Topic: Addition and Subtraction of polynomials

Directions: Simplify each rational expressions

please answer with solution.​

We have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.

Given,

The quantity of medicine added to the original mixture = 15 ounces

New quantity of medicine in the mixture = 18 ounces

Quantity of water in the mixture = 7 ounces

Total new quantity of mixture = 18 + 7 = 25 ounces

Original quantity of medicine in the mixture = 18 - 15 = 3 ounces

Original quantity of water in the mixture = 7 ounces

Total original quantity of mixture = 3 + 7 = 10 ounces

We have to find the amount of water to add into the new mixture to make the proportion of medicine and water same as the original mixture.

Here,

Proportion of medicine and water in original mixture = 3:7

Quantity of medicine and water in new mixture = 18:7

Now,

18 ÷ 3 = 6

Then, 7 × 6 = 42

So, 42 - 7 = 35

Therefore, we have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.

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To form a system with an infinite number of solutions, the equation -4x + 6y = 3 must be combined with D. 0.75 + x = 1.5 y.

A system of equations is a set of two or more equations which includes common variables.

To form a system with an infinite number of solutions, the lines should be the same or overlapping. These lines must have the same slope and y-intercept. The equations of these lines must be the multiple of one another.

Given the equation -4x + 6y = 3, rewrite this in the form c + ax = by(same as the form of the choices).

-4x + 6y = 3   ⇒   3 + 4x = 6y

To make 6y into 1.5y, divide both sides by 4.

3 + 4x = 6y   ⇒   0.75 + x = 1.5 y

Hence, the equation -4x + 6y = 3 must be combined with 0.75 + x = 1.5 y to form a system with an infinite number of solutions.

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The distance between each pair of parallel lines with the given equations y = -2x+1 and y = -2x+16 is 15 units.

We can find the points passing through the lines.

Hence,

The points passing through the line y = x - 11  are:-

Let x = 0

y = -2(0) +1

(0,1)

and;

Let x = 1/2

y = -2(1/2) + 1 = -1 +1

(-1/2,0)

The points passing through the line y = -2x + 16 are:-

Let x = 0

y = -2(0) + 16 =16

(0,16)

and;

Let x = 8

y = -2(8) + 16 = -16 + 16

(8,0)

Hence, using distance formula, the distance between the parallel lines will be:-

[tex]\sqrt{(16-1)^2+(0-0)^2} = \sqrt{15^2+0}=\sqrt{225} = 15[/tex] units.

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The result of multiplying the numbers 234 x 0.35 is 81.9

The numbers are given as:

234 and 0.35

Express the numbers in a product expression

So, we have

234 x 0.35

Express 234 as 200 + 34

So, we have

234 x 0.35 = (200 + 34) x 0.35

Expand the bracket

So, we have

234 x 0.35 = 200 x 0.35 + 34 x 0.35

Evaluate the product

So, we have

234 x 0.35 = 70 + 11.9

Evaluate the sum

So, we have

234 x 0.35 = 81.9

Hence, the result of multiplying the numbers 234 x 0.35 is 81.9

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Answer:

Step-by-step explanation:

(i)

[tex]2.014^2-2.012^2=\\(2.014+2.012)(2.014-2.012)=\\4.026*0.002=\\0.008052=\\8.052*10^{-3}[/tex]

(ii)

[tex]12^3+8^3=\\(12+8)(12^2-(12)(8)+8^2)=\\20*(144-96+64)=\\20*112=\\2240[/tex]

(iii)

[tex]9^3-5^3=\\(9-5)(9^2+(9)(5)+5^2)=\\4*(81+45+25)=\\4*151=\\604[/tex]

Answer: 1000

Step-by-step explanation:

4000/4

Answer:

1000

Step-by-step explanation:

blank can be written as x. since this is a multiplication problem we need to the opposite of multiplying, which is dividing. rewrite the problem as 4000/4=x

solve by dividing 4000 by 4 to get 1000

Solving for y in terms of x gives y = 31 - 5x

The subject of a formula is defined as the variable that is expressed in terms of the other variables in an equation or given expression.

It is also described as the variable that is being worked out in a given equation.

Given the equation;

5x +y = 31

Let's make 'y' the subject

We have to make 'y' stand alone by taking the other variables or terms over the equality sign, we have

y = 31 - 5x

Thus, solving for y in terms of x gives y = 31 - 5x

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Triangles are congruent if their matching interior angles and sides are all congruent.

What is congruence in math?

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.

Congruent figures: what are they?

What is congruent shapes?

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Answer:

13

Step-by-step explanation:

first use PEMDAS= P= Parentheses E= Exponents M= Multiplication D= Division A= Addiction S= Subtraction.

(3+6)+6-2=

9+6-2=

15-2=

13

Add 3+6 which is 9

Add 3+6 which is 9then add 9+6 equal to 15

Add 3+6 which is 9then add 9+6 equal to 15finally subtract 2 from 15

Add 3+6 which is 9then add 9+6 equal to 15finally subtract 2 from 15boom that's how you do it

Answer:

22

Step-by-step explanation:

Use Pemdas

P means parenthesis so add the numbers in the parenthesis

3 + 6 = 9

2(9) + 6 - 2 =

Next is E, but there are no exponents so now there is M

multiply 2 times 9, you will get 18.

18 + 6 - 2 =

So next is A which is addition, add 18 + 6

18 + 6 = 24.

24 - 2

And lastly, S which is subtraction.

24 - 2 = 22

So the answer is 22

Answer:

Solution on Screen

Step-by-step explanation:

It's okay don't worry

Answer:

[tex]y=18x+ 12[/tex]

Step-by-step explanation:

Given equation:

[tex]2+\dfrac{1}{6}y=3x+4[/tex]

Subtract 2 from both sides:

[tex]\implies 2+\dfrac{1}{6}y-2=3x+4-2[/tex]

[tex]\implies \dfrac{1}{6}y=3x+2[/tex]

Multiply both sides by 6:

[tex]\implies 6 \cdot \dfrac{1}{6}y= 6 \cdot3x+ 6 \cdot2[/tex]

[tex]\implies y=18x+ 12[/tex]

Answer:12+2y

Step-by-step explanation:

Answer:

12 + 2y

Hope this helps :)

Step-by-step explanation:

When it says "sum," this means the answer to 2 numbers you add. The first number would be 12, and the other number will be y 2 times. So y plus y equals 2y. The final equation is 12 + 2y.

Answer:

-2/5

Step-by-step explanation:

Hi there!

We find slope by using rise over run.

For this problem, identify two points on the line. I'll use (0, 3) and (5, 1).

[tex] m = \frac{{y} - {y} }{ {x} - {x}}[/tex]

You can plug the coordinates into this formula, making sure they stay in the right order. Subtract the first y coordinate from the second y coordinate, and the first x coordinate from the second x coordinate. (Just make sure one point is on the left, and the other on the right).

[tex] \frac{3 - 1}{0 - 5} = \frac{2}{ - 5} [/tex]

2/-5 is the same as -2/5, so that is your answer

Answer:

Recurring Decimal

Recurring Decimal, also called as repeating decimal, is a decimal number only that consists of digits repeating after a fixed interval after the decimal. For example, 46.374374374..., 5173.838383... etc. Decimals can be classified into different categories depending upon what type of digits occur after the decimal point, whether the digits are repeating, non-repeating, end, or unending (infinite digits after the decimal point).

Examples are

0.6666666666,

1.456456456

Step-by-step explanation:

Set as brainliest

Answer:

The answer is 36

Step-by-step explanation:

12+6=18

18/3=6

6 squared is 36

36 simplified is still 36

Answer:

The first 2 and the 2nd to last equations

Step-by-step explanation:

Angles 8 and 10 are alternate interiors, which would only work if m and n are parallel.

Angles 1 and 9 are congruent angles, which would only work if m and n are parallel.

Angle 1 and 3 are on the same line, so that can't prove it.

m8 and m9 could only add up to 180 if m and n are parallel, which makes this also true.

Angles 7 and 10 add up to 180, but can't be congruent.

Using least common multiple (LCM), the Vasquez family both visit their grandmother and host the neighbor hood party after 24 weeks. After 48 weeks, all three events will occur at the same time.

A common multiple is defined as a whole number, that is a shared multiple of each set of numbers. The least common multiple (LCM) of two integers is the smallest positive integer that is divisible by both numbers.

If the Vasquez family visit their grandmother every 3 weeks and host a neighbor hood party every 8 weeks, to know when will these event will occur at the same time, solve for the LCM of 3 and 8.

3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . .

8 : 8, 16, 24, 32, 40, . . .

LCM = 24

Hence, after 24 weeks, both will occur at the same time.

To know when will the three events will occur at the same time, solve for their LCM.

3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, . . .

8 : 8, 16, 24, 32, 40, 48, . . .

16 : 16, 32, 48, . . .

LCM = 48

Hence, after 48 weeks, all three events will occur at the same time.

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Answer:

why did the teacher give an exam

What is the sum of the finite geometric series?

a. -15+30-60+120-240+480= 315

Given:

a=-15

r= -2

n=6

[tex]S_n=\frac{a(1-r^{n})}{1-r} \\\\S_6=\frac{-15(1-(-2)^{6})}{1+2}\\\\S_6=\frac{-15(1-64)}{3}\\\\S_6=\frac{-15(-63)}{3}\\\\S_6=5*63=315[/tex]

What is a finite geometric series?

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When only three sides are provided without any information regarding the angle, such as a = 5 m and b = 9 m, c = 6m we can either create no triangle or create an unique triangle. Hence, either 0 or 1 Triangle.

For example :

How many different triangles may be formed with side lengths of 5m,9m and 6 m ?

Create a triangle with the following measurements: 5 meters, 9 meters , and 6meters, by protractor-adjusted to the given length of sides. You have constructed a triangle.

We can only create one triangle here, as no choice can be made in the given length of side as they are prefixed.

This implies that you cannot chose the side length independently. So, only one triangle which is unique will be formed. Hence, 0 or 1 triangle is formed

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Answer:

$3,985.00

Step-by-step explanation:

The formula for the amount accrued, A if you invest an amount P at r% compounded annually for n years is given by the formula

[tex]A = P\left(1 + \dfrac{r}{100}\right)^n[/tex][tex]A = P\left(1 + \dfrac{2}{100}\right)^{30} \\\\= P\left(1 + 0.02\right)^{30} \\\\= P\left(1 .02\right)^{30} \\\\= \; \$3,985.00[/tex]

The division by 100 is necessary to allow r% to be reduced to a decimal

So using this formula directly by substituting values gives

Answer:

Negative

Step-by-step explanation:

Answer: i believe its 3.2 cups per cake

Step-by-step explanation:

9.6 / 3 = 3.2

According to the given statement The sum of pair of vectors are  =  (-16 , -28).

The operation of combining two or even more vectors into a vector sum is known as vector addition. The rule for addition and multiplication of two or more vectors is given by the so-called parallelogram law. When two vectors are placed head to tail, the vector total is determined by drawing this same vector from of the free tail towards the free head.

Given two vectors are:

a =(6,-31)

b = (-22,3)

The vector sum is,

M = (a1 + b1, a2 + b2)

   = (Mx, My).

Substitution of the value we  get:

M = (6 + (-22), (-31) + (3))

   = (-16 , -28)

The sum of pair of vectors are  =  (-16 , -28).

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Answer:

1. Room size (length * width) for carpet

2. From window top to floor for curtains

Step-by-step explanation:

Answer:

"Games played in a workplace environment to achieve status, advancement and money"

Answer:

Step-by-step explanation:

Rate: 54000 brochures per hour

Formula: D=RT   Distance=Rate x Time (In this case distance is the amount)
(I’m not sure if you meant to type 3 1/4 or 314. I’ll include both)
D=54,000(3 1/4)

Two ways

1. 54,000(3 1/4)=175,500

2. 54,000x3 is 162,000, and 1/4 of 54,000 is 54,000/4=13,500. 162,000+13,500=175,500.

(54,000 x 314 = 16,956,000)

Hope this helps!

The area of triangle is 12 square units.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Given:

The given points are

A=(1,2)

B=(1,8)

C=(5,2)

According to given question we have

By the use of distance formula , we get

[tex]AC=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\AC=\sqrt{(5-1)^{2} +(2-2)^{2} }\\\\AC=\sqrt{(4)^{2} +(0)^{2} }\\\\AC=4 units\\\\\\AB=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\AB=\sqrt{(1-1)^{2} +(8-2)^{2} }\\\\AB=\sqrt{(0)^{2} +(6)^{2} }\\\\AB= 6 units[/tex]

Area of right triangle(A) is given by:

[tex]Area =\frac{1}{2} base *height[/tex]

where,

base of the triangle =4 units

height of the triangle =6 units.

[tex]Area =\frac{1}{2} base *height\\\\Area =\frac{1}{2}* 4 *6\\\\Area =12 square units[/tex]

Therefore, the area of triangle is 12 square units.

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The expression that represents the difference between the student's guess and the actual number of marbles will be 1206 - 2m.

When there are 1206 marbles in a jar and a student makes a guess of m marbles. The expression for the guesses will be:

= 2 × m

= 2m

The expression that represents the difference between the student's guess and the actual number of marbles will be:

= 1206 - 2m

= 2(603 - m)

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