Mathematics College

DIVIDING ALGEBRAIC FRACTIONS

2p/4p^2 divided by 6p^3/6p+3

Answers

Answer 1
To multiply two fractions, you multiply the numerators together and you multiply the denominators together
= 2p(6p + 3) / 6p^3(4p^2 - 1)

Next, we can factor out a 3 in the numerator
= 6p(2p + 1) / 6p^3(4p^2 - 1)

Next, we can factor the denominator
= 6p(2p + 1) / 6p^3(2p - 1)(2p + 1)

Since we have (2p + 1) in the top and bottom, we can cancel it
= 6p / 6p^3(2p - 1)

We can also cancel a 6p in the top and bottom
Answer: 1 / p^2(2p - 1)

hope I helped

Related Questions

Derivative of sin (x^(1/3)) + (sinx)^(1/3)

Answers

1/3 x^(-2/3) cos (x^1/3) + 1/3(sinx)^-2/3 .cos x



[tex]\bf sin\left( x^{\frac{1}{3}} \right)+[sin(x)]^{\frac{1}{3}}\\\\ -------------------------------\\\\ cos\left( x^{\frac{1}{3}} \right)\cdot \cfrac{1}{3}x^{-\frac{2}{3}}+\cfrac{1}{3}[sin(x)]^{-\frac{2}{3}}\cdot cos(x)\impliedby \textit{chain-ruling both terms} \\\\\\ \cfrac{cos(\sqrt[3]{x})}{3\sqrt[3]{x^2}}+\cfrac{cos(x)}{3\sqrt[3]{sin^2(x)}}[/tex]

A reel of electrical cable holds 80 metres when full.

3/16 of the reel has been used.

How much cable is there left on the reel?

Answers

I3/I6(8O)= 65m of electrical cable left

HELLLLPPPPP MMMEEEEE!

Answers

you have 2 angles given 50 and 110

50+110 = 160

so 180-160 = 20

A = 20 degrees

How do I solve this 6x + 3 = 5x + 10

Answers

Subtract 5x from both sides
x+3=10

Subtract 3 from both sides
x=7

Final answer: x=7
Move all terms containing xx to the left side of the equation.Since 5x5x contains the variable to solve for, move it to the left side of the equation by subtracting 5x5x from both sides.6x−3−5x=−56x-3-5x=-5Subtract 5x5x from 6x6x to get xx.x−3=−5x-3=-5Move all terms not containing xx to the right side of the equation.Since −3-3 does not contain the variable to solve for, move it to the right side of the equation by adding 33 to both sides.x=3−5x=3-5Subtract 55 from 33 to get −2-2.x=−2

Use Cramer's Rule to solve the following system: –2x – 6y = –26 5x + 2y = 13

Answers

[tex]\bf \begin{cases} -2x-6y&=-26\\ \quad 5x+2y&=13 \end{cases}\stackrel{\textit{determinant of the coefficients}}{D= \begin{bmatrix} -2&-6\\5&2 \end{bmatrix}}\implies (-4)-(-30) \\\\\\ D=-4+30\implies \boxed{D=26}\\\\ -------------------------------\\\\[/tex]

[tex]\bf x=\cfrac{D_x}{D}\implies x=\cfrac{ \begin{bmatrix} \boxed{-26}&-6\\\\ \boxed{13}&2 \end{bmatrix}}{D}\implies x=\cfrac{(-52)-(-78)}{26} \\\\\\ x=\cfrac{-52+78}{26}\implies x=\cfrac{26}{26}\implies \boxed{x=1}\\\\ -------------------------------\\\\ y=\cfrac{D_y}{D}\implies y=\cfrac{ \begin{bmatrix} -2&\boxed{-26}\\\\ 5&\boxed{13} \end{bmatrix}}{D}\implies y=\cfrac{(-26)-(-130)}{26} \\\\\\ y=\cfrac{-26+130}{26}\implies y=\cfrac{104}{26}\implies \boxed{y=4}[/tex]

What radius of a circle is required to inscribe a regular hexagon with an area of 210.44 cm2 and an apothem of 7.794 cm?

Answers

[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap\quad \begin{cases} a=apothem\\ p=perimeter\\ -------\\ a=7.794\\ A=210.44 \end{cases}\implies 210.44=\cfrac{1}{2}(7.794)p \\\\\\ 420.88=7.794p\implies \cfrac{420.88}{7.794}=p\implies 54\approx p \\\\\\ \textit{a \underline{hexa}gon has 6 sides, so }\cfrac{54}{6}\implies \stackrel{\textit{length of one side}}{9}[/tex]

so.. now, if we know one side is of 9 units long... ok, bear in mind that a regular hexagon, splits the center of the circumscribing circle in 6 even angles, that'd be 60° each, if you run a bisector from that angle, it'd split into two 30° angles, check the picture below.

So it ends with a 30-60-90 triangle with one side being just half of the 9 units, and we can just use the 30-60-90 rule to get the radius itself, which is just one of the sides of the 30-60-90 triangle.

Answer:

The answer is D) 9cm

6 equilateral triangles in a regular hexagon

210.44

6

= 35.073 cm2

The apothem cuts each equilateral triangle into two right triangles.

35.073

2

= 17.5367 cm2

Base of each right triangle.

area =  

1

2

bh

17.5367 =  

1

2

b(7.794)

b = 4.5

Thus, the sides of each equilateral triangle is 2b = 2(4.5) = 9; which is also the radius of the circle needed to construct the inscribed regular hexagon.

Brainliest? You can read me work unlike the other

The team manager mixes 0.6 kg of Gatorade powder with water in the 5-gallon water coolers for the football team. Gatorade donates new 7-gallon water jugs. How much powder should the manager use in a new 7-gallon cooler to maintain the same Gatorade mixture?

Answers

Since it's 0.6 kg for 5 gallons, we'd want to find the unit rate aka the amount of kg's per gallon. To find that, we have to see how many times 5 goes into 0.6, which is 0.6/5=0.12 for 1 gallon. Multiply that by 7 to get 0.84 for 7 gallons!

The service elevator in a high-rise building travels between the lowest underground parking level and the seventeenth story of the building. The lowest parking level is 15 meters below street level, and the seventeenth story is 51 meters above street level. If the elevator rises at a rate of 2 meters per second, how long, in seconds, could a person ride the elevator when starting from the lowest level? Assume the elevator makes no extra stop.

Answers

15 +51 = 66 meters total

66 /2 = 33 seconds 

and that is your answer


The person will reach to the seventeenth in 33 seconds.

Given that,
The lowest parking level is 15 meters below street level, and the seventeenth story is 51 meters above street level.
To determine how long, in seconds, could a person ride the elevator when starting from the lowest level.

What is speed?

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
Total height to cover = height of lowest parking to street level + height of 17 stories from street level.
Total height = 15 + 51
Total height = 66 meters
Time to reach to the 17th story
Speed = distance / time
2 = 66 / time
time = 66 / 2
Time = 33 seconds

Thus,  the person will reach to the seventeenth in 33 seconds.

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What is the base 8 representation for 112

Answers

Final answer:

In base 8 (also known as octal), the conversion of the decimal number 112 is done by repeatedly dividing by 8 and considering the remainder. Following this process, the base 8 representation of 112 is 160.

Explanation:

In base 8 (also known as octal), each position in a number represents a power of 8. To convert the decimal number 112 to base 8, we need to determine how many times 8 can fit into 112, along with the remainder.

Here's how we do it:

Divide 112 by 8. The result is 14 with no remainder. There's your first Octal digit, at the least significant digit (rightmost). Now divide the whole number quotient from the previous step (14) by 8. The result is 1 with a remainder of 6. The whole number quotient (1) is the next Octal digit, and keep 6 as the next step's quotient.Finally, you have 1 (from the last step) which can be divided by 8, results in 0 and a remainder of 1. So, the remainder is the final Octal digit, at the most significant digit (leftmost).

So, the base 8 representation for 112 is 160.

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8 to the power of x+3=16 to the power of x-1

Answers

8^x+3=16^x+1, 2^3(x+3)=2^4(x+1), 2^3x+9=2^4x+4, same bases. 3x+9=4x+4, 3x-4x=4-9, -x=-5, x=5
[tex]\bf 8^{x+3}=16^{x-1}\qquad \begin{cases} 8=2\cdot 2\cdot 2\\ \qquad 2^3\\ 16=2\cdot 2\cdot 2\cdot 2\\ \qquad 2^4 \end{cases}\implies (2^3)^{x+3}=(2^4)^{x-1} \\\\\\ 2^{3(x+3)}=2^{4(x-1)}\impliedby \begin{array}{llll} \textit{since the bases are the same}\\ \textit{the exponents must also be the same} \end{array} \\\\\\ 3(x+3)=4(x-1)\implies 3x+9=4x-4\implies 9+4=4x-3x \\\\\\ \boxed{13=x}[/tex]

Ivy corporation gave 90 people a bonus. If ivy had given 8 more people bonuses, ivy would have rewarded 2/3 of the workforce. How large is Ivy's workforce?

Answers

Hey! Hope that I can help.

With the info you've given me, I know that 98 people is 2/3 of their workforce. Divide that by 2 to get 1/3, and then multiply that number by 3 to get your answer.

98 / 2 = 49 x 3 = 147
Answer: 147 people
they rewarded 90 folks, if they had made it 98, that'd be 2/3 of their workforce, so hmmm  if say 98 is 2/3, how much is the 3/3, or the whole amount?

[tex]\bf \begin{array}{ccll} workers&\stackrel{total}{workforce}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 98&\frac{2}{3}\\\\ x&\frac{3}{3} \end{array}\implies \cfrac{98}{x}=\cfrac{\frac{2}{3}}{\frac{3}{3}}\implies \cfrac{98}{x}=\cfrac{\frac{2}{3}}{1} \\\\\\ \cfrac{98}{x}=\cfrac{2}{3}\implies \cfrac{98\cdot 3}{2}=x\impliedby \textit{total amount of workers}[/tex]

The quotient of nine and the difference of four and a number

Answers

We write this in math as 9/(4-n) this cannot be simplified any further.
Final answer:

The quotient of nine and the difference of four and a number is obtained by dividing nine by the difference of four and the number (4 - x), after subtracting the number from four first. This expression can be simplified to get the final result.

Explanation:

The quotient of nine and the difference of four and a number can be expressed as:

9 / (4 - x)

To simplify this expression, we need to subtract the number x from 4 first, and then divide 9 by the result. For example, if the number x is 2, the expression would be:

9 / (4 - 2) = 9 / 2 = 4.5

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A cell phone that is on sale for $70 has a markdown of 45% off the regular price. What is the regular price of the cell phone? Round to the nearest cent.

Answers

vjghfjghfhggvbgvjyhfg cghgfc fgjfgtydfjnhgjhyuvgk
the equation here is 70*.45= x then u add x to the $70 and thats your answer

Solve for z in the following equation: 2-3iz = 3 + 2iz$

Answers

2-3iz=3+2iz
-5iz=1
iz=-1/5
z=i/5

Ans.) i/5


The value of 'z' for the given linear equation is [tex]- \frac{1}{5i}[/tex].

What is a linear equation?

A linear equation is an equation where there are one or multiple variables. However, the highest power of any variable is one.

Given linear equation is

[tex]2-3iz = 3 + 2iz[/tex]

⇒ [tex]2iz + 3iz= 2-3[/tex]

⇒ [tex]5iz = -1[/tex]

⇒ [tex]z = \frac{-1}{5i}[/tex]

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97 cars making up a freight train,56 are boxcars and 41 are not.Find the fraction of the cars that are not boxcars?

Answers

56/97 are boxcars, 41/97 are not boxcars. Neither fraction will reduce, so 41/97 is the correct fraction of cars that are not boxcars.

If u, v, and w are nonzero vectors in r 2 , is w a linear combination of u and v?

Answers

Not necessarily. [tex]\mathbf u[/tex] and [tex]\mathbf v[/tex] may be linearly dependent, so that their span forms a subspace of [tex]\mathbb R^2[/tex] that does not contain every vector in [tex]\mathbb R^2[/tex].

For example, we could have [tex]\mathbf u=(0,1)[/tex] and [tex]\mathbf v=(0,-1)[/tex]. Any vector [tex]\mathbf w[/tex] of the form [tex](r,0)[/tex], where [tex]r\neq0[/tex], is impossible to obtain as a linear combination of these [tex]\mathbf u[/tex] and [tex]\mathbf v[/tex], since

[tex]c_1\mathbf u+c_2\mathbf v=(0,c_1)+(0,-c_2)=(0,c_1-c_2)\neq(r,0)[/tex]

unless [tex]r=0[/tex] and [tex]c_1=c_2[/tex].

water weighs about 8.34 pounds per gallon. About how many ounces per gallon is the weight of the water?

Answers

Use a conversion factor and turn pounds to ounces. 1 pound = 16 ounces so
[tex] \frac{8.34pounds}{gallon} \times \frac{16 ounces}{ 1 pound} =133.44 \frac{ounces}{gallon} [/tex]

Please help!!
A road trip of 400 miles require a total of 8 hours to drive. For the first portion of the trip, an average speed of 63 miles per hour was maintained; on the last portion of the trip, the average speed was only 443 miles per hour due to highway construction project. How much time, in hours, to the nearest tenth of an hour, was spent driving at each of the two speeds, and what was the total time for the entire trip?

Answers

2.8 hours at 63 mph 5.2 hours at 43 mph Total time spent driving = 8.0 hours. I'm assuming based upon context that your value of 443 miles per hour is a typo and the correct value is 43 miles per hour. The solution provided is for the two speeds of 63 mph and 43 mph. First make an expression detailing what you know. X = duration spent at 63 mph (8 - X) = duration spent at 43 mph 63X + 43(8-X) = 400 Solve for X 63X + 43(8-X) = 400 63X + 344 - 43X = 400 63X - 43X = 56 20X = 56 X = 2.8 So you spent 2.8 hours at 63 mph and 8-2.8 = 5.2 hours at 43 mph

f(x)= 2x-3x^2 evaluate f(-3)
A. -33
B. 6
C. 33
D. -21

Answers

f(-3) = 2(-3) - 3(-3)²
f(-3) = -6 - 3(9)
f(-3) = -6 - 27
f(-3) = -33

What is the gcf of 14 and 22

Answers

The multiples of 14 are 1,2,7,14
the multiples of 22 are 1,2,11,22
Therefore 2 is the GCF

For the equation, 2x^4 -5x^3+10=0 find the number of complex roots and the possible number of real roots.
A. 3 complex roots; 0, 2 or 4 real roots
B. 3 complex roots; 1 or 3 real roots
C. 4 complex roots; 0, 2 or 4 real roots
D. 4 complex roots; 1 or 3 real roots

Answers

The given equation is
2x⁴ - 5x³ + 10 = 0

Because this is a 4th degree polynomial, there are 4 possible real and complex roots.

Let f(x) = 2x⁴ - 5x³ + 10
Apply Descartes' Rule of signs.
There are 2 sign changes, so there are 2 possible positive real roots.

f(-x) = 2x⁴ + 5x³ + 10
There are no sign changes, so there are no negative real roots.

This means that
(a) There are possibly 2 real positive roots, and a conjugate pair of  2 complex roots;
(b) 0 real roots, and 2 pairs of 4 complex roots.

Of the given answers, only C. can be correct.
Note that complex roots always occur as conjugate pairs, so A and B are incorrect.

Answer: C
4 complex roots; 0, 2, or 4 real roots

What is 6,403.5 rounded to the nearest thousand?

Answers

It is 6,000. 6,403.5 rounds down to 6,000. Hope this helps!

Can u plz mark me as brainliest?? I really need it!

When given an algebraic expression involving subtraction, why is it best to rewrite the expression using addition before identifying the terms?

Answers

Since it doesn't mention multiplication, no. What would be the point of rewriting an expression from 3-2 to 3+(-2)?

The area of a circle is 99 in.² what’s the radius

Answers

The radius is ≈ 5.61in. I hope this helps love! :)

What is the median of the following string of values?
55, 18, 58, 49, 8, 77, 62, 26, 7, 91

A.55

B.52

C.49

D.58

Answers

the median is 52, so the answer would be B.

Answer:

Option B is correct

The median of the following string of values is 52

Step-by-step explanation:

Median defined as the median is the middle number.

To find the median of the following string of values:

55, 18, 58, 49, 8, 77, 62, 26, 7, 91

Arrange the string of  values from least to greatest.

7, 8, 18 , 26, 49, 55, 58, 62, 77, 91

As you can see that we have two numbers, there is no middle number.

Simply, take the mean of the two middle numbers.

then;

Median = [tex]\frac{49+55}{2} = \frac{104}{2} = 52[/tex]

Therefore, the median of the following string of values is 52


Find the equation of the line that contains the given points. P1(−8, 5), P2(−8, −5)

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -8}}\quad ,&{{ 5}})\quad % (c,d) &({{ -8}}\quad ,&{{ -5}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-5-5}{-8-(-8)} \\\\\\ \cfrac{-10}{-8+8}\implies \stackrel{und efined}{\cfrac{-10}{0}}[/tex]

that simply means, is a vertical line, check the picture below.

What is the common ratio for this geometric sequence?

Answers

Answer is c 3 because it is multiplied 3 everytime

Answer:

Common ratio for the sequence is 3

Step-by-step explanation:

Given sequence is

5, 15, 45, 135,.....

To find out common ratio, divide the second number by the first number

[tex]\frac{15}{5} =3[/tex]

[tex]\frac{45}{15} =3[/tex]

[tex]\frac{135}{45} =3[/tex]

we got 3 that is our common ratio 3

Common ratio for the sequence is 3

Estimate the sum 458+214

Answers

Final answer:

To estimate the sum of 458+214, round each number to the nearest ten to get 460 and 210, then add to find the estimated sum of 670. The actual sum is 672, confirming the estimate's accuracy.

Explanation:

To estimate the sum of 458+214, you can round each number to the nearest ten and then add them together. You would round 458 to 460 and 214 to 210. When you add 460 and 210, you get 670. Therefore, an estimate for the sum of 458 and 214 is 670.

To verify if our estimation is accurate, we can perform the actual addition: 458 + 214 equals 672. Our estimate of 670 is very close to the actual sum, demonstrating the effectiveness of the estimation method.

You and your brother are readibg the same novel you wnat to get ahead of him in the book so you decide to read 30 minutes longer than your brother reads how many minutes will you read if your brother reads for 15 minutes

Answers

45 minute 30+15= 45 easy

Answer:

45 minute 30+15= 45 easy

Step-by-step explanation:

what is 2x+square root x+1=8 solve for x

Answers

[tex]\bf 2x+\sqrt{x+1}=8\implies \sqrt{x+1}=8-2x\quad \leftarrow \textit{now we square both sides} \\\\\\ (\sqrt{x+1})^2=(8-2x)^2\implies x+1=8^2-32x+(2x)^2 \\\\\\ x+1=64-32x+2^2x^2\implies x+1=64-32x+4x^2 \\\\\\ 0=4x^2-32x-x+64-1\implies 0=4x^2-33x+63 \\\\\\ 0=(4x-21)(x-3)\implies \begin{cases} 0=4x-21\\ 21=4x\\\\ \boxed{\frac{21}{4}=x}\\ --------\\ 0=x-3\\ \boxed{3=x} \end{cases}[/tex]
Hello,

On my keybord i have no touch "square root (√)" but "V" yes .

[tex]2x+ \sqrt{x+1} =8\\ \sqrt{x+1} =8-2x\\ x+1=(8-2x)^2\\ x+1=64-32x+4x^2\\ 4x^2-33x+63=0\\ x= \frac{21}{4} \ or\ x=3\\ [/tex]

Verification:
if x=3 then 2*3+√(3+1)=6+2=8

if x=21/4 then 13≠8 is to exclude.

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