It costs $32 per day to rent a medium-sized car, plus $0.25 for each mile driven over 150 miles. The equation that represents this situation is y = 0.25x + 32, where y represents the total cost of renting a car, and x represents the number of miles driven over 150 miles.
a.) What is the slope and what does it represent in the context of this problem?

b.) What is the y- intercept and what does it represent in the context of this problem?

Answer:

x = 12

Step-by-step explanation:

equation:

x + 4 = 16

to solve for x, subttract 4 on each side:

x + 4 - 4 = 16 - 4

x = 12

Answer:dont worry :) its right! hit enter!

Step-by-step explanation:

Answer:

Step-by-step explanation:

w' = (1, - 1 ) check

C' = ( 4, 2 ) check

Answer:  h= 5/g−3/2

Step-by-step explanation:

h=  5 over g minus   3 over 2

Answer:

[tex]h\neq -3/2[/tex]

Step-by-step explanation:

Divide both sides by h+3/2;

g(h+3/2)/h+3/2=5/h+3/2

simplify

g=10/2h+3; h[tex]\neq[/tex]-3/2

Answer:

27°

Step-by-step explanation:

I'm assuming you have learned basic trigonometry: SOH CAH TOA. In this diagram to find the angle x we are given the opposite side and the hypotenuse, therefore we will use SOH. sinθ = opp/hyp. Plugging in those values we get sinθ = 5/11 -> θ = sin⁻¹ (5/11) = 27.03569179° = 27°

Answer:

70°, ,have a nice day

Answer:

∠BCO = 70°

Step-by-step explanation:

AO = CO = BO because all radii of the same circle are equal.

∠ACO = 20° because it is an isosceles triangle.

∠BCA = 90° because a triangle with it's hypotenuse being the diameter of a circle is a right triangle.

∠BCA - ∠ACO = ∠BCO

90° - 20° = 70°

∠BCO = 70°

Answer:

6108795

Step-by-step explanation:

To obtain the number of ways the committee can be selected :

4 teachers from the 12 teachers available and 3 students from the 43 students available

Using combinatorics :

12C4 * 43C3

recall :

nCr = n! ÷ (n - r)!r!

Using calculator :

12C4 = 495

43C3 = 12341

12C4 * 43C3

495 * 12341

= 6108795

Answer:

The answer is 16 stones

Step-by-step explanation:

It's 8:16 because

8/1 = 8

and

2 x 8 = 16

To check your answer to see if its correct :

1/2 = 2

16/2=8

Hope this helps!! ;)

Answer:

x ≈ 261 ft

Step-by-step explanation:

Using the sine ratio in the right triangle

sin50° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{200}{x}[/tex] ( multiply both sides by x )

x × sin50° = 200 ( divide both sides by sin50° )

x = [tex]\frac{200}{sin50}[/tex] ≈ 261 ft ( to the nearest foot )

x ≈ 261 ft

that is the answer

Answer:

The penguin will walk 75.15 feet in 45 seconds. It will take the penguin 26.95 seconds to walk 45 feet

Step-by-step explanation:

hope it helps !

Answer: 75 feet

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

10/2 $5 per pack

110/5= 22 packs

How I was taught all of these problems is in terms of r, x, and y. Where sin = y/r, cos = x/r, tan = y/x, csc = r/y, sec = r/x, cot = x/y. That is how I will designate all of the specific pieces in each problem.

#3

Let's start with sin here. [tex]\frac{2\sqrt{5}}{5} = \frac{2}{\sqrt{5}}[/tex] Therefore, because sin is y/r, r = [tex]\sqrt{5}[/tex] and y = +2. Moving over to cot, which is x/y, x = -1, and y = 2. We know y has to be positive because it is positive in our given value of sin. Now, to find cos, we have to do x/r.

cos = [tex]\frac{-1}{\sqrt{5}} = \frac{-\sqrt{5}}{5}[/tex]

#4

Let's start with secant here. Secant is r/x, where r (the length value/hypotenuse) cannot be negative. So, r = 9 and x = -7. Moving over to tan, x must still equal -7, and y = [tex]4\sqrt{2}[/tex]. Now, to find csc, we have to do r/y.

csc = [tex]\frac{9}{4\sqrt{2}} = \frac{9\sqrt{2}}{8}[/tex]

The pythagorean identities are

sin^2 + cos^2 = 1,

1 + cot^2 = csc^2,

tan^2 + 1 = sec^2.

#5

Let's take a look at the information given here. We know that cos = -3/4, and sin (the y value), must be greater than 0. To find sin, we can use the first pythagorean identity.

sin^2 + (-3/4)^2 = 1

sin^2 + 9/16 = 1

sin^2 = 7/16

sin = [tex]\sqrt{7/16}[/tex] = [tex]\frac{\sqrt{7}}{4}[/tex]

Now to find tan using a pythagorean identity, we'll first need to find sec. sec is the inverse/reciprocal of cos, so therefore sec = -4/3. Now, we can use the third trigonometric identity to find tan, just as we did for sin. And, since we know that our y value is positive, and our x value is negative, tan will be negative.

tan^2 + 1 = (-4/3)^2

tan^2 + 1 = 16/9

tan^2 = 7/9

tan = -[tex]\sqrt{7/9} = \frac{-\sqrt{7}}{3}[/tex]

#6

Let's take a look at the information given here. If we know that csc is negative, then our y value must also be negative (r will never be negative). So, if cot must be positive, then our x value must also be negative (a negative divided by a negative makes a positive). Let's use the second pythagorean identity to solve for cot.

1 + cot^2 = [tex](\frac{-\sqrt{6}}{2})^{2}[/tex]

1 + cot^2 = 6/4

cot^2 = 2/4

cot = [tex]\frac{\sqrt{2}}{2}[/tex]

tan = [tex]\sqrt{2}[/tex]

Next, we can use the third trigonometric identity to solve for sec. Remember that we can get tan from cot, and cos from sec. And, from what we determined in the beginning, sec/cos will be negative.

[tex](\frac{2}{\sqrt{2}})^2[/tex] + 1 = sec^2

4/2 + 1 = sec^2

2 + 1 = sec^2

sec^2 = 3

sec = -[tex]\sqrt{3}[/tex]

cos = [tex]\frac{-\sqrt{3}}{3}[/tex]

Hope this helps!! :)

Answer:

sin(θ)=√7/4

tan(θ)= - √7/3

Step-by-step explanation:

c^2= √(4^2-(-3^2))

c^2= √(16-9)

c^2= √7

sin(θ)= opp/hyp=√7/4

tan(θ)= (opp )/adj= - √7/3

Answer:

The Y intercept is two

Step-by-step explanation:

The y intercept is the point on a graph where the graph crosses the y axis.

Basically, it is the value of y when x is 0 is (x,y)

Looking at the attached graph, our y intercept is (0,2), meaning that the y-intercept is 2.

The answer is: the Y-INTERCEPT is 2

Answer:

x=-1

Step-by-step explanation:

because 2^3 is 8

and when you do -1+4 you get left with 3

so x=-1

Answer:

x = -1

Step-by-step explanation:

Answer:

p = 5k - 40

Step-by-step explanation:

Since we're finding the profit (p), it's not the last answer choice because it's finding kids (k).

Because we have to take out from her profit whatever Katie spent, we would have -40.

Because she'd charging $5 per kid, or $5 per k, we would have 5k.

So now we know the profit is whatever she makes, then minus whatever she spent. So:

p = 5k (what she makes) - 40 (what she spent)

p = 5k - 40

Answer:

O p = 40k + 5

Step-by-step explanation:

Katie is raising money to buy  a dog. She starts a  neighborhood babysitting service.

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

Answer:

Step-by-step explanation:

With 22% decrease the value after the year is:

To find 78% we need to multiply the current value by 0.78.

The same number is multiplied each year to find the decreased value.

The formula for the car would be:

The decay factor is 0.78

Correct choice is B

Answer:

m. m, .;.

Step-by-step explanation:

Answer:

x=d/a - by/ac

Steps:

ax+by/c=d

(cax+by)/c=d

cax+by=cd

cax=cd-by

x=(cd-by)/ca

x=cd/ca - by/ca

x=d/a - by/ac

Answer:

3.95

Step-by-step explanation:

R = 7.9/2 = 3.95

Answer:

Step-by-step explanation:

rate of change is the slope of the line

plot the data and calculate the slope or simple find the delta cost divided by the delta people

    (cost x - cost y) / (people x - people y)  = rate of change

you can pick any cost as long as you use the coresponding people

    (19.75 - 7.90) / (5 - 2)  = rate of change

    ( 11 .85) / (3)   = rate

     3.95 = rate

try it for different cost and people and see if you get the same rate, it looks linear to me

Answer:

The answer is C.

Step-by-step explanation:

Answer:

I cant see picture

Step-by-step explanation:

Answer:

m = 1; n = 0.5

Step-by-step explanation:

5m - 2n = 4; m - 4n = - 1

It's might be answer C but im not sure :\

Answer:

Boys= 12

Girls= 6

Step-by-step explanation:

Let no: of girls be 'x'

No: of boys= 2x

boys after= 2x-6

girls after = x+6

according to the question,

2(2x-6)=x+6

4x-12=x+6

3x=18

x=6

No: of girls at first= 6

No: of boys at first=2*6=12

Answer:

$ 20,189.65

Step-by-step explanation:

Jake's parents want $100,000 at the end of 40 years. They put their money in an account that yields 4% per year compounded continuously. How much money should jakes parents deposit?

From the above question, we are to find the Principal. The formula for Principal compounded continuously =

P = A / e^rt

Where:

A = Amount after time t = $100,000

r = Interest rate = 4%

t = Time in years = 40 years

First, convert R percent to r a decimal

r = R/100

r = 4%/100

r = 0.04 per year,

Then, solve our equation for P

P = A / e^rt

P = 100,000.00 / e ^(0.04×40)

P = $ 20,189.65

Therefore, the amount Jake's parents should invest = $ 20,189.65

Answer:

1

Step-by-step explanation:

3 divided by 1/3 is 9, and 9-9=0

0+1=1

1

Step-by-step explanation:

Answer:

4.90m

Step-by-step explanation:

A sector of a circle of diameter 11 cm is formed from an angle of size 51. Find the length of the arc rounded to two decimal places

Length of an arc = 2πr(θ/360)

(θ) = 51°

r = Diameter/2 = 11/2

= 5.5

Length of an arc = 2 × π × 5.5(51/360)

= 4.89565m

Approximately = 4.90m

Answer:

a trapezoid

Step-by-step explanation:

Answer:

D: Trapezoid.

Step-by-step explanation:

Because you can see that the shape has only one set of parralel sides it is a trepezoid.