A family has a hybrid car that gets 40 miles per gallon (mpg) and a pickup truck that gets 17 mpg. They drive at least 500 miles per week using both vehicles but don't want to use more than 20 gallons of gas. Make a recommendation for using each vehicle. Part A Write an expression that represents the total amount of gasoline used. Then write an inequality to show the maximum amount of gasoline that the family wants to use. Define the variables and list any constraints on the variables.

Answers

Answer 1

Answer:

[tex]Z=x+y[/tex]

[tex]x+y<20[/tex]

Step-by-step explanation:

Let the gallons of fuel used in the hybrid per week car be [tex]x[/tex] and [tex]y[/tex] be the number of gallons used in the pickup truck per week.

Number of miles driven using both vehicles is at least 500 per week. The inequality that represents the number of miles driven is.

[tex]40x+17y\geq 500[/tex]

The expression of total amount of fuel used would be [tex]Z=x+y[/tex].

Now the sum of the fuels used in both the cars is more than 20 gallons per week. The inequality that represents the total amount of gasoline used is

[tex]x+y<20[/tex]


Related Questions

Plz help I will give brainliest

Answers

Answer:bc

Step-by-step explanation:

There is a hiking trail that is 2,080 feet long. There is 1 person hiking for every 10 feet of the length of
the trail. Write and solve an equation to find how many people are hiking on the trail.

Answers

Answer:

208

Step-by-step explanation:

2080 Divided by 10 = 208

Which number line represents the solution for the inequality |2p+3|>7

will give 20 points and brainliest

Answers

Answer:

Graph A

Step-by-step explanation:

Answer:

its graph A

Step-by-step explanation:

whats the midpoint? im pretty confused

Answers

the mid point is (7, 7/2)

Is this equation linear or non linear

Answers

Answer:

Non-linear

Step-by-step explanation:

This equation represents a reciprocal function.

You can't divide by zero so it never passes the y-axis, therefore it cannot be linear.

The graph of this equation is attached below.

I hope this helps!!

- Kay :)

Non-linear. In linear equations, you don't divide a number by x.

Jason is 10 years older than Alex. Mark is 11 years younger than Alex. If the total of their ages is 68, how old is the youngest of them?

Answers

Answer:

Mark is 12 years old.

Step-by-step explanation:

Let's just define some variables:

J = Jason

A = Alex

M = Mark

Next, let's put the information given in the question into equations.

Since Jason is 10 years older than Alex we can represent it like this:

J = A + 10

Since Mark is 11 years younger than Alex we can represent it like this:

M = A - 11

All of their ages add up to 68 so we can represent that like this:

J + A + M = 68

We can now do some substitutions to the J and M in this equation, like this:

(A + 10) + A + (A - 11) = 68

Combine like terms:

3A - 1 = 68

Solve for A

3A = 69

A = 23

Now that we found that Alex is 23 we can plug that back in to the first equations to find their ages:

J = 23 + 10

J = 33

M = 23 - 11

M = 12

Mark is the youngest out of the siblings being 12 years old.

Check:

23 + 33 + 12 = 68

68 = 68 :)

I hope this helps!!

- Kay :)

At what value of x does the second
function's output exceed (get bigger
than) the first function's output?
Explain your solution steps.
f(x)= x+7 and f(x)= x²)

Answers

The second function's output exceeds (get bigger than) the first function's output for x∈(-∞,[tex]\frac{1-\sqrt{29} }{2}[/tex])∪([tex]\frac{1+\sqrt{29} }{2}[/tex],∞)

Given the functions f(x)=x+7 and f(x)=[tex]x^{2}[/tex]

To know when to exceed, need to equate both functions.

⇒[tex]x^{2} =x+7[/tex]

⇒[tex]x^{2} -x-7=0[/tex]

x=[tex]\frac{-b+\sqrt{D} }{2a}[/tex] and [tex]\frac{-b-\sqrt{D} }{2a}[/tex]

⇒x=[tex]\frac{1-\sqrt{29} }{2}[/tex],[tex]\frac{1+\sqrt{29} }{2}[/tex]

f(x)=[tex]x^{2}[/tex] decreases from -∞ to 0 and increases from 0 to ∞ it cuts the graph of x+7 two times and for  x∈(-∞,[tex]\frac{1-\sqrt{29} }{2}[/tex])∪([tex]\frac{1+\sqrt{29} }{2}[/tex],∞) f(x)=[tex]x^{2}[/tex]  is greater than f(x)=x+7

Therefore,The second function's output exceeds (get bigger than) the first function's output for x∈(-∞,[tex]\frac{1-\sqrt{29} }{2}[/tex])∪([tex]\frac{1+\sqrt{29} }{2}[/tex],∞)

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Put these 3 problems in order from least to greatest: (WILL GIVE BRAINLIEST)
-15.2, -15.9, 3.6, -3.6


-15.9, -15.2, -3.6, 3.6


2.03, -2.3, -2.03, 3.0

Answers

1.) -15.9, -15.2, -3.6, 3.6
2.) second one is already correct
3.)-2.3, -2.03, 2.03, 3.0

John buys two types of tree saplings. One starts out at 40 cm and will grow 10 cm every three months. The other sapling starts at 20 cm and will grow 10 cm every two months. After how many months will they be the same height, and how tall will they be? solve for y and x

Answers

Answer:

They will at the same height of 80cm at 12 months.

Step-by-step explanation:

Sapling A:

y = 10/3x + 40

Sapling B:

y = 5x + 20

Set the equations to equal each other.

10/3x + 40 = 5x + 20

10/3x - 5x = 20 - 40

10x - 15x = 60 - 120

-5x = -60

x = 12

Sub x = 12 into one of the two equations (It doesn't matter which one you choose)

y = 5(12) + 20

y = 80

-3x-6y=6 y=x+8 infinite solution no solution one solution

Answers

Answer:

3x-6y=6

y=x+8

3x - 6(x+8) = 6

3x - 6x - 48 = 6

-3x - 48 = 6 / +48

-3x = 54 // -3

x = - 18

y = -18 +8 = 10

Step-by-step explanation:

Fiona is 7 years older than Gavin. Alex is 12 years younger than Gavin. If the total of their ages is 73, how old is the youngest of them?

Answers

the youngest of them is 42

i hope this was helpful:)

Which of the following has no solutions?
A) 5x + 5 = -4x - 5
B) -4x + 5 = -4x - 4
C) 4x + 5 = -4x + 5
D) -4x + 5 -4x - 5

Answers

Answer: B is the answer

Step-by-step explanation:

The answer for A) is x=-9/10

The answer for B) is no solution

The answer for C) is x=0

The answer for D) is =-8x

2/5 of a number is what percentage of that number?​

Answers

Answer:

40%

Step-by-step explanation:

2×100%5divide 5 by 100 percen2×20=40% .this is my answer

CAN SOMEONE HELP PLS

Answers

C=2 r = 2* *5= 31.24

Graph the following line. y=3/2x -5

Answers

Answer:

See the attached image.

Step-by-step explanation:

Remember the equation of the line is y = mx + b.

m = 3/2 (slope) ... rise/run. up 3 over 2.

b = -5 (y-intercept)

*These lines go on forever.

The graph of the line y = (3/2)x - 5 is given below.

Given that:

Equation of the line is y = (3/2)x - 5

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

Convert the equation into intercept form, then we have

y = (3/2)x - 5

(3/2)x - y = 5

x / 3.33 + y / (-5) = 1

The graph of the line is given below.

More about the linear equation link is given below.

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Find the values of x and y that make these triangles congruent by the HL theorem

Answers

Answer:

A. x = 3, y = 2

Step-by-step explanation:

The hypotenuse and the length of one leg of one right triangle must be equal to the hypotenuse and corresponding length of the one leg of the other ∆ for both triangles to be equal by the HL Congruence Theorem.

Thus, let's find x and y by setting the corresponding lengths of the two right ∆s equal to each other.

Therefore:

x = y + 1 ----› eqn. 1

2x + 3 = 3y + 3 ----› eqn. 2

Substitute x = (y + 1) into eqn. 2, and solve for y.

2x + 3 = 3y + 3 ----› eqn. 2

2(y + 1) + 3 = 3y + 3

2y + 2 + 3 = 3y + 3

2y + 5 = 3y + 3

Collect like terms

2y - 3y = -5 + 3

-y = -2

Divide both sides by -1

y = 2

Substitute y = 2 into eqn. 1.

x = y + 1 ----› eqn. 1

x = 2 + 1

x = 3

The water pump for a swimming pool can move 166.5 gallons of water in 3 minutes. The number of gallons, g, is proportional to the number of minutes,m, that the pump operates. Which of the following equations represents the relationship between g and m? Select all that apply.


A) m= 1/55.5g

B) g= 55.5m

C) g= 0.02m

D) g= 166.5/3 m

E) m= 55.5g

Answers

Answer:

A,B,D

Step-by-step explanation:

The equation that represents the relationship between g and m is; y = 55.5x

What is Proportionality?

If two objects are proportional to each other, the link between them can be described by y = kx, where ‘k’ is the constant ratio of y-values to corresponding x-values.

Given that the water pump for a swimming pool can move 166.5 gallons of water in 3 minutes.

Here we need to determine the relationship between the water pump and the time for filling.

Consider x to be the number of minutes and y to be the amount of water that follows on the pump.

Then the proportionality is written as,

y = kx

Where k refers to the amount of water that flows in one minute.

Thus, equals,

=> 166.5/3

=> 55.5

Therefore, the value of k is; 55.5.

Hence, the equation that represents the relationship between g and m is; y = 55.5x

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Combine and Simplify:
48 (1/4x - 1/3y - 2/6x - 3/8y - 2/3
WRITE 2 WAYS!

Answers

Answer:

Combining and simplifying [tex]48(\frac{1}{4}x-\frac{1}{3}y-\frac{2}{6}x-\frac{3}{8}y-\frac{2}{3})[/tex] we get  [tex]\mathbf{-4x-34y-32}[/tex] or we can write as [tex]\mathbf{48(\frac{-x}{12} -\frac{17y}{24}- \frac{2}{3})}[/tex]

Step-by-step explanation:

We need to combine and simplify

[tex]48(\frac{1}{4}x-\frac{1}{3}y-\frac{2}{6}x-\frac{3}{8}y-\frac{2}{3})[/tex]

First we will combine like terms and then perform the mathematical operations like addition or subtraction.

Like terms: terms having same variable

[tex]48(\frac{1}{4}x-\frac{2}{6}x-\frac{1}{3}y-\frac{3}{8}y-\frac{2}{3})[/tex]

Now we take LCM of like terms

[tex]=48(\frac{1}{4}x-\frac{2}{6}x-\frac{1}{3}y-\frac{3}{8}y-\frac{2}{3})\\=48(\frac{x*3-2x*2}{12} +\frac{-y*8-3y*3}{24}- \frac{2}{3})\\=48(\frac{3x-4x}{12} +\frac{-8y-9y}{24}- \frac{2}{3})\\=48(\frac{-x}{12} +\frac{-17y}{24}- \frac{2}{3})\\=48(\frac{-x}{12} -\frac{17y}{24}- \frac{2}{3})[/tex]

Now, we can multiply 48 with terms inside the bracket.

we can simplify the terms if they are both divisible by same number.

[tex]=48(\frac{-x}{12} -\frac{17y}{24}- \frac{2}{3})\\=48(\frac{-x}{12} )-48(\frac{17y}{24})-48(\frac{2}{3}))\\=-4x-34y-32[/tex]

So, Combining and simplifying [tex]48(\frac{1}{4}x-\frac{1}{3}y-\frac{2}{6}x-\frac{3}{8}y-\frac{2}{3})[/tex] we get  [tex]\mathbf{-4x-34y-32}[/tex] or we can write as [tex]\mathbf{48(\frac{-x}{12} -\frac{17y}{24}- \frac{2}{3})}[/tex]

a circle has a center at . the point is on the circle. what is the area of the circle to the nearest tenth of a square unit?

Answers

So area of the Circle ≈ 157.1 sq. unit .

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

Distance formula, Algebraic expression that gives the distances between pairs of points in terms of their coordinates (see coordinate system). In two- and three-dimensional Euclidean space, the distance formulas for points in rectangular coordinates are based on the Pythagorean theorem.

Point P(3,7) is on the Circle having Centre C(8,2).

Therefore, the Distance between points P and C is the radius r of the circle. To calculate r, use the distance formula .

Therefore, [tex]r^2=(8-3)^2+(2-7)^2=50[/tex]

∴ Area of the Circle =π×[tex]r^{2}[/tex]≈ (3.1416) ×(50)=157.08≈ 157.1 sq. unit ( nearest tenth).

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Rahul is going to an amusement park. The price of admission into the park is $15, and once he is inside the park, he will have to pay $4 for every ride he rides on. How much money would Rahul have to pay in total if he goes on 7 rides? How much would he have to pay if he goes on rr rides?

Answers

Using a linear function, the costs are given as follows:

7 rides: $43.r rides: 15 + 4r.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For this problem, we have that:

The admission fee is the intercept.The cost per ride is the slope.

Hence the cost for r rides is given by the following linear function:

C(r) = 15 + 4r.

The cost for 7 rides is given by:

C(7) = 15 + 4(7) = 15 + 28 = $43.

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In which pair of triangles is Triangle E F G is congruent to triangle R T S?

For triangles G E F and S R T, sides E G and S T are congruent, sides G F and S R are congruent, and sides E F and R T are congruent.
For triangles G F E and S T R, sides E G and T R are congruent, sides G F and T S are congruent, and sides E F and S R are congruent.
For triangles G F E and R S T, sides E G and R S are congruent, sides G F and R T are congruent, and sides E F and T S are congruent.
For triangles E G F and T S R, sides E G And S R are congruent, sides G F and S T are congruent, and sides E F and T R are congruent.

Answers

Answer:

Step-by-step explanation:Last pair of triangles represent congruence.

Step-by-step explanation:

If , it can be deducted the following:

Also,

Notice that the last imag shows the correct congruence, because it shows the congruence between sides as we said before.

Answer:

D

Step-by-step explanation:

I am doing the test

Write an equation of the line in slope-intercept form.

slope: 6
y-intercept: 3

Answers

y=6x+3


ywwwwwwwwwwww :)

Answer:

y=6x+3

Step-by-step explanation:

anyone know??? I’m not sure

Answers

9514 1404 393

Answer:

  UW = 24

Step-by-step explanation:

Midsegment XY is half the length of base UW, so we can write ...

  UW = 2·XY

  73 -7x = 2(54 -6x) . . . . substitute the given expressions

  73 -7x = 108 -12x . . . . . eliminate parentheses

  5x = 35 . . . . . . . . . . . . . add 12x-73

  x = 7 . . . . . . . . . . . . . . . divide by 5

Now, we can find UW:

  UW = 73 -7x = 73 -7·7

  UW = 24

what is 25 rounded to the hundreds place

Answers

Answer:

0

Step-by-step explanation:

because if the number is not higher than 50, you have to round down.

A company advertises on a website. A worker tracked the number of visits to the website and the number of clicks on the advertisement. The table shows the data for several days. A linear function can be used to model the data. based on the table, what is the best prediction of the number of clicks on the advertisement if 1,500 people visit the website?

Answers

Answer:

I think it's 83

Step-by-step explanation:

Teacher explanation I still don't understand

If Patrick was pushing directly downward on the rock with a force of 10 N. How much work did Patrick do? Show/explain your work.

Answers

Answer:

Patrick from spongebob? He dosent do work

Step-by-step explanation:

Let w =Vector O R where O(–5, 6) and R(4, –2). What is the component form of One-fifthw?

LeftAngleBracket negative 0.2, 0.8 RightAngleBracket
LeftAngleBracket negative 5, 20 RightAngleBracket
LeftAngleBracket 1.8, negative 1.6 RightAngleBracket
LeftAngleBracket 45, negative 40 RightAngleBracket

Answers

Answer:

C) (1.8, -1.6)

Step-by-step explanation:

1.
For the function f(x) =
8x + 10, find the inverse function.
O
x2 - 10
f-4x) =
-,X20
8
O
(x - 10)2
f-1(x) =
x2 10
8
f-1(x)
X2 + 10
8
,*20
x2 - 10
f-4(x) =
-, X30
8

Answers

Answer:

The inverse of [tex]f(x)=8x+10[/tex] is [tex]\mathbf{f^{-1}(x)=\frac{x-10}{8}}[/tex]

Step-by-step explanation:

[tex]f(x)=8x+10[/tex]

We need to find inverse of the function.

For finding inverse of function,

let [tex]y=8x+10[/tex]

Now, solving to find value of x

Subtracting 10 on both sides

[tex]y-10=8x+10-10\\y-10=8x[/tex]

Divide both sides by 8

[tex]\frac{8x}{8}=\frac{y-10}{8} \\x=\frac{y-10}{8}[/tex]

Now replace y with x and x with [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x)=\frac{x-10}{8}[/tex]

So, the inverse of [tex]f(x)=8x+10[/tex] is [tex]\mathbf{f^{-1}(x)=\frac{x-10}{8}}[/tex]

Answer:

The answer is [tex]f^(-1)(x)= (x^(2) - 10)/(8), x > =0[/tex]

professor duque will participate in a lottery that will be played by five hundred participants. he buys a ticket for five dollars. if the lucky randomly selected winner gets one hundred dollars as a prize, what would duque's expected winnings or losses be?

Answers

Expected winning of professor Duque = -$4.8

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Total no of participation = 500

The prize winner will be decided at random.

Number of favorable outcomes divided by the total number of outcomes gives Duque a chance of winning the reward.

Out of the 500 competitors, only one will be the winner.

Duque's chances of winning the prize are 1 in 500, or 0.002.

If a person wins, they will receive $100 as their prize.

The price of a ticket is $5.

Thus, the net amount prize pool is $100 - $5 = $95 total.

Participants 499  will not be successful.

Probability of losing is 499/500, which is 0.998.

Loss from losing = - $5 (negative sign represents loss).

For discrete random variable X:

E(X) = ∑[tex]_{i=0}^{n} x_{i}*p(x_{i})[/tex]

E(X) = [tex]x_{1}*p(x_{1})+x_{2}*p(x_{2})\\[/tex]

Given,

[tex]x_{1}=[/tex]$95 and [tex]p(x_{1})[/tex]=1/500

[tex]x_{2}[/tex]= -$5 and [tex]p(x_{2})\\[/tex] = 499/500

[tex]E(X)=(95*\frac{1}{500})+(-5*\frac{499}{500}) \\= -4.8\\[/tex]

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30 POINTS AND I'LL MARK YOU BRAINLIST IF YOU ANSWER!!

Troy made a scale drawing of the Statue of Liberty which has an actual height of 305 feet. He decides to use a scale in which 1 inch represents 25 feet. What is the height in inches of Troy's drawing?

Answers

Answer:

Step-by-step explanation:

The height of statue is 12.2 inches in Troy's drawing.

Step-by-step explanation:

Given,

Actual height of statue = 305 feet

Scale used by Troy;

25 feet = 1 inch

1 feet =

305 feet =

305 feet =

305 feet = 12.2 inches

The height of statue is 12.2 inches in Troy's drawing.

Answer:

12.2 inches

Step-by-step explanation:

The scale is 1 inch = 25 ft

305 ft * (1 inch)/(25 ft) = 305/25 inches = 12.2 inches

Answer: 12.2 inches

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