Hank’s pickup can travel 75 miles on 5 gallons of gas. How many gallons will Hank’s pickup need to travel 60 miles?

Hank’s pickup will need blank gallons of gas to travel 60 miles.

Answer:

the next 3 terms are 64, 128, and 256

Answer:

answer is D

Step-by-step explanation:

5(-2) + y = 1      5(1) + y = 1   5(6) + y = 1  

-10 + y = 1          5 + y = 1      30 + y = 1

y - 10 = 1            y + 5 = 1       y + 30 = 1

y = 11                 y = -4            y= -29

The corresponding range function 5x + y=1 which has the domain (-2, 1, 6) will be option (D) {11,-4,-29}

A function is a correspondence or rule that assigns to each element in one set, called the domain D, exactly one element from a second set, called the range R.

The Steps are as follow:

Function = 5x + y = 1

domain  = (-2 , 1, 6)

Corresponding range = ?

let x = -2

∴ 5x + y =1

∴ 5(-2) + y =1

∴  -10 + y =1

∴ y = 11

x = 1

∴ 5x + y = 1

∴ 5(1) + y = 1

∴ 5 + y = 1

∴ y = -4

x = 6

∴ 5x + y =1

∴ 5(6) + y = 1

∴ 30 + y =1

∴ y = -29

So the corresponding range function 5x + y=1 which has the domain (-2, 1, 6) will be option (D) {11,-4,-29}

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Answer:

-327

Step-by-step explanation:

20+22-369=-327

The answer is 14 2/3

I hoped this helped youuuuu!!!!!

Answer: (x−4)(x2+4x+16)

Step-by-step explanation:

x^3 − 64 ←is a difference of cubes

. xa^3 −b^3 = ( a − b ) (a^2 + ab + b^2)

here a = x and b =4 → (4)^3 = 64

⇒ x^3 − 64 = (x − 4) (x^2 + 4x + 16 )

Answer:

[tex][{x}^{2} + 4x + 16][x - 4][/tex]

Step-by-step explanation:

Take the cube root of this expression using the Difference of Cubes [(a + b)(a² - 2ab + b²)]:

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

Now, since the divisor\factor is in the form of [tex]x - c[/tex], use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

4| 1 0 0 −64

↓ 4 16 64

__________

1 4 16 0 → [tex]{x}^{2} + 4x + 16[/tex]

You start by placing the c in the top left corner, then list all the coefficients of your dividend [x³ - 64]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², the 4x follows right behind it, and bringing up the rear, 16, giving you the other factor of [tex]{x}^{2} + 4x + 16[/tex]. Attach this to the first factor you started out your work on:

[tex][x - 4][{x}^{2} + 4x + 16][/tex]

I am joyous to assist you anytime.

Answer:

_

1/3, or 0.3 is there difference

Answer:

PS = 37

Step-by-step explanation:

The opposite sides of a rectangle are congruent, thus

perimeter = 2(3x + 1) + 2(4x - 3) = 136 ← distribute and simplify left side

6x + 2 + 8x - 6 = 136

14x - 4 = 136 ( add 4 to both sides )

14x = 140 ( divide both sides by 14 )

x = 10

Hence

PS = 4x - 3 = (4 × 10) - 3 = 40 - 3 = 37

Answer:

2. [tex]f(x)=\frac{x^2}{x+5}[/tex]

Step-by-step explanation:

When you replace x=5 into those functions you obtain:

[tex]1. f(x)=\sqrt{x^2-36} = \sqrt{5^2-36} = \sqrt{-11} \\2. f(x)=\frac{x^2}{x+5}=\frac{5^2}{5+5}=\frac{25}{10}[/tex]

We can see that the function number 1, when the x=5 is replaced, falls into the imaginary numbers or complex domain, so the function is not continuous in the real domain.

On the other hand, the second function falls into the real domain whe x=5 is replaced, so the function is continuous in the real domain!

I hope you understand!

Final answer:

In this problem, we are given the percentage (25%) and the amount (40), and we need to find the base. To find the base, we can set up an equation and solve for x. The base in this problem is 160.

Explanation:

In this problem, we are given the percentage (25%) and the amount (40), and we need to find the base. The base represents the whole quantity or number that the percentage is taken from.

Let x be the base. We can set up the equation: 25% of x is equal to 40, or 0.25x = 40.

To find the base, we divide both sides of the equation by 0.25: x = 40 / 0.25.

Simplifying, we get x = 160. Therefore, the base is 160.

To summarize, the percent is 25%, the amount is 40, and the base is 160.

Answer:

x = 13

Step-by-step explanation:

Given

[tex]\frac{3}{5}[/tex](x + 2) = x - 4

Multiply through by 5 to clear the fraction

3(x + 2) = 5x - 20 ← distribute left side

3x + 6 = 5x - 20 ( subtract 5x from both sides )

- 2x + 6 = - 20 ( subtract 6 from both sides )

- 2x = - 26 ( divide both sides by - 2 )

x = 13

Answer:

14 miles.

Step-by-step explanation:

Let the distance traveled from home to destination = x miles.

Speed while going to friend's house = 35 miles per hour.

Speed while coming back = 40 miles per hour.

Total Time taken for the journey = 45 minutes = 0.75 hours.

Let the time taken while going to friend's house = y hours.

Therefore, the time taken while going to friend's house = (0.75 - y) hours.

To find x and y, model the speeds of both the journeys.

Speed while going to friend's house = Distance/Time.

35 = x/y.

x = 35y (Equation 1).

Speed while coming back = Distance/Time.

40 = x/(0.75 - y).

x = 40(0.75 - y) (Equation 2).

Since x = x, therefore:

35y = 30 - 40y.

75y = 30.

y = 30/75.

y = 0.4 hours.

Put y = 0.4 hours in Equation 1:

x = 35y.

x = 35(0.4).

x = 14.

Therefore, the distance between my friend's house and my house is 14 miles!!!

Answer:

The distance from my house to friend's house is 14 miles

Step-by-step explanation:

* Lets explain how to solve the problem

- Driving to the friend's house rate is 35 miles per hour

- Driving to my home rate is 40 miles per hour

- The round trip took 45 minutes

- We need to find the distance from my house to my friend's house

* At first lets change 45 minutes to hour because the rate of driving

 unit is miles per hour

∵ 1 hour = 60 minutes

∴ 45 minutes = [tex]\frac{45}{60}=\frac{3}{4}[/tex] hour

- Assume that the distance from my house to friend's house is d,

 the time for the trip from my house to the friend's house is [tex]t_{1}[/tex]

 and the time from friend's house to my house is [tex]t_{2}[/tex]

∵ The distance between the two houses is d

∵ Distance = rate of driving × time of the trip

∴ d = 35 × [tex]t_{1}[/tex] = [tex]35t_{1}[/tex]

∴ d = 40 × [tex]t_{2}[/tex] = [tex]40t_{2}[/tex]

- Equate the two equations

∴ [tex]35t_{1}[/tex] = [tex]40t_{2}[/tex]

- Divide both sides by 35

∴ [tex]t_{1}=\frac{40}{35}t_{2}=\frac{8}{7}t_{2}[/tex]

∴ [tex]t_{1}=\frac{3}{4}t_{2}[/tex] ⇒ (1)

- The time of the round trip is [tex]\frac{3}{4}[/tex] hour

∴ [tex]t_{1}+t_{2}=\frac{3}{4}[/tex] ⇒ (2)

- Substitute equation (1) in equation (2)

∴ [tex]\frac{8}{7}t_{2}+t_{2}=\frac{3}{4}[/tex]

∴ [tex]\frac{15}{7}t_{2}=\frac{3}{4}[/tex]

- Divide Both sides by [tex]\frac{15}{7}[/tex]

∴ [tex]t_{2}=0.35[/tex] hour

∵ d =  [tex]40t_{2}[/tex]

- Substitute the value of [tex]t_{2}[/tex] in the equation above

∴ d = 40(0.35) = 14

∵ d represents the distance from my house to friend's house

∴ The distance from my house to friend's house is 14 miles

The roads are two lines and they intersect at  90° .

Intersecting lines cross each other at some arbitrary angle .

Two geometric objects are perpendicular if they intersect at a right angle. A line is said to be perpendicular to another line if the two lines intersect at a right angle.

According to the question

Roads have 2 lanes and have crossing lane .

Now,

Those roads  are two lines and they intersect at a right angle by making 90° at there point of intersection .

So,

They are perpendicular lines .

Hence, the roads are two lines and they intersect at  90° .

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Answer:D. 2(3x-5)^2

Step-by-step explanation:

18x^2-60x+50=2(9x^2-30x+25)

Answer:

D. 2(3x - 5)²

Step-by-step explanation:

18x² - 60x + 50

The expression can be factorize as follows;

18x² - 60x + 50

divide through by 2

2(9x² - 30x + 25)

The bracket equation can be factorized further

Find the square value that can be multiplied to get 9x² and 25

The values are 3x and 5

2( (3x- 5)(3x - 5) )

2(3x - 5)²

Answer:

See explanation

Step-by-step explanation:

To subtract mentally 81 from 304, complete following steps:

Step 1: Write number 304 as

[tex]304=300+4\\ \\304=200+100+3+1\\ \\304=200+20+80+3+1[/tex]

Step 2: Write number 81 as

[tex]81=80+1[/tex]

Step 3: Now subtract 80 and 1 from number 304:

[tex]304-81=(200+20+80+1+3)-(80+1)\\ \\304-81=200+20+3\\ \\304-81=223[/tex]

Final answer:

To mentally subtract 304-81, round 81 to 100, subtract from 304 to get 204, then add back the difference (19) for a result of 223.

Explanation:

To calculate 304-81 mentally, we can round 81 up to 100 to make the numbers easier to work with. We know that 304 - 100 = 204.

Since we've subtracted too much by rounding up, we need to add back the difference between 81 and 100, which is 19.

So the full calculation would be 304 - 81 = 304 - 100 + 19 = 204 + 19 = 223.

The coherent sequence of equations aligning with this reasoning would be:

Answer:

From the table shown the years in which there was a budget deficit are

2002,2003,2005,2006,2008,2010

Step-by-step explanation:

Budget deficit is said to be when expenditure exceed or is greater than the budgeted revenue.

For 2002:

Revenue = $5 trillion and expenditure = $7 trillion

To check for budget deficit = Revenue - expenditure ( $5 trillion - $7 trillion)

=  -$2 trillion ( there was a budget deficit of $2 trillion)

For 2003:

Revenue = $8 trillion and expenditure = $10 trillion

to check for budget deficit = Revenue - expenditure ($8 trillion - $10 trillion)

= -$2 trillion (there was a budget deficit of $2 trillion)

For 2005:

Revenue = $15 trillion and expenditure = $18 trillion

to check for budget deficit = Revenue - expenditure ($15 trillion - $18 trillion)

= -$3 trillion (there was a budget deficit of $2 trillion)

For 2006:

Revenue = $8 trillion and expenditure = $10 trillion

to check for budget deficit = Revenue - expenditure ( $8 trillion - $10 trillion)

= -$2 trillion (there was a budget deficit of $2 trillion)

For 2008:

Revenue = $2 trillion and expenditure = $4 trillion

to check for budget deficit = Revenue - expenditure ( $2 trillion - $4 trillion)

= - $2 trillion ( there was a budget deficit of $2 trillion)

For 2010:

Revenue = $5 trillion and expenditure = $9 trillion

to check for budget deficit = Revenue - expenditure ( $5 trillion - $9 trillion)

= -$4 trillion (there was a budget deficit of $4 trillion)

From the table shown the years in which there was a budget deficit are

2002,2003,2005,2006,2008,2010

Budget deficit is said to be when expenditure exceed or is greater than the budgeted revenue.

For 2002:

Revenue = $5 trillion and expenditure = $7 trillion

To check for budget deficit = Revenue - expenditure ( $5 trillion - $7 trillion)

=  -$2 trillion ( there was a budget deficit of $2 trillion)

For 2003:

Revenue = $8 trillion and expenditure = $10 trillion

to check for budget deficit = Revenue - expenditure ($8 trillion - $10 trillion)

= -$2 trillion (there was a budget deficit of $2 trillion)

For 2005:

Revenue = $15 trillion and expenditure = $18 trillion

to check for budget deficit = Revenue - expenditure ($15 trillion - $18 trillion)

= -$3 trillion (there was a budget deficit of $2 trillion)

For 2006:

Revenue = $8 trillion and expenditure = $10 trillion

to check for budget deficit = Revenue - expenditure ( $8 trillion - $10 trillion)

= -$2 trillion (there was a budget deficit of $2 trillion)

For 2008:

Revenue = $2 trillion and expenditure = $4 trillion

to check for budget deficit = Revenue - expenditure ( $2 trillion - $4 trillion)

= - $2 trillion ( there was a budget deficit of $2 trillion)

For 2010:

Revenue = $5 trillion and expenditure = $9 trillion

to check for budget deficit = Revenue - expenditure ( $5 trillion - $9 trillion)

= -$4 trillion (there was a budget deficit of $4 trillion)

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Answer:

≠

Step-by-step explanation:

it would be unequal to

Answer:

5.7

Step-by-step explanation:

Answer:

7-x^2

Step-by-step explanation:

The required expression will be x² - 7

Expressions are functions separated by an operation sign.

For the given statement:

7 less than number means we are to subtract 7 from the result x² as shown

F(x) = x² - 7

Hence the required expression will be x² - 7

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Answer:

Step-by-step explanation:To convert part-to-part ratios to fractions:

Use the total number as the denominator: 6 + 8 = 14.

Use each of the ratio terms as the numerator in a fraction: ...

Reduce each fraction to lowest terms: ...

The part-to-part ratio 6 : 8 converts into the fractions:

To convert a rational expression to a fraction, create a common denominator, multiply by the inverse when dividing fractions, and simplify by canceling out common factors after prime factorization.

Converting a rational expression to a fraction involves creating a common denominator for the terms involved. When dividing fractions, the process is to change the division to multiplication by the inverse of the second fraction and then multiplying the numerators and denominators as above. A conversion factor in a measurement context is simply a fraction equal to one, with the original unit in the denominator to cancel it out and the new unit in the numerator.

When simplifying fractions it's useful to remember that multiplying or dividing both numerator and denominator by the same number does not change the value of the fraction; this is often referred to as multiplying by a fraction that equals one (1/2, 2/2, 3/3, etc.). Simplifying a fraction may involve finding these 'fractions equal to one' to cancel out the same factors in both the numerator and denominator.

Answer:

a. the ratio is 73:100

b. the ratio is 27:73

Answer: 6 inches

Step-by-step explanation:

formula for area of a rectangle is length times width

LW=A

substitute

7(W)=42

divide 7 on both sides

42/7 = 6

Answer: 6

There are 169 boys and 195 girls in the first-grade class at Park Elementary School.

Let's assume the number of boys in the first-grade class is x. Since there are 26 more girls than boys, the number of girls would be x + 26. The total number of students in the class is 364, so we can calculate the equation:

x + (x + 26) = 364

Simplifying the equation, we get:

2x + 26 = 364

Subtracting 26 from both sides:

2x = 338

Dividing both sides by 2:

x = 169

So there are 169 boys and 169 + 26 = 195 girls.

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Answer:

$7.90 tip the total is $47.40

Step-by-step explanation:

Final answer:

To find the total cost of a $39.50 family dinner after adding a 20% tip, first calculate the amount of the tip by multiplying the cost of the dinner by the tip percentage. Then, add the tip to the cost of the dinner to get the total amount.

Explanation:

To find the total cost of a $39.50 family dinner after adding a 20% tip, you first need to calculate the amount of the tip. Tip is calculated by multiplying the cost of the dinner by the tip percentage. In this case, the tip would be 20% of $39.50, which is

$39.50 × 0.20 = $7.90

Next, you add the tip to the cost of the dinner to get the total amount:

$39.50 + $7.90 = $47.40

So, the total cost of the family dinner after adding a 20% tip is $47.40.

Answer:  (a) 43  (b) 25.5  (c) 17.5

Step-by-step explanation:

f(x) = 51

Replace f(x) with 51

a) f(x) - 8   = 51 - 8    = 43

[tex]b)\quad \dfrac{1}{2}f(x)\qquad =\dfrac{1}{2}\cdot 51\qquad =\dfrac{51}{2}\qquad =25.5[/tex]

[tex]c)\quad \dfrac{1}{2}f(x)-8\qquad =25.5-8\qquad =17.5[/tex]

Answer:

(4 , 5)

Step-by-step explanation:

Note the point: (x , y) = (11 , 10)

Note that if you are moving left or right, you are changing the x variable.

Note that if you are moving up or down, you are changing the y variable.

In this case, you are starting at (11 , 10)

You move 7 units left (subtract 7 from x):

(11 - 7 , 10) = (4, 10)

You then move 5 units down (subtract 5 from y):

(4 , 10 - 5) = (4 , 5)

(4 , 5) is your answer.

~

Answer:

C = [tex]\frac{3L+120}{4}[/tex]

Step-by-step explanation:

Given

L = [tex]\frac{4}{3}[/tex](C - 30)

Multiply through by 3 to clear the fraction

3L = 4(C - 30) ← distribute

3L = 4C - 120 ( add 120 to both sides )

3L + 120 = 4C ( divide both sides by 4 )

[tex]\frac{3L+120}{4}[/tex] = C

√16 + √40 = √4×4 + √4×10

= 4 + √2×2×10

= 4 + 2√10

If you need a better explanation just as in the comments.

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Answer:

4+ 2*√10

Step-by-step explanation:

√16 = 4

√40 = √4* √10    

√4=2

√40 = 2 *√10

the square root of 16 plus the square root of 40 simplified is

4+ 2*√10