2 4/7 / 1 3/6 using a complex fraction. what is the answer

Answer:

[tex]\frac{3x + 8}{36 - 2x} / \frac{27x^2 + 72x}{3x^2 - 27} = \frac{(x - 3)(x+3)}{6x(18 - x)}[/tex]

Step-by-step explanation:

Given

[tex]\frac{3x + 8}{36 - 2x} / \frac{27x^2 + 72x}{3x^2 - 27}[/tex]

Required

Solve

Change / to *

[tex]\frac{3x + 8}{36 - 2x} * \frac{3x^2 - 27}{27x^2 + 72x}[/tex]

Factor out 3

[tex]\frac{3x + 8}{36 - 2x} * \frac{3(x^2 - 9)}{3(9x^2 + 24x)}[/tex]

[tex]\frac{3x + 8}{36 - 2x} * \frac{(x^2 - 9)}{(9x^2 + 24x)}[/tex]

Factorize:

[tex]\frac{3x + 8}{36 - 2x} * \frac{(x^2 - 9)}{3x(3x + 8)}[/tex]

Cancel out 3x + 8

[tex]\frac{1}{36 - 2x} * \frac{(x^2 - 9)}{3x}[/tex]

Factorize:

[tex]\frac{1}{2(18 - x)} * \frac{(x^2 - 9)}{3x}[/tex]

Combine

[tex]\frac{x^2 - 9}{2*3x(18 - x)}[/tex]

[tex]\frac{x^2 - 9}{6x(18 - x)}[/tex]

Express the numerator as a difference of two squares

[tex]\frac{(x - 3)(x+3)}{6x(18 - x)}[/tex]

Hence:

[tex]\frac{3x + 8}{36 - 2x} / \frac{27x^2 + 72x}{3x^2 - 27} = \frac{(x - 3)(x+3)}{6x(18 - x)}[/tex]

Question:

For which value of x must the expression √97x be further simplified?

A. 5    B. 10     C. 15     D. 20

Answer:

[tex]D.[/tex]  [tex]x = 20[/tex]

Step-by-step explanation:

Given

[tex]\sqrt{97x[/tex]

Required

For what value of x can it be simplified

From the list of options, only (D) is correct

D. 20

Substitute 20 for x in [tex]\sqrt{97x[/tex]

[tex]\sqrt{97 x} = \sqrt{97 * 20}[/tex]

Express 20 as 4 * 5

[tex]\sqrt{97 x} = \sqrt{97 * 4 * 5}[/tex]

Reorder

[tex]\sqrt{97 x} = \sqrt{4 *97 * 5}[/tex]

Split

[tex]\sqrt{97 x} = \sqrt{4} *\sqrt{97 * 5}[/tex]

[tex]\sqrt{97 x} = 2*\sqrt{97 * 5}[/tex]

[tex]\sqrt{97 x} = 2*\sqrt{485}[/tex]

[tex]\sqrt{97 x} = 2\sqrt{485}[/tex]

With other values of x, the given expression can not be simplified.

Hence:

[tex]x = 20[/tex]

Answer:

8) 0.46

Step-by-step explanation:

54% = 0.54 because 0.54*100 = 54% so 54%/100 = 0.54

100% - 54% = 46%

46%/100 = 0.46

You're #6 is unclear, what is V?

Answer:

6y + 1.25x

$61

Step-by-step explanation:

Diego works at a vegetable farm and earns $6.00/hour plus $1.25 for every full wagonload of picked vegetables. Write an expression to represent how much Diego earns if he works y hours and fills x wagonloads. Instruction : In the expression, let the term containing y come before the term containing x.

If Diego works six hours and fills 20 wagonloads, how much does he earn?

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

Let's Start!

So, we know Diego earns $6.00/hour.

We can write that as 6y, where y is the number of hours worked.

We also know that he earns $1.25 for every wagonload of picked vegetable.

We can write that as 1.25x, where x is the number of wagonloads filled.

So, to make our algebraic expression, we will separate the terms by a plus sign.

6y + 1.25x

PART TWO:

"If Diego works 6 hours"

6(6) + 1.25x =

"And Diego fills 20 wagonloads"

6(6) + 1.25(20) =

Simplify.

36 + 25=  61

So, Diego will earn $61

Hope I helped, have a nice day!

              -Aadi x

Answer:

I believe it's choice (3) because the exponent of x is 25 and it's the largest exponent of the choices.

Step-by-step explanation:

Answer:

C. 25x^10+3x-15

Step-by-step explanation:

The degree of 3x^8-2x^7+x^6 is 8

The degree of 5x-100 is 1

The degree of 25x^10+3x-15 is 10

The degree of 134x^2 is 2

Therefore the largest degree is 10

Answer:

When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor. Example: the GCF of 12 and 16 is 4, because 1, 2 and 4 are common factors of both 12 and 16, and 4 is the greatest of them.

Step-by-step explanation:

When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor. Example: the GCF of 12 and 16 is 4, because 1, 2 and 4 are common factors of both 12 and 16, and 4 is the greatest of them.

Answer:

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

Step-by-step explanation:

Example: 6,8,20

6-1,2,3,6

8-1,2,4,8

20-1,2,4,5,20

GCF is 2

Answer:

8

Step-by-step explanation:

12 divided by 3 is 4 and since its 2/3 you multiple 4 times 2 giving you 8

Answer:

8

Step-by-step explanation:

Multiply amount of books by the fraction of

Answer:

substitute it into the value that they give then expand the formula which is

a^2-2ab+b^2

Step-by-step explanation:

Answer:

25 rides

Step-by-step explanation:

has $28.50

15.75 + 0.50r [tex]\leq[/tex] 28.50

Subtract 15.75

0.50r [tex]\leq[/tex] 12.75

r [tex]\leq[/tex] 25.5

you can't have half rides, so 25 rides

Answer:

33.44

Step-by-step explanation:

Use this calculator to find percentages. Just type in any box and the result will be calculated automatically.

Calculator 1: Calculate the percentage of a number.

For example: 38% of 88 = 33.44

Calculator 2: Calculate a percentage based on 2 numbers.

For example: 33.44/88 = 38%

Answer:

x=1, y=1

Step-by-step explanation:

Sub y=2x-1 into 3x+8y=11

3x+8(2x-1)=11

3x+16x-8=11

19x=11+8

19x=19

x=1

Sub x=1 into y=2x-1

y=2(1)-1

y=2-1

y=1

Answer:

100 degrees

Step-by-step explanation:

all angles in a triangle add up to 180 degrees, so,

45+35=80

180-80=100

hope this helps!!!

Answer:

The shaded region is [tex]353.25m^2[/tex].

Step-by-step explanation:

The area of a circle is defined by the multiplication of the square of its radius, or half its diameter, by pi, or simply [tex]A=\pi r^2[/tex].

15m is the radius of the large circle, and also the diameter of the smaller circles.

The area of the shaded region will be the subtraction of the area of the two smaller circles from the area of the larger circle.

As such:

[tex]A=\pi(15)^{2}-2(\pi(\frac{15}{2} )^{2})\\\\A=(3.14)(15)^{2}-2(3.14)(\frac{15}{2} )^{2}\\A=706.5-353.25\\A=353.25[/tex]

Answer:

Step-by-step explanation:

Shaded region is the difference in the area of the bigger circle and two smaller circles.

The shaded area:

Step-by-step explanation:

3x^2-2x+1

3(2)^2-2(2)+1

3(4)-4+1

12-4+1

8+1=9 Answer

Step-by-step explanation:

3(2)^2 - 2x + 1

=3x4 - 2x + 1

=12 - 2x + 1

= 13 - 2x

Answer: 13 - 2x

Answer:

34 because 50 percent of 68 is 34

Answer:

There are 34 red marbles in the bin

Step-by-step explanation:

50% is basically 1/2. So half of 68 is 34.

Answer:

Both 1 and 2

Step-by-step explanation:

Answer:

where is the figure. please provide a figure.

Answer:

144(3/4)^1-n

Step-by-step explanation:

This is a geometric sequence, so if you divide 192 by 144 you will find that the common ratio r is 4/3. This would make the equation an=144(4/3)^n-1. However, that's not one of the options. If you plug in some numbers, you can see that 3/4 (the reciprocal of 4/3) can work as well if it's 3/4^1-n. 4/3^-1=3/4 and n-1(-1)=1-n

Answer:

21

Step-by-step explanation:

[tex] \sqrt{440 + 1} \\ = \sqrt{441 } \\ = 21[/tex]

Answer:

b

Step-by-step explanation:

Answer:

Im pretty sure its 114 m^2 sorry if im wrong

Answer:

The total surface area of the figure would be 114m.

Answer:

the answer should be 9, im not sure tho I vaguely remember this

Answer:

0.31% = 0.0031 in decimal form.

Step-by-step explanation:

Percent means 'per 100'. So, 0.31% means 0.31 per 100 or simply 0.31/100. If you divide 0.31 by 100, you'll get 0.0031 (a decimal number).

Answer:

250

Step-by-step explanation:

If they asked 50 people, and 25 said yes, that means you could excpect about 50% to buy fresh fruit, or 250 out of 500.  500/2=250

Step-by-step explanation:

The answer is 254.57142857

Answer:

3,900 Babies

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

312000 x0.0125 / 100 = 39

I hope this helps a little bit.

Answer:

3 times (18+ 2) - 100

3 (18+2) - 100 = -40