a man drove to work at an average rate of speed 60 miles per hour and
returned over thesame route driving at an average rate of speed of 40 miles per hour. If his total driving time was 1 hour, what was the total number of miles in
the round trip?

A yard is a unit of length. Hence, the Rebeccas have  [tex]\frac{11}{20}[/tex] a yard of ribbon.

What is the yard?

A yard is a unit of length in both US Customary and British Imperial Systems of Measurement.

Here, Rebecca had [tex]\frac{9}{10}[/tex] a yard of ribbon, and Rebecca gives [tex]\frac{7}{20}[/tex] of a yard of a friend.

Now, we have to subtract [tex]\frac{7}{20}[/tex] from the original [tex]\frac{9}{10}[/tex].

Since the denominator is the same as the rules of fractions.

Now, we multiply [tex]\frac{9}{10}[/tex] by [tex]\frac{2}{2}[/tex] so that the denominator [tex]10[/tex] and [tex]20[/tex] would be the same.

Therefore,

[tex]\frac{9}{10}[/tex]×[tex]\frac{2}{2}[/tex]=[tex]\frac{18}{20}[/tex].

Here, both the denominator are the same, we can subtract [tex]\frac{7}{20}[/tex] from the [tex]\frac{18}{20}[/tex].

[tex]\frac{18}{20}-\frac{7}{20}\\=\frac{11}{20}[/tex]

Hence, the Rebeccas have  [tex]\frac{11}{20}[/tex] a yard of ribbon.

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Final answer:

Rebecca has 11/20 of a yard of ribbon left after subtracting the 7/20 yard she gave to a friend from her initial 9/10 yard of ribbon by converting both fractions to have a common denominator.

Explanation:

Rebecca started with 9/10 of a yard of ribbon and gave away 7/20 of a yard. To find out how much ribbon she has left, we need to subtract the amount she gave away from the amount she started with. This can be done following these steps:

Ensure that both fractions have a common denominator. The least common multiple of 10 and 20 is 20, so multiply the numerator and the denominator of the first fraction (9/10) by 2 to get the equivalent fraction with a denominator of 20, which gives us 18/20.

Now subtract the second fraction (7/20) from the first fraction (18/20) since they now have a common denominator. This gives us 18/20 - 7/20 = 11/20.

Therefore, Rebecca has 11/20 of a yard of ribbon left.

Answer:

As given : Graph in the coordinate plane with title Julia’s volleyball digs. Vertical axis goes from 0 to 60 in increments of 5 and is labeled number of digs. Horizontal axis goes from 0 to 10 in increments of 1 and is labeled games played. A ray on the graph starts at point begin ordered pair 0 comma 25 end ordered pair and goes through points begin ordered pair 4 comma 37 end ordered pair and begin ordered pair 8 comma 49 end ordered pair.

As the ray passes through (0,25) and (4,37) and (8,49).

Equation of line passing through (a, b) and (p,q) is given by:

 →  [tex]\frac{y-b}{x-a}=\frac{q-b}{p-a}[/tex]

→Equation of line passing through (0,25) and (4,37) is :

[tex]\frac{y-25}{x-0}=\frac{37-25}{4-0}=3\\\\y -25=3x\\y =3x + 25[/tex]

As , y= 3 x + 25,  also passes through (8,49) also.

Equation of line is : y = 3 x + 25 or in Standard form : - 3 x + y = 25

Option (D) is the standard form of line which is : - 3 x + y = 25

The value of a number such that The difference between three-fifths of that number and 7 is -36 is -145/3.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

Subtraction = Minus of any two or more numbers with each other called subtraction.

Let's say that number is x.

Three-fifth of x ⇒ (3/5)x

The difference of (3/5)x and 7 will be,

(3/5)x - 7 = -36

Add 7 on both sides

(3/5)x = -29

Multiply 5/3 on both sides

x = -29(5/3)

x = -145/3

Hence "The value of a number such that The difference between three-fifths of that number and 7 is -36 is -145/3".

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Answer: Add 7 7 times

Step-by-step explanation: if you add 7 7 times like this 7+7+7+7+7+7+7 then that is your answer easy way too.

rate of change for 2x+4y=10

here rate of change can be found by finding slope

the general form for slope is y=mx+b

isolating y on the left side:

2x+4y=10

4y=[tex] y=\frac{-2x+10}{4}

[/tex]-2x+10

from here slope is -1/2

Rate of change =-1/2

A linear equation or function is always a representation of a straight line in the coordinate plane. The equation of the line that passes through points (4, 5) and (−3, −1) is y = (6/7)x + 9/7.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

The equation of a straight line is given by, y = mx + c

Where m is the slope while c is the y-intercept.

The slope of line passing by two points (x₁, y₁) and (x₂, y₂)

Slope(m) = (y₂ - y₁)/(x₂ - x₁)

The slope of the line that passes through  (4, 5) and (−3, −1) will be,

m = (-1 -5)/(-3-4)

m = -6/-7 = 6/7

So equation converts as, y = (6/7)x + c

Substitute, (4,5)

5 = (6/7)4 + c

c = 9/7

So, y = (6/7)x + 9/7 will be the equation.

Hence "The equation of the line that passes through points (4, 5) and (−3, −1) is y = (6/7)x + 9/7".

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Final answer:

Thomas will earn $2415 per month after a 15% raise on his current salary of $2100, which results in a raise amount of $315.

Explanation:

Thomas currently earns $2100, and with a 15% raise, we need to calculate the increase in his monthly pay. To find the amount of the raise, we calculate 15% of his current earnings. That is, we multiply his earnings by the raise percentage expressed in decimal form: $2100 × 0.15 = $315.

After finding the raise amount, we add it to his current salary to find his new monthly earnings. $2100 + $315 = $2415 per month. Therefore, after a 15% raise, Thomas will make $2415 per month.

The simplifying value of the expression is,

⇒ 3q - 6

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 4p + 12 - 3q - 4p - 18 + 6q

Now,

Simplify the expression as;

⇒ 4p + 12 - 3q - 4p - 18 + 6q

⇒ 4p - 4p - 3q + 6q + 12 - 18

⇒ 0 + 3q - 6

⇒ 3q - 6

Thus, The simplifying value of the expression is,

⇒ 3q - 6

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the correct order from greatest to least is:

0.863, 0.6833, 0.386, 0.3

Answer: The slope (m) of the line using two points where the line goes through is:

m = - 4 (negative 4).

Solution:

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

Taking two points in the graph where the line goes through:

P1=(0,2)=(x1,y1)→x1=0, y1=2

P2=(1,-2)=(x2,y2)→x2=1, y2=-2

Replacing in the formula of the slope:

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

m=(-4) / (1)

m=-4

The expression that uses the greatest common factor and the distributive property to rewrite the sum 75 + 45 is B. 15(5 + 3)

The distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is

A(B + C) = AB + AC

This property is known by distributive law and applies to subtraction also.

Given; the distributive property to rewrite the sum 75 + 45

First find the greatest common factor.

75: 1, 3, 5, 15, 25, 75

45: 1, 3, 5, 9, 15, 45

Their GCF is 15.

To get 75, we will multiply 15 by 5.

To get 45, we will multiply 15 by 3.

Therefore, 15(5 + 3) = 75 + 45.

The expression that uses the greatest common factor and the distributive property to rewrite the sum 75 + 45 is B. 15(5 + 3)

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The rate at which the water level is rising when the water is 8 inches deep in the trough is 13/30 ft/min.

To find how fast the water level rises when the water is 8 inches deep, we need to use the equation V = 30h^2, which represents the volume of the trough as a function of its height h. We are given that the trough is being filled at a rate of 13 ft^3/min, so we can set dV/dt (the rate of change of volume) equal to 13.

Substituting the given values into the equation dV/dt = 60h * dh/dt, we get 13 = 60 * h * dh/dt. Since h = 0.5 (in feet), we can solve for dh/dt which turns out to be 13/30 ft/min.

Therefore, the water level is rising at a rate of 13/30 ft/min when the water is 8 inches deep.

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