HELP YOU ONLY HAVE TO ANSWER 1 BUT YOU CAN DO ALL IF YOU WANT

1. Kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get 36. How old is each sister?

(a) Write an equation that represents the situation. Explain any variable used.
(b) Solve the equation from Part (a). Show your work. State your solution as a complete sentence.


2. Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither.

(a) 6x + 4x - 6 = 24 + 9x
(b) 25 - 4x = 15 - 3x + 10 - x
(c) 4x + 8 = 2x + 7 + 2x - 20


3. At a bargain store, Tanya bought 3 items that each cost the same amount. Tony bought 4 items that each cost the same amount, but each was $2.25 less than the items that Tanya bought. Both Tanya and Tony paid the same amount of money. What was the individual cost of each person's items?

(a) Write an equation. Let x represent the cost of one of Tanya's items.
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences.

1/9

Short Cut That My Teacher Taught Me :)

0.1 repeating has 1 digit repeating after the decimal point, so there is one digit in the denominator. Put the repeating digit in the numerator place. That's your answer. You can do the same to any repeating decimal: 2 digits after the point has 99 as the denominator, 3 digits is the repeating number over 99, and so on. 

The population of Pleasanton is 17 % higher. (Right choice: D)

According to the statement, the population of Pleasanton is reduced by a factor of 0.9 in the 1980s and increased by a factor of 1.3 in the 1990s. The increase rate is found by means of this formula:

[tex]x =[(0.9)\cdot (1.3)-1]\cdot 100[/tex]

[tex]x = 17\,\%[/tex]

The population of Pleasanton is 17 % higher. (Right choice: D)

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The population of Pleasanton at the end of the 1990s is 17% higher than the population in 1980.

To compare the population of Pleasanton in the 1990s with the population in 1980, we need to consider the changes that occurred in each decade. In the 1980s, the population decreased by 10%. This means that if the population in 1980 was represented by 100, it would have decreased to 90 by the end of the decade.

In the 1990s, the population increased by 30%. Using the population of 90 at the beginning of the decade, the population at the end of the 1990s would be 90 + (30% of 90) = 90 + 27 = 117.

So, the population of Pleasanton at the end of the 1990s is 117, which is 17% higher than the population in 1980. Therefore, the correct answer is D) It is 17% higher.

It will take 20 months for the costs of Apartment A and Apartment B to be the same.

To find out how many months it will take for the costs of Apartment A and Apartment B to be the same, we need to set up an equation. Let's say it takes x months for the costs to be equal. The equation would be: 1000 + 1200x = 1500 + 1175x. We can solve this equation to find the value of x.

First, we can simplify the equation by subtracting 1175x from both sides: 1000 + 25x = 1500. Then, we can subtract 1000 from both sides to isolate the variable: 25x = 500.

Finally, we can divide both sides of the equation by 25 to solve for x: x = 20. Therefore, it will take 20 months for the costs of Apartment A and Apartment B to be the same.

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Answer: [tex]3068.18\text{ miles per hour}[/tex]

Step-by-step explanation:

We know that 1 hour = 60 minutes

1 minute = 60 seconds

Then by Unitary method , 1 hour=[tex]60\times60=3600\text{ seconds}[/tex]

Also, 5280 ft = 1 mi

Given speed =  4500 feet per second

To convert it into miles per hour.  we divide it by 5280 and multiply it by 3600 we get

[tex]4500\times\dfrac{3600}{5280}\\\\=3068.18181818\approx3068.18\text{ miles per hour}[/tex]

Hence, the correct answer = [tex]3068.18\text{ miles per hour}[/tex]

Answer: 24.0

Step-by-step explanation:

divide 492 and 20.5

The value of given percent 28.2% of 92 is equal to 25.94

To calculate 28.2% of 92,  follow these steps:

Convert the percentage to a decimal by dividing it by 100. In this case, 28.2% becomes 0.282 (28.2 ÷ 100 = 0.282).

Multiply the decimal by the number you want to find the percentage of. here, 0.282 multiplied by 92:

0.282 ×92 = 25.944

Round the result to an appropriate number of decimal places. In this case, we'll round it to two decimal places:

28.2% of 92 is approximately 25.94.

Therefore, 28.2 percent of 92 is equal to 25.94.

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Answer: It will take the bus 2.5 hours to travel 125km at 50km/h.

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given.

So, to find the time we have to divide the distance by the speed:

We have to apply: time = distance/speed

Replacing with the values given:

Time = 125 / 50 = 2.5 hours

It will take the bus 2.5 hours to travel 125km at 50km/h.

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The multiplication problem using 2-digit factors with a resulting product that falls between 7,000 and 8,000 is 81x90 = 7290.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that:

The number are 7,000 and 8,000

Let A and B be the two-digit number with a resulting product that falls between 7,000 and 8,000:

Let two numbers are:

81 and 90

The product of the numbers:

81x90 = 7290

The product of number falls between 7,000 and 8,000.

Thus, the multiplication problem using 2-digit factors with a resulting product that falls between 7,000 and 8,000 is 81x90 = 7290.

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The unknown number is = 3/4

Let the unknown number be X

4(X)  +  7 =  10

Minus 7 from the both sides:

4x  +7  -7 =  10 -7

4x + 0 = 3

4x = 3

Make x the subject of formula by dividing both sides by 4,

4x/4 = 3/4

Therefore,

x= 3/4

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The following system of equations,  x + y = 4 x - y = 6 represents an Independent System.

A formula that expresses the connection between two words on each side of an indication. A calculation with an integer multiple is referred to as an equation. Algebra is widely used in equations. In performing calculations but unsure of the precise amount, algebra is utilized.

When there is only one solution, a set of linear regression is persistent and independent. The diagrams of the platform's lines intersect at precisely one spot if this is the case. If a set of linear equations would have no resolutions, it is inconsistent. There is only one solution pair for an autonomous state (x,y). The sole solution is the intersection of the two lines. A system that is incongruous cannot be fixed.

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Surface area of the rectangle prism is 88 sq. units.

Given:

height of the rectangle prism (h) = 4 units

width of the rectangle prism (w) = 2 units

length of the rectangle prism (l) = 6 units

Recall:

Formula for surface area of a rectangle prism is:

[tex]SA = 2(lw +wh +lh)\\[/tex]

Plug in the values:

[tex]SA = 2(6\times 2 +2\times4 +6\times4)\\SA = 2(12 + 8 + 24)\\SA = 2(44)\\SA = 88[/tex]

Therefore, the surface area of the rectangle prism is 88 sq. units.

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The original gross margin is (2.50 / 1.00) - 1 = (2.5 - 1) = 1.5  =  150%

the cost increases 0.25, is an increase of (0.25 / 1.00) = 25%

  in order to keep the same gross margin, you need to increase the sale price by 25%

2.50*1.25 = 3.125

Then the gross margin is (3.125 / 1.25) - 1 = (2.5 - 1) = 1.5 = 150% ( same as original )