A vehicle travels 55 miles per hour and 20 miles per gallon.
a. Write an equation that represents the distance d (in miles) that the vehicle travels in t hours. Then write an equation that represents the distance d (in miles) that the vehicle travels using g gallons of gasoline.
b. Write an equation that relates g and t. Then solve the equation for g.
c. Thevehicletravelsfor6hours.Howmanygallons of gasoline does the vehicle use? How far does it travel? Explain.

Answer: Change = - 2.8 gallons

Step-by-step explanation:

Let X be the starting amount of paint in the can, in gallons.

"Removes 5/8 gallon" can be written -(5/8)gal

"Adds 3/8 gallon" becomes +(3/8)gal

The result is :  X - (5/8)gal + (3/8)gal = Remaining Paint (gallons)

Consolidating:  Remaining (gallons) = X - (2/8)gal

If we want the overall increase/decrease, subtract the initial volume:

Initial - Remaining = Change in amount of paint in can

Change =  (X-(2/8)gal) - X = - (2/8) gallons

Answer:

So the answer would be 20 for 50-[20+[50-40]]

Step-by-step explanation:

50 - 40 =10 and 20 +10 = 30 so we 50 minus 30 which is 20

If its the other one it is 9 because 3 times 2 is 6 and 8 minus 6 is 2 and 7 plus 2 equals 9

$ 86.67 , Steve and his five friends has to pay $86.67 each to rent limo for four hours.

According to the question,

rent of limo for five hours = $130

now by multiplication ,

rent of limo for four hours = $130 * 4

                                           = $520

now we know that there are six people including Steve hence we divide this $520 by 6 to get the share of each individual,

by division ,

hence the amount for each = $520 / 6

                                              = 86.666666

amount round up to the nearest dollar is $86.67

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The equations which could represent Relationship B which has a greater rate than Relationship A as described in the task content are; y = 2.2x and y = 3x.

It follows from the task content that the equation which could represent Relationship B given that it has a greater rate than Relationship A be determined.

It can be evaluated from the graph given that the slope of relationship A which is a measure of it's rate is;

Slope, m = (y2 - y1)/(x2 - x1)

m = (8 -4)/(4-2)

m = 4/2

m = 2.

Ultimately, since the rate of Relationship A is 2, and the rate of Relationship B has to be greater, it follows that the equations which are required are;

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The fraction that Alice, Billy, and Anna should bring when they are spending the weekend baking cookies for winter holiday is 11/12 cups.

It should be noted that based on the information, for each batch of cookies, they’ll need 2 1/2 cups of flour and 1 1/4 cups of butter.

In this case, it should be noted that there are 3 people.

The fraction will be:

= (2 1/2 + 1 1/4) / 3

= 3 3/4 ÷ 3

= 11/12

Therefore, the fraction will be 11/12 cups for each person.

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Alice, Billy, and Anna are spending the weekend baking cookies for.winter holiday gifts. For each batch of cookies, they’ll need 2 1/2 cups of flour and 1 1/4 cups of butter. Each person contributed supplies from their mothers’ kitchens and met at Anna’s house. What fraction should each person bring?

The hypotenuse of the right triangle is found to be 6√2 ft.

The formula is as follows:

H² = B² + P²

where, H is the hypotenuse.

B is the base

P is the perpendicular.

In the given question, hypotenuse is to be calculated.

Lets, base B = 6 ft and

Perpendicular P = 6 ft.

Thus, put the values in the formula;

H² = 6² + 6²

H² = 2×6²

Taking square root on both sides.

H =  6√2

Thus, the value of the hypotenuse if the right angled triangle is found as  6√2 ft.

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 5 +2}{2}~~~ ,~~~ \cfrac{ -1 +4}{2} \right) \implies \left(\cfrac{ 7 }{2}~~~ ,~~~ \cfrac{ 3 }{2} \right)\implies \left(3\frac{1}{2}~~,~~1\frac{1}{2} \right)[/tex]

Given the function and interval, the average rate of change of the function over the given interval is 1.

The average rate of change of a function is calculated by dividing the change in y-values over the change in x-values of the two point.

r = ( f(1) - f(0) / ( (1) - (0) )

Given the data in the question;

f(x) = 2x² - x - 2

Intervals: [0, 1]

Plug the given values into the average rate of change formula and simplify.

r = ( f(1) - f(0) / ( (1) - (0) )

r = ( (2(1)² - (1) - 2) - ( 2(0)² - (0) - 2 )) / ( (1) - (0) )

r = ( (2 - 1 - 2) - ( 0 - 0 - 2 )) / 1 -0

r = ( (-1) - (-2 )) / 1r = ( -1 - (-2 ) / 1

r = ( -1 + 2 ) / 1

r = 1/1

r = 1

Therefore, the average rate of change of the function over the given interval is 1.

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The average rate of change of the function f(x) = 2x² - x - 2 over the intervals of 0 to 1 is 1.

The average rate of change of a function is calculated by dividing the change in y-values over the change in x-values of the two point.

AVR = ( f(1) - f(0) / ( (1) - (0) )

Given the data in the question;

Plug the given values into the average rate of change formula and simplify.

r = ( f(1) - f(0) / ( (1) - (0) )

r = ( (2(1)² - (1) - 2) - ( 2(0)² - (0) - 2 )) / ( (1) - (0) )

r = ( (2 - 1 - 2) - ( 0 - 0 - 2 )) / 1 -0

r = ( (-1) - (-2 )) / 1

r = ( -1 - (-2 ) / 1

r = ( -1 + 2 ) / 1

r = 1/1

r = 1

The average rate of change of the function f(x) = 2x² - x - 2 over the intervals of 0 to 1 is 1.

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The simple interest that Su Young paid for borrowing $2,900 for 15 months at 5.5% per year is $199.375.

Simple interest is interest that is not compounded.

Compounding involves adding earned interests to the principal when computing the next period's interest.

Principal = $2,900

Period = 15 months or 1.25 years

Interest Rate = 5.5%

Simple interest amount = Principal x Period x Rate

= $199.375 ($2,900 x 1.25 x 5.5%)

Thus, based on simple interest, Su Young paid $199.375.

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Answer: f(4) = 8,                     f(-5) = -19,                 f(2-x) = -3x+2

Step-by-step explanation:

Let's start by analyzing what we are given:

f(x)=3x-4

In this equation, f is the name of the function.

The number in the parentheses represents x.

The 3x-4 tells us what the equation does. In this instance, we multiply x by 3 and then subtract 4.

Let's start with (a).

f(4)

Since we have established that the number in the parentheses is x, we can plug 4 in for x into the equation f. We must abide by the order of operations. Therefore, we can obtain the following:

f(4) = 3(4) -4

f(4) = 12 -4

f(4) = 8

We can continue this for part (b).

f(-5) = 3(-5) -4

f(-5) = -15-4

f(-5) = -19

Part (c) is slightly different, but applies the same principles we established previously. On this part, we must recall the distributive property. The 3 multiples the 2 and the x. We must also remember to combine like terms.

f(2-x) = 3(2-x) -4

f(2-x) = 6 - 3x -4

f(2-x) = -3x +2

The radical expression ∛24  is between integers 2 and 3

The expression is given as

∛24

The above expression is a radical expression .

So, we have:

Express 24 as the product of 8 and 3

So, we have

∛24 = ∛(8 * 3)

Take the cube root of 8

So, we have

∛24 = 2∛3

Take the cube root of 3

So, we have

∛24 = 2 * 1.44

Evaluate the product

∛24 = 2.88

2.88 is between integers 2 and 3

Hence, the radical expression ∛24  is between integers 2 and 3

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Categorical variable: job titles, location

Quantitative variable: starting salary, number of years post-experience

Categorical variables represent many data kinds that can be grouped. Race, sex, age, and educational level are a few examples of categorical variables.

In addition, categorical variables are any variables where the data represent groups, as opposed to quantitative variables, which are any variables where the data indicate amounts, such as height, weight, or age.

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Christopher's age given the sum of the ages of the three siblings is 23.

An odd number is a number that is not perfectly divisible by 2. An odd number can be a positive number or a negative number. An example of an odd number is 3 and 7.

Consecutive odd integers are odd integers that follow each other on the number line. Consecutive odd integers increase by a value of (x + 2). Examples of consecutive odd integers are 11, 13, 15.

Let x represent the youngest sibling's age

Second sibling's age : x + 2

Christopher's age : x + 4

x + x + 2 + x + 4 = 63

3x + 6 = 63

3x = 63 - 6

3x = 57

x = 57 / 3

x = 19

Christopher's age : x + 4 : 19 + 4 = 23

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The fraction 13/20 of Duo's dumplings have vegetarian fillings.

A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.

Given:

Duo makes 65 percent of his dumplings with vegetarian fillings.

According to given question we have

A percentage is a number or ratio expressed as a fraction of 100.

65 percent

=65 %

=65/100

Simplify fraction into simpler fraction,

⇒13/20

Therefore, the fraction 13/20 of Duo's dumplings have vegetarian fillings.

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Answer:of not

Step-by-step explanation: ops

The answer to this question is:

No. of cups of milk will Paula use = 3/8

Given that recipe requires 3/4 cups of milk.

Paula is making half (1/2) of the recipe.

And we are asked to find that No. of cups of milk will Paula use.

To solve this question,  we have to multiply the quantity of milk required by the quantity she is going to make.

The quantity of milk required * the quantity she is going to make

= 3/4 * 1/2

= 3/8

Therefore, No. of cups of milk will Paula use = 3/8

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Answer:

-28

Step-by-step explanation:

Simplify those in parenthesis first.

( 30 - 3) - (60 - 5)

27 - 55

= -28

Answer:

42,307,0102,014 is the number form

For every hour spent watching television, the amount of time spent sleeping drops by an Graph hour.

Graph: A graph is a visual representation, such as a picture or diagram, that shows information or values in a structured way.

The relationships between two or more items are frequently represented by the points on a graph.

Various Graph Types

Pictograph

The term "pictograph" refers to the visual depiction of information. Each graphic represents a specified number of objects.

Line Graph:

In a line graph, dots are connected by lines to depict changes over time.

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If Sam says that 2/7 to the power of 2 times 1/3 to the power of 5 can be rewritten as 2/21 to the power of 7 Sarah says it can be rewritten as 2/21 to the power of 10 Steve says it cannot be rewritten as either of these expression. The person that is correct is: Steve.

2/7 to the power of 2 times 1/3 to the power of 5 can be rewritten or express as [(2/7²)× (1/3^5)].

This implies that both Sam and Sarah are wrong, Only Steve is correct because  2/7 to the power of 2 times 1/3 to the power of 5 can either of the two expression that was mentioned by Sam and Sarah.

Therefore if Steve says it cannot be rewritten as either of these expression. The person that is correct is: Steve.

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The measures of the angles are

1. Angle TLN, MZQ and NLM

The angles TLN and NLM are supplementary angles

So, we have

TLN + NLM = 180

This gives

3x - 18 + y = 180

Also, we have

TLN + MZQ = 180

So, we have

3x - 18 + 5x + 14 = 180

Evaluate the like terms

8x -4 = 180

This gives

8x = 184

Divide

x = 23

Substitute x = 23 in 3x - 18 + y = 180

3 x 23 - 18 + y = 180

Evaluate

51 + y = 180

So, we have

y = 129

The above computations imply that:

TLN = 3 x 23- 18 = 51

NLM = y = 129

MZQ = 5 x 23 + 14 = 129

2. Angle JZQ and TLN

The above means that

JZQ = TLN

So, we have

9x + 9 = 8x + 19

Evaluate

x = 10

So, we have

JZQ = TLN = 9 * 10 + 9

JZQ = TLN = 99

3. Angle ZMR, LMO and LMR

The angles ZMR and LMO are congruent angles

So, we have

ZMR = LMO

This gives

x + 14 = 2x - 6

Evaluate

x = 20

Also, we have

LMR + LMO = 180

So, we have

y + 2x - 6 = 180

y + 2 x 10 - 6 = 180

y + 14 = 180

So, we have

y = 166

The above computations imply that:

LMO= ZMR = 20 + 14 = 34

LMR = y = 166

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The inverse of the function y = log(x ₋ 6) is y = 10ˣ + 6.

Given the function is :y = log₁₀ (x ₋ 6)

we are asked to find the inverse of the function.

steps to find inverse function are:

Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.

Here, find y and solve for x = ay + b.

Then we get :

y = (x - b/a).

Finally, we can substitute y = f⁻¹(x) with f⁻¹(x) = (x - b)/a.

now interchange the positions of x and y in the function.x = log₁₀(y ₋ 6)

the next step is to isolate the dependent variables.

y = 10ˣ + 6

hence we get the inverse of the function y = log₁₀ (x ₋ 6) as y = 10ˣ + 6.

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The primary difference between expression and equation has an equal sign. An equation has a left side , a right side and an equal symbol separating the sides. But an expression by contrast does not have any sides and equal symbol.

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) Expressions can be thought of as similar to phrases.

The primary difference between expression and equation is an equal sign. An equation has a left side , a right side and an equal symbol separating the sides. But an expression by contrast does not have any sides and equal symbol.

For example

ax2+by+c is an expression.

4x+3y+8=5 is an equation.

Therefore expression and equation both are different.

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None of the given option is equivalent to 6 [tex]\sqrt81x^{4}y^{8}[/tex].

squares are the products of numbers which comes out when the no. is multiplied by itself twice .

and square root helps to find the no. which is multiplied twice to get that no. inside the root.

6 [tex]\sqrt81x^{4}y^{8}[/tex]

= 6 * 9 [tex]x^{2} y^{4}[/tex]

= 54 [tex]x^{2} y^{4}[/tex]

Since from the given option none of the option is equivalent to 6 [tex]\sqrt81x^{4}y^{8}[/tex]

because you can see that all of the option are given in cube roots but the question is in square root .

so , there are two possibilities that maybe the question is typed wrong or the options are incorrect . But if everything present in the question is correct then none of the given values are equivalent to the given expression.

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The simplified value of radical expression 4√16 x¹² is 2x^3.

By considering the given expression

4√16 x¹²

=(16x^12)^1/4

=(2^4)^1/4( x^12)^1/4

=2x^3.

An expression with a square root is referred to as a radical expression. Radicand: A value or phrase contained within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.

The 'V'-shaped portion of the radical symbol will have a superscript number when it is used to represent any root other than a square root. For instance, the expression 3(8) denotes the cube root of 8.

The radical symbol, which resembles a check mark, the index, a small number written outside the radical symbol, and the radicand, a quantity written beneath the horizontal bar of the radical symbol, are the three main components of the radical expression ab.

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The midpoint of the segment is (7, 4).

According to the section formula-

If a point (x , y) divides a line in the ratio of m : n, where the two endpoints of the line are (x1, y1) and (x2, y2), then-

x = (nx1 + mx2)/ (m + n)

and y = (ny1 + my2)/ (m + n)

Here, we are given two points- (9, 6) and (5, 2)

Therefore,

x1 = 9, y1 = 6

x2 = 5, y2 = 2

Since, midpoint divides a line segment into two equal halves, m : n = 1 : 1

Now, substituting the values in the section formula we get-

x = (9 + 5)/2

x = 14/2

x = 7

and y = (6 + 2)/2

y = 8/2

y = 4

Thus, the midpoint of the segment is (7, 4).

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The value of x can not be told as there is no answer to the question "x+26".

Hence, can not be solved and it is left as 'x+26'

Answer:

It is Perpendicular