1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
gulaghasi [49]
2 years ago
10

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 th

is 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?
Mathematics
1 answer:
Olin [163]2 years ago
4 0

Answer:

Read explanation

Step-by-step explanation:

A)The slope is the number before the X so 0.25, this represents the amount of money people have to pay for each mile driven over 150 miles.

B) The y-intercept is the number after the X so 32, this number represents the amount people have to pay rent the car before actually using it.

You might be interested in
Which rule can be used to find the output numbers in this table?
Anton [14]
A. Multiple the input by 11.
7 0
3 years ago
What are the ordered pairs of the
9966 [12]

Start by writing the system down, I will use y to represent f(x)

y=x^2-5x+3\wedge y=-3

Substitute the fact that y=-3 into the first equation to get,

-3=x^2-5x+3

Simplify into a quadratic form (ax^2+bx+c=0),

x^2-5x+6=0

Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,

x^2+x(m+n)+mn=0

which then must factor into

(x+m)(x+n)=0

And the solutions will be m,n.

Clearly for small coefficients like ours 5,6, this is very easy to figure out. To get 5 and 6 we simply say that m=3, n=2.

This fits the definition as 5=3+2 and 6=2\cdot3.

So as mentioned, solutions will equal to m=3, n=2 but these are just x-values in the solution pairs of a form (x,y).

To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.

So the solution pairs are (2,0) and (3,0).

Hope this helps :)

5 0
2 years ago
The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new functio
kap26 [50]

Answer:

The new function is (x + 7)² - 47 ⇒ the 3rd answer

Step-by-step explanation:

* Lets put the function f(x) in the vertex form at first and then make

 the translation

∵ The general form of the quadratic function is

  f(x) = ax² + bx + c

∵ The x-coordinate of the vertex of the function is -b/2a

∵ The y-coordinate of the vertex of the function is f(-b/2a)

- Lets find a , b from the function two find the vertex point

∵ f(x) = x² + 22x + 58

∴ a = 1 , b = 22 , c = 58

∵ x-coordinate of the vertex = -b/2a

∴ x-coordinate of the vertex = -22/2(1) = -11

∵ y-coordinate of the vertex = f(-11)

∴ f(-11) = (-11)² + 22(-11) + 58 = 121 - 242 + 58 = -63

∴ The vertex point is (-11 , -63)

- The vertex form of the quadratic function is f(x) = (x - h)² + k , where

  (h , k) are the coordinates of the vertex point

∵ The vertex point is (-11 , -63)

∴ h = -11 , k = -63

∴ f(x) = (x - -11)² + -63

∴ f(x) = (x + 11)² - 63

* lets revise the rules of the translation

- If the function f(x) translated horizontally to the right  

 by m units, then the new function g(x) = f(x - m)

- If the function f(x) translated horizontally to the left  

 by m units, then the new function g(x) = f(x + m)

- If the function f(x) translated vertically up  

 by n units, then the new function g(x) = f(x) + n

- If the function f(x) translated vertically down  

 by n units, then the new function g(x) = f(x) – n

∵ f(x) will translate 4 units to the right

∴ m = 4

∵ f(x) ⇒ f(x - m)

∴ (x + 11)²  ⇒ (x + 11 - 4)² = (x + 7)²

∵f(x) will translate 16 units up

∴ -63 will add by 16

∴ n = 16

∴ f(x) ⇒ f(x) + n

∵ -63 + 16 = -47

∴ The new function is (x + 7)² - 47

5 0
3 years ago
Read 2 more answers
Let sin A= -3/5 with 270°&lt; A&lt; 360°. Find the following.<br> sin A/2
GREYUIT [131]

Answer:

1/sqrt10

Step-by-step explanation:

1) Find out cosA using formula (cosA)^2+(sinA)^2=1

The module of cosA= sqrt (1- (-3/5)^2)= sqrt 16/25=4/5

So cosA=-4/5 or cosA=4/5.

Due to the condition 270degrees< A<360 degrees, 0<cosA<1 that's why cosA=4/5.

2) Find sinA/2 using a formula cosA= 1-2sinA/2*sinA/2 where cosA=4/5.

(sinA/2)^2= 0.1

sinA= sqrt 0.1= 1/ sqrt10 or sinA= - sqrt 0.1= -1/sqrt10

But 270°< A< 360°, then 270/2°<A/2<360/2°

135°<A/2<180°, so sinA/2 must be positive and the only correct answer is

sin A/2= 1/sqrt10

6 0
3 years ago
8 less than twice a number is twelve .
kvv77 [185]
8 - -2×2=12.............
8 0
3 years ago
Read 2 more answers
Other questions:
  • Key Features of Graphs of Functions - Part 1
    15·2 answers
  • The triangles are similar. Find the value of x.
    15·2 answers
  • 15=3-(z+6) solve the equation and check your solution
    10·2 answers
  • Help asap<br><br><br> Factor completely.<br><br> x^2−5x−24<br><br> Enter your answer in the box.
    5·2 answers
  • Determine the domain and range of the given function.<br> The domain is<br> The range is
    5·2 answers
  • What is the difference<br> between:<br> 1X + 3) = 10 &amp; 1X1 + 3 = 10
    11·1 answer
  • Factor -4 + 8a - 4a^2
    10·2 answers
  • Consider the table of values and the equation, which both represent a function,
    10·1 answer
  • To make purple plum paint, the paint store mixes blue and red paint in a ration of 8:5 if a customer needs 65 gallon of paint ho
    12·1 answer
  • Hi i know im desperate but pls ill give you BIG BIG points…
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!