Which expression has a solution of 27, if r = 3?

Answer:

[tex]4(x + 1)^{2}(x - 1)^{2}[/tex]

Step-by-step explanation:

STEP 1:

The equation at the end of step 1

[tex]((4 (x^4)) - 2^3x^2) + 4[/tex]

STEP 2:

The equation at the end of step 2:

[tex](2^2x^4 - 2^3x^2) + 4[/tex]

STEP 3:

STEP 4: Pulling out like terms

4.1 Pull out like factors:

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

Trying to factor by splitting the middle term

4.2 Factoring [tex]x^4 - 2x^2 + 1[/tex]

The first term is, [tex]x^4[/tex] its coefficient is 1.

The middle term is,  [tex]-2x^2[/tex]  its coefficient is -2.

The last term, "the constant", is +1.

Step-1: Multiply the coefficient of the first term by the constant   1 • 1 = 1

Step-2: Find two factors of  1  whose sum equals the coefficient of the middle term, which is -2.

-1 + -1 = -2 That's it

Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  -1

                    x4 - 1x2 - 1x2 - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x2 • (x2-1)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x2-1)

Step-5 : Add up the four terms of step 4 :

                   (x2-1)  •  (x2-1)

            Which is the desired factorization

Trying to factor as a Difference of Squares:

4.3      Factoring:  x2-1

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check :  x2  is the square of  x1

Factorization is :       (x + 1)  •  (x - 1)

Trying to factor as a Difference of Squares:

4.4      Factoring:  x2 - 1

Check : 1 is the square of 1

Check :  x2  is the square of  x1

Factorization is :       (x + 1)  •  (x - 1)

Multiplying Exponential Expressions:

4.5    Multiply  (x + 1)  by  (x + 1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (x+1)  and the exponents are :

         1 , as  (x+1)  is the same number as  (x+1)1

and   1 , as  (x+1)  is the same number as  (x+1)1

The product is therefore,  (x+1)(1+1) = (x+1)2

Multiplying Exponential Expressions:

4.6    Multiply  (x-1)  by  (x-1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (x-1)  and the exponents are :

         1 , as  (x-1)  is the same number as  (x-1)1

and   1 , as  (x-1)  is the same number as  (x-1)1

The product is therefore,  (x-1)(1+1) = (x-1)2

Final result :

 4 • (x + 1)2 • (x - 1)2

Answer:

Step-by-step explanation:

I still...really don't know

Answer:

500

Step-by-step explanation:

40×100÷8=500

Number 40 is 8 percent of 500.

The percentage refers to a number that is out of 100. When describing components of a whole in mathematics, percentages are employed similarly to fractions and decimals. When employing percentages, the idea is that there are 100 equal pieces that make up the whole. In addition to the shorthand "pct," which is used less frequently, the symbol "%" is used to indicate that a number is a percentage.

Let the unknown number be "x" whose 8% is 40.

Hence,

8% of x = 40

1% of x = 40/8 = 5

Thus, the value of x = 500

Therefore, 8 percent of 500 if 40.

Learn more about percentages here:

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Answer:

8

Step-by-step explanation:

Jimarcus plans to build a fence of 5 1/3 yards longs

He want to divide it into 2/3 yard sections

Therefore the number that will be produced can be calculated as follows

= 5 1/3 ÷ 2/3

= 16/3 ÷ 2/3

= 16/3 × 3/2

= 16/2

= 8

Answer:

0.96 kg

Step-by-step explanation:

0.56+0.40=0.96

95.4

Add the numbers of kilograms. Remember to line up the decimal points. You can write extra zeroes to make equivalent decimals.

Answer:

4bb

Step-by-step explanation:

Answer:

4bb

Step-by-step explanation:

Because you need to combine like terms

Hope this helped!! :)

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Brainliest?!?!

(This is too easy)

Answer:Kirk is taller than Joey by 8 inches

Step-by-step explanation:

Step 1

Kirk's height is given as  =5 feet 4 inches tall.

Joey's  height 4 feet 8 inches tall

Difference in height = 5 feet 4 inches

                                    - 4 feet   8 inches

                                 =

Step 2

Bear in mind that 12 inches = 1 feet . Now,8 cannot be subtracted from 4 , so we borrow 1 feet from 5feet,  which is equivalent to 12 inches and add to inches  so it becomes

4 feet  (12+4)inches     =                   4 feet     16inches

- 4 feet   8 inches                             - 4 feet   8 inches

                                                     =                   8 inches

Therefore Kirk is taller than Joey by 8 inches

Answer:

b

Step-by-step explanation:

Answer:

9. A loebskesşbxksjlejs

Answer:

60000

Step-by-step explanation:

You should treat the first son with the 1 ratio as x. Because of this, the second son would be 3x and the third would be 6x. All of them need to equal 120000 so 10x=120000. Next you isolate the and x= 12000. Fill in 1200 for x and the first son gets 12000, the second gets 36000, and the third gets 72000. Lastly you subtract and you get 60000.

Answer:

Because it's not a quadratic function.

Step-by-step explanation:

The imaginary roots of a quadratic equation will always be in form of a ± b thus 3 and 2 + 3i will be incorrect.

The roots of an equation are the solution of that equation, since an equation consists of hidden values of the variable so to determine them by different processes and then the resultant is called roots.

The standard form of a quadratic equation is,

ax² + bx + c = 0

The root of it is given by,

x = [-b ± √(b²-4ac)]/2a

For being this as imaginary the term b²-4ac < 0

Let's say b²-4ac = -m then

x = (-b/2a) ± (m/2a)i so both root will be imaginary.

Given that one root is real (3) and the second is imaginary (2 + 3i) is not possible.

Hence "The imaginary roots of a quadratic equation will always be in form of a ± b thus 3 and 2 + 3i will be incorrect".

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Answer:

11.2

Step-by-step explanation:

The answer is 11.2

11.2*.25=2.8

11.2-2.8=8.4

Answer:

n = 4

Step-by-step explanation:

3 = 2 + n/4

1 = n/4

4 = n

Answer:

n = 4

Step-by-step explanation:

take the 2 and subtract it from itself then you gotta do it to the other side so it be 3 -2 and you get 1 then you multiply 4 to n/4 and it crosses it out and what you do to one side you do to the other so you multiply 4 by 1 & get 4

Answer:

y=-2/3x-1

Step-by-step explanation:

Answer:

y=-2/3x-1

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

all quadrilateral angle sums are 360° no matter how you change it

Answer:

1 = -9

Step-by-step explanation:

Just substitute 3 for g

then 3/3 = 1

Answer:

Since 1 pound of copper costs 3.18, C = 3.18p

Answer:

243

Step-by-step explanation:

[tex]5( \sqrt{ {x}^{2} + 2x - 14} + x) = 20 \\ \\ \sqrt{ {x}^{2} + 2x - 14} + x= \frac{20}{5} \\ \\ \sqrt{ {x}^{2} + 2x - 14} + x= 4 \\ \\ \sqrt{ {x}^{2} + 2x - 14} = 4 - x\\ \\ {(\sqrt{ {x}^{2} + 2x - 14} )}^{2} = {(4 - x)}^{2} \\ \\ \cancel{ {x}^{2}} + 2x - 14 = 16 - 8x + \cancel{ {x}^{2} } \\ \\ 2x - 14 = 16 - 8x \\ \\ 2x + 8x = 16 + 14 \\ \\ 10x = 30 \\ \\ x = \frac{30}{10} \\ \\ x = 3 \\ \\ 3 {x}^{4} = 3 {(3)}^{4} = 3 \times 81 \\ \\ \huge \red {3 {x}^{4}= 243}[/tex]

Answer:

4900

Step-by-step explanation:

so what you're going to do first is you're going to do 114* 43 which equals 4902 then you round that and you're going to have 4900I am not a hundred percent sure

Answer:

Point C

Step-by-step explanation:

Points are read as (x, y).

This means that 2 = x and y = 3.

X is the bottom line, whilst Y is the line going up.

Answer:

translation of ABC to A'B'C' is 5,3

Answer:

The second one

Answer:

196-49 pi

Step-by-step explanation:

diameter of circle is 14

radius-7

7^2=49

49 pi

14^2=area of square

196-49pi= area of shaded area.

Answer:

im pretty sure the area is 196

Step-by-step explanation:

because when finding the area of a rectangle/ square you use the formula Length * Width and as we can see the sides of the shaded are are equivalent and as we know the length of the shaded area is 14.

we would just plug in our information.

L*W

14*14= 196

Answer:

3.764

Step-by-step explanation:

Answer:

20 pounds of Gummyballs and 5 pounds of caramel was ordered

Step-by-step explanation:

Let :

Gummyball = a

Caramel = b

a + b = 25 - - - (1)

5a + 8b = 140 - - - (2)

From (1)

a = 25 - b

Put into (2)

5(25 - b) + 8b = 140

125 - 5b + 8b = 140

125 + 3b = 140

3b = 15

b = 5

From a = 25 - b

a = 25 - 5

a = 20

Hence,

20 pounds of Gummyballs and 5 pounds of caramel was ordered

Answer:

3.5

Step-by-step explanation:

the median is the dotted lines.

median of girls height: 65.5

median of boys height: 69

69-65.5=3.5

Answer:

The final bill was $912

Step-by-step explanation:

Since there is 14% tax in order to get the final cost we would need to multiply the cost of the jerseys by 1.14, and so we get...

800 x 1.14 = $912