What is the slope between the points (-2,4) and (-3,5)

the graph shows your budget and the total cost of x gallons of gasoline and a car wash you want to determine the possible amount

Yuki888 [10]

Answer:

Part a) The budget is $40

Part b) The cost of one gallon of gasoline is $3.55 and the cost of the car wash is $8

Part c) $x \leq 9.01\ gal$

Part d) see the explanation

Step-by-step explanation:

The complete question in the attached figure

Part a) What is your budget?

The budget is given by the equation

y=40

therefore

The budget is $40

Part b) How much does a gallon of gasoline cost? how much does a car wash cost?

Let

y ------> the cost of a gallon of gasoline plus the cost of a car wash

x -----> the amount of gasoline in gallons

we have

y=3.55x+8

In this problem

For x=0

y=3.55(0)+8=8

The y-intercept is the cost of the car wash

so

The cost of the car wash is $8

Find the cost of one gallon of gasoline

we know that

The slope of the linear equation is

m=$3.55 per gallon

therefore

The cost of one gallon of gasoline is $3.55

Part c) Write an inequality that represent the possible amounts of gasoline you can buy

we have

$3.55x+8 \leq 40$

Solve for x

$3.55x \leq 40-8$

$3.55x \leq 32$

$x \leq 9.01\ gal$

Part d) Use the graph to estimate the solution of the inequality in part c)

we have the system

y=40

y=3.55x+8

The solution of the system is the intersection point both graphs

Looking at the graph the intersection point is about (9,40)

That means ----> The maximum amount of gasoline you can buy with the budget is about 9 gallons

7 0

2 years ago

A system of equations is given below. y=1/2x-3 and -1/2x-3. Which of the following statements best describes the two lines?

pantera1 [17]

"They have different slopes but the same y-intercept, so they have one solution" is the statement which best describes the two lines.

Answer: Option D

<u>Step-by-step explanation:</u>

Given equations:

$y=\left(\frac{1}{2} \times x\right)-3$

$y=\left(-\frac{1}{2} \times x\right)-3$

As we know that the slope intercept form of a line is

y = m x + c

So, from equation 1 and equation 2 we can see that

$m_{1}=\frac{1}{2} \quad \text { and } c_{1}=-3$

$m_{2}=-\frac{1}{2} \text { and } c_{2}=-3$

So, from the above expressions, we can say that both lines have different slopes but have same y – intercept with one common solution when x = 0.

4 0

3 years ago

Read 2 more answers

THIS IS MULTIPLE CHOICE!

Troyanec [42]

Answer:

there is a cluster from 1-4

there is a gap from 5-7

The spread is from 1-8

Step-by-step explanation:

These are all true if you look... there is a bunch from 1-4, there is none from 5-7, and all of them are within 1-8, but the highest amount isn't at 3.

7 0

3 years ago

I need help please take a look at this

Reika [66]

Answer:

$y = x-1$

$-x+\dfrac32=-y\\\implies y=x-\dfrac32$

The equations have the same slope but different y-intercepts. This means the lines are parallel and there is no solution (since they do not intersect).

5 0

2 years ago

Read 2 more answers

a current of 9 amps flows through a circuit lamp. which formula could be used to determine the resistance of the circuit when th

maxonik [38]

As, the formula of power=P = V*I
By using ohms law( V=I*R)
The formula of power become
P= I² * R
342/(9)²=R
R= 4 Ω

5 0

3 years ago