3 A trainer for a soccer team keeps track of the amount of water players consume during practice. The trainer observes that the average amount of water consumed by the team is a linear function of the temperature. The graph and equation for this function are shown. Choose True or False for each statement. True у 7.8 a. For every degree increase in temperature, the average amount of water consumed increases by 0.0875 gallons. False 7.2 b. When the temperature is below 74 degrees, the team consumes no water. Water (gal) True 6.6 64 False 6.0 0 X True 0 74 76 78 80 82 84 86 88 90 92 94 C. When the temperature is 86 degrees, the team consumes somewhere between 7 gal and 7.2 gal of water. Temperature (°F) False w = 0.0875t – 0.45, where w represents the average amount of water consumed, and t represents the temperature on that day. True d. The amount of water consumed by the team decreases by 0.45 gallons for every degree the temperature falls, False S​

Answer:

j = 2/3

Step-by-step explanation:

-1/3 = -1/2 j

Multiply each side by -2

-1/3 * -2 = -1/2 j * -2

2/3 =j

Answer:

j = 2/3

Step-by-step explanation:

-2/3 = -j

j = 2/3

Answer:

[tex]\cos(A + B) = \frac{23}{265}[/tex]

Step-by-step explanation:

Given

[tex]\tan A=\frac{28}{45}[/tex]

[tex]\cos B=\frac{3}{5}[/tex]

Required

[tex]\cos(A+B)[/tex]

In trigonometry:

[tex]\cos(A+B) = \cos\ A\ cosB - sinA\ sinB[/tex]

We need to solve for cosA, sinA and sinB

Given that:

[tex]\tan A=\frac{28}{45}[/tex] and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),

So, we have:

[tex]x =28[/tex] and [tex]y = 45[/tex]

For this angle A, we need t calculate its hypotenuse (z).

Using Pythagoras,

[tex]z^2 = x^2 + y^2[/tex]

[tex]z = \sqrt{x^2 + y^2[/tex]

[tex]z = \sqrt{28^2 + 45^2[/tex]

[tex]z = \sqrt{2809[/tex]

[tex]z = 53[/tex]

From here, we can calculate sin and cos A

[tex]\sin A= \frac{opposite}{hypotenuse}[/tex] and [tex]\cos A= \frac{adjacent}{hypotenuse}[/tex]

[tex]\sin A= \frac{x}{z}[/tex]

[tex]\sin A= \frac{28}{53}[/tex]

[tex]\cos A= \frac{y}{z}[/tex]

[tex]\cos A= \frac{45}{53}[/tex]

To angle B.

Give that

[tex]\cos B=\frac{3}{5}[/tex] and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),

So, we have:

[tex]a = 3[/tex] and [tex]b = 5[/tex]

For this angle B, we need to calculate its opposite (b).

Using Pythagoras,

[tex]c^2 = a^2 + b^2[/tex]

[tex]5^2 = 3^2 + b^2[/tex]

[tex]25 = 9 + b^2[/tex]

Collect like terms

[tex]b^2 = 25 - 9[/tex]

[tex]b^2 = 16[/tex]

[tex]b = \sqrt{16[/tex]

[tex]b = 4[/tex]

From here, we can calculate sin B

[tex]\sin B= \frac{opposite}{hypotenuse}[/tex]

[tex]\sin B = \frac{b}{c}[/tex]

[tex]\sin B = \frac{4}{5}[/tex]

Recall that:

[tex]\cos(A+B) = \cos\ A\ cosB - sinA\ sinB[/tex]

and

[tex]\cos B=\frac{3}{5}[/tex]      [tex]\sin B = \frac{4}{5}[/tex]       [tex]\sin A= \frac{28}{53}[/tex]      [tex]\cos A= \frac{45}{53}[/tex]

[tex]\cos(A + B) = \frac{45}{53} * \frac{3}{5} - \frac{28}{53} * \frac{4}{5}[/tex]

[tex]\cos(A + B) = \frac{135}{265} - \frac{112}{265}[/tex]

[tex]\cos(A + B) = \frac{135-112}{265}[/tex]

[tex]\cos(A + B) = \frac{23}{265}[/tex]

The value of [tex]\cos (A+B)[/tex] is [tex]-\frac{96}{265}[/tex].

Trigonometrically speaking, the sine, cosine and tangent of an angle are described by the following formulas:

[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (1)

[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (2)

[tex]\tan \theta = \frac{y}{x}[/tex] (3)

Where:

And we have the following trigonometric identity for the cosine of the sum of angles:

[tex]\cos (A+B) = \cos A\cdot \cos B - \sin A \cdot \sin B[/tex] (4)

By (1) and (2), we rewrite (4):

[tex]\cos (A+B) = \frac{x_{A}\cdot x_{B}}{\sqrt{x_{A}^{2}+y_{A}^{2}}\cdot \sqrt{x_{B}^{2}+y_{B}^{2}}} - \frac{y_{A}\cdot y_{B}}{\sqrt{x_{A}^{2}+y_{A}^{2}}\cdot \sqrt{x_{B}^{2}+y_{B}^{2}}}[/tex]

If we know that [tex]x_{A} = 28[/tex], [tex]y_{A} = 45[/tex], [tex]x_{B} = 3[/tex] and [tex]y_{B} = 4[/tex], then the cosine for the sum of angles is:

[tex]\cos (A+B) = \frac{28\cdot 3}{\sqrt{28^{2}+45^{2}}\cdot \sqrt{3^{2}+4^{2}}}-\frac{45\cdot 4}{\sqrt{28^{2}+45^{2}}\cdot \sqrt{3^{2}+4^{2}}}[/tex]

[tex]\cos (A+B) = -\frac{96}{265}[/tex]

The value of [tex]\cos (A+B)[/tex] is [tex]-\frac{96}{265}[/tex].

We kindly invite to check this question on trigonometric identities: https://brainly.com/question/24836845

Answer:

x = 8

Step-by-step explanation:

7x-3x= 32

4x=32

/4    /4

x= 8

Answer:

1.) $1

2.)$4

3.)$12

4.)3/4

Step-by-step explanation:

32(.5)=16

she had 16 left after lunch. 16(.25)=4

16-4=12

1/2=2/4

2/4+1/4=3/4

Answer:

1) lunch 16

2) coffee 4

3) 12

4) 3/4ths or .75 or 75%

Answer:

I think its A

Step-by-step explanation:

Please mark brainliest

Answer:

(f*g)(5.7)= -452.6, hopefully that answers your question

Answer:

no solution

Step-by-step explanation:

y = -2x + 3

6x + 3y = -3

the substitution method means you plug one equation into the next, because the first equation gives us a solution for y we can go ahead and plug that into y of the second equation

6x + 3(-2x + 3) = -3

6x - 6x + 9 = -3

9 = -3

which is false meaning that there are no solutions and the lines don't touch at any point

Answer:

10,15

Step-by-step explanation:

Answer:

AC=39

Step-by-step explanation:

-x+25=3(2x-8)

-x+25=6x-24

49=7x

x=9

AC = 2(-9+25)=-11+50=39

Answer:

He makes $1 every 2 minutes

Step-by-step explanation:

If you break it down 60 minutes is in an hour and he works for 3 hours total so you multiply 60×3 which is 180 that's how many minutes he works for. Then you take the money he made and take the minutes and divide it by the money 180÷90=2 so he make $1 every 2 minutes

Answer:125 students

Step-by-step explanation:if 5 out of every 32 students bikes

5=32

X=800

800(5)=4000

4000/32=125

Answer:I'm pretty sure its -7

Step-by-step explanation:

Answer:

286.16

Step-by-step explanation:

To find the area, you simply multiple length by width. And the product of 29.2 and 9.8 is 286.16

Answer:

Like terms have to have the same variables and powers

Answer:

and powers

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hey! I also asked this question before lol! Someone solved it so this is not my work:

"N+ 1 = 3+2/2

The answer is 3

This is a odd number"

Hope this helps ∞<3

Answer:

x = 3/4

y = 2.5

Step-by-step explanation:

No there is just one.

Equate the ys

-2/3 x + 3 = 2/3 x + 2                        Add 2/3 x to both sides

3 = 2/3 x + 2/3x + 2                          Combine

3 = 4/3 x + 2                                     Subtract 2

3-2 = 4/3 x                                        Multiply by 3

1 * 3 = 4x                                          Divide by 4

3/4 = x

====================

y = 2/3 x + 2

y = 2/3 * 3/4 + 2

y = 6/12 + 2

y = 1/2 + 2

y = 2 1/2

y = 2.5

Answer:

115

Step-by-step explanation:

Answer:

y=1+2/3x

Step-by-step explanation:

1 is y intercept

2/3 is slope

Answer:

-145/88z+4

Step-by-step explanation:

Answer: -4/11z - 4

Step-by-step explanation: We can combine like terms to simplify the expression 2/11z - 5/11z + 4 - 1/11z - 8. The terms 2/11z, -5/11z, and -1/11z are like terms because they all have the same variable part z. When we add them together, we get (2 - 5 - 1)/11z = -4/11z. The constants 4 and -8 are also like terms. When we add them together, we get 4 + (-8) = -4. So the simplified expression is -4/11z - 4.

Answer:

A

Step-by-step explanation:

Geometry has nothing to do with driving.

Answer:

there is a greater chance that she selects a even number because there are 4 even numbers and 3 odd numbers

Answer:

D.(x,y) → (x,-y)

Step-by-step explanation:

If it is reflected across the X-axis, then the X variable will stay the same and the Y variable will change.

I hope this helps!! Good luck!!

(Sorry if I'm wrong! It's kinda awkward because it is placed in the second quadrant instead of the first.)

Answer:

its d

Step-by-step explanation:

Answer:

Gravity.

Step-by-step explanation:

Gravity is what holds the planets in orbit around the sun and what keeps the moon in orbit around Earth. The gravitational pull of the moon pulls the seas towards it, causing the ocean tides. Gravity creates stars and planets by pulling together the material from which they are made.

This is actually a physics problem, but the force of Gravity keeps us from flying into the sky. Gravity is the force by which a planet or other body draws objects toward its center. This force gives us a tendency to remain on the ground and not to float off into the atmosphere.

Answer: -2

Step-by-step explanation: 4-8= -4 then it ends up being -2r-4=0

Then you add 4 to 0 so -2r=4 then divide

Answer:

where's the graph rn ?

Step-by-step explanation:

is this question complete?

Answer:

you didn't add options for the sentences, but

x-5 =-10 (add 5 to both sides to get x alone)

x= -5

so anything that has to do with x equaling - 5 would be correct

after reading through the sentences, the correct answer is:

a number subtracted from five is equal to negative ten

because that sentence is saying " 5 - n = - 10 " and that's not what's happening

Step-by-step explanation:

Answer:

x = -2.5 or -5/2

Step-by-step explanation:

Answer:

$200 and $450

Step-by-step explanation:

We can start by assigning variables to our unknowns.

Our unknowns are the price for a DVD player and the price for a television.

x= price of a television

y= price of a DVD player

Next, let's translate the given information into a system of equations.

two televisions and three DVD players for $1750

2x+3y=1750

four televisions and one DVD player for $1250

4x+y=1250

Since the instructions did not specify, I will use substitution to solve, however you can also use elimination.

First, from the second equation, we subtract 4x from both sides.

4x+y-4x=1250-4x

y=1250-4x

Now we plug 1250-4x for y in the first equation.

2x+3y=1750

2x+3(1250-4x)=1750

Distribute.

2x+3*1250-3*4x=1750

Simplify.

2x+3750-12x=1750

Combine like terms.

-10x+3750=1750

Subtract 3750 from both sides

-10x+3750-3750=1750-3750

-10x=-2000

Divide both sides by -10

x=200

A television costs $200.

Now using that, we can plug that into one of the original equations. I'll use the second one.

4x+y=1250

4(200)+y=1250

800+y=1250

Subtract 800 from both sides.

y=450

A DVD player costs $450

You can plug those values back into the other equation (the first one) to double-check if you'd like as well.

Answer:

y=2

Step-by-step explanation: