ab + 3c = 2x, for b

 AC and BD are perpendicular bisectors of each other.

=> ABCD is rhombus.

AD = 13

AE = √(13^2 - 12^2) = 5

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.

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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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

Answer:

4680 is correct

Step-by-step explanation:

Answer:

r=8 8 is the answer

Step-by-step explanation:

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

To make the equation (4.8 × 10^–3)(n) = 9.6 × 10^9 true, the value of n is 2 × 10^12.

To make the equation (4.8 × 10–3)(n) = 9.6 × 109 true, we need to find the value of n. Let's solve the equation:

First, divide both sides of the equation by (4.8 × 10–3). This simplifies the equation to n = (9.6 × 109) / (4.8 × 10–3).

Next, simplify the right side of the equation by dividing the numbers and subtracting the exponents: n = (9.6 / 4.8) × 109-(-3) = 2 × 1012.

Therefore, the scientific value for n that makes the equation true is 2 × 1012.

Final answer:

To solve for n in the equation (4.8 × 10–3)(n) = 9.6 × 10⁹, divide both sides by 4.8 × 10–3. After dividing the coefficients and subtracting the exponents, the scientific value for n is 2 × 10².

Explanation:

To find the scientific value for n that makes the equation (4.8 × 10–3)(n) = 9.6 × 10⁹ true, we need to isolate n by dividing both sides of the equation by 4.8 × 10–3.

Divide each side by 4.8 × 10–3 to get:

n = (9.6 × 10⁹) / (4.8 × 10–3)

Now, we divide the coefficients (9.6/4.8) and subtract the exponents of 10 (9 - (-3)) to find n:

n = 2 × 10²

So, the scientific value for n is 2 × 10².

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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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.

The markup percentage for the video games is 66.67%.

Markup Percentage Calculation:

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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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.

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 phrase 'three increased by the quotient of a number and two' translated into an algebraic expression is '3 + n/2'.

To convert the given phrase 'three increased by the quotient of a number and two' into an algebraic expression, we first need to understand the mathematical operations involved in the phrase. 'increased by' is typically addition, 'the quotient of a number and two' signifies division.  Using 'n' to represent 'a number', 'the quotient of a number and two' can be represented as 'n/2'. Now, 'three increased by the quotient of a number and two' can be written as '3 + n/2'. So, the algebraic expression for 'three increased by the quotient of a number and two' is '3 + n/2'.

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Answer:

premium answer :D

Step-by-step explanation:

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].