A closet contains 5 cases of laundry detergent. Each case contains 12 bottles. Each bottle contains 3 liters of detergent.

How many liters of laundry detergent in all are in the closet?

Answer:

[tex]\displaystyle \large{x=\pm \sqrt{y}}[/tex]

Step-by-step explanation:

We are given the equation:

[tex]\displaystyle \large{y=x^2}[/tex]

Make ‘x’ the subject of the formula by square root both sides:

[tex]\displaystyle \large{\sqrt{y}=\sqrt{x^2}}[/tex]

Cancel the square root and square in RHS and write plus-minus in LHS:

[tex]\displaystyle \large{\pm \sqrt{y}= x}\\\displaystyle \large{x=\pm \sqrt{y}}[/tex]

Therefore, the solution is [tex]\displaystyle \large{x=\pm \sqrt{y}}[/tex]

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Summary

To make a variable as the subject of equation means to isolate that variable. For an example, if you want to make y as the subject, you’ll have to isolate y-term.

You may also be curious why do you have to add plus-minus on another side when cancelling [tex]\displaystyle \large{\sqrt{x^2}}[/tex] because [tex]\displaystyle \large{\sqrt{x^2}=|x|}[/tex] and [tex]\displaystyle \large{|x|}[/tex] for their positive and their counterparts (opposite/negative) will always give same y-value.

From an example:

[tex]\displaystyle \large{\sqrt{x^2}=4}[/tex] can be rewritten as [tex]\displaystyle \large{|x|=4}[/tex], cancel absolute sign/square root then write plus-minus which the solution is [tex]\displaystyle \large{x=\pm 4}[/tex] and if you substitute x = 4 or -4, the equation will be true for both values.

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Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

Answer:

100°

Step-by-step explanation:

the total of all angles around O on one side of AD is 180° (as that would represent a half-circle).

and the sum of the arc angles AB + BC + CD covers the whole 180°.

so, we have

180 = 55 + BC + 25

180 = 80 + BC

BC = 100°

Answer:

220 millimeters

Step-by-step explanation:

If you take 22 cm * 10mm/1cm you get 220 mm

Please rate!

Answer:

Mean: 5.19 or 5.2

Median: 5

Range: 17

Step-by-step explanation:

Range: Q3 - Q1

0, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 17

Here, we have 26 numbers

Minimum: 0

Maximum: 17

Median: 5 + 5 = 10/2 = 5

Lower quartile (Q1): 3

Upper quartile (Q3): 7

Range (biggest # - the smallest #): 17 - 0 = 17

Mean (add up all the numbers, and divide it by 26): 135/26 = 5.19 or 5.2

Hope this helps!

Take one side

Scale factor (A to B)

[tex]\\ \rm\rightarrowtail \dfrac{3}{9}=\dfrac{1}{3}[/tex]

#2

Scale factor Bto A:-

Scale factor (Ato B)=3/2

Answer:

The scale factor can either increase or decrease the size of an object. To find the scale factor of dilation:

[tex]\textsf{Scale factor} = \dfrac{\textsf{Dimension of the new shape}}{\textsf{Dimension of the original shape}}[/tex]

For these questions:

Question 1

[tex]\sf \implies scale \ factor=\dfrac{9}{3}=3[/tex]

Question 2

[tex]\sf \implies scale \ factor=\dfrac46=\dfrac23[/tex]

Answer:

y=3x+1

Step-by-step explanation:

The function (fg)(x) is a composite function

The value of the function (fg)(x) is 2x^3 + 7x^2 - 19x - 20

The functions are given as:

f(x) = 2x^2 - 3x - 4 and g(x) = x + 5.

To calculate (fg)(x), we make use of

(fg)(x) = f(x) * g(x)

So, we  have:

(fg)(x) = (2x^2 - 3x - 4) * (x + 5)

Expand

(fg)(x) = 2x^3 - 3x^2 - 4x + 10x^2 - 15x - 20

Collect like terms

(fg)(x) = 2x^3 - 3x^2 + 10x^2 - 4x - 15x - 20

Evaluate

(fg)(x) = 2x^3 + 7x^2 - 19x - 20

Hence, the function (fg)(x) is 2x^3 + 7x^2 - 19x - 20

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75 ÷ 15 = 5

the width is 5 inches

Answer:

25(m+3)

Step-by-step explanation:

25 is multiplied by (m+3)

'the sum of m and 3' is a quantity which must be indicated using parentheses

Hello!

The sum of means we add:

m+3

Multiply it times 25:

25(m+3)

The answer is Option C.

Now, the option you selected is wrong for the following reasons:

If you translate it into a verbal phrase, this is what it means:

25 plus the product of m and 3

Hence, Option C is correct.

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power! :-)

Answer:

Here,

n(A)={0,1,3,5,6}

n(B)={1,2,3,7}

n(AUB)=?

we know that,

AUB={0,1,2,3,5,6,7}

Step-by-step explanation:

is it okay ?

hopefully it works <3 ❣️

Answer:

the answer is (0, 0) trust me

The exponential function that passes through (0,2) and (3,54) is a growth function

The exponetial function is y = 2 * 3^x

The points are given as:

(x,y) = (0,2) and (3,54)

An exponential function is represented as:

y = ab^x

Substitute the points in the equation

2 = ab^0 and 54 = ab^3

Solve 2 = ab^0

a = 2

Substitute 2 for a in 54 = ab^3

54 = 2b^3

Divide by 2

27 = b^3

Take the cube roots of both sides

b = 3

So, we have:

y = ab^x

This becomes

y = 2 * 3^x

Hence, the exponetial function is y = 2 * 3^x

Read more about exponential functions at:

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Answer:

East

Step-by-step explanation:

Arkansas is East of Oklahoma.

Refer to the image below:

Answer: East

Step-by-step explanation:

Answer:

9 or 9 months (if you have to add units)

Step-by-step explanation:

Subtract 15 from his savings:

420-15 = $405

This is the amount left he has to  pay the monthly membership

405/45 = 9

9 is the number of months

Answer:

9 months

Step-by-step explanation:

Set up and solve the equation 15 + 45x = 420.  Begin by subtracting 15 from both sides.  After paying 15 dollars for the deposit, He will have $405 dollars left.  Divide both sides of the equation by 45.  When you divide 405 by 45 that will tell you how many months the membership can be paid.

Answer:

2

Step-by-step explanation:

gradient =y² -y¹ /x²-x¹

=9-1/2--2

=8/4

=2

Answer:

y = 2x + 5

Step-by-step explanation:

There are 2 ways to find this equation:

The first way:  We have: y = ax + b (this is the line, right?)

The line is through the point (-2, 1) so we have:

1 = (-2)a + b      (1)

The line is also through the point (2, 9) so we have:

9 = 2a + b.       (2)

From (1) and (2) we get a equals 2, b equals 5. Then:
y = 2x + 5

The second way:

Let A(-2, 1) and B(2, 9), then AB = (4, 8).

=> The normal vector of this line is n = (-2, 1).

The line that is through the points A(-2, 1) and B(2, 9), and has the normal vector n=(-2, 1) has the equation:

[tex]-2(x - 2) + 1(y - 9) = 0[/tex]

[tex]-2x + y - 5 =0\\ < = > y = 2x + 5[/tex]

Answer:

9n + 2

Step-by-step explanation:

Answer:

[tex]9p+2[/tex]

Hope This Helps! Please give Brainliest!

Answer:

[tex]x = -5 \pm \sqrt{26}[/tex]

Step-by-step explanation:

[tex]x^2+10x-1=0\\\\\implies x^2+2\cdot 5 x +5^2-5^2-1=0\\\\\implies (x+5)^2-25-1=0\\\\\implies (x+5)^2 -26=0\\\\\implies (x+5)^2 = 26\\\\\implies x +5 = \pm\sqrt{26}\\\\\implies x = -5 \pm \sqrt{26}[/tex]

Answer:

x=2.16

Step-by-step explanation:

1. Cross multiply.  3.5x(5) = 9(4.2)

2. Simplify. 17.5x=37.8

3. Divide both sides by 17.5. x=2.16

Answer:

Part A: 512 ft²

Part B: 3 cans

Step-by-step explanation:

Part A:

We can divide the shape into 2 areas or rectangles.

The top rectangle's area: 20 x 12 =240

The bottom: 34 x 8 = 272

add these 2 up, 240 +272, and you get 512, the area of this figure.

Part B:

We have to divide the number of feet covered by the area:

512/200 = 2.56

However, we half to round up, cause we cant buy part of a can, we have to buy a whole one.

So, we get 3 cans.

Answer:

48% chance to be female and 52% chance to be male.

Step-by-step explanation:

14 female + 15 males =  29 total people

a) 14 females/29 total = 0.48... * 100 = 48%

b) 15 males/29 total = 0.57.... * 100 = 52%

Answer:

[tex]\displaystyle [-2, 7][/tex]

Step-by-step explanation:

You want to eradicate one pair of variables so they are set to zero. It does not matter which pair is selected:

[tex]\displaystyle \left \{ {{4x + 2y = 6} \atop {-2x + 2y = 18}} \right.[/tex]

{½[4x + 2y = 6]

{−2x + 2y = 18

>> [tex]\displaystyle \left \{ {{2x + y = 3} \atop {-2x + 2y = 18}} \right. \\ \\ \frac{3y}{3} = \frac{21}{3} \\ \\ \\ y = 7[/tex]

Plug this back into the system to get the x-value of [tex]\displaystyle -2.[/tex]

I am joyous to assist you at any time.

Answer:

− (45m+2084)/40

Step-by-step explanation:

I do not have one sorry,

Answer: 3/8

Step-by-step explanation: 6/8 x 2/4 = 3/8

The fraction of attendees of legal age who are women are 3/8

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have in a stadium, 6/8 of the attendees are older and of these 2/4 are women.

The fraction of attendees of legal age who are women are -

2/4 of 6/8

2/4 x 6/8

12/32

3/8

Therefore, the fraction of attendees of legal age who are women are 3/8

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English translation of question -

In a stadium, 6/8 of the attendees are older and of these 2/4 are women, what fraction of the attendees of legal age are women?

Spanish translation of answer -

Tenemos en un estadio, 6/8 de los asistentes son mayores y de estos 2/4 son mujeres.

La fracción de asistentes mayores de edad que son mujeres son:

2/4 de 6/8

2/4 x 6/8

32/12

3/8

Por tanto, la fracción de asistentes mayores de edad que son mujeres son 3/8

Answer:

32x^7y^15

Step-by-step explanation:

x^2(2xy^3)^5

can be simplified by adding up the x and y values.

Answer:

78°

Step-by-step explanation:

Angles on a straight line = 180°

AD is the straight line

Angle BFA = 48

Angle CFD = 54

54 + 48 = 102

180 - 102 = 78

Therefore, Angle BFC = 78°

Answer:

To figure out the change, we subtract the original temperature by the following after temperature.

18°F - original

-9°F - subsequent time after original

So we set up the equation;

18°F - (-9°F)

(Two negatives combine to form a positive)

18°F + 9°F

= 27°F was the change in temperature.

The change in temperature from 2:00 PM to 10:00 PM is -27° F.

Temperature is a physical quantity that measures the coldness or hotness of an object in reference to some standard value.

Change in temperature can be defined by the difference of the final temperature with that of the initial temperature.

Temperature is usually measured in degree Celsius or degree Fahreheit.

Temperature at 2:00 PM = 18° F

Temperature at 10:00 PM = -9° F

Change in temperature = Final temperature - Initial temperature

                                       =  -9° F - 18° F

                                       = -27° F

Hence, the change in temperature can be calculated as -27° F.

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Answer:

50°

Step-by-step explanation:

90-40= 50° ............

Answer:

what is your question??????

Step-by-step explanation:

Answer:

a) x = 12  y = 9

b) x = -2   y = -4

c) x = 6   y = -2

Step-by-step explanation:

a)

Equation 1:  6x - 7y = 9

Equation 2:  3x + 2y = 54

Multiply Equation 2 by 2:

⇒ 6x + 4y = 108

Subtract equations:

   6x + 4y = 108

-    6x - 7y = 9      

           11y = 99

Divide both sides by 11:

⇒ y = 9

Substitute found value of y into Equation 1 and solve for x:

⇒ 6x - 7(9) = 9

⇒ 6x - 63 = 9

⇒ 6x = 72

⇒ x = 12

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b)

Equation 1:  4x - 5y = 12

Equation 2:  2x - 3y = 8

Multiply Equation 2 by 2:

⇒ 4x - 6y = 16

Subtract equations:

   4x - 6y = 16

-   4x - 5y = 12      

           -y = 4

Divide both sides by -1:

⇒ y = -4

Substitute found value of y into Equation 1 and solve for x:

⇒ 4x - 5(-4) = 12

⇒ 4x + 20 = 12

⇒ 4x = -8

⇒ x = -2

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c)

Equation 1:  4x - 2y = 28

Equation 2:  3x + 3y = 12

Multiply Equation 1 by 3:

⇒ 12x - 6y = 84

Multiply Equation 2 by 4:

⇒ 12x + 12y = 48

Subtract equations:

     12x - 6y = 84

-   12x + 12y = 48  

            -18y = 36

Divide both sides by -18:

⇒ y = -2

Substitute found value of y into Equation 1 and solve for x:

⇒ 4x - 2(-2) = 28

⇒ 4x + 4 = 28

⇒ 4x = 24

⇒ x = 6

Answer:

∠B = 70 and ∠C = 40

Step-by-step explanation:

The image is not loading for me but with isosceles triangles there will two angles that are the same and one different angle.

All the angles will add up to equal 180 degrees.

In this case the different angle would angle C as the two same lines meet at that point.

From this you can that angle A and B are the same, both 70, so angle C would be:

180 (all the angles of a triangle added together) - 70 - 70 = 40

I'm assuming that x and y are angles B and C as they are not stated so they would be: ∠B = 70 and ∠C = 40.

Here is a diagram to demonstrate this: