A new hybrid car has a 18-gallon gas tank. On one tank of gas, the owner can drive 540 miles. The number of miles traveled varies directly with the number of gallons of gas the car uses.

a. Write an equation that relates the number of miles traveled with the number of gallons of gas used.

b. How many miles can the owner travel on 12 gallons of gas?

Answers

Answer 1
To find the amount of miles/gallon, we have 540 miles/18 gallons=30 miles/gallon. As we add 30 miles for every gallon, the amount of miles traveled is 30*x (e.g. if x is 1 then 0+30=30 and if x is 2 then 30+30 (2 times)=60) with x being the amount of gallons. For b, we just plug 12 in for x to get 20*12=360

Related Questions

The length of a rectangle is 4 in longer than its width. if the perimeter of the rectangle is 28 in , find its area.

Answers

The area is 45 inches squared

Show why the function f(x) = 3rad x is not differentiable at x=0

Answers

[tex]f(x) = 3\sqrt{x}[/tex]
[tex]f'(x) = -\frac{3}{2\sqrt{x}}[/tex]

When x = 0, f'(0) becomes undefined. Thus, we know that there is no derivative at x = 0. You could also show it by taking the limits, which is the fundamental of calculus. Show that as x approaches 0 from the negative side is not equal to the value as x approaches 0 from the positive side.

What this tells us is that there is no uniquely distinct point that satisfies the continuity of the curve in order for the graph to have a specific gradient at x = 0; thus, this means there is no gradient at x = 0, and hence, the function is not differentiable at x = 0

does this equation describe a linear function
Y=2/x-28

Answers

no soulation would be it
it's not a straight line so it's not a function :3


Which of the following is more than 0.35 but less than 0.41
A.
8/25
B.
3/10
C.
2/5
D.
9/26

Answers

its B because 3/10ths is a little bit more than 0.35, but way less than 0.41

Answer:

C. [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Let x be the number which is more than 0.35 but less than 0.41,

⇒ 0.35 < x < 0.41

[tex]\implies \frac{35}{100}< x < \frac{41}{100}[/tex]

[tex]\implies \frac{7}{20} < x < \frac{41}{100}[/tex]

∵ Only [tex]\frac{2}{5}[/tex] is between [tex]\frac{7}{20}[/tex] and [tex]\frac{41}{100}[/tex],

Hence, option C is correct.

The top of a manhole cover is shaped like a circle. The area of the manhole cover is 380 square inches. What is the circumference of the manhole cover, to the nearest inch? 

Answers

need to find the radius first

 area = pi*r^2

380 = PI *r^2

380/PI = r^2

r^2 = 121

r = sqrt(121) = 11 inches

 radius is 11 inches


 now calculate circumference:

 c = 2*PI*r

 C = 2 * 3.14 * 11

circumference = 69.08 = 69 inches

How would I solve -x^2 = -36?

Answers

Let's solve your equation step-by-step.
-x^2 = -36

Step 1: Divide both sides by -1.
-x^2/-1 = -36/-1
x^2 = 36

Step 2: Take square root.
x=±√36
x=6 or x=−6

Answer: x=6 or x=−6

I hope this helps you! :)


 the answer to your question is x=6

If f(x)=-2(5)^x what is f(2)

Answers

What the question is asking is for you to evaluate the function f at x=2, which means you'll need to substitute the x in the function for 2, giving you:

f(2) = -2(5)²

Which of the following characteristics of a parallelogram leads to the conclusion that every square can always be classified as a parallelogram? Select all that apply.

four equal sides
two pair of opposite equal angles
bisecting diagonals
two pair of opposite parallel sides

Answers

The properties of a parallelogram that lead to the conclusion that a square is a type of parallelogram are 2nd, 3rd and 4th options.

Answer:

two pair of opposite equal angles

bisecting diagonals

two pair of opposite parallel sides

Jill is 7 kilometers away from joe. both begin to walk toward each other at the same time. jull walks at 1.5 kilometers per hour. they meet in 2 hours. how fast is joe walking?

Answers

it would be 21 kilometers

If a sports car is traveling at 95 miles per hour, how long would it take the sports car to overtake a family car traveling at 35 miles per hour that left the same starting point 4.5 hours earlier?

Answers

distance = speed * time
d = st

The sports car travels d distance for t time at speed, s, 95 mph until it overtakes the family
car.
The equation for the sports car is
d = 95t

The family car travels the same distance, d, but since it left 4.5 hours earlier  than the sports car, it travels for t + 4.5 time until it is overtaken. It travels at speed, 35 mph.
The equation for the family car is
d = 35(t + 4.5)

We solve the two equations as a system of equations.

d = 95t
d = 35(t + 4.5)

Since d = d, set the right sides of the equations above equal to each other.

95t = 35(t + 4.5)

95t = 35t + 157.5

60t = 157.5

t = 2.625

The answer is 2.625 hours, or 2 hours, 37 minutes, and 30 seconds.

Check:
In 2.625 hours, the sports car travels: 95 mph * 2.625 h = 249.375 miles
The family car traveled 2.625 hours plus the extra 4.5 hours, or 7.125 hours.
In 7.125 hours, the family car travels 35 mph * 7.125 h = 249.375 miles.
The cars have traveled the same distance 2.625 hours after the sports car left, so our answer is correct.

If number is added to its square, the result is 56. find the number.

Answers

Answer:

  -8 or +7

Step-by-step explanation:

Let x represent the number. The the problem statement tells us ...

  x² + x = 56

  x² +x -56 = 0 . . . . . subtract 56 to put into standard form

  (x +8)(x -7) = 0 . . . . factor

Solutions to the equation are values of x that make the factors zero:

  x = -8 . . . or . . . x = +7

The number could be -8 or +7.

_____

Check

For x = -8, the square is (-8)² = 64. Adding -8 to that gives 64-8 = 56.

For x = 7, the square is 7² = 49. Adding 7 to that gives 49+7 = 56.

At tennis practice, Tim practices his backhand and his serve at least 2 hours each day. He works less on his backhand than his serve and practices his serve more than 1/2 hour daily.
Which system of inequalities represents Tim’s daily tennis practice if x represents the number of hours spent practicing his backhand and y represents the number of hours practicing his serve?
 

The images below are the possible answers,


Answers

He practices his backhand(x) and serve(y) AT LEAST(≥) 2 hours each day
x+y≥2

He practices his backhand(x) LESS THAN(<) his serves(y)
x<y

He practices his serves(y) MORE THAN(>) .5 hours
y>.5

Answer:

[tex]\left\{\begin{matrix}x+y\geq 2\\ x< y\\ y> \frac{1}{2}\end{matrix}\right.[/tex]

Step-by-step explanation:

Let  x represents the number of hours spent practicing his backhand

Let y represents the number of hours practicing his serve.

Since we are given that Tim practices his backhand and his serve at least 2 hours each day i.e. he practices his backhand and serves for two hours or more than two hours

⇒ x+y≥2 --(a)

We are also given that He works less on his backhand than his serve

⇒x < y --(b)

And we are also given that he practices his serve more than 1/2 hour daily.

⇒ y > 1/2 --(c)

Thus the inequalities are :

[tex]\left\{\begin{matrix}x+y\geq 2\\ x< y\\ y> \frac{1}{2}\end{matrix}\right.[/tex]

Thus the Option C is correct .




WHO IS GOOD AT MATH!!!!! Solve this problem.
326-9²+32= ?

Answers

277; You want to use the order of operations so first, figure out 9 squared which is 81 so you take 326-81+32 , 326-81=245 then 245+32=277

5,550 divide 10 to the power of 3

Answers

This would be 5.55

5550÷10^3=5.55

Hope this helps

The solution involves dividing 5,550 by 1,000, which gives 5.55. The expression 10³ represents 1,000, simplifying the division. Therefore, 5,550 divided by 10 to the power of 3 equals 5.55.

To solve the problem 5,550 divided by 10 to the power of 3, follow these steps:

First, understand that 10 to the power of 3 is equivalent to 10³.Calculate 10³: 10 × 10 × 10 = 1,000.  Now, divide 5,550 by 1,000: 5,550 ÷ 1,000 = 5.55.

Therefore, 5,550 ÷ 10³ = 5.55.

what is w reduced by 22? f(w)=

Answers

w reduced by 22 means that 22 will be subtracted from every w - value.

So, to every w-value corresponds a value equal to w - 22.

Using the notation of functions, w is the independent variable or input and f(w) is the function that returns the dependent value or output:

inpunt       otuput

w               f(w) = w - 22

Answer: f(w) = w - 22

5.Thomas walked 1 1/4 miles from his home to his school. Jackson walks 1 2/3 miles from his home to work. How much farther does Jackson walk to school than Thomas?

Answers

Jackson walks 5/12 miles farther than Thomas to work. So, Jackson walks approximately [tex]\( \frac{5}{12} \)[/tex] miles farther than Thomas.

To find out how much farther Jackson walks to work than Thomas, we need to subtract the distance Thomas walks from the distance Jackson walks.

Thomas walks 1 1/4 miles, which is equivalent to 5/4 miles. Jackson walks 1 2/3 miles, which is equivalent to 5/3 miles.

To subtract fractions, we need a common denominator, which in this case is 12. So, 5/3 is equivalent to 20/12, and 5/4 is equivalent to 15/12.

Now, subtracting, we get 20/12 - 15/12 = 5/12 miles.

Therefore, Jackson walks 5/12 miles farther than Thomas.

write an expression for the quotient of a number and 5 decreased by 4

Answers

q=x/5-4

let me know if you have any questions

After 2 months on a diet, John’s weight dropped from 168 pounds to 147 pounds. By what percent did John’s weight drop?

Answers

Final answer:

John's weight dropped by 12.5%.

Explanation:

To calculate the percent by which John's weight dropped, we need to find the difference between his initial weight and final weight, and then divide that difference by his initial weight. We can then multiply the result by 100 to express it as a percentage.

Initial weight = 168 pounds
Final weight = 147 pounds

Difference = 168 - 147 = 21 pounds

Percent drop = (Difference / Initial weight) x 100

Percent drop = (21 / 168) x 100 = 12.5%

Therefore, John's weight dropped by 12.5%.

Final answer:

To calculate the percent by which John's weight dropped, subtract his final weight from his initial weight, and divide the difference by his initial weight, then multiply by 100. John's weight dropped by 12.5%.

Explanation:

To calculate the percent by which John's weight dropped, you need to find the difference between his initial weight and his final weight, then divide that difference by his initial weight and multiply by 100.

Difference in weight = Final weight - Initial weight = 147 - 168 = -21 Percent weight drop = (Difference in weight / Initial weight) * 100 = (-21 / 168) * 100 = -12.5%

So, John's weight dropped by 12.5%.

PLEASE HELP QUICK I'M OFFERING 12PTS AND BRAINLIEST ANSWER
what is the solution set for the open sentence with the given replacement set w^2 + 9 = 6w, (0,3,6,9)

Answers

do you mean solve it 

At Chelsea's workplace, 30 people drink 2 cups of coffee a day on average. A pot of coffee has 10 cups of coffee. How many pots of coffee are needed each day?

Answers

6 pots would be the answer. 
30*2=60
1 pot=10
60 divided by 10 = 6

6 pots

6 pots

6 pots

6 pots

What is the value of x?

Answers

the answer would be 35 because you take 120 and add 25 and get 145. then because it can make a straight line you do 180-145 and that equals 35.

is 3.774447444744474447444 a rational number

Answers

No it is an irrational number because it is a decimal with repeating numbers.

Seth is reading a long novel. if he reads 45 pages per hour, how many hours will it take him to read 585 pages?

Answers

It will take Seth 13 hours to read the novel.
This is true because:
You need to divide 585 by 45, and you get the answer, 13.

Find the missing measures for the rectangle.

l = _?_
w = 2 cm
A = _?_
P = 25 cm

A) 12.5 cm; 25 cm2

B) 10.5 cm; 21 cm2

C) 12.5 cm; 21 cm2

D) 10.5 cm; 25 cm2

Answers

P = 2(L + W)
P = 25
W = 2

25 = 2(L + 2)
25 = 2L + 4
25 - 4 = 2L
21 = 2L
21/2 = L
10.5 = L.......so ur length is 10.5 cm

A = L * W
A = 10.5 * 2
A = 21 cm^2

so ur answer is B. 10.5 cm, and 21 cm^2

How to find the perimeter of a polygon with vertices

Answers

Step 1 Draw the triangle in a coordinate plane by plotting the vertices and connecting them. Step 2 Find the lengths of the base and height.
Final answer:

To find the perimeter of a polygon with vertices, calculate the sum of the lengths of all the sides of the polygon by taking the distance between each pair of consecutive vertices and adding them together.

Explanation:

To find the perimeter of a polygon with vertices, you need to calculate the sum of the lengths of all the sides of the polygon. The perimeter is the distance around the polygon. You can do this by taking the distance between each pair of consecutive vertices and adding them together. For example, if you have a triangle with vertices A, B, and C, you would calculate the length of AB, BC, and AC, and then add these lengths together to find the perimeter of the triangle.

Learn more about perimeter of a polygon here:

https://brainly.com/question/15387363

#SPJ12

At 1 P.M., there were 16 seagulls on the beach. At 3p.m., there were 40 seagulls. What is the constant rate?

Answers

at 1 p.m. there were 16 seagulls....at 3 p.m. there were 40 seagulls....that means in 2 hrs (from 1 to 3) there was an increase of (40 - 16) = 24 birds....
24 birds in 2 hrs = 24/2 = 12 birds per hr....ur constant rate is 12 per hr

BRAINLIESTTTT!!!

1. Which of the following statements best describes the graph of x + y = 4?

It is a line which intersects the x-axis at (4, 4).
It is a line which intersects the y-axis at (4, 4).
It is a line joining the points whose x- and y-coordinates add up to 8.
It is a line joining the points whose x- and y-coordinates add up to 4.

Answers

Problem 1

A is false because any point on the x axis will have y = 0
B is false because any point on the y axis will have x = 0
C is false; the coordinates add up to 4
D is the only thing left. It's true since x+y = 4 indicating that the coordinates add up to 4

Answer: choice D

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

Problem 2

You're close but the answer is actually choice C. The shaded region is below the slanted line so we'll have a "less than or equal to" sign instead of a "greater than or equal to" sign for the first inequality.

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

Problem 3

Using geogebra (see attached image) I'm getting the graph that matches with choice A

So it looks like you have the correct answer. Nice job.

How do you solve this equation

Answers

Answer:

  -4

Step-by-step explanation:

Use your knowledge of multiplication facts.

  [tex]\sqrt[3]{-64}=\sqrt[3]{(-4)^3}=-4[/tex]

__

Your calculator may be able to do this for you.

[11 (y- 10)] = (4y- 5) what is y

Answers

[11(y-10)=(4y-5)

11y-110 = 4y -5
    +110       +110
11y = 4y + 105
-4y   -4y
7y = 105

y= 15

Please help!! Rewrite the expression as the product of two binomials. What are the two binomials for the expression? x(x-8)-9(x-8)

Answers

that would be (x-9) (x-8)
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