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butalik [34]
1 year ago
10

What is the product? StartFraction 3 k Over k + 1 EndFraction times StartFraction k squared minus 1 Over 3 k cubed EndFraction S

tartFraction k + 1 Over k squared EndFraction StartFraction k minus 1 Over k squared EndFraction StartFraction negative 1 Over k EndFraction StartFraction 1 Over k EndFraction
Mathematics
1 answer:
Nana76 [90]1 year ago
4 0

Answer:

StartFraction negative 1 Over k cubed EndFraction

Step-by-step explanation:

3k / (k + 1) × (k²- 1) / 3k³

= 3k(k² - 1) / (k + 1)(3k³)

= 3k³ - 3k / 3k⁴ + 3k³

= -3k / 3k⁴

= -1/k³

StartFraction k + 1 Over k squared EndFraction

(k + 1) / k²

StartFraction k minus 1 Over k squared EndFraction

(k - 1)/k²

StartFraction negative 1 Over k cubed EndFraction

= -1/k³

StartFraction 1 Over k EndFraction

= 1/k

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8. Finley has 152 yellow, red, and blue marbles in a bag. He has seven more red marbles than yellow marbles, and three times as
DochEvi [55]

Let number of yellow marbles = x

Let number of red marbles = y

Let number of blue marbles = z


Given that Finley has 152 yellow, red, and blue marbles in a bag.

So we get equation:

x+y+z=152...(i)


"He has seven more red marbles than yellow marbles" means:

y=x+7...(ii)

"three times as many blue marbles as yellow marbles." means:

z=3x...(iii)

Now we just need to solve those equations to find the answer.


Plug (ii) and (iii) into (i)


x+(x+7)+(3x)=152

x+x+7+3x=152

Which looks similar to choice (B)


5x+7=152

5x=145

x=29

Hence final answer is choice B.

Required equation is

x+x+7+3x=152

Number of yellow marbles = 29

5 0
2 years ago
Write the phrase as a rate in simplest form. 320miles on 34gallons
Katena32 [7]

Answer:

160/17 miles per gallon

Step-by-step explanation:

The typical rate of distance and gallons is distance per gallons, so divide the distance by the number of gallons.

(320 miles)/(34 gallons) = 160/17 miles per gallon

7 0
2 years ago
Read 2 more answers
What is the simplified form of the following expression? 2 StartRoot 18 EndRoot + 3 StartRoot 2 EndRoot + StartRoot 162 EndRoot
ExtremeBDS [4]

Answer:

18\sqrt2

Step-by-step explanation:

To simplify:

2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 }

First of all, let us write 18 and 162 as product of prime factors:

18 = 2 \times \underline{3 \times 3}\\162 = 2 \times \underline{3 \times 3} \times \underline{3 \times 3}

The pairs are underlined as above.

While taking roots, only one of the numbers from the pairs will be chosen.

Now, taking square roots.

\sqrt{18} =3 \sqrt2

162 = 3 \times 3 \times \sqrt 2  = 9 \sqrt2

So, the given expression becomes:

2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 } = 2 \times 3\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow 6\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow \sqrt2(6+3+9)\\\Rightarrow \bold{18\sqrt2}

So, the answer is:

18\sqrt2 or 18 StartRoot 2 EndRoot

7 0
2 years ago
Which is the solution of the quadratic equation (4y-3)^2=72 ?
max2010maxim [7]
Hello : 
<span>(4y-3)²=72 
4y-3 = </span>√72   or  4y-3 = - √72
y= (3+√72) /4   or y= (3 - √72) /4
7 0
2 years ago
0.2x + (-0.9) + 1.7 = 9.6<br> 0.2x + 0.8 = 9.6<br> X= <br> WHAT DOES x =
Andru [333]

Answer:

x =44

Step-by-step explanation:

0.2x + (-0.9) + 1.7 = 9.6

Combine like terms

.2x +.8 = 9.6

Subtract .8 from each side

.2x +.8 -.8 = 9.6 -.8

.2x = 8.8

Divide each side by .2

.2x/.2 = 8.8/.2

x =44

3 0
2 years ago
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