5. (10.01 MC) If sin = 1 over 4 and tan > 0, what is the value of cos ? (1 point)

5. (10.01 MC) If sin θ = 1 over 4 and tan θ > 0, what is the value of cos θ? (1 point)

Answers

Answer 1

To find the value of cos θ when sin θ = 1/4 and tan θ > 0, use the Pythagorean identity. As the angle is in the first quadrant, cos θ is positive and equals the square root of 15/16 or √15/4.

If sin θ = 1/4 and tan θ > 0, we need to determine the value of cos θ. When the sine of an angle is positive and the tangent is positive, we know the angle must be in the first quadrant, where all trigonometric functions are positive. To find cos θ, we utilize the Pythagorean identity sin2 θ + cos2 θ = 1. Rewriting this identity for cos θ, we get cos2 θ = 1 - sin2 θ.

Substituting the given value of sin θ, we have:

cos2 θ = 1 - (1/4)2
cos2 θ = 1 - 1/16
cos2 θ = 15/16

Since θ is in the first quadrant, and cos θ is positive, the value of cos θ is the positive square root of 15/16:

cos θ = √(15/16)
cos θ = √15/4 or approximately 0.9682

Related Questions

Draw a tree diagram to support the area model.
Draw a maze that fits her plan.
Find P(Y). Explain your reasoning.
Find P(N). Explain your reasoning.
Ms. Sweet predicts 50 people will enter the maze next year. Based on your findings, give Ms. Sweets a recommendation for the number of pumpkins to place in the maze.

Answers

As a tree diagram, I'd draw this with 2 branching levels. You obviously have a starting point, which branches into 3 levels for each row of the plan.

Then a second branch level off each of those 3 for the possible outcomes by the columns in that row. So the branch for the top row would have 4 further branches, the second row splits into 2 branches etc.

I'm assuming the probability is based off the area of each box, and that the splits are done equally each time.

As for drawing a maze, it's the same as the tree, just in a bit of a maze sort of shape (corners etc).

P(Y), P(N) and the number of pumpkins should come easily from the tree diagram.

The drop that riders experience on Dr. Doom's Free Fall can be modeled by the quadratic function, h(t)9.8t2 5t 39 where h is height in meters and t is time in seconds. From what height are the riders dropped? What is the height of the riders after 1.5 seconds?

Answers

The correct answer is 53.55 meters.

To solve this problem, we need to analyze the given quadratic function h(t) = [tex]9.8t^2 - 5t + 39[/tex], where h is the height in meters and t is the time in seconds.

The given quadratic function: [tex]h(t) = 9.8t^2 - 5t + 39[/tex]

Part 1: From what height are the riders dropped?

[tex]h(0) = 9.8(0)^2 - 5(0) + 39[/tex]

[tex]h(0) = 39[/tex]

The riders are dropped from a height of 39 meters.

Part 2: What is the height of the riders after 1.5 seconds?

[tex]h(1.5) = 9.8(1.5)^2 - 5(1.5) + 39[/tex]

[tex]h(1.5) = 9.8(2.25) - 7.5 + 39[/tex]

[tex]h(1.5) = 22.05 - 7.5 + 39[/tex]

[tex]h(1.5) = 53.55[/tex]

The height of the riders after 1.5 seconds is 53.55 meters.

Suzie drew the line of best fit on the scatter plot shown.

What is the approximate equation of this line of best fit in slope-intercept form?

y = 6 over 5x + 3
y = 3x + 6 over 5
y = 5 over 6x + 3
y = 3x + 5 over 6

Answers

Hey there!

Slope intercept form is defined as:

y = mx +b

In this form for lines, m is the slope, and b is the y intercept. Hence, slope intercept. That means that in order to write it in this form, we need to know both the slope and y intercept. We'll start with the former.

Slope is defined as ride over run, or up over right (you know it's negative when it goes left). In order to calculate this, we can take two points that lie directly on a coordinate and put them into a fraction as rise/run.

We have;

(0,3) and (5,9)

As we can see, the difference between the two points is that (5,9) is 5 more to the right, and is 6 higher. We get 6/5. We can even see that in the coordinates, because they're written as (x, y). Additionally, you can use the slope given two points formula:

y2-y1/x2-x1 =

9-3/5-0 = 6/5

Notice how we get the same thing, because in both methods you're finding the difference between the two coordinates based off of rise/run. That's why it's y2 minus y1.

Now that we have our slope, we need the y intercept. The y intercept is simply where the line crosses the y axis. As we can see, it crosses at (0,3) - so the intercept is 3. Now we can create our equation

Slope = 6/5
Y intercept = 3

y = mx + b --> y = 6/5x + 3

Your answer is A, the first option.

Hope this helps!

what is the image of n for a 144° counterclockwise rotation about the center of the regular pentagon

A. A
B. E
C. P
D. T

Answers

I believe the answer would be C. P
144 is two fifths of 360 so for a pentagon, it would cause the point to shift two places

Answer:

The correct option is C. The image of N for a 144° counterclockwise rotation about the center is P.

Step-by-step explanation:

The number of vertices of a regular pentagon is 5.

The central angle between two consecutive vertices is

[tex]\frac{360}{5}=72[/tex]

It means the central angle between two consecutive vertices is 72 degrees.

We have to find the image of N for a 144° counterclockwise rotation about the center.

If pentagon rotates 72 degree counterclockwise rotation about the center, then the image of N is E.

If pentagon rotates (72+72) degree counterclockwise rotation about the center, then the image of N is P.

The image of N for a 144° counterclockwise rotation about the center is P.

Therefore the correct option is C.

MATH HELP PLEASE WILL GIVE BRAINLIEST!
This figure shows circle Z with chords AB and RS .

mAR=55°
mRB=66°
AB=8 m
RS=8 m

What is mRS ?

Enter your answer in the box.

Answers

Because AB=RS=8m, ArcRS=Arc AB=ArcAR+ArcRB=55+66=121

How can you divide 133 nickels into 8 bags so that there are the same number of nickels in each bag and the number in each bag is odd and there are none left over?

Answers

There is no way to divide them because 133 is odd, so 133 divided by 8 would be 16.625.

A bakery receives an order for 1600 cookies if 12 cookies are packed in each bag how many bags are needed

Answers

134 bags.

You get this by dividing the 1600 by 12 and rounding up.

134 bags are needed to pack all the cookies.

To solve this problem, you need to divide the total number of cookies by the number of cookies that fit in each bag.

Start with the total number of cookies:

1600 cookies.

Each bag can hold 12 cookies:

1 bag= 12 cookies

Divide the total number of cookies by the number of cookies per bag:

1600 ÷ 12.

Using division:

1600 ÷ 12

= 133.33.

Since you can't have a partial bag, you need to round up to the next whole number.

So, you will need 134 bags to pack all the cookies.

A builder has 7200kg of sand.
A) write 7200 in grams
B) Give our answer in standard form,

Answers

7200kg in grams is 7200 x 1000= 7200000g, since 1 kilogram equals 1000 grams. This is also 7.2 x 10^6, which is found by moving the decimal point six places to the left and indicating it as multiplied by that many powers of ten.

EASY MEDAL !!!!!
Given the trinomial, what is the value of the coefficient 'B' in the factored form?

2x2 - 12xy - 32y2 = 2(x - 8y)(x + By)

B= ____________

Numerical Answers Expected!,

Answers

Let's start with the given polynomial:
2x² - 12xy - 32y²

As a first step, we want to regroup 2:
= 2(x² - 6xy - 16y²)

Now, we want to re-write the term -6xy in order to be able to perform a partial factoring. In this case, we can write:
-6xy = -8xy + 2xy
Therefore, the polynomial becomes:
= 2(x² - 8xy + 2xy - 16y²)

Now we factorize x within the first two terms and 2y within the last two:
= 2[x(x - 8y) + 2y(x - 8y)]

We can now regroup the common term:
=2(x - 8y)(x + 2y)

Your answer is hence B = 2

Which of the following problem types CANNOT be solved using the law of sines?

**Choose ALL that apply!!!***

A. SAA

B. SSS

C. AAA

D. SAS

E. ASA

**I'm confused :( can you please explain? thank you :)

Answers

Law of sines in a triangle with angles A, B, C and sides a,b,c states that
(sin A)/a =(sinB)/b = (sinC)/c
To use the above ratios, you need at least one angle and one side and one of either an angle or a side. So SSS and AAA don't work

Answer:

B) SSS C AAA D) SAS

Step-by-step explanation:

The sine rule is used when we are given

a) Two angles and one side (SAA)

b) Two angles and included side (ASA)

Sine rule can not be used in SSS,AAA or SAS.

Among the given options sine rule can not be used in cases B) SSS C AAA D) SAS

The product of what number and 7 is less than 49?

Answers

Answer:

All real numbers less than 7

Step-by-step explanation:

Let

x ----> the number

we know that

The inequality that represent the situation is

[tex]7x < 49[/tex]

Solve for x

Divide by 7 both sides

[tex]x < 49/7[/tex]

[tex]x < 7[/tex]

The solution is the interval -----> (-∞, 7)

All real numbers less than 7

Evaluate log10 0.001

Answers

[tex]0.001=\dfrac1{1000}=10^{-3}[/tex]

[tex]\implies\log_{10}0.001=\log_{10}10^{-3}=-3\log_{10}10=-3[/tex]

Final answer:

The operation 'log10 0.001' means 'the power to which we must raise 10 in order to obtain 0.001'. The answer is -3 because 0.001 can be represented as 10^-3.

Explanation:

The question asks you to evaluate log10 0.001. To solve this, we examine the concept of 'logarithms'. In this case, the logarithm in question is base 10 (often written simply as 'log'), and we're being asked for the power to which we need to raise 10 to obtain 0.001.

We know that 0.001 can be written as 10^-3. Therefore, log10 0.001 = -3. This is because the logarithm indicates the exponent that the base number (10, in this case) must be raised to in order to obtain the specified number (0.001, here). So, when we say log10 0.001 = -3, we're saying '10 raised to power -3 gives us 0.001'.

Learn more about Logarithms here:

https://brainly.com/question/37287488

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The graph shown is the graph of which function?

Answers

square root function. f(x)= square root x x> or = to 0

Answer:

The function of the graph is y = f(x) = x².

Step-by-step explanation:

From the graph we have

At x = 0, y = 0

Therefore f(x) = ax + c where c = 0

At x = 1 y = 1

At x = 4 y = 2

At x = 9 y = 3

At x = 16 y = 4

Therefore the graph is of the form, y= f(x) = x²

That is the graph can be plotted with a slope given by dy/dx = 2x an an intercept of c = 0.

Values of the graph are as follows

x y

1 1

2 √2

3 √3

4 2

5 √5

6 √6

7 √7

8 2√2

9 3.

You roll an fair number cube. The six possible outcomes when rolling are one, two, three, four, five, six. What are the favorable outcomes when rolling an odd number?

1, 3, 5

2, 4, 6

1, 2, 3, 4, 5, 6

1, 2, 3

Answers

The favorable outcomes are the outcomes we want (aka the outcomes we favor or like). Think of it as a gambling game. If the goal is to roll an odd number, then we need to roll a 1, a 3 or a 5. We don't want 2, 4 or 6 as those are even.

The answer is choice A) 1, 3, 5

A pile of sand is in the shape of a cone. The diameter of the sand pile is 18 feet and the height is 10 feet.

What is the volume of the sand pile?

Use 3.14 for pi.

Enter your answer as a decimal

Answers

v=pi*(r )upper 2 * h
v= 3.14 (9*9 ) * 10
=847.8

The volume of pile of sand having diameter of 18 feet and height of 10 feet is 847.8[tex]feet^{3}[/tex].

What is volume?

Volume is basically the amount of something which the container can hold in its capacity or the amount of material with the help of which it is formed.

How to determine volume?

It is told that the pile of sand is of cone shaped and it is having diameter 18 feet and height 10 feet. So the volume of sand pile will be

Volume=1/3π[tex]r^{2} h[/tex]

Radius=diameter/2

=18/2

=9 feet

Volume=1/3*3.14*[tex]9^{2}[/tex]*10

=1/3*3.14*81*10

=254.34/3

=847.8 [tex]feet^{3}[/tex]

Hence the volume of the sand pile of diameter 18 feet and height 10 feet is 847.8 [tex]feet^{3}[/tex].

Learn more about volume at https://brainly.com/question/463363

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12-packs of skwunch apple juice cost $3.00 after a 40% discount.Which equation would allow you to find the original price of the 12-packs?

Answers

The answer is 8
Hope this help and plz give me points thank u :)

Answer:

The Iready Answer:

0.6x = 3

Jeanette purchased a concert ticket on a web site.The original price of the ticket was $75.She used a coupon code to receive a 20% discount.This website applied a 10% service fee to the discounted price.Jeanette ticket was less than the original price by what percent?

Answers

STEP 1:
Find discounted price.
Discounted $= original $ - (original $ * % discount)

Discounted $= $75 - ($75 * 20%)
Discounted $= 75 - 15
Discounted $= $60

STEP 2:
Find discounted $ plus service fee.
Price plus fee= discounted $ + (discounted $ * service fee %)

Price plus fee= $60 + ($60 * 10%)
Price plus fee= 60 + 6
Price plus fee= $66

STEP 3:
Find % change.
% change formula= (new # - original #) ÷ original # x 100

% change= (66-75)÷ 75 x 100
% change= -9 ÷ 75 x 100
% change= -0.12 x 100
% change= -12%

***the negative indicates a decrease

ANSWER: Her ticket was less than the original by 12%.

Hope this helps! :)

The area of a rectangular classroom is given by the trinomial 10x^2 + 3x - 4
What are the possible dimensions of the classroom? Use Factoring.
A.(5x - 4) and (2x + 1)
B.(5x - 4) and (2x - 1)
C.(5x + 4) and (2x - 1)
D.(5x + 4) and (2x + 1)

Answers

Answer: C is the correct factored form of the equation.

To solve this, you can factor the polynomial by grouping. There are numerous ways to do this.

If you are given a multiple choice question like this, you can use the FOIL method to test the answers until you get the correct one.

Choice C with the FOIL method.

(5x + 4)(2x - 1)
10x^2 - 5x + 8x - 4
10x^2 +3x - 4

It is correct!

Luisa sells stuffed animals.she sells a stuffed elephant for $34.90, and the sale tax is 6% of the sale price.about how much is the sales tax on the elephant

Answers

To solve this problem you must follow the proccedure below:

1. You have that Luisa sells a stuffed elephant for $34.90 and the sale tax is 6% of the sale price.

2. Then, you only have to multiply $34.90 by the sale tax, as below:

6/100=0.06

Sales tax on the elephant=$34.90x0.06
Sales tax on the elephant=$2.094

About how much is the sales tax on the elephant?

The answer is: $2.094

Suppose the velocities of golf swings for amateur golfers are normally distributed with a mean of 95 mph and a standard deviation of 3.9 mph.

What is the difference in velocities between a golfer whose z-score is 0 and another golfer whose z-score is −1?

1.95 mph

2.9 mph

3.9 mph

7.8 mph

Answers

to get the difference between the golfers we proceed as follows;
the z-score is given by:
z=(x-μ)/σ
the score for golfer with z-score of 0 will be:

μ- mean
σ- standard deviation
0=(x-95)/3.9
the value of x will be
0=x-95
x=95

the score for the golfer with z-score of -1 is:
-1=(x-95)/3.9
-3.9=x-95
x=-3.9+95
x=91.1
the difference in the score of the golfers will be:
95-91.1
=3.9
the answer is C] 3.9 mph

which letter has at least one line of symmetry?
D
J
G
P
DOES ANYONE HAVE THE WHOLE QUIZ???? UNIT 4 Compositions of Isometries

Answers

D.

The letter D has a line of symmetry that runs horizontally down the middle. If you were to fold the letter D in half, you would see that the upper and lower half of the letter look the exact same.

A hose dispenses 1,413 cm³ of water every minute into a cone with a radius of 60 cm and a height of 150 cm. How long will it take to fill the cone? Use 3.14 to approximate pi. Enter your answer in the box.

Answers

Hm. Have you ever dispensed water from a hose unto a cone? I know I haven’t, but math can give us a good idea of what it would be like — or at least, how long it would take.

We are told that the hose spills 1413 cm^3 of water every minute. We are also told the cone has a height of 150 cm and a radius of 60 cm. So far, so good.

First things first, we need to find out how much water can fit in the cone. That means volume. The volume of a cone is

π • r^2 • (h/3)

Let’s go ahead and plug in (remember we use 3.14 for π)

(3.14) • (60)^2 • (150/3)

The volume of the cone is 565,200 cm^3

Wait, I’m lost. What were we supposed to do again? Oh, right. We needed to find how long it would take for the hose to fill in the cone. Well, if we know the hose dispenses 1413 cm^3 per minute, and there is a total of 565,200 cm^3 the cone can take, we can divide the volume of the cone by the amount the hose dispenses per minute to get the number of minutes it’d take to fill it.

565200/1413

400 minutes. Wow, ok. I wouldn’t want to wait that long. That’s like watching 3 movies!

whats the surface area of a cylinder with a base of 12in and hieght of 40in

Answers

3920.71 so it wants like djehf ewfewvhe veiv

HOW DO YOU FIGURE OUT THE SLOPE OF A LINE ON A GRAPH?!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

To calculate the slope of a line you need only two points from that line, (x1, y1) and (x2, y2). The equation used to calculate the slope from two points is: On a graph, this can be represented as: There are three steps in calculating the slope of a straight line when you are not given its equation.

Answer:

There are different ways to find the slope of a line on a graph

Step-by-step explanation:

One way to find the slope of a line is by putting your line into the equation y=mx+b

In case you don't know m= the slope and b= the y-intercept

If you want to put your equation into y=mx+b; you will need to do rise/run

This means you count how much your line goes up on the y-axis so you rise however many and then you go to the right or left and count until you get to the point that is in line with the y and x axis'.

Also you can use the equation Y2-Y1/X2-X1

You will do that by finding 2 points from the line and take the numbers and make it into Y2-Y1/X2-X1

For Example if you had,

(4,3)(6,8) you would do

8-3/6-4= 5/2 so your m, or your slope would be 5/2

I hope this helps!

If you were asked to find the 87th term in a sequence, which formula would you want to be given?
A) analog form
B) digital form
C) explicit form
D) recursive form,

Answers

If you were asked to find the 87th term in a sequence, the formula you would want to be given is the explicit form. The correct answer to your questions is letter C. It is a formula that allows direct computation of any term for a sequence a1, a2, a3..an

Answer:

C) explicit form

Step-by-step explanation:

Since the explicit form is written in terms of the number of the term, it would be the most useful to find the 87th term. To use the recursive form, you would have to know the 86th term.

PLEASE HELP ME!!!!!!! Estimate the correlation coefficient for each data set. Explain your reasoning.

Answers

The closer the set of data is to a line the closer the correlation coefficient is to 1

in a you can see somewhat of a line so you should pick a value between 0.5 and 0.7

in b you can see a line, the value you should estimate should be greater than 0.9

In c you kinda maybe imagine a line, but worse than a. so you should pick a number between 0.2 and 0.4

Find the area of the regular pentagon if the apothem is 4.9 m and a side is 7.1 m. round to the nearest whole number. 62 m2 34 m2 87 m2 17 m2

Answers

we know that
[Area of the regular pentagon]=5*[side length * apothem] / 2
side length=7.1 m
apothem=4.9 m
then
Area=5*[7.1 * 4.9] / 2-----------> 86.975 m²----------> 87 m²

the answer is 87 m²

Please help me thank you.

Answers

The measure of a circle is 360°. The major arc is that portion of the circle that does not include the 50° minor arc. Hence the measure of the major arc is 310°. You designate the major arc by naming another point on it (in addition to the end points).

The 3rd selection is appropriate.

A rectangular field has a diagonal of 360 feet. One of the side of the field is 160 feet long. What is the perimeter of the field? Enter your answer, rounded to the nearest hundredth, in the box.

Answers

We need to calculate the other triangle side.
Using the Pythagorean Theorem,
3rd side^2 = 360^2 -160^2
3rd side^2 = 129,600 - 25,600
3rd side^2 = 104,000
3rd side = 322.49
Perimeter = 2 * (160 + 322.49)
Perimeter = 964.98 feet

Answer:

Perimeter of rectangle rounded to the nearest hundredth is 964.98 feet.

Step-by-step explanation:

Given : A rectangular field has a diagonal of 360 feet. One of the side of the field is 160 feet long.

To find : What is the perimeter of the field? Enter your answer, rounded to the nearest hundredth, in the box.

Formula used : perimeter = 2* length + 2√[tex]d^{2} -l^{2}[/tex].

Solution : We have diagonal of 360 feet and length = 60 feet .

plugging all the values of d and , l in formula .

perimeter = 2* 160 + 2√[tex]360^{2} -160^{2}[/tex].

perimeter = 320 + 2√[129600 -25600].

perimeter = 964.98 feet = nearest hundredth = 964.98 feet.

Therefore, Perimeter of rectangle rounded to the nearest hundredth is 964.98 feet.

The rectangular room is given by the trinomial x^2+4x-12. What are the possible dimensions of the rectangle? Use factoring. (1 point) (x-6) and (x-2) (x+6) and (x+2) (x-6) and (x+2) (x+6) and (x-2) 17. What is the factored form of the following expression? X^2+2xy-48y^2 (1 point) a. (x+6y)(x-8y) b. (x-6y)(x-8y) c. (x+6y)(x+8y) d. (x-6y)(x+8y) 18. The area of a rectangular art studio is given by the trinomial 24x^2-4x-8. What are the possible dimensions of the studio? Use factoring. a. (3x-2) and (8x-4) b. (3x-2) and (8x+4) (3x-2) and (8x-4) (3x+2) and (8x-4)

Answers

Given that the rectangle is x²+4x-12, the possible sides will be given by:
a]
x²+4x-12
=x²+6x-2x-12
=x(x+6)-2(x+6)
=(x-2)(x+6)
thus the dimensions are (x-2) units (x+6) units

b]
x²+2xy-48y²
factorizing the above is:
x²+8xy-6xy-48y²
=x(x+8y)-6y(x+8y)
=(x+8y)(x-6y)

c]
24x²-4x-8
factoring the above we get:
=4(6x²-x-2)
=4(6x²+3x-4x-2)
=4(3x(x+2)-2(x+2))
=4(3x-2)(x+2)
=(12x-8)(4x+8)

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Which of the following illustrations show atoms of the same element? (Yellow=electrons, red=protons, gray=neutrons). If $7300 is invested in a savings account for which interest is compounded monthly, and if the $7300 turns into $8600 in 2 years, what is the interest rate of the savings account? which state removed a physician's license to practice medicine. what is the intersection points of f(x)=2x+7 and g(x)=x^2-1 Read the following passage from Susan B. Anthony:Sally Ann never failed to locate the trouble or to untangle the yarn. Yet she was never made overseer, and this continued to puzzle Susan.[1]Based on the context, what does the word puzzle most likely mean?piece togetherconfusebreak apartpersuade The sum of r and t is equal to 42. Let r = 25. What is the value of t? Antibodies that act against a particular foreign substance are released by ________. plasma cells t lymphocytes lymph nodes medullary cords What would happen to a monthly payment if the interest rate increased Choose an equation for the relationship between the measures of the segments, angles, and arcs. Melinda goes blowing on Saturday afternoon. She bowls three games nand pays for shoe rental. Define a variable and write an expression to represent the total cost Melinda pays. Then find the total cost if one game cost 4$ two important influences of dissolving a solute in a solution are temperature and ______. Which of the equations below shows the relationship in the table? [X] [15] [5] [3] [1] ------------------------------------------ [Y] [1] [3] [5] [15]] A. y = 15x B. y = x - 14 C. y = x + 2 D. y = 15 x How is Peter, as well as perhaps James, introduced to Jesus Last year, a person wrote 134134 checks. let the random variable x represent the number of checks he wrote in one day, and assume that it has a poisson distribution. what is the mean number of checks written per day? what is the standard deviation? what is the variance? Which of the following cellular materials is solely composed of DNA and proteins? A. ribosomes B. Golgi complex C. chromosomes D. mitochondria There is a 20% probability that a person inoculated with a particular vaccine will get the disease anyway. a county health office inoculates 83 people. What is the probabythat exactly 10 of them will get the disease at some point their lives? Which two of the following tasks would most likely be completed by a biomedical engineer Dennis can load the car in 28 min. If Andy helps him it takes 21 min to load the car how long will it take Andy alone? true Value Hardware buys 200 snow blowers for $90 each to stock the store for the winter. If True Value sells the 200 snow blowers at $120 each, what is the profit? Add the two expressions.6.3x+4 and 1.5x6Enter your answer, in simplified form, in the box.