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You want to make a banner that says HAPPY BIRTHDAY. You want the letters to be 3 inches high. You make a sketch of the banner with letters that are 2 inches high. The length of the phrase in your sketch is 20 inches long. What length of paper should you buy to make the banner? ​

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:

220 millimeters

Step-by-step explanation:

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

Please rate!

Jonathan will need a warping paper of 420.78m^2

Data;

To find the amount of warping paper used, we can use the formula of surface area of an equilateral triangle since the triangle used here is an equilateral triangle.

[tex]Surface Area = base area + \frac{1}{2}(perimeter * slant height)[/tex]

Let's calculate the base area and perimeter of the triangle.

base area of an equilateral triangle is given as

[tex]B.A = \frac{\sqrt{3} }{4} a^2[/tex]

Let's substitute the value and solve

[tex]B.A = \frac{\sqrt{3} }{4} a^2\\B.A = \frac{\sqrt{3} }{4}*10.39^2\\B.A = 46.74m^2[/tex]

The base area is 46.74m^2

Let's calculate the perimeter of the triangle

[tex]P = 3a\\[/tex]

Substitute the value into the equation and solve

[tex]P = 3a \\P = 3 * 10.39\\P = 31.17m^2[/tex]

We can proceed to substitute the values of the base area and perimeter of the triangle into the formula of the surface area of an equilateral triangle.

[tex]S.A = base area + \frac{1}{2}(perimeter * slant height)\\S.A = 46.74 + \frac{1}{2}(31.17*12)\\S.A = 46.74 + 374.04\\S.A = 420.78m^2[/tex]

The surface area of the equilateral triangle is 420.78m^2

Jonathan will need a warping paper of 420.78m^2

Learn more on surface area of an equilateral triangle here;

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Answer:c

Step-by-step explanation:

Answer:

$5.40

Step-by-step explanation:

First, find Dave's purchase. To do this, you multiply 15 by the tax percent and add that to the original.

So:

15 x 8% = 15 x 0.08 = 1.2

15 + 1.2 = 16.2

Next, do the same for Mel's purchase:

20 x 8% = 20 x 0.08 = 1.6

20 + 1.6 = 21.6

Then, you subtract Dave's purchase from Mel's:

21.6 - 16.2 = 5.4

This comes out to $5.40

Answer:

3

Step-by-step explanation:

Select an ordered pair: (2, 7)

Select another ordered pair: (6, 19)

slope = (difference in y)/(difference in x)

slope = (19 - 7)(6 - 2)

slope = 12/4

slope = 3

Answer:

Step-by-step explanation:

Pick any two points.

(2 ,7)  & (4, 13)

x₁  = 2  ; y₁ = 7    & x₂ = 4  ; y₂ = 13

[tex]Slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         [tex]=\dfrac{13-7}{4-2}\\\\\\=\dfrac{6}{2}\\\\\\= 3[/tex]

Answer:

22

Step-by-step explanation:

You add the to numbers together and the answer will be 22

I hope it helps! Have a great day!

Muffin ^^

Answer:

Step-by-step explanation:

As ABCD is a rectangle, ∠A = 90°.

Diagonal BD will be the hypotenuse.

[tex]Sin \ 53^{ \circ} = \sf \dfrac{opposite \ of \ angle \ 53}{hypotenuse}\\\\\\0.7986=\dfrac{AB}{42.3}\\\\\\0.7986*42.3=AB\\\\\bold{AB = 33.8}[/tex]

Length = AB = 33.8 cm

[tex]\sf Cos \ 53^{ \circ} =\dfrac{adjacent \ side \ to \ angle \ 53}{hypotenuse}\\\\\\0.6018 = \dfrac{AD}{42.3}\\\\\\0.6018*42.3 =AD\\\\\bold{AD = 25.5 }[/tex]

Width = 25.5 cm

Answer:

2000j

Step-by-step explanation:

Kinetic Energy = mgh

= 20 x 10 x 10 J

= 2000J

Dilation is the change in size of of object. The length of the side OB' will be 3 units

From the given diagram, we can see that there is a change in the side of the triangle OAB to OA'B'

Given the following parameters

OB = 3/4 units

Scale factor = 4 units

The measure of OB' = 4 * 3/4 = 3 units

Hence the length of the side OB' will be 3 units

Learn more on dilation here: https://brainly.com/question/10253650

Answer:

3

Step-by-step explanation:

edg 2022

To find the solutions to the quadratic equations

    ⇒ factor the equation

           [tex]x^2-2x = 8\\x^2-2x-8=0\\(x-4)(x+2) = 0[/tex]

Now to find the exact solutions, we have to set 'x - 4' and 'x + 2' equal to 0

     [tex]x - 4 = 0\\x = 4\\\\x + 2 = 0\\x = -2[/tex]

Thus the solution to this problem is -2 and 4

Hope that helps!

Answer:

4 and - 2

Step-by-step explanation:

x² - 2x = 8

x² - 2x - 8 = 0

x² + 2x - 4x - 8 = 0

x ( x + 2 ) - 4 ( x + 2 ) = 0

( x + 2 ) ( x - 4 ) = 0

x + 2 = 0

x = - 2

x - 4 = 0

x = 4

The values of x are - 2 and 4.

Hello!

Let's use the Distributive Property & simplify:

6(8x+1)

distribute 6 by multiplying it times 8x and 1:

48x+6

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning

:-)

Answer:

[tex]\displaystyle 6 + 48x[/tex]

Step-by-step explanation:

[tex]\displaystyle 6[8x + 1] \hookrightarrow \boxed{48x + 6}[/tex]

I am joyous to assist you at any time.

Answer: 7xy + 2x^2t

Step-by-step explanation:

Answer:

5/5 out of the 7/5 make ONE whole while 2/5 is left over.

The ONE whole is added to nine to make 10 and the remaining 2/5 is also added to the 10 hence 9 7/5 = 10 2/5

Step-by-step explanation:

5/5 out of the 7/5 make ONE whole while 2/5 is left over.

The ONE whole is added to nine to make 10 and the remaining 2/5 is also added to the 10 hence 9 7/5 = 10 2/5

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:

1,000

Step-by-step explanation:

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.

To learn more on Temperature, click:

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Answer:

length= 1115 inches

width= 545 inches

Step-by-step explanation:

The perimeter of the rectangular rug is the sum of the lengths of all its sides.

Start by defining the variables that we are going to use throughout our working.

Let the length and the width of the rug be L and W inches respectively.

Perimeter= 2(L +W)

Given that the length is 25 inches more than twice the width,

L= 2W +25 -----(1)

3320= 2(2W +25 +W)

Divide both sides by 2:

1660= 2W +W +25

1660= 3W +25

3W= 1660 -25

3W= 1635

Divide both sides by 3:

W= 1635 ÷3

W= 545

Substitute W= 545 into (1):

L= 2(545) +25

L= 1115

Thus, the length and width of the rug is 1115 and 545 inches respectively.

Answer:

Two terms ( [tex] x [/tex] and [tex] n [/tex])

Step-by-step explanation:

If simplified it gives 3n+4x+5

And cannot be factored

=======================================================

We're given the following expression:

[tex]\bigstar{\boxed{4x+3n+5}[/tex]

Here,

4x is a term

3n is a term

5 is a term

4 is the coefficient of x

x is a variable

3 is the coefficient of n

n is a variable

5 is a constant

Details:-

A coefficient is a number before a variable

A variable is a letter

A constant is a number without any variables next to it

=========================================================

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Answer:

at aircraft(at z) sported by

Answer:

22

Step-by-step explanation:

5x + 8 = 118

5x = 110

x = 22

Answer:

200g/0.2kg

Step-by-step explanation:

8 × 25g = 200g

The total mass of the pencil is 200 grams.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that,

A pencil has a mass of 25 grams.

there are 8 pencils.

Total number of pencils = 8

Mass of each pencil = 25 grams

Total mass of the pencils = 8 × 25 = 200 grams

Hence the total mass is 200 grams.

Learn more about Multiplication here :

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Answer:

4x-11=73,

x=21

Step-by-step explanation:

11 subtracted from means -11

four times a number means 4(x) because x is the number

is = equals

so

4x-11=73

+11      +11

4x=84

/4    /4

x=4

Answer:

40

Step-by-step explanation:

Angle KPJ is going to have the same measure as Angle DPE. This problem is a bit tricky, but I'll try my best to explain it. A straight angle is basically just a straight line, and it equals 180 degrees. Angle FPG is a straight angle.

To find the measure of Angle KPJ, we first have to find the measure of angle DPE, and the way we're gonna do that is add together the other angles in the straight angle (which would be Angle FPD and Angle EPG) and then subtract that from 180 (measure of a straight angle).

That might have sounded a bit confusing, but that's the best way I could explain it. Now, let's add Angle FPD and Angle EPG.

105 + 35 = 140

Now, let's subtract that from 180.

180 - 140 = 40

We now know that the measure of Angle DPE is 40, and since it's equivalent to Angle KPJ, our answer is 40!

I know that was confusing, but I hope it helped a little bit! Have a lovely day!! :)

Answer:

[D]

Step-by-step explanation:

Graph using the end point and a few selected points.

x            y

0           2

1            3

2        3.41

Graph is below:

[RevyBreeze]

Answer:

Angle ABC = 6x

Step-by-step explanation:

this is an isosceles triangle so the values of angle ACB and angle ABC are the same.

Answer:

4

Step-by-step explanation:

2+2 = 4