Expand and simplify
(7 + V6 )^2

Answer:

After 10 months, both salespersons will sell 160 cars.

Step-by-step explanation:

We are given two different salesperson's statistics of sales. We can use this information to set up a system of equations and solve for our variable.

Let us name the first salesperson Person 1 and the other salesperson Person 2.

Now, for Person 2:

Now, because we have these equations, we can set up a table that will determine the number of months that will elapse before the salespersons will sell the same amount of cars.

For Person 1, the equation will be the increase of the y-value by 13 cars after an initial sale of 30 vehicles. Therefore, we can create a table of values.

[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 30 \\ \cline{1-2} 1 & 43 \\ \cline{1-2} 2 & 56 \\ \cline{1-2} 3 & 69 \\ \cline{1-2} 4 & 82 \\ \cline{1-2} 5 & 95 \\ \cline{1-2} 6 & 108 \\ \cline{1-2} 7 & 121 \\ \cline{1-2} 8 & 134 \\ \cline{1-2} 9 & 147 \\ \cline{1-2} 10 & 160 \\ \cline{1-2} \end{array}[/tex]

For Person 2, we can use the same formatting to create a table. However, the rule changes - we must start at 50 cars being sold and increase it by only 11 cars a month.

[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 50 \\ \cline{1-2} 1 & 61 \\ \cline{1-2} 2 & 72 \\ \cline{1-2} 3 & 83 \\ \cline{1-2} 4 & 94 \\ \cline{1-2} 5 & 105 \\ \cline{1-2} 6 & 116 \\ \cline{1-2} 7 & 127 \\ \cline{1-2} 8 & 138 \\ \cline{1-2} 9 & 149 \\ \cline{1-2} 10 & 160 \\ \cline{1-2} \end{array}[/tex]

Now, we need to see where the y-values are the same in both tables. We can see that we have a value of (10, 160) in both tables, so after 10 months, the salespersons will sell the same amount of cars.

There is an alternative method of solving the problem that is much quicker and will require much less work.

We are given two equations that are both equal to y. Therefore, we can set them equal to each other (dropping the y) and solving for x.

Our value of x will be the amount of months in which the sales are equal.

[tex]\displaystyle{13x+30=11x+50}\\\\2x + 30 = 50\\\\2x = 20\\\\\boxed{x = 10}[/tex]

Therefore, after 10 months of sales, the salespersons will have sold the same amount of cars. We can plug this information into one of the equations to see how many cars will be sold at that point.

[tex]y = 13(10) + 30\\\\y = 130 + 30 \\\\y = 160[/tex]

In 10 months, 160 cars will be sold. If we set the equations equal to each other and substitute x, we should get a true statement.

[tex]13(10)+30=11(10)+50\\\\130 + 30 = 110 + 50\\\\160 = 160[/tex]

Because we get a true statement, each salesperson will sell 160 cars after 10 months of initial sales.

Answer:

- 19

Step-by-step explanation:

Step 1:

d + 7 ÷ - 3 = 4        Equation

Step 2:

d + 7 = - 12        Multiply

Step 3:

d = - 12 - 7      Subtract

Answer:

d = - 19

Hope This Helps :)

Answer:

56

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

-2(9)+4= -14  and -14 is equal to -14.

Answer:

3.16

Step-by-step explanation:

Hope this helps!

Answer:

This should help

Step-by-step explanation:

1.05, 1.09 and 1.1 are close to each other so I marked where each one should go

Answer:12

Step-by-step explanation:

it’s 12 because 4 x 3 = 12

Answer:

48π units³

Step-by-step explanation:

The volume (V) of a cylinder is calculated as

V = πr²h ( r is the radius of the base and h the height )

Here r = 4 and h = 3 , thus

V = π × 4² × 3

   = π × 16 × 3

    = 48π units³ ← exact answer

Answer:

Vertex form is y=(x-5)^2-43

Step-by-step explanation:

Given expression: x^2-10x-18

Take half of b:

-10/2=-5

Square the result:

-5^2=25

Add and subtract into original expression:

x^2-10x+25-25-18

Factor and simplify:

(x^2-10x+25)-25-18

(x-5)^2-25-18

(x-5)^2-43

So the vertex form is y=(x-5)^2-43

Answer:

124.8

Step-by-step explanation:

Because the formula of a prism is v=bh so you would multiply 16x7.8 and get 124.8

Answer:

[tex]x=(-12,0)[/tex]

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

Step-by-step explanation:

x-intercept

[tex]-2(x-4y)=24[/tex]

[tex]x-4y=-\frac{24}{2}[/tex]

[tex]x-4y=-12[/tex]

[tex]x=4y-12[/tex]

[tex]x=4(0)-12[/tex]

[tex]x=-12[/tex]

y-intercept

[tex]-2(x-4y)=24[/tex]

[tex]x-4y=-\frac{24}{2}[/tex]

[tex]x-4y=-12[/tex]

[tex]-4y=-12-x[/tex]

[tex]y=-\frac{-12-x}{4}[/tex]

[tex]y=-\frac{-12-(0)}{4}[/tex]

[tex]y=\frac{12}{4}[/tex]

[tex]y=3[/tex]

Step-by-step explanation:

2 /4

3. 5

doing reciprocal

2× 5

3. 4

= 8×15

12

= 120

12

=10 ans

hope it help u..

Answer:

13/16 is the answer. Bad handwriting but try to understand .

Answer:

The answer is most likely c.)

Step-by-step explanation:

It says that they sold 40 scarves and hats at the Winter Festival, but it never told us exactly how many hats total and how many scarves total that they sold. So we leave it as "s+h=40" Next we have the price of the scarves and hats, not the numbers sold. Since the scarves cost $18 and the hats cost $14, we know that a certain amount of each equals $700. Since we don't know the exact number of each that were sold, we leave it at "18s+14h=700." Sorry if you got a bit lost.

Answer:

it would be -18

Step-by-step explanation:

because you would divide 108 by 6 and you will get -18 each second

Answer:

B

Step-by-step explanation:

I am sorry if this is wrong

Answer:

sin^2α

Step-by-step explanation:

I will just  pose  x instead  of alpha  here to make things simpler

[tex]\tan ^2\left(x\right)\left(2\cos ^2\left(x\right)+\sin ^2\left(x\right)-1\right)\\\\[/tex]

we know that sin^2x = 1 -  cos^2x so...

[tex]=\left(-1+1-\cos ^2\left(x\right)+2\cos ^2\left(x\right)\right)\tan ^2\left(x\right)[/tex]

[tex]=\cos ^2\left(x\right)\tan ^2\left(x\right)[/tex]

we can rewrite using trigonometric identities (tan = sin/cos)...

[tex]=\left(\frac{\sin \left(x\right)}{\cos \left(x\right)}\right)^2\cos ^2\left(x\right)\\= \sin ^2\left(x\right)[/tex]

Answer:

0.1,0.2,1.8,2.3

Step-by-step explanation:

Answer:

.02, .1, 1/8, 2/3

Step-by-step explanation:

Answer:

$276.25

Step-by-step explanation:

$325 times (100% -15%)

$325 times 0.85

Answer:

1) c=100

2) x^4-40x^3+400x^2

Step-by-step explanation:

When I write ^# that means it's squared and has a number above it :)

You're welcome :)

Answer:

Axis is a vertical line at x = 2

Vertex is (2, -1)

y-intercept is (0, 3)

Solutions are x = 1 and x = 3

Step-by-step explanation:

To draw the graph of the quadratic equation you must find at least 5 points lie on the graph by choose values of x and find their values of y

Let us do that

Use x = -1, 0, 1, 2, 3, 4, 5

∵ y = x² - 4x + 3

∵ x = -1

∴ y = (-1)² - 4(-1) + 3 = 1 + 4 + 3 = 8

→ Plot point (-1, 8)

∵ x = 0

∴ y = (0)² - 4(0) + 3 = 0 + 0 + 3 = 3

→ Plot point (0, 3)

∵ x = 1

∴ y = (1)² - 4(1) + 3 = 1 - 4 + 3 = 0

→ Plot point (1, 0)

∵ x = 2

∴ y = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1

→ Plot point (2, -1)

∵ x = 3

∴ y = (3)² - 4(3) + 3 = 9 - 12 + 3 = 0

→ Plot point (3, 0)

∵ x = 4

∴ y = (4)² - 4(4) + 3 = 16 - 16 + 3 = 3

→ Plot point (4, 3)

∵ x = 5

∴ y = (5)² - 4(5) + 3 = 25 - 20 + 3 = 8

→ Plot point (5, 8)

→ Join all the points to form the parabola

From the graph

∵ The axis of symmetry is the vertical line passes through the vertex point

∵ x-coordinate of the vertex point is 2

∴ Axis is a vertical line at x = 2

∵ The coordinates of the vertex point of the parabola are (2, -1)

∴ Vertex is (2, -1)

∵ The parabola intersects the y-axis at point (0, 3)

∴ y-intercept is (0, 3)

∵ x² - 4x + 3 = 0

∵ The solutions of the equation are the values of x at y = 0

→ That means the intersection points of the parabola and the x-axis

∵ The parabola intersects the x-axis at points (1, 0) and (3, 0)

∴ Solutions are x = 1 and x = 3

Answer:

25%

Step-by-step explanation:

Mrs. Loar has to grade 75 papers. Mrs. Holt is helping her grade. Mrs. Loar graded 60 papers and Mrs. Holt graded the rest.

Hence, the amount of papers Mrs Holy graded is = 75 - 60

= 15 papers

What percent of the papers did Mrs. Holt grade?

This is calculated as:

15/60 × 100 = 25%

Hence, Mrs Holy graded 25% of the papers

Answer:

use the corner ofa paper to see if its obtuse it should be long and wide if its acute it should be a corne

Step-by-step explanation:

Answer:

the time needed to get to the arch is 6 per hour

Step-by-step explanation:

The computation of the time needed to get to the arch is shown below:

As we know that

Speed = distance ÷ time

where,

Speed is 65 miles per hour

And, the distance is 390 miles

So, the time is

= 390 ÷ 65

= 6 per hour

Hence, the time needed to get to the arch is 6 per hour

We simply applied the above formula so that the correct value could come

And, the same is to be considered  

Answer: 24

Step-by-step explanation:

i did the problem and got it right

Answer:

Yep it's C) 40°

Step-by-step explanation:

and rest one is 70°