A pool gained 10 gallons of water on Friday due to rain. How could the owner of the pool bring the water level back to its previous level? Select all that apply. Let 10 gallons of water evaporate. Add 10 gallons of water with a hose. Increase the amount of water by 10 gallons due to rain. Let her kids play in the pool and splash out 10 gallons of water. Drain 10 gallons of water from the pool. Fill 10 old milk gallons with water and dump them into the pool.​

Answer:

x=5

Step-by-step explanation:

step 1 : exapnding 2(x+4) will give you 2x +8 , the student made an error in expanding

so it should then be 2x+8 = 6x-12

and then if you move the letters to one side and the numbers to the other you will get :

-4x = -20

x=5

hope this works :)

x=5

Step-by-step explanation:

the student added a minus in 2x and 8 when it's suppose to be an addition that is the error

2(x+4)=6(x-2)

2x+8=6x-12

2x-6x=-8-12

-4x=-20

x= -20/-4= 5

x=5

The roots of the quadratic equation represented by the graph are;  x = -2.5 and x = 2.5.

The solutions to the equation 2x² + x = 11 will be given by the points at which the graph intercepts the x-axis.

By looking at the graph, we can clearly see that the graph intercepts the x-axis at x = -2.5 and x = 2.5.

The roots are located between -3 and 3.

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Answer:

Step-by-step explanation:

Here is a simple example of set-builder notation set builder notation it says " the set of all x's, such that X is greater than 0".

Answer:

***4.4+ 1.5 * 2 / 0.5*** = 10.4

***3-2.5/3+1 1/3*** = 3.5

Step-by-step explanation:

Table:

Miles    Hours

  5          4

  40       32

  45       36

The ratio between Miles and Hours is 5:4

In the table, miles = 40 is got by 8 x 5 = 40

So corresponding hours = 8 x 4 = 32

In the table, hours = 36 is got by 9 x 4 = 36

So corresponding miles = 9 x 5 = 45

So the ratios are 5:4 , 40:32, 45:36

Graph can be plotted with number of miles in the x-axis and number of hours in y-axis.

The points to be plotted are (5, 4), (40,32) and (45, 36). Joint these points to get a straight line on the graph.

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Answer:

13 • -2 = -26

Step-by-step explanation:

-13 + -13= -26

The solution of the graph of the solution set y< 2x - 8 and y > -1/2 x - 3 is shown in image by purple shade.

What is Inequality?

To compare two or more mathematical expression in a relation is called an Inequality.

Given that;

The solution sets are;

y < 2x - 8

y > -1/2 x - 3

Now, We draw graph of inequalities.

Then we get,

The graph of the solution set y< 2x - 8 and y > -1/2 x - 3 is shown in image by purple shade.

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The total cost is T(x)={ 90x if 0≤x≤2, 180+50x if x > 2}

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

An algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition(+), subtraction(-), multiplication(×), and division(/).

Given:

T(x)={a if x≤2, b if x > 2}

let us take

a= 90x, 0≤x≤2

and, b = 180 + 50x  for x>2

Hence. the total cost be T(x)={ 90x if 0≤x≤2, 180+50x if x > 2}

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Using the motion equation we can get:

a) s = -16*t^2 + 1028

b) 992 feet above the ground.

c) after 8 seconds, the coin will hit the ground.

First, we know that the general height equation is:

s = -16*t^2 + v0*t + s0

In this case, the coin is dropped, so the initial velocity v0 is zero.

And the coin is dropped from a height of 1028 ft, then s0 = 1028

Replacing that in the equation we get:

s = -16*t^2 + 1028

b) The height after 1.5 seconds is what we get by evaluating the height equation in t = 1.5

s = -16*(1.5)^2 + 1028 = 992

This means that the height after 1.5 seconds is 992 ft above the ground.

c) The coin will strike the ground when s = 0, then we need to solve:

s = 0 = -16*(t)^2 + 1028

Solving that for t, w eget:

16*t^2 = 1028

t^2 = 1028/16

t = √(1028/16) = 8

This means that the coin will hit the ground after 8 seconds.

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The typical pace of change since the slide's start, -14/3.

Let, the average rate of change is k

(x1,y1) (x2,y2), k= (y2-y1)/(x2-x1)

=10-80/15

=-70/15

k=-14/3

Average = -14/3

Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in measurable parameters like average speed or average velocity calls for the knowledge of the average rate of change.

The average rate of change is a measure of how quickly on average one quantity changes in relation to another. It provides a general sense of the function's change in value per unit throughout the specified time period. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another. Let's take a closer look at the average rate of change formula.

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Answer:

83/100

Step-by-step explanation:

To turn a decimal into a fraction, place decimal number over its place value.

Place value = 100

Decimal number = 83

Answer:

[tex] \large \sf \: 6y - 8[/tex]

Step-by-step explanation:

Let's simplify step-by-step.

8y−2(y+4)

Distribute:

=8y+(−2)(y)+(−2)(4)

=8y+−2y+−8

Combine Like Terms:

=8y+−2y+−8

=(8y+−2y)+(−8)

=6y+−8

=6y−8

Answer:

6y - 8

Step-by-step explanation:

This is a simplifying problem, so we just need to separate and link the like terms.

First we start with the parenthesis by distributing

-2*y + -2*4

-2y - 8

We can the put it back into the equation

8y - 2y + 8

8y and -2y are like terms so we can put them together to get 6y

6y +8

Answer:

y = -1/12x + 11

Step-by-step explanation:

An ordered pair is the form (x,y)  Us the x and y from the point and the slope to find the y intercept and then you can write the equation.

Use o for x and  11 and or y and - 1/12 for m

y = mx + b

11  = (-1/12)(0) + b

11 = b

y = -1/12x + 11

Answer:

Y = -1/12 x + 11

Step-by-step explanation:

Start with point (0,11)   slope ( -1/12)  form :

(y-11) = -1/12 (x-0)

      re-arrange to slope intercept form just by adding 11 to both sides

y = -1/12 x + 11    

Answer:

a) 3

b) draw a rectangle

Step-by-step explanation:

___

|___| combine the rectangle (3 bottom lines, 3 top lines, 2 left lines, 2 right lines)

Yes, the pole will fit in the box when kept diagonally.

In order to fit the pole in rectangular prism or cuboid, it has to be kept diagonally. Now, we need to calculate the length of body diagonal of cuboid. The length of body diagonal of cuboid should be greater than pole to fit it.

The length of body diagonal of cuboid can be calculated by the formula -

Diagonal = √(l² + b² + h²)

Keep the values in formula to find the diagonal of rectangular prism

Diagonal = √(10² + 9² + 8²)

Taking square of the three numbers to find the diagonal of rectangular prism

Diagonal = √100 + 81 + 64

Taking sum of numbers present on Right Hand Side of the equation

Diagonal = √245

Taking square root of the number

Diagonal = 15.65 feet

Hence, as the diagonal of rectangular prism is greater than shower curtain pole, it will definitely fit.

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Answer:

I think the answer is Answer: 1.17 per cup

Step-by-step explanation:

Work  

If one 1-pint is 2 cups

Then  2 *  8 = 16 cups

so then  $18.72 divided by 16

1.17 US

Hope this help pls like

Answer:

[tex]r \times \cos( 0) = - 6 \\ r = - \frac{6}{ \cos(0) } \\ r = - 6 \sec(0) \\ \\ r \times \cos(0) = 10 \\ r = \frac{10}{ \cos(0) } \\ r = 10 \sec(0) [/tex]

Answer

this question is impossible!11!1!!!!

Step-by-step explanation:

none

If you solve the inequality you will have a final answer w ≤ 10. The greatest value being 10.

According to the statement

We have to find that the value of the width.

So, For this purpose, we all know that the

A rectangle may be a form of quadrilateral, whose opposite sides are equal and parallel.

From the given information:

the length of a rectangle is fourfold its width. if the perimeter is at the most 106 centimeters

Then

L = 4w --------The length of a rectangle is fourfold its width.

2w + 2L ≤ 106 ------- the perimeter is at the most 130 centimeters.

Now, if substitute the primary equation into the second inequality you may get

2w + 2 • (4w) ≤ 106.

Therefore, the inequality model becomes 2w + 2 • (4w) ≤ 106.

So, If you solve the inequality you will have a final answer w ≤ 10. The greatest value being 10.

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Greetings from Brasil...

Using set theory to solve this question

Let

D = Dogs Set

C = Cats Set

R = Classroom Set

n(D ∪ C) = n(D) + n(C) - n(D ∩ C)

n(D ∪ C) = 14 + 11 - 3

n(D ∪ C) = 22

Then,

Total = n(D ∪ C) + 24

Total = 22 + 24

Answer:

b

Step-by-step explanation:

Answer:

x/12

Step-by-step explanation:

In terms of x with no dollar numbers provided, the amount LESS for 4 people versus 3 would be x/3 - x/4.  Getting 12 as the LCD and subtracting gives x/12 less to pay.

Answer:

0.5L

Step-by-step explanation:

240ml = 1 cup

120ml = 1/2 cup

80ml = 1/3 cup

60ml = 1/4 cup

^ add together and get 500ml, change unit to liters and your set will hold 0.5l

Two numbers are drawn without replacement. The only way their product is zero is if one of these numbers is zero. The probability of this happening is

[tex]\dfrac{\dbinom11 \dbinom51}{\dbinom62} = \dfrac{1\cdot5}{15} = \boxed{\dfrac13}[/tex]

In other words,

• there is 1 zero in the list - we draw it with [tex]\binom11 = 1[/tex] way of doing so;

• there are 5 non-zero numbers in the list - we draw 1 of these, with [tex]\binom51 = 5[/tex] ways of doing so;

• there is a total of 6 numbers in the list - we draw 2 of these, with [tex]\binom62 = 15[/tex] ways of doing so.

On the other hand, if the numbers are drawn with replacement and independently of one another, then each number has the same probability of getting drawn each time. There are 6×6 = 36 possible outcomes, each with 1/36 probability of occurring. Their product is zero if at least one of the numbers drawn is zero. The probability of this happening is

[tex]\dbinom21 \dfrac16 \times \dfrac56 + \dbinom22 \left(\dfrac16\right)^2 = \dfrac{11}{36}[/tex]

That is,

• there is 1/6 chance of drawing a zero and 5/6 chance of not drawing a zero. This can selection can happen in [tex]\binom21=2[/tex] ways (zero is drawn first or last);

• there is 1/6 chance of drawing a zero for either selection. This can happen in [tex]\dbinom22=1[/tex] way (zero is drawn both times).

While the probabilities are close, they are not the same! Be careful with which interpretation you choose.

[tex]\dfrac13 = \dfrac{12}{36} > \dfrac{11}{36}[/tex]

Answer:

  11)  KI = 28

  12) PR = 22

Step-by-step explanation:

You want the base segment lengths KI and PR, given relations between those segments and the corresponding midsegment of the triangle.

A midsegment is a line segment that joins midpoints of other line segments, usually the midpoints of triangle sides or opposite sides of a quadrilateral. In the case of a triangle, the midsegment is parallel to the third side, and half its length. This relation is used to solve these problems.

  KI = 2·AB

  (x +37) = 2(x +23) . . . . substitute given expressions

  x +37 = 2x +46 . . . . . . eliminate parentheses

  37 = x +46 . . . . . . . . . . subtract x

  28 = x +37 . . . . . . . . . . subtract 9

The length of KI is 28 units.

  PR = 2·HG

  (x +30) = 2(19 +x) . . . . substitute given expressions

  x +30 = 38 +2x . . . . . eliminate parentheses

  22 = x +30 . . . . . . . . subtract (x+8)

The length of PR is 22 units.

__

Additional comment

As you can see here, there is no real reason to find the value of x, then substitute it back into the expression for the segment of interest. We can, and did, solve directly for the value of that expression.

As with any algebraic manipulation, any operation performed on one side of the equal sign must also be performed on the other side of the equal sign. When we say "subtract ()", we mean "subtract () from both sides of the equation."

In problem 11, x=-9. In problem 12, x=-8. Negative values of x work just fine, as long as the resulting segment lengths are positive.

From the given linear function, it is found that each descent by 88 meters was 11 seconds long.

The graph of the linear function is missing, and it is given at the end of the answer.

A linear function is modeled by:

y = mx + b

In which:

Given two points on the graph, the slope is given by change in y divided by change in x. For this problem, the points are given as follows:

(0, 440) and (40,0).

Hence the slope is:

m = (0 - 440)/(40 - 0) = -11.

Meaning that in each minute, he descended 8 meters. Thus the time to descend 88 meters is given by:

t = 88/8 = 11 seconds.

Each descent by 88 meters was 11 seconds long.

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The approximate length of string lights the staff needs to decorate the ceiling is 40.25

The complete question is added as an attachment

From the attached figure, we have the following coordinates

A = (5, 16)

B = (17, 10)

C = (14, 4)

D = (2, 10)

Calculate the lengths AB and BC using the following distance formula

d = √[(x2 - x1)^2 + (y2 - y1)^2]

This gives

AB = √[(5- 17)^2 + (16- 10)^2] = 13.4

BC = √[(14- 17)^2 + (4- 10)^2] = 6.7

The approximate length of string lights the staff needs to decorate the ceiling is then calculated as

P = 2 * (AB + BC)

This gives

P = 2 * (13.4 + 6.7)

Evaluate

P = 40.2

Hence, the approximate length of string lights the staff needs to decorate the ceiling is 40.25

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Answer: 40.25

Step-by-step explanation:

Answer:

y = m(x) + t

Step-by-step explanation:

Pretty sure this is the right answer...

Hope this helps! :D

The nut that has the higher unit price is pecans.

The pecans cost $0.65 more than cashews.

Looking at the table of the cost of pecan, it can be seen that the cost of pecan increase by $10 for every 1 pound increase in weight.

Cost of one pound of pecan : $5 / 0.5 = $10

A linear function is a function that has one dependent variable and one independent variable. A linear function represents a straight line on a coordinate plane.

A linear function has the form: a + bx

Where:

y = 9.35x

Cost of one pound of cashew : 9.35 x 1 = $9.35

Difference in cost = $10 - $9.35 = $0.65

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