality shows that "2n - 5" is between -3 and 15. This means that the possible values of "n" should satisfy both inequalities:

-3 ≤ 2n - 5 and 2n - 5 ≤ 15

Alternatively, you can simplify the compound inequality to:

-3 + 5 ≤ 2n ≤ 15 + 5

Which becomes:

2 ≤ 2n ≤ 20

Finally, divide the entire inequality by 2 to isolate "n":

1 ≤ n ≤ 10

Thus,

The compound inequality representing the range of numbers that William might be thinking of is 1 ≤ n ≤ 10.

This means William's number "n" could be any integer from 1 to 10, including both 1 and 10.

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Answer:

do you need the value of x?

x=7+6y+2z

-2(7+6y+2z)+5y+2z=-1 -7y=13+2z

-14-12y-4z+5y+2z=-1

-14-7y-2z=-1

-7y-2z=-1+14

-7y-2z=13

Answer:

x= -1, y= -1 and z= -1

Step-by-step explanation:

x-6y-2z= 7 (Equation 1)

-2x+5y-2z= -1 (Equation 2)

-5x+6y+5z= -6 (Equation 3)

The above three are your system of equations and you need x3 answers!

Use equations (1) and (2) to eliminate z. Multiply equation (1) by −1 and then add to equation (2) to eliminate z. Resulting in:

−x+6y+2z= -7 (1)

−2x+5y−2z= -1 (2)

Adding them together results in your 4th equation:

-3x+11y= -8 (4)

Use equations (1) and (3) to eliminate z. Multiply equation (1) by −5 and equation (3) by −2 and then add to eliminate z. Resulting in:

−5x+30y+10z= -35 (1)

10x-12y-10z= 12 (3)

Add them to get:

5x+18y= -23 (5)

Use equations (4) and (5) to solve for x. Multiply equation (4) by 18 and equation (5) by −11 and then add to eliminate y.

−54x+198y= -144

-55x-198y= 253

-109x=109 (Divide -109 from both sides to isolate x)

x= -1 <---- ANSWER 1

Substitute x=−1 into equation (4) to find:

−3x+11y= -8

-3(-1)+11y= -8

3+11y= -8 (Subtract 3 from both sides)

11y=-11 (Divide 11 from both sides to isolate y)

y=-1 <---- ANSWER 2

Now we can substitute x=−1 and y=−1 into equation (1) to find:

x-6y-2z= 7

(-1)-6(-1)-2z=7

-2z+5=7 (Subtract 5 from both sides to isolate z)

z= -1 <---- ANSWER 3

Hope this explains it for you! Enjoy! <3

Answer:

the answer is A) 35°.

Step-by-step explanation:    

Solution

To solve this problem, we need to use the information given about the angles and arcs. We know that arc VY = 132° and ∠YUV = 41°.

We can use the properties of a triangle to find the measure of arc XV. Since arc VY and arc XV are supplementary angles (their sum is 180°), we can write the equation:

arc VY + arc XV = 180°

We are given arc VY = 132°, so:

132° + arc XV = 180°

Now, we can solve for arc XV:

arc XV = 180° - 132° arc XV = 48°

However, since the given options do not include 48°, we can use the information about ∠YUV to find the closest answer. Since ∠YUV = 41° and arc VY = 132°, we can find the measure of arc VY by adding ∠YUV to it:

arc VY + ∠YUV = 132° + 41° arc VY = 173°

Now, we can use this new value of arc VY and the fact that arc VY and arc XV are supplementary to find the closest answer:

arc VY + arc XV = 180° 173° + arc XV = 180°

Now, we can solve for arc XV:

arc XV = 180° - 173° arc XV = 7°

Since 7° is not among the given options, we can consider the closest option, which is 35°.

So, the answer is A) 35°.

Answer: the answer is 2.375 and as a mixed fraction is 2 3/8

Step-by-step explanation: first you subtract 3 5/8 from 6 so 6-3= 3 and in order to get the 3/8 you have to make one more number divisible by 1 which in this case was

Over 8 so then you do 8/8 which gives you a whole then you subtract the 5-8/8 which is 3/8 plus the 2 you had left

Mark runs 27 feet in 6 seconds.

To find out how many feet Mark runs in 6 seconds, we need to determine how many yards he runs in 6 seconds first. We are given that Mark runs 6 yards every 4 seconds, so we can set up a proportion: 6 yards / 4 seconds = x yards / 6 seconds. Cross-multiplying and solving for x, we find that x = 9 yards. Now, since there are 3 feet in 1 yard, we can convert 9 yards to feet by multiplying by 3: 9 yards * 3 feet/yard = 27 feet. Therefore, Mark runs 27 feet in 6 seconds.

Answer:

5+(23xN)

I think this is right. Sorry if I'm wrong.

Answer:

They will finish in time for Jamal to catch the bus.

Step-by-step explanation:

Jamal agreed to bring four dozen i.e. 48 cupcakes in for sale.

He started icing cupcakes at 7:40 a.m. at a rate of 3 cupcakes per minute up to 7:50 a.m. that is the time when he needs to be out of his house to catch his bus.

So, with in this 10 minutes (7:40 a.m. to 7:50 a.m.) he would be able to make (10 × 3) = 30 cupcakes.

Now, at 7:44 his older sister started icing cupcakes too. she iced them at a rate of 4 cupcakes per minute.

So, in this 6 minutes (7:44 a.m. to 7:50 a.m.) she will be able to make (4 × 6) = 24 cupcakes.

Therefore, in total Jamal will be able to made (30 + 24) = 54 cupcakes.

Since, 54 > 48 so, they will finish in time for Jamal to catch the bus. (Answer)

Answer:

The answer is 20% :)

Answer:

9

Step-by-step explanation:

5/5 = 1

1 x 9 = 9

Answer:

9

Step-by-step explanation:

Answer:2/6

Step-by-step explanation:

Answer:

2/1

Step-by-step explanation:

If we use ratios, it would be 4:2 which is the same as 4/2. But, we can simplify them both by 2. So 4/2=2 and 2/2=1. So the fraction would be 2/1