Ben participated in a race. During the first half of the race, he walked 3 miles and ran at a rate of 5 miles per hour for x hours. During the second half of the race, he walked for 2 miles and ran at a rate of 5.5 miles per hour for x hours. What equation could you write to solve for the number of hours Ben ran during each half of the race? Let y represent the number of miles in half the race. Write two equations, one for the first half of the race and one for the second half. How could you transform these two equations to be the same as the original equation you wrote to solve for x? What do you think this means about solving for the variables in a situation represented by two equations?

Answer:

Therefore, [tex] \angle ABC = 48\degree[/tex]

Step-by-step explanation:

We need to find the [tex] \angle ABC[/tex]

Since, [tex] \angle DBC = 180\degree[/tex]      ( since DBC is straight line )

[tex](7x-1)+(3x-9)=180\degree[/tex]

[tex]10x-10=180 \degree[/tex]

Add both the sides by 10 in above expression

[tex]10x-10+10=180\degree+10[/tex]

[tex]10x=180 \degree+10[/tex]

[tex]10x=190 \degree[/tex]

divide both the sides by 10 in above expression

[tex]x=\frac{190}{10}[/tex]

[tex]x=19 [/tex]

Hence, the value of x is 19.

Now, we will calculate [tex] \angle ABC[/tex]

[tex] \angle ABC = 3x-9[/tex]

Put x = 19 in above

[tex] \angle ABC = 3(19)-9[/tex]

[tex] \angle ABC = 57-9[/tex]

[tex] \angle ABC = 48[/tex]

Therefore, [tex] \angle ABC = 48[/tex].

let apple juice = x

 milk = 2x

 fruit punch = 3x

3x + 2x + x = 660

6x = 660

x = 660/6

x = 110 apple juices

2*110 = 220 milks

3*110 = 330 fruit punches

To determine the greatest number of full batches of trail mix that can be made, divide the total quantity of each ingredient by the required amount per batch.

To determine the greatest number of full batches of trail mix that can be made, we need to compare the quantities of granola and peanuts. First, we calculate the number of full batches we can make using granola. Since each batch requires 12 cups of granola, we divide the total quantity of granola (12 cups) by the required amount per batch (12 cups). The result is 1 full batch.

Next, we determine how many batches we can make using the peanuts. Since each batch requires 8 1/2 cups of peanuts, we divide the total quantity of peanuts (8 1/2 cups) by the required amount per batch (8 1/2 cups). The result is 1 full batch.

Therefore, the greatest number of full batches of trail mix that can be made is 1 batch.

 AC and BD are perpendicular bisectors of each other.

=> ABCD is rhombus.

AD = 13

AE = √(13^2 - 12^2) = 5

Answer:

Average speed: 585/11 or 53 2/11

Step-by-step explanation:

Let distance from New York to Boston, and vice-versa, be D

Then, time taken to travel from Boston to New York is: D/45

Also, time taken to travel from New York to Boston is: D/65

Total time taken for entire trip: D/45+D/65

Average speed: total distance/total time

Average speed: 2D/22D/585

Average speed:  53 2/11 or 585/11 mph

Answer: C P’(9,-6), L’(3,1)

The coordinates of P' and L' after the translation are (9, -6) and (3, 1) respectively.

A translation rule in mathematics describes the process of moving a geometric figure from one location to another without changing its shape or orientation. It involves shifting the figure horizontally or vertically by a certain distance. Translation rules are essential in geometry and are used to analyze and manipulate shapes on a coordinate plane.

The segment PL has endpoints P(4, -6) and L(-2, 1). To find the coordinates of P' and L' after being translated using the mapping (x, y) → (x + 5, y), we simply add 5 to the x-coordinates of P and L. Therefore, the coordinates of P' are (4 + 5, -6) which is equal to (9, -6), and the coordinates of L' are (-2 + 5, 1) which is equal to (3, 1).

The amount he paid for per dairy is (rounded to the nearest hundredth would be) $0.31 (31 cents)

Division is the process of splitting a number or an amount into equal parts.

Here, given that,

Leon bought a dozen dairies for $3.75

i.e. cost of 12 dairies = $3.75

Then, cost of per dairy = $3.75÷12

                                      =$0.3125

(The answer would be $3.75/12 which equals to $0.3125. )

Hence, The amount he paid for per dairy is $0.31.

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Both plans will work for achieving the goal.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Two plans for reaching a goal are given below.

Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7.20 per hour.

Then the total amount after 8th weeks will be

⇒ 8 x 9 x 7.20

⇒ $518.4

Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6.50 per hour.

Then the total amount after 8th weeks will be

⇒ 6 x 15 x 6.5

⇒ $585

Both plans will work for achieving the goal.

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To multiply 7 x 462 using place value and expanded form, we first write 462 as the sum of the products of its digits and their place values (400 + 60 + 2). We then multiply each component by 7 and add the results to get 3234.

To multiply 7 x 462 using place value and expanded form, you first need to break down the number 462 into expanded form. This means you write it as the sum of the products of its digits and their place values. We start at the right and move to the left: 2 (units), 60 (tens), and 400 (hundreds). So 462 in expanded form is 400 + 60 + 2.

The next step is to multiply each component by 7: 7 x 400 = 2800, 7 x 60 = 420, and 7 x 2 = 14. You add those results together to get your final answer: 2800 + 420 + 14 = 3234. So, 7 x 462 = 3234.

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It would be: 8 - (1 1/4 + 2 3/8)

8 - (5/4 + 19/8)

8-29/8

64-29/8

35/8 inches OR  4.375 is your answer

to convert a fraction to a decimal, divide the top number by the bottom number

 2 divided by 7 = 0.2857

rounded to the nearest thousandth = 0.286

The required money that the boy has is $13.50 initially.

Given that,
A boy spent one-half of his money on a book and one-third of his money on a pen. The remaining $2.25 he saved, how much money he had originally to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the money boy has to be x,
According to the question,
x - x/2 -x /3 = 2.25
x(1 / 6) = 2.25
x = 2.25 × 6
x = $13.50

Thus, the required money that the boy has is $13.50 initially.

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Answer:

premium answer :D

Step-by-step explanation:

Answer:

Joe

Step-by-step explanation:

Jon wrote 13 out of 18

Dividing 13 by 18 we get, decimal form

[tex]\frac{13}{18}=0.722........[/tex]

Jim wrote .7 (repeated .7)

0.777..........

Joe reduced his to 5/6

Dividing 5 by 6 we get, decimal form

[tex]\frac{5}{6}=0.833........[/tex]

These numbers are irrational numbers

0.833......>0.777........>0.722......

So, Joe had the higher grade.

Final answer:

It would take 6 workers 4 hours to paint the fence, as the total amount of work, 24 worker-hours, divided by 6 workers, gives 4 hours.

Explanation:

Let's tackle the problem by first determining the total amount of work done when 8 workers paint a fence in 3 hours. This work can be considered as 24 worker-hours (since 8 workers * 3 hours = 24 worker-hours). This total amount of work would stay the same regardless of the number of workers. So if 6 workers are going to do the same job, we'd divide the total work by the number of workers to find out how many hours it would take for 6 workers to complete the task.

Dividing the 24 worker-hours by 6 workers, we get:

24 worker-hours / 6 workers = 4 hours

Therefore, it would take 6 workers 4 hours to paint the fence.

Answer:

The answer is true

Step-by-step explanation:

Inductive reasoning is a principle in mathematical and philosophical logic where general conclusions are derived from specific situations. Its contrary is deductive reasoning where we use a general rule to explain particular situations, reasoning commonly used in mathermatics. Example: all right angles measure 90 degrees, AB is right angle so AB measure 90 degrees,

In inductive reasoning we use the opposite logic that can take to incorrect general principles due to a bias. Example, my friend is tall and a good basket player, Joe is tall and also plays good basketball so All tall people are good basket players is a biased conclusion.  

Answer:

5/9-2/3×5/2=

5/9-5/3=

-10/9

Step-by-step explanation: