Show that the system of rational expressions is closed under addition, or give an example showing the contrary.

Answers

Answer 1
Answer: Let p/q, r/s be elements of Q , the set of rational numbers, where q and s are non zero.We need to show that the sum is also a rational number.p/q + r/s =  (p*s + q*r ) /(q*s)
Since q and s are non zero, the sum is a rational number.

Related Questions

Anyone know the answer?
Please answer quick guys! 3. Given LJ ≅ MK, and LK ≅ MJ, prove ∠L ≅ ∠M (Picture is below)
AB+C=50BC+A=41What is A, B, C
Graph f(x)=-4|x 1|-3
The tangent, cotangent, and cosecant functions are odd , so the graphs of these functions have symmetry with respect to the:

Solve the equation for a: r=a+k/b a= ?

Answers

r = a + k/b

a = r - k/b

a = 1/b (r.b - k)

(4,?) is on the line 8x – 3y = -10. Find the other half of the coordinate

Answers

(4, ?) is on 8x - 3y = -10

The ? is the missing y coordinate.  (4, y) satisfies 8x - 3y = -10

8x - 3y = -10.      From point (4, y),  we would replace x = 4 in the equation below. y remains the unknown.

8*4 - 3y = -10

32 - 3y = -10

-3y = -10 - 32

-3y = - 42

y = -42/-3

y = 14
We need to plug 4 in place of x into the equation of the line and find the y-value.

8x - 3y = -10
8(4) - 3y = -10
32 - 3y = -10

Add 3y on both sides.

32 = -10 + 3y

Add 10 on both sides.

42 = 3y

Divide 3 on both sides.

y = 14

The point is (4, 14).

1. You have a 4 quart bottle of 70% pure apple juice. You want to mix it with 90% pure apple juiceto obtain 85% pure apple juice. How much of the 90% pure apple juice should you use?

Answers

Answer:

12 quarts of the 90% pure apple juice should be used

Step-by-step explanation:

Here, we want to calculate the number of quarts of the 90% pure apple juice to be used.

Let the number of quarts of the 90% pure apple juice to be used be x;

This brings the total of the 85% result to (4 + x)

By mathematical convention;

4 quarts of 70% + x quarts of 90% = (4 + x) of 85%

70% = 70/100 = 0.7

90% = 90/100 = 0.9

85% = 85/100 = 0.85

Thus, mathematically;

(0.7 * 4) + (0.9 * x) = 0.85(4 + x)

2.8 + 0.9x = 3.4 + 0.85x

Let’s collect like terms

3.4 -2.8 = 0.9x -0.85x

0.6 = 0.05x

x = 0.6/0.05

x = 12

Final answer:

To get an 85% pure mixture, you need to combine 4 quarts of 70% pure apple juice with 4 quarts of 90% pure apple juice. This is obtained by setting and solving an algebraic equation based on percentage purity and volume.

Explanation:

This problem relates to an area of mathematics known as algebra. We are trying to find the amount of 90% pure apple juice needed to achieve an 85% pure mixture with a 4 quart bottle of 70% pure apple juice.

First, let's set up an equation based on the given information:

70%(amount of 70% pure apple juice) + 90%(amount of 90% pure apple juice) = 85%(total amount of apple juice mix)

Since the 70% pure apple juice is 4 quarts, the equation becomes:70%(4 quarts) + 90%(x) = 85%(4 quarts + x)

Next, we will solve for x. To do this, convert the percentages into decimals, multiply through, simplify and solve.

0.7(4) + 0.9x = 0.85(4+x)  

2.8 + 0.9x = 3.4 + 0.85x

Solving for x, we get that x = 4 quarts.

So, you would need 4 quarts of the 90% pure apple juice to get an 85% pure mixture with your 4 quart of 70% pure apple juice.

Learn more about algebra here:

brainly.com/question/32436021

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On the map of an amusement park on a coordinate grid, the skating rink is at (−1.5, −1).Coordinate grid shown from negative 3 to positive 3 on x-axis and negative 3 to positive 3 on y-axis. There are increments of 1 over 2 for each grid line on each of the two axes. Only the whole numbers are labeled on either side of the axis.

Which of these shows how to plot the point to mark the skating rink?

From the origin, move 1.5 units to the left along the x-axis and 1 unit vertically down, and place the point.
From the origin, move 1 unit to the left along the x-axis and 1.5 units vertically down, and place the point.
From the origin, move 1 unit to the right along the x-axis and 1.5 units vertically down, and place the point.
From the origin, move 1.5 units to the right along the x-axis and 1 unit vertically down, and place the point.

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Answer:

The correct option is 1.

Step-by-step explanation:

It is given that the skating rink is at (−1.5, −1).

Here, x-coordinate is -1.5 and y-coordinate is -1.

In a point P(a,b),

If a>0, then the point P is a units right from the origin and if a<0, then the point P is a units left from the origin.

If b>0, then the point P is b units up from the origin and if b<0, then the point P is b units down from the origin.

It the given point (-1.5, -1), a=-1.5 and b=-1 both are negative.

From the origin, move 1.5 units to the left along the x-axis and 1 unit vertically down, and place the point.

Therefore the correct option is 1.

The first option is correct.

Moving 1.5 units to the left (or -1.5 units to the right).
Moving 1 unit down (or -1 unit up).

Therefore you get the result of (-1.5, 1) as is the location of the rink.

If prices increase at a monthly rate of 1.5% by what percentage do they increase in a year

Answers

The question says that prices increase at a monthly rate of 1.5%.
We know that there are 12 months in a year.
To to find the percentage of yearly increase, we just need to multiply the monthly percentage by the number of months in a year.

1.5% = 0.015

0.015 * 12 = 0.18

0.18 = 18%

Therefore, the prices increase 18% in a year.

Which word or phrase best completes the sentence?I used to be ________, with a quick temper, but I had to learn how to calm down.

A.
hotheaded

B.
peachy

C.
heart of stone

D.
crystal clear

Answers

hotheaded

This phrase means to be short tempered.