3. Your car gets 30 mpg on the highway. If gas costs $4.20 per
gallon, how much does it cost to drive your car per mile?​

To find how much of 5/8 is you would need to divide 1/2 by 5/8:

X = (1/2) / (5/8)

When dividing fractions, you reverse the second fraction and multiply:

X = (1/2) x (8/5)

X = 8/10

Simplify:

X = 4/5

The fractional amount of the fraction 5 over 8 in the fraction 1 over 2 is the fraction 4 over 5. Therefore, Option B is correct.

From the information given;

We are to find how much  the Fraction 5 over 8 is in the Fraction 1 over 2

This implies that we need to divide the fraction 5 over 8 i.e.  [tex]\mathbf{\dfrac{5}{8}}[/tex]  by the fraction 1 over 2 i.e. [tex]\mathbf{\dfrac{1}{2}}[/tex]

Mathematically;

[tex]\dfrac{1}{2} \div \dfrac{5}{8}[/tex]

[tex]\mathbf{= \dfrac{1}{2} \times \dfrac{8}{5} }[/tex]

[tex]\mathbf{= \dfrac{4}{5}}[/tex]

Therefore, we can conclude that the fractional amount of the fraction 5 over 8 in the fraction 1 over 2 is the fraction 4 over 5.

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Answer:

all work is shown and pictured

The given family of facts can be completed as follows:

2 8 6 0 -4 -2 22 86.

by observing the given number pattern.

To complete the family of facts,  observe the pattern and determine the missing numbers.

Starting with the first number, 2, observe that each subsequent number is obtained by multiplying the previous number by 4 and then subtracting 2.

So, to find the next number, multiply 6 by 4 and subtract 2, giving  22.

Similarly, to find the next number after 22, we multiply 22 by 4 and subtract 2, resulting in 86.

Therefore, the completed family of facts is 2 8 6 0 -4 -2 22 86.

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Answer:

-7 degrees

Step-by-step explanation:

-28 divided by 4 equals -7. -7 x 4 = -28

Answer:

[tex]-7^{\circ}F[/tex]

Step-by-step explanation:

Let x represent temperature change per hour.

We have been given that the temperature is going to steadily drop over the next 4 hours and the temperature changes by the same amount each hour.

So temperature change in 4 hours would be [tex]4x[/tex].

We are also told that the temperature changes by a total of -28°F, so we can represent this information in equation as:

[tex]4x=-28^{\circ}F[/tex]

Let us solve for x.

[tex]\frac{4x}{4}=-\frac{28^{\circ}F}{4}[/tex]

[tex]x=-7^{\circ}F[/tex]

Therefore, the temperature changes [tex]-7^{\circ}F[/tex] each hour.

Answer:

(attached is the formulas and equations)

Answer:

20 boxes can fit

Step-by-step explanation:

15x2×4=120 so 120 is the area of the storage locker

3×2×1=6 so 6 is the area of the boxes

120÷6=20

The domain of the function is the set of values for x, given as {2,3,4}. The range, which is the set of all output values for y that result when substituting each x value in the domain into the equation, is {8,6,4}.

In this problem, we are given an equation y + 2x = 12 and a domain D = {2,3,4}, which means x takes the values 2, 3, and 4. The domain of a function is all the possible values that x can take. Therefore, in this case, the domain (D) is {2,3,4}.

The range, on the other hand, includes all the corresponding output values that y takes for each x in the domain. The output is determined by plugging each value of the domain (x) into the equation and solving for y:

Hence, the range for this equation, given the domain {2,3,4}, is {8,6,4}.

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Answer:

One gallon of paint is not enough to paint the bedroom floor

Step-by-step explanation:

step 1

Find the area of the bedroom floor

The area is in the shape of rectangle

so

[tex]A=(11.4)(12.5)=142.5\ ft^2[/tex]

Remember that the bedroom floor will be painted with two coats of paint

so

Multiply the area by two

[tex]A=(2)142.5=285\ ft^2[/tex]

A gallon of paint will cover approximately 150 square feet

[tex]285\ ft^2 > 150\ ft^2[/tex]

therefore

One gallon of paint is not enough to paint the bedroom floor

Final answer:

No, one gallon of paint will not be enough to paint the bedroom floor with 2 coats of paint.

Explanation:

To determine if one gallon of paint will be enough to paint the bedroom floor with 2 coats of paint, we need to calculate the total area of the floor and then divide it by the coverage area of a gallon of paint.

The area of the bedroom floor is calculated by multiplying the length and width together: 11.4 feet * 12.5 feet = 142.5 square feet.

Since we need to apply 2 coats of paint, we need to double the area: 142.5 square feet * 2 = 285 square feet.

Since one gallon of paint covers approximately 150 square feet, one gallon of paint will not be enough to paint the bedroom floor with 2 coats of paint.

Answer:

First Equation answer: r > 2

Second Equation answer: 7 (r+3)

Step-by-step explanation:

First Equation Explanation: Move variable to the left side (2r + 2r + 8 > 16)

See the like terms (4r > 16-8)

Divide both sides by inequality of 4 (4r > 8) 4r----> r > 2

Second Equation Explanation: Factor out 7.

same thing here, let's pick two points, any two points off the table to get the slope.

[tex]\bf \begin{array}{|cc|ll} \cline{1-2} tables&cost\\ \cline{1-2} 1&10\\ 2&18\\ 3&24\\ 4&28\\ \cline{1-2} \end{array} \begin{array}{llll} \\[1em] \leftarrow \\\\ \leftarrow \end{array}\qquad \qquad (\stackrel{x_1}{2}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{28})[/tex]

[tex]\bf \stackrel{\textit{\large average rate of change}}{\stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{28}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}}\implies \cfrac{10}{2}\implies 5}[/tex]

Answer:

The equation has only one solution

Step-by-step explanation:

* Lets explain how to solve the problem

- There are three types of solutions for the equations

Case (1)

# Two sides of the equation have different coefficient of the variable

   and same or different numerical terms, then the equation has only

   one solution

- Ex: 2x + 5 = x + 5, lets solve it

∵ 2x + 5 = x + 5

- subtract x from both sides

∴ x + 5 = 5

- Subtract 5 from both sides

∴ x = 0

- Zero is a solution

∴ The solution of the equation is x = 0

- If the numerical terms are different x will be any other value, so the

 equation has only one solution

∴ The equation has one solution

Case (2)

# Two sides of the equation have same coefficient of the variable,

  and different numerical terms, then the equation has no solution

- Ex: 14x - 20 = 14x + 10, lets solve it

∵ 14x - 20 = 14x + 10

- Subtract 14x from both sides

∴ - 20 = 10

- The left hand side not equal the right hand side , then there is

  no value of x can make the two sides equal

∴ The equation has no solution

Case (3)

# Two sides of the equation have same coefficient of the variable,

  and same numerical terms, then the equation has infinitely

  many solutions

- Ex: 3x + 5 = 3x + 5, lets solve it

∵ 3x + 5 = 3x + 5

- Subtract 3x from both sides

∴ 5 = 5

- The left hand side is equal to the right hand side , then x can be

  any value because the two sides is already equal without x

∴ The equation has infinitely many solutions

∵ He will write two expressions simplified , not equal , have different

  coefficients on the variables and equate them, then it is like

  the first case

- That means not same coefficient of the variable, and may be not

 same numerical term

∴ The equation has only one solution

Answer:

the correct answer is 30

Step-by-step explanation:

Answer:

Minute hand moves 6 degrees, hour hand moves .5 degrees.

Step-by-step explanation:

Doing the math we agree that in 1 minute the little hand (hours) will move .5 degrees and the big hand (minutes) will move 6 degrees.

Answer:

Dylan and Nadhii agree. The value of both of their ratios is equivalent, so their ratios are also equivalent.

Good luck<3

Looking at the line graph any - number to the left of the -4 would be less than -4.

This would make A true, -8 is less than -4

Answer:

The answer for this question is A: −8 < −4

Step-by-step explanation:

If you have 0 on the number line and label the points - 4 would be closer to 0 than -8 . The greater number is the number that is closer to the 0.

Answer:

1:0,2,4,6,8,10

2:0,5,10,15,20,25

Step-by-step explanation:

Answer:

7/6

Step-by-step explanation:

Firstly we have to distribute it and write in this form

1/4*12x-1/4*5.6=0.5*3x+0.5*0.7

3x-1.4=1.5x+0.35 ( now that we have multiplied and simplified it we will combine like terms remember whenever you move it to the other side of equal signs it turns the opposite of the sign value eg positive to negative.

subtract 0.35 from both sides leaving the equations as 3x-1.75=1.5x

now we move 3x on other side to combine with 1.5x and 3x becomes negative

-1.75=1.5x-3x

-1.75= -1.5x (divide -1.5 from both sides

-1.75/-1.5=1.5x/-1.5

1.166666666666667=x  

or 7/6 if you left the fraction as it is and didn't simplify further.

Let me know if you don't understand  or need more help .

The student's algebraic equation 1/4 (12x−5.6)=0.5(3x+0.7) simplifies to x = 1.17. This is found by distributing numbers, rearrangement of terms, and final division to solve for x.

The question is an algebraic equation that needs to be simplified and solved. First, distribute the numbers in front of the parentheses to both the terms inside. This gives:

Next, rearrange terms to bring all terms involving x to one side of the equation and constants to the other side. This gives:

Simplify the equation to get:

Finally, divide by 1.5 on both sides to solve for x:

So, x = 1.17 (rounded to two decimal places).

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Answer:

is equidistant from the sides of the angle

Step-by-step explanation:

Answer:

equidistant from the sdie of the angles

Step-by-step explanation:

The ratios 1:2, 29:30, and 52:12 can be represented in different situations, such as recipe measurements, voting results, and quantities of colored marbles.

a. 1 to 2: In a recipe for pancakes, the ratio 1:2 could be used to represent the ratio of flour to milk. For every 1 cup of flour, you would need 2 cups of milk.

b. 29 to 30: Suppose a group of students are voting for their favorite ice cream flavor, and there are 29 votes for chocolate and 30 votes for vanilla. The ratio of 29:30 represents the ratio of votes for chocolate to votes for vanilla.

c. 52:12: Let's say you have a bag of different colored marbles, and there are 52 red marbles and 12 blue marbles. The ratio 52:12 would then represent the ratio of red marbles to blue marbles in the bag.

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Answer:

$16

Step-by-step explanation:

$2 x 5 = $10

1 pound = $9

2/3 = $6

10+6=16

Hey!

--------------------------------------------------------

Solution:

Ratio is 4/1

Add.

4 + 1 = 5

Divide.

150 / 5 = 30

Multiply for Ivan.

30 x 4 = 120

30 x 1 = 30

Check.

120 + 30 = 150

Subtract.

120 - 30 = 90

--------------------------------------------------------

Answer:

Ivan has £90 more than Tanya has!

--------------------------------------------------------

Hope This Helped! Good Luck!

Answer:

90

Step-by-step explanation:

Since the ratio is 4:1 there are 5 (4+1) parts you should divide it into.

150 ÷ 5 = 30

30 = 1 part

30 × 4 = 120

Ivan has 120 while Tanya has 30. to find the difference you subtract the two.

120 - 30 = 90

Answer:

The perimeter is 30 and the angle is 53.

Step-by-step explanation:

The perimeter is found by adding the length of all four sides. Two sides are 10 units and two sides are 5 units. 10+10+5+5 = 30.

The angle is found by subtracting angle ABC's value from 180.

180 - 127 = 53.

The perimeter of a parallelogram ABCD is 30 units and the measure of angle BCD is 53°.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Given that, from given parallelogram ABCD, m∠ABC=127°.

The length of BC Is 10 units, and the length of AB is 5 units.

Here, the perimeter of of a parallelogram is AB+BC+CD+DA

= 10+5+10+5

= 30 units

Here, m∠ABC+m∠BCD=180° (Sum of co-interior angles is 180°)

127°+m∠BCD=180°

m∠BCD=180°-127°

m∠BCD=53°

Therefore, the perimeter of a parallelogram ABCD is 30 units and the measure of angle BCD is 53°.

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Answer:

Lamb is the difference

Step-by-step explanation:

Answer:

range

Step-by-step explanation:

Answer:

Step-by-step explanation:

6*x=36

the inverse operation is the division  x = 36/6 = 6

Answer:7

Step-by-step explanation:

1.flip the equation 4y-12=16

2.add 12 to both sides 4y-12+12=16+12

3.divide both sides by 4

4y/4 =28/4

Y=7

Answer:

5

Step-by-step explanation:

4+5x=4x+9

-4x -4x

4+x=9

-4 -4

x=5

The equation to relate the number of weeks a computer programmer works to the number of hours worked is h = 40w, where h represents the total hours worked and w represents the number of weeks.

To relate the number of weeks w that a computer programmer works to the number of hours h he or she spends working, we can use a simple multiplication equation. Since we know the programmer works 40 hours per week, the relationship between hours worked and number of weeks can be represented as:

h = 40w

This equation states that the total hours worked (h) is equal to 40 times the number of weeks worked (w). For example, if the programmer works for 2 weeks, the total hours worked would be h = 40 * 2, which equals 80 hours.

Answer: [tex]y=8[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

We know that this is a horizontal line. This means that:

[tex]m=0[/tex]

Knowing that this line contains the point (-4,8) we can substitute  this coordinates and [tex]m=0[/tex] into [tex]y=mx+b[/tex], and then solve for "b":

[tex]8=0(-4)+b\\\\b=8[/tex]

Therefore, the equation of this line in Slope-intercept form is:

[tex]y=(0)x+8\\\\y=8[/tex]

Final answer:

The equation of the horizontal line that contains the point (-4,8) is y = 8 and it demonstrates that for a horizontal line, the slope is 0 and the y-coordinate remains constant along the line.

Explanation:

The equation of a horizontal line that contains a given point can be determined by looking at the y-coordinate of that point. Since a horizontal line has a slope of 0, the y-coordinate of any point on the line does not change. Therefore, the equation of the horizontal line that contains the point (-4,8) is simply y = 8. This equation indicates that the y-value will always be 8, regardless of the x-value, which is characteristic of a horizontal line. In the slope-intercept form of the equation of a line, which is y = mx + b, the slope (m) is 0, and the y-intercept (b) is 8.

To prove that angle 1 is equal to angle 3, we can use the given information and the properties of supplementary angles. Using substitution and algebraic manipulations, we can show that angle 1 is indeed equal to angle 3.

To prove that angle 1 is equal to angle 3, we can use the given information and the properties of supplementary angles.

Given: angle 2 = angle 4 and angle 2 and angle 3 are supplementary.

Since angle 2 and angle 4 are equal, we can substitute angle 4 with angle 2 in the given statement, giving us angle 2 = angle 2. Now, since angle 2 and angle 3 are supplementary, their sum is 180 degrees. So angle 2 + angle 3 = 180 degrees. We can rewrite this equation as angle 2 = 180 - angle 3. Now, we can substitute angle 2 in the equation with angle 4 (which is equal to angle 2), giving us angle 4 = 180 - angle 3. Rearranging this equation, we get angle 3 = 180 - angle 4. Since angle 4 = angle 2, we can substitute angle 4 with angle 2 in the equation, giving us angle 3 = 180 - angle 2. Finally, since angle 3 = 180 - angle 2, and angle 2 = angle 4 (from the given information), we can conclude that angle 1 = angle 3.

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Final answer:

The geometry proof demonstrates that angle 1 is congruent to angle 3 by using properties of supplementary and congruent angles.

Explanation:

The student is asking for help with a proof in geometry, a branch of mathematics. The proof involves understanding the properties of supplementary angles and congruent angles. Here is a step-by-step explanation addressing the problem:

Consequently, we have proven that angle 1 is congruent to angle 3.