MATHEMATICS
HIGH SCHOOL

7^2x^-3y/49x^-3y^-2

Answer:

The answer is: y^3.

The answer is: y^3.

Answer: This is the answer I got

x(xy-7)^2

x(xy-7)^2

MIDDLE SCHOOL

Find the sum of the first 40 terms of the arithmetic sequence 17, 24, 31, 38,...

The sum of the first 40 terms of 17, 24, 31, 38,..., with a common difference of 7 is: 6,140.

Recall:

- Formula for finding the sum of the first n terms of an arithmetic progression/sequence is given as:
- d = common difference between terms
- a = the first term of the sequence

Thus, the first term of the sequence, 17, 24, 31, 38,..., is: 17

- a = 17

Common difference (d) = 38 - 31 = 31 - 24 = 24 - 17 = 7

- d = 7

- n = 40 (sum of the first 40 terms is what is required

Plug in the values into the formula for finding the sum of the first n terms:

Therefore, the sum of the first 40 terms of 17, 24, 31, 38,..., with a common difference of 7 is: 6,140.

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Answer:

6120

Step-by-step explanation:

First let's calculate the 40th term. Here a(n) = 17+7(n-1), so a(40) = 17 + 7(39). This works out to 290.

To find the sum of the first 40 terms, add together the first and last terms and then divide the result by 2 (which gives us the average of the first and last terms), and then mult. this result by 40, the number of terms:

40(17 + 290)/2 = 40(306)/2 = 6120

HIGH SCHOOL

Julian needs to spend at least seven hours each week practicing the drums. He has already practiced five and one third hours this week. He wants to split the remaining practice time evenly between the last two days of the week. Write an inequality to determine the minimum number of hours he needs to practice on each of the two days.

Answer:

70 min

Step-by-step explanation:

If we take the hypothesis that by the end of the fifth day he had 5h20min drums practice then the remaining time to get to 7 hours practice time would be 1h40min.

MIDDLE SCHOOL

You are making a welding fixture and must cut down a length of steel tubing from 19 3/8 inches to 11 9/16 inches. When you cut the tubing, you will waste 1/16 inch of it because of the width of the saw cut. If the leftover piece is long enough, you will use it in another fixture. How long will this leftover piece be?

The length of the left over steel tubing is 7 3/4 inches.

What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

The original length of steel tubing = 19 3/8 inch

The cut down length of steel tubing = 11 9/16 inch

Length of the steel tubing wasted = 1/16 inch

Thus the length of the left over steel tubing is

⇒

⇒

⇒

⇒

⇒

⇒

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Hence we can conclude that the length of the left over steel tubing is 7 3/4 inches.

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7 3/4 inches will be left.

19 6/16 - 11 9/16

310/16 - 185/16 = 125/16 or 7 13/16

7 13/16 - 1/16 = 7 12/16 or 7 3/4

19 6/16 - 11 9/16

310/16 - 185/16 = 125/16 or 7 13/16

7 13/16 - 1/16 = 7 12/16 or 7 3/4

HIGH SCHOOL

Write 3.1818 as a fraction in simplest form.

First we will convert it to fraction and than we will see if it can be wrote in simpler way.

Fraction can be represented as:

A/B where A and B are integers. When you are writing decimal number as fraction you do it this way:

number A is your number but without decimal point.

A = 31818

number B is number 1 with four 0 numbers because there is four decimal numbers.

B = 10000

Our fraction looks like this:

we can divide both numbers with 2 and we get

Fraction can be represented as:

A/B where A and B are integers. When you are writing decimal number as fraction you do it this way:

number A is your number but without decimal point.

A = 31818

number B is number 1 with four 0 numbers because there is four decimal numbers.

B = 10000

Our fraction looks like this:

we can divide both numbers with 2 and we get

It would be equal to 31818/10000

MIDDLE SCHOOL

Jasmine is baking and selling cupcakes for $15 per dozen she would like to make more than $120 in cupcake sales which number line below represents the solution to the situation

Answer:

i'll explain it to you

Step-by-step explanation: look for a number line that has 180, 120, and 15 you see you have to multiply 15 by 12 dozen cupcakes which equals to 180 that way she earns more than $120

MIDDLE SCHOOL

What is equivalent fraction of 4/5

You can double the numerator and the denominator (8/10), triple, etc.

As for decimals, divide 4 by 5, which equals 0.8.

As for decimals, divide 4 by 5, which equals 0.8.

HIGH SCHOOL

Which is an equivalent expression for 14+10x+6−8x?14+10x+6−8x?

= (10 -8)x +(14+6)

= 2x +20

= 2x +20

HIGH SCHOOL

Find the angle of elevation of the sun when a 12.5 meter tall telephone pole casts an 18 meter long shadow.

To answer this problem, you should know the formula that we will be using and this would be:

Angle of elevation = arc tan( (vertical height)/(length of the shadow)).

Angle of elevation = arc tan( (vertical height)/(length of the shadow)).

Plugging in the values in the formula. Here, this angle is:

arc tan (12.5/18) = 34.78 degrees

The answer would be approximately 34.78 degrees

MIDDLE SCHOOL

Explain why drawing a quick picture helpful when adding decimals

Drawing a quick picture is useful when adding decimals because it provides a visual representation of the answer. It also allows you to be certain that you got the correct answer because adding computations can contain errors.

Why is drawing a picture important n decimal?The "draw a picture" problem-solving strategy involves students creating a visual representation of the problem. This resource will assist you in teaching your students how to use a fundamental problem-solving strategy that is easily understood by students of all abilities.

The decimal numeral system is the most widely used system for representing both integer and non-integer numbers. It is the Hindu-Arabic numeral system's extension to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system

To add decimals, arrange the numbers in a column with the decimal points aligned. Place a decimal point directly below the decimal points in the addends to keep the decimal point in your sum. Align the decimal point in the sum with the decimal point in the addends, and if necessary, add a zero. Drawing a picture will make it easier.

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