13. Consider the two repeating decimals shown
below.
0.31313131...
0.02020202...
a. By simply looking at the decimal
representations, what is the sum of these
two rational numbers? Write as a decimal
and as a fraction.
b.
Verify your answer by finding fractions that
represent each decimal. Add the fractions.
c. Write the difference of the two numbers as a
repeating decimal.

Answer:

x=45+5b

Step-by-step explanation:

x is  the total

The solutions of the linear equations are below:

(1/3)*x + 7 = 3 + (2/3)*x  is true if x = 12

5r−8=9r−12   is true if r = 1

(5/9)t− 27 = (1/9)t + 21   is true if t = 108

−(1/2)(−5y+4) = 2 + 1/2y  is true if y = 2.

a) The first linear equation we have is:

(1/3)*x + 7 = 3 + (2/3)*x

To solve this, move all the like terms together (I will move the ones with x to the left side and the ones without x to the right side).

(1/3)*x - (2/3)*x = 3 - 7

Now we just simplify:

-1/3*x = -4

Now we isolate x:

x = -3*-4 = 12

x = 12

That is the solution of the linear equation, so remember, you just need to isolate the variable.

Let's do the same for the other ones:

2) 5r−8=9r−12

5r - 9r = -12 + 8

-4r = -4

r = -4/-4 = 1

r = 1

3)  (5/9)t− 27 = (1/9)t + 21

(5/9)*t - (1/9)*t = 21 + 27

(4/9)*t = 48

t = (9/4)*48 = 108

4) −(1/2)(−5y+4) = 2 + 1/2y

Here we start by expanding the product in the left side, we will get:

(5/2)*y - 2 = 2 + (1/2)*y

(5/2)*y - (1/2)*y = 2 + 2

(4/2)*y = 4

2*y = 4

y = 4/2 = 2

y = 2

And so on, that is the general method to solve linear equations, just isolate the variable in one side of the equation and simplify the other side.

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Answer:

Step-by-step explanation:

we now that [tex]\sqrt[n]{x} *\sqrt[n]{y} =\sqrt[n]{xy}[/tex]

so:

[tex](\sqrt[3]{5} )(\sqrt[5]{25} )= \sqrt[3]{125} = 5[/tex]

The equation of the table is y = 28x

The slope intercept equation of a linear equation is as follows:

y = mx + b

where

Therefore, let's find the slope using (1, 28)(2, 56)

m = slope = 56 - 28 / 2 - 1 = 28

Therefore, let's find the y-intercept as follows:

using (1, 28)

28 = 28(1) + b

b = 28 - 28

b = 0

Hence, the equation of the table is y = 28x

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Answer:

AM= 2x+4

MB= 5x-8

AB= ?

So to get AB, you would need to find the total measurements of AM and MB.

AM=MB

2x+4=5x-8

2x=5x-12

-3x=-12

x=4

So now to find the measurement of AB, you need to plug it into AM and MB.

2(4)+4+5(4)-8= 24!!!

So the measure of AB would be 24.

Step-by-step explanation:

Step-by-step explanation:

Given that

To find

So, according to the question

we have,

So, we know that

The equation of parabola, that reflected over the  y axis, and horizontally compressed by a factor of m and translated up c units:

                  x = - my² + c ---------------(1)

Where,

    m show the a factor, c showing translation.

    And - sign show the compression.

Now, put the all given values in equation (1),

So, we will get

                  x = - my² + c ---------------(1)    

                   x = - [tex]\frac{1}{2} y^2[/tex] + 6          

Answer:

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Answer:

2years 6 months

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year.

I = P × R × T/100

Solving our equation:

$350 = $3500 × 4 × T /100

Let's solve your equation step-by-step.

350=(3500)(4)t/100

Step 1: Multiply both sides by 100.

350=(3500)(4)t/100

(350)*(100)=((3500)(4)t/100)*(100)

35000=(3500)(4)t

Step 2: Simplify both sides of the equation.

35000=14000t

Step 3: Flip the equation.

14000t=35000

Step 4: Divide both sides by 14000.

14000t/14000=35000/14000

t=5/2

t = 2.5 years

2.5 years = 2years 6 months

In linear equation ,the time taken by Evian, Toby and J are 10, 9 and 12 minutes respectively.

What is linear equation?

Using the concept of proportional relationship, the time taken by Evian, Toby and J are 10, 9 and 12 minutes respectively.

Using the concept of proportional relationship :

For Evian :

1.5 miles = 15 minutes

1 mile = x

1.5x = 15

x = 15 / 1.5

x = 10 minutes

For Toby :

2/3 miles = 6 minutes

1 mile = x

2/3x = 6

x = 6 ÷ 2/3

x = 9 minutes

For J :

0.75 miles = 9 minutes

1 mile = x

0.75x = 9

x = 9 / 0.75

x = 12 minutes

Therefore, the time taken by Evian, Toby and J are 10, 9 and 12 minutes respectively.

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The complete question is -

Students at Polk Middle School are given a fitness test. The results of their tests are shown in the table. Use the table to answer questions d-c. a. Find the time it takes each student to run 1 mile. FITNESS TEST RESULT Evian 1 1/2 miles in 15 minutes Toby: 2/3 miles in 6 minutes Jillian 3/4 miles in 9 minutes.​

The function, after the transformations is y'' = 1/4(x +84)

The function equation is given as:

y = |x|

1) Reflect the function about the y-axis.

This is represented as

(x, y) = (-x, y)

So, we have:

y' = |-x|

This gives

y' = |x|

This is represented as

(x, y) = (x, 1/4y)

So, we have:

y'' = 1/4y'

This gives

y'' = 1/4|x|

This is represented as

(x, y) = (x + 84, y)

So, we have:

y'' = 1/4(x +84)

Hence, the function, after the transformations is y'' = 1/4(x +84)

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Answer:

Try no solution

Step-by-step explanation:

Solving for the solution the answer is 4

Solving for x the answer is no solution

According to the given statement

Money is spent on food =8640

on rent is = 3240

Savings refers to the money that is left over after consumer expenditure is deducted from disposable income during a specific time period. Savings, then, is the net amount of money that a person or household has left over after all bills and commitments have been paid.

Savings are retained as cash or cash equivalents (such as bank deposits), which carry negligible risk of loss but also negligibly low returns. Savings can increase through investing , but doing so necessitates risking some of the money.

According to the given value;

saving = 36000 x 2/5

= 7200 x 2

=14400

=36000- 14400

=21600. left

food = 40/100 x 21600

=40 x 216

=8640

rent = 15/100 x 21600

=15 x 216

=3240

Money is spent on food =8640

and on rent is = 3240

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Answer:

  m∠B = 53°

Step-by-step explanation:

You want the measure of the acute angle, given that consecutive interior angles of the trapezoid have measures (32x-1) and (14x-3).

Consecutive interior angles between the bases of a trapezoid are supplementary:

  (32x -1) +(14x -3) = 180

Simplifying the equation, we get ...

  46x -4 = 180

  46x = 184 . . . . . . add 4

  x = 4 . . . . . . . . divide by 46

The smaller angle is ...

  14(4) -3 = 56 -3 = 53

The measure of angle B is 53°.

__

Check

The measure of angle C is 32(4) -1 = 127. This is the supplement of the measure of angle B, as it should be.

Answer:

Neither is correct

Step-by-step explanation:

Look at each side of the smaller figure and compare it to the larger figure. That will give you the scale: (Larger figure length)/(Smaller figure length)

Let's take the base
Smaller figure is 6 units
Larger figure is 9 units

Scale = 9/6 = 1.5

Take the vertical height
Smaller figure = 4

Larger figure = 8
So here the scale is 2

Scaling is inconsistent for different sides of the figure

So neither of them is right. For a figure to be scaled, all its sides must be scaled by the same number

Step-by-step explanation:

To know wgich scale factore the Original sketch was increased with Compare the measurements of the original sketch and the student's sketch.

HOW?

do the proportion with relations to each and every side to see by how much each side increased.

For the bases it will be>>>>>>> The base of the student's sketch/ The base of the Original sketch(distance)

=10/7

10/7Adjacent side of the Student's Sketch/Adjacent side of the Original sketch

10/7Adjacent side of the Student's Sketch/Adjacent side of the Original sketch=9/5

upper side os student's sketch / upper side of original sketch

upper side os student's sketch / upper side of original sketch =4/3

Before I go any further you can see that for any side there is no certain(constant) scale factor whuch was used to increase the original Sketch to the Student's Sketch. Fir each and every side the Scale factor keeps on Changing This brings us to a conclusion that NEITHER OF SASHA AND RANDY IS CORRECT.

HOPE THIS HELPS

11 > x is the possible values for the number.

In algebraic formulations, numbers are represented by letters or alphabets without their numerical values being specified. The fundamentals of algebra taught us how to represent an unknown value using letters like x, y, and z. Here, these letters are referred to as variables. A mathematical expression may have both variables and constants. A coefficient is any value that is introduced before and increased by a variable.

Given that :The sum of a number x and 33 is greater than the product of 4 and that number.

x + 33 > 4x

33 > 3x

11 > x

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Answer: 5x+6y=13

               6x-12y=14

The area of the remaining part of a large rectangle is 8m².

It should be noted that the original rectangle had sides of 8m by 6m.

In this case, it was stated that 4m was cut out from each side. The value of the remaining sides will be:

Area = Length × Width

Area = (8 - 4) × (6 - 4)

Area = 4 × 2

Area = 8m²

Therefore, the area of the remaining part of a large rectangle is 8m².

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Answer:

No solution

Step-by-step explanation:

First I plugged the value of y into the equation 10x-2y=, which gave me
10x- 2(5x - 3) = 7. Then you can distribute the -2 into the parenthesis giving you 10x - 2(5x)(-2 x -3) = 7. This leaves us with 10x- 10x + 6 = 7, because two negatives multiplied together form a positive. Now you subtract six from both sides to keep it equal, and you're left with 10x-10x= 1. This gives you 0= 1, which is not possible, so there is no solution.

We can check our work by putting 10x -2y= 7 into y=mx+b format, by subtracting 10x from both sides, leaving you with -2y = -10x+ 7. then you can divide out the -2, giving you y= 5x+ 7/5. Notice how the slopes in both our equations are 5x. This means that they are a group of parallel lines, bc they both stay at the same rate, despite having different y-intercepts or starting points.

I hope this helps and please let me know if you have any other questions or need somethign to be explained more :D

The slope of the line represented by the graph of a linear function is  -2/3.

The general equation of a straight line is -

y = mx + c

where -

m → slope of line

c → y - intercept of line

Given in a question a linear function that decreases from left to right passing through the coordinates A(2, 0) and B(5, -2).

A linear function is a function of general equation → y = ax + b which is same as y = mx + c. So, it represents a straight line.

The line passes through the points A (2, 0) and  B (5, -2). The Slope of the given line can be calculated using the following formula -

m = (y[2] - y[1]) / (x[2] - x[1])

m = (- 2 - 0) / (5 - 2)

m = -2/3

Therefore, the slope of the line represented by the graph of a linear function is  -2/3.

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The slope of the line represented by the graph of a linear function is  -2/3.

What is the general equation of a straight line?

The general equation of a straight line is -

y = mx + c

where -

m → slope of line

c → y - intercept of line

Given in a question a linear function that decreases from left to right passing through the coordinates A(2, 0) and B(5, -2).

A linear function is a function of general equation → y = ax + b which is same as y = mx + c. So, it represents a straight line.

The line passes through the points A (2, 0) and  B (5, -2). The Slope of the given line can be calculated using the following formula -

m = (y[2] - y[1]) / (x[2] - x[1])

m = (- 2 - 0) / (5 - 2)

m = -2/3

Therefore, the slope of the line represented by the graph of a linear function is  -2/3.

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The number of  mozzarella sticks that will be in the larger sample will be 5.

Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s). The sign used to express ratios is :.

The first step is to determine the ratio of mozzarella sticks to pretzel bites in the smaller sample. This can be done by dividing the quantity of  mozzarella sticks by the number of pretzel bites.

Number of mozzarella sticks / number of pretzel bites = 2 : 8  or 1 : 4.

Now, divide the number of pretzel bites in the larger sample by the ratio of mozzarella sticks and pretzel bites in the smaller sample.

The ratio of mozzarella sticks in the larger sample = 20 / 4 = 5

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The nearest whole number (ones place).

$14.59+ $5.83 + $0.89 =21 rounding off

Given,

$14.59+ $5.83 + $0.89

Whole no. is 0,1,2..

If we add these number we get 21.31 is 21

When rounding numbers, there are several basic guidelines that must be observed.

We must first determine our rounding digit. This is the digit that will be affected in the end.

Following that, we must examine the digit to the right of this location, which will determine the fate of the rounding digit.

We do not modify the rounding digit if the digit to the right is less than 5. All digits to the right of the rounding digit, however, are altered to 0.

If the digit to the right is 5 or greater, the rounding digit is increased by one, and all digits to the right of the rounding digit are converted to 0.

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Answer:

It's 366. 53*7=371 | 371-5 because the 0th term is -5

Answer:

£1.6

Step-by-step explanation:

we can round 1.252 to 1.25

to find how much 2 euros is, we first have to make 1.25 into 2.

to do that, we will use the same equation to get the answer for £

1.25/5*8=0.25*8=2. now we repeat for £1

1/5*8=0.20*8=1.6

hope it helps

Answer:

Step-by-step explanation:

12(5m-n)

Answer:

x=|4/3|

Step-by-step explanation:

3|2x|=12-4

|2x|= 8/3

x=4/3

The value of the expression in scientific notation is 1.2913 * 10^5

The expression is given as:

(1.28 × 105) + (1. 13 × 10³)

Rewrite properly as

(1.28 × 10^5) + (1. 13 × 10^3)

Express 10^3 as 10^-2 * 10^5

So, we have

(1.28 × 10^5) + (1. 13 × 10^3) = (1.28 × 10^5) + (1. 13 × 10^-2 * 10^5)

Factor out 10^5

So, we have:

(1.28 × 10^5) + (1. 13 × 10^3) = (1.28 + 1. 13 × 10^-2) * 10^5

This gives

(1.28 × 10^5) + (1. 13 × 10^3) = (1.28 + 0.0113) * 10^5

Evaluate the sum

(1.28 × 10^5) + (1. 13 × 10^3) = 1.2913 * 10^5

Hence, the value of the expression in scientific notation is 1.2913 * 10^5

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The scientific notation of (1.28 × 105) + (1. 13 × 10³) is  1.2913 × 10⁵

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.

The proper format for scientific notation is a × 10ᵇ

where

Therefore, let's evaluate (1.28 × 10⁵) + (1. 13 × 10³)

(1.28 × 10⁵)  = 128000

(1. 13 × 10³)  = 1130

Hence,

(1.28 × 10⁵) + (1. 13 × 10³) = 128000 + 1130 = 129130

In scientific notation,

(1.28 × 10⁵) + (1. 13 × 10³) = 129130 = 1.2913 × 10⁵

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The solution to the system of the equations h = (1/2)t + 4 and h = (1/4)t + 5.5 will be 7 cm and 6 weeks.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Half a centimeter grows on a 4 cm bean plant per week. One-fourth of a centimeter is added to a 5.5 cm bloom per week.

Let h be the height of the plant and t be the number of weeks. Then the equations will be

h = (1/2)t + 4

h = (1/4)t + 5.5

The solution to the equations will be

(1/2)t + 4 = (1/4)t + 5.5

(1/2 - 1/4)t = 5.5 - 4

t / 4 = 1.5

t = 6

Then the height of the plant will be

y = (1/2)6 + 4

y = 3 + 4

y = 7

The solution to the system will be 7 cm and 6 weeks.

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Answer:

131232- This is the answer

Answer:

3,1,2,1,3,2

Step-by-step explanation:

3,1,2,1,3,2

Answer:

35/20 yards

Step-by-step explanation:

We know the keyword “cut” means to divide, so we now know we have to use division.

7 3/4÷5/1

First, make 7 3/4 an improper fraction.

7 x 4 = 28

28+7= 35

Remember to keep the denominator.

35/4 ÷ 5/1

Then, use the method Keep, Change, & Flip.

(35/4)(1/5) = 35/20

Therefore…

Each piece will be 35/20 yards long.

An equation that models the balance y after x months​ y = 1070 - 172.5x.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

Zachary purchased a computer for $1070. The first step is to calculate the purchase he paid after 2 months.

= 1070 - 725

= $345

Then the purchase after 1 month is

= $345/2

= $172.5 per month

The equation can be written as:-

y = mx + c

y = 1070 - 172.5x.

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Answer: The answers are (-8,8) and (2,-12)

Step-by-step explanation: I substituted the coordinates into the equations and on both sides they matched!

Hope this helps! :3