The square of a non-zero number is equal to 70% of the original number. What
is the original number?

An expression has numbers, variables, and mathematical operations. The factors of the expression 4x³+x²-8x-2 by grouping are x²(4x+1)-2(4x+1).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The factors of the expression by grouping can be done as,

[tex]4x^3+x^2-8x-2[/tex]

Take x² as the common factor from the first two terms while -2 from the last two terms,

[tex]4x^3+x^2-8x-2\\\\=x^2(4x+1)-2(4x+1)[/tex]

Thus, the factors of the expression 4x³+x²-8x-2 by grouping are x²(4x+1)-2(4x+1).

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Using proportions, it is found that the unit rate is of 1.33 cups of brown sugar for a batch of cookies.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

2/3 cups of brown sugar are used for half a batch of cookies. The unit rate is the amount used for one batch. Hence, the rule of three is given by:

2/3 cups - 1/2 batch

x cups - 1 batch.

Applying cross multiplication:

[tex]\frac{1}{2}x = \frac{2}{3}[/tex]

[tex]x = \frac{4}{3}[/tex]

The unit rate is of 1.33 cups of brown sugar for a batch of cookies.

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Answer:

rises sharply on the right

Step-by-step explanation:

The approximate area of the decagon with a side of 8cm comes to be 492.40 cm².

The side of the regular decagon = 8cm

A regular decagon is a polygon with 10 sides that are equal to each other.

The area of a regular decagon with side a is:

[tex]A=\frac{5}{2} a^{2} \sqrt{5+2\sqrt{5} }[/tex]

So, the area A of the regular decagon with a side of 8cm:

[tex]A=\frac{5}{2} 8^{2} \sqrt{5+2\sqrt{5} }[/tex]

[tex]A=160\sqrt{5+2\sqrt{5} }[/tex]

A=492.40 cm²

Therefore, the approximate area of the decagon is 492.40 cm².

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Since f(x) ≠ f(- x) then f(x) is not an even function. (–x)^4 – (–x)^3 is equivalent to x^4 – x^3.

A function is defined as a relation between the set of inputs having exactly one output each.

We need to find f(x) = x^4 – x^3 is an even function

If 2 functions are even, then

f(x) = f(- x)

f(x) =  [tex]- x^3[/tex]

f(- x) = [tex]- (- x)^3 = + x^3[/tex]

Since f(x) ≠ f(- x) then f(x) is not an even function.

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Answer:

A

Step-by-step explanation:

Answers:

Final velocity = 29 m/s

Distance traveled = 73.5 meters

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

Work Shown:

The given data is

[tex]v_i = 20 \text{ m}/\text{s} = \text{initial velocity}\\\\a = 3 \text{ m}/\text{s}^2 = \text{acceleration}\\\\t = 3 \text{ s} = \text{time duration}\\\\[/tex]

This leads to

[tex]v_f = v_i + a*t\\\\v_f = 20 + 3*3\\\\v_f = 20 + 9\\\\v_f = 29\\\\[/tex]

The final velocity is 29 m/s.

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We can use that final velocity to find the distance traveled.

[tex]x = 0.5*(v_i+v_f)*t\\\\x = 0.5*(20+29)*3\\\\x = 0.5*(49)*3\\\\x = 24.5*3\\\\x = 73.5\\\\[/tex]

The distance traveled is 73.5 meters.

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An alternative way to calculate the distance is to do this

[tex]x = \frac{(v_f)^2 - (v_i)^2}{2a}\\\\x = \frac{(29)^2 - (20)^2}{2*3}\\\\x = \frac{841 - 400}{6}\\\\x = \frac{441}{6}\\\\x = 73.5\\\\[/tex]

Or you could do this

[tex]x = v_i*t + 0.5*a*t^2\\\\x = 20*3 + 0.5*3*3^2\\\\x = 20*3 + 0.5*3*9\\\\x = 60 + 13.5\\\\x = 73.5\\\\[/tex]

For more information, check out the Kinematics equations.

Answer:

Step-by-step explanation:

First Container.

Total = 7 + 2 + 6 = 15

Probility blue = 7 / 15 = 0.467

Second Container

Total = 4 + 2 +2 =  8

Probability Blue = 4/8 = 1/2 = 0.5

Answer: You are much better off drawing from the Second Container.

Answer:
To convert 27 kg to mg, you would move the decimal point 6 places to the right.

hope that's helpful to you!

Answer:

Side = 3 cm

Step-by-step explanation:

Given:

[tex]\text{Volume of cube} = 27 \ \text{cm}^{3}[/tex]

The formula to calculate the volume is (Side)³.

Thus, we obtained the following equation:

[tex](\text{Side})^{3} = 27 \text{cm}^{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Side}^{3} = \text{Volume of cube}][/tex]

Cube root both sides to obtain the side length of the cube:

[tex]\implies \sqrt[3]{\text{(Side)}^{3}} = \sqrt[3]{27 \ \text{cm}^{3} }[/tex]

Evaluate the side of the cube:

[tex]\implies \sqrt[3]{\text{(Side)}^{3}} = \sqrt[3]{27 \ \text{cm}^{3} }[/tex]

[tex]\implies \sqrt[3]{\text{(Side)}\text{(Side)(Side})} = \sqrt[3]{3 \times 3 \times 3 \times \text{(cm)(cm)(cm)}}[/tex]

[tex]\implies \text{Side = 3 cm}[/tex]

Answer:

3 cm

Step-by-step explanation:

Formula

Volume of a cube = [tex]a^3[/tex]  (where a is the side length)

Given that the volume of the cube is 27 cm³, to find the side length, substitute the given volume into the equation and solve for [tex]a[/tex]:

[tex]\implies 27\: \sf cm^3=a^3[/tex]

Cube root both sides:

[tex]\implies \sqrt[3]{27\: \sf cm^3} =\sqrt[3]{a^3}[/tex]

[tex]\implies \sqrt[3]{27}\sqrt[3]{\sf cm^3} =\sqrt[3]{a^3}[/tex]

[tex]\implies 3\: \sf cm=a[/tex]

[tex]\implies a=3\: \sf cm[/tex]

Therefore, the length of each side of the cube is 3 cm.

[tex]~~~~~~2(x-12)+x=36\\\\\implies 2x-24+x = 36\\\\\implies 3x = 36+24\\\\\implies 3x = 60\\\\\implies x = \dfrac{60}3\\\\\implies x = 20[/tex]

2(x+12)+x=36

or,2x+24+x=36

or,3x+24=36

or,3x=36-24

or,3x=12

or,x=12/3

or,x=4

Thus, 20 is your answer

Answer:

1 (one)

Step-by-step explanation:

Answer:

1

----------------------------------------------------------------------------------------------------------

First things first, evaluate all square roots in order, starting with the square root of 12

The next step is to divide, despite multiplication always coming before division, you cannot multiply without first knowing the values of the division.

[tex]3.5 / 3.2 = 1.09\\\\2.2 / 2.4 = 1.09[/tex]

Now, you can multiply.

[tex]1.09 * 1.09 = 1.1881[/tex]

That said, 1.1881 is closest to 1 because it has a 1 in the tenths place, the greatest place in a decimal number.

The percent of the initial set-up and operation costs that Sam needs to finance with a lender or investor is A. 19%.

From the information given, Sam is planning to start a pool cleaning business from his home. he has developed a cost analysis for the set-up and operation.

Here, the percent of the initial set-up and operation costs that Sam need to finance with a lender or investor is simply 19%.

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#SPJ1

Answer:

y/x

Step-by-step explanation:

Answer: y/x

water/time = unit rate = y/x

Answer:

(-2,1)

Step-by-step explanation:

1 unit up will change the y-value as it is moving vertically. Will make it (-2,-1)

Then, reflecting over x-axis means x-value stays the same and the sign of y-value switches.

so,

(-2,1)

it's 46/99

whenever you get a question like this, you need to think: what would those fractions even be?

well it sure is not a bc 3/6 is already 0.5 and you need a lower number

it's not b either bc 4/16= 1/4 and that is 0.25

and well it can't be d either bc 13/16 is that not far away from 1

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

Explanation:

Let x = 0.464646...

Multiplying both sides by 100 gets to 100x = 46.464646... which moves the decimal point over two spots to the right.

Then subtract the two equations

100x - x = 46.464646... - 0.464646...

99x = 46

x = 46/99

Notice how the decimal portions cancel out when we subtract. This is because they line up perfectly.

To confirm the answer, your calculator should show that

46/99 = 0.46464646

The "46"s going on forever.

At some point, your calculator may round the last '4' to a 5 to have it read something like 0.464646465 but this is of course rounding error.

On some calculators I tried, I noticed it displayed 0.46464646464647 which is even more strange considering the next digit (4) isn't five or larger. So that 6 shouldn't have bumped up to the 7.

Answer:The J C Penney Company stock would have been the best investment option, because the stock provided a rate of return of 18.82 percent to investors during the past year. The Apple stock offered a lower return of 13.29 percent. The Ford Motor Company gave a negative return of 0.51 percent, which means investors in this stock lost a small amount of their investment over the past one year.

Step-by-step explanation: ANSWER FOR EDMENTUM/PLATO

(Answers may vary.)

The J C Penney Company stock would have been the best investment option, because the stock provided a rate of return of 18.82 percent to investors during the past year. The Apple stock offered a lower return of 13.29 percent. The Ford Motor Company gave a negative return of 0.51 percent, which means investors in this stock lost a small amount of their investment over the past one year.

Step-by-step explanation: edmentum/ plato exact

Answer:

Hope the picture will help you.......

Answer:

what how

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

900/6000

which is the same as 900÷6000

900÷6000= 0.15

0.15 as a percent in 15%

1200 cards

All measurements should be taken in centimeters

Calculate the area of large rectangular card:

Calculate the area of each small cards:

Divide the area of large card by area of small card

Number of small cards: 1200 cards

For bigger rectangle:-

Area:-

For smaller rectangle

Area:-

Total cards:-

Answer:

$4500 in interest.

Step-by-step explanation:

9% of 10,000 is 900, 900 x 5 is 4500

Answer:

2.5

Step-by-step explanation:

3 hours after 7 is 10 so add 1.9 to 0.6

Answer: x=1 y=1

Step-by-step explanation:

ax+by=a−b .......... (1)

bx−ay=a+b .......... (2)

Multiply equation (1) with a  and  equation (2) with b ,

a

2

x+aby=a

2

−ab ..........(3)

b

2

x−aby=ab+b

2

 ......... (4)

Adding (3) and (4), we get,

(a

2

+b

2

)x=a

2

+b

2

⇒x=1

Now, from (1),

ax+by=a−b

a+by=a−b

by=−b

y=−1

Answer:

please check photo for detailed explanation

Answer:200

Step-by-step explanation: There are 15balls and the probability of picking a blue ball once is 4/15

The ball is returned and repeated 750 Times. Multiply 4/15 by 750

A 200Answer:

Step-by-step explanation:

↪Given 15 cot A = 8. Find sin A and sec A

Hope this helps...☆

Answer:

I will not give in answer but will give an example

Step-by-step explanation:

The area of irregular shapes can be determined by dividing the given shape into smaller regular shapes. The area of irregular shapes can be determined by dividing the given shape into smaller regular shapes.

In real life figures are often irregular shapes - a little bit messy. Think of your messy bedroom once more ‐ is it a perfect rectangle?

The trick is to break these figures into shapes that you know well and whose area you know how to find.

1. Find the area of this room:

3- 2 -4 -6 irregular shape

This can be done in two different ways but ill only give one example on how to find an area.

Method #1

Divide the figure into two rectangles and find all missing lengths.

The larger rectangle has an area of

4cm x 7cm = 28cm2

The smaller rectangle has an area of

4cm x 2cm = 8cm2

If we combine these we will find the total area:

28cm2 x 8cm2 = 36cm2

hope this helps :)

Answer:

you have to solve the first equation for y

Step-by-step explanation:

Step-by-step explanation:

At first put the value of y that is 3x in equation 2x=y-1.

Then put the value of x in equation y=3x that comes from the first solving part.