MATHEMATICS
MIDDLE SCHOOL

x + y = 1

Answer:

Solution of the system:

x = 8

y = -7

Step-by-step explanation:

In this problem, we have to solve a system of 2 equations. The system is the following:

We proceed in the following way:

1) First, we find x from the 1st equation. We add +2 on both terms of the 1st equation, and we get:

Then, we multiply by -1 both sides of the equation, and we get:

2) Now we replace x = 8 into the 2nd equation, and we solve for y. We find:

Subtracting 8 on both sides,

So, the solution of the system is

x = 8

y = -7

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MIDDLE SCHOOL

What is the perimeter of a rectangular building that is 80 feet wide and 140 feet deep?

Answer:

= 440 ft

Step-by-step explanation:

The perimeter of a rectangle is found by adding up all the sides. We use the formula

P =2(l+w)

where l is the length and w is the width

The length is 140 and the width is 80

P = 2(140+80)

= 2(220)

= 440 ft

MIDDLE SCHOOL

50 POINTS***** Why is partitioning a directed line segment into a ratio of 1:3 not the same as finding the length of the directed line segment?

The ratio given is part to whole, but fractions compare part to part.

The ratio given is part to part. The total number of parts in the whole is 3 – 1 = 2.

The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.

The ratio given is part to whole, but the associated fraction is .

Answer:

The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.

Step-by-step explanation:

We know that partitioning a directed line segment into a ratio of 1:3 means that we are dividing the given line segment into two parts whose first part is 1 times the of some quantity while the another part is 3 times of the same quantity. So basically we are comparing part to part in by ratio. And total number of parts in the whole will be just sum of both so we get 1+3=4

Hence choice (3) is correct answer.

"The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4."

The one third length of the directed line segment is as the length of the directed line segment is divided into the ratio of .

Further explanation:

Ratio is the numerical relation between two different things.

Given:

It is given that a directed line segment is separated in the ratio of .

Step by step explanation:

Step 1 :

The directed line segment is separated in the ratio of .

It means that there are total 4 shares as it contains four pieces.

One part is before the required point and 3 remaining parts are after the required point.

Step 2:

The one third length of the directed line segment means there are three parts of equal size.

Step 3:

Consider an example a ribbon has length of 8cm.

Now divide the ribbon into the ratio of .

Therefore, the ribbon is separated in the ratio of as

Now divide the ribbon equally in three parts that is of the ribbon.

Therefore, the ribbon is partitioned into one third as .

Thus, it has been proved the given explanation.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Fractions

Keywords: directed, line segment, length, one third, ratio, units, line, thing, quantitative relation, number, comparison, different things, ribbon, equally divided.

HIGH SCHOOL

Jacob drove from town a to town b at an average rate of x miles per hour, then returned along the same route at y miles per hour. if he then drove back to town b at z miles per hour along the same route, what was jacob's average rate of speed for the entire trip, in miles per hour?

The answer is 1,000 miles

HIGH SCHOOL

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x , [0, 9]

Answer:

Step-by-step explanation:

The following information is missing in the given question:

Using this we may solve the question as:

We are given the following in the question:

We have to find the number c such that f(x) satisfies the Mean value theorem.

Mean Value theorem:

It states that if the function is differentiable in the closed interval [a,b], differentiable in the interval (a,b), then there exist c in (a,b) such that:

Now,

Continuity in [0,9]

Since a polynomial function is continuous everywhere, f(x) is continuous in [0,9]

Differentiability in (0,9)

Since a polynomial function is differentiable everywhere the given function is differentiable in interval (0,9)

Then, by mean value theorem: