Just need someone to clarify things with me!
As I was solving this equation, I got:
x^-2
-------
x^10
I moved x^-2 down with x^10
So in x^-2's place, I placed a positive 1.
1
----------------------
x^10 times x^-2
The radical rule here is to pretty much subtract ahead. However, this extremely smart person said something like if I move a negative number to the denominator, it becomes positive. However, in this case, x^-2 stays the same.
Anyone explain here??
Answers
Answer:
[tex]\frac{1}{x^{12} }[/tex]
Step-by-step explanation:
Given [tex](\frac{x}{x^{-5}})^{-2}[/tex]
The Negative Exponent Rule states that, [tex]a^{-n} = \frac{1}{a^{n}}[/tex]
Basically, since you're raising the fraction inside the parenthesis to a negative exponent, the whole fraction becomes a denominator of 1: [tex]\frac{1}{(\frac{x}{x^{-5}})^{2}}[/tex]
Then, you'll have to work on the denominator:
[tex]\frac{1}{(\frac{x}{x^{-5}})^{2}} = \frac{1}{\frac{x^{2} }{(x^{-5})^{2}}}[/tex]
Next, you'll have to work on the divisor of x² (in the denominator), [tex](x^{-5})^{2}[/tex] by using the Power-to-Power Rule of Exponents: [tex](a^{m})^{n} = a^{mn}[/tex], which results in:
[tex](x^{-5})^{2} = x^{-10}[/tex]
Since it is a negative exponent, you'll have to apply the Negative Exponent Rule once again to the denominator.
[tex]\frac{1}{(\frac{x}{x^{-5}})^{2}} = \frac{1}{\frac{x^{2} }{(x^{-5})^{2}}} = \frac{1}{\frac{x^{2} }{x^{-10}}} = \frac{1}{\frac{x^{2} }{\frac{1}{x^{10}}}}[/tex]
At this point, you could apply the Fraction rule onto the denominator: [tex]\frac{a}{\frac{b}{c}} = \frac{a*c}{b}[/tex]
So the denominator now becomes:
[tex]\frac{1}{\frac{x^{2} }{\frac{1}{x^{10}}}} = \frac{1}{x^{2}*x^{10} }[/tex]
Finally, you could apply the Product Rule of Exponents, [tex]a^{m}a^{n} = a^{m + n }[/tex] onto the denominator:
[tex]\frac{1}{x^{2}*x^{10} } = \frac{1}{x^{2+10}} = \frac{1}{x^{12} }[/tex]
Therefore, the correct answer is: [tex]\frac{1}{x^{12} }[/tex]
Related Questions
Which statement correctly compares the function shown on this graph with
the function y = 5x + 5?
-10-8-642
2 4 6 8 10
A. The function shown on the graph has a smaller rate of change and
a lower starting point.
B. The function shown on the graph has the same rate of change, but
a lower starting point.
OC. The function shown on the graph has the same rate of change, but
a higher starting point.
D. The function shown on the graph has a smaller rate of change, but
the same starting point.
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Find the area of the following
trapezoid:
8 cm
5 cm
4 cm
16 cm
A = [?] cm2
PLEASE HELP
Answers
Answer:
48 cm²
Step-by-step explanation:
Area of trapezoid = [tex]\frac{a + b}{2}[/tex] × h
Area = (8 + 16)/2 x 4
Area = 24/2 x 4
Area = 12 x 4
Area = 48 cm²
of the students in the lunch room 40% are girls there are 20 girls in the the lunch room how many students are in the lunch room
Answers
Answer:
50 students
Step-by-step explanation:
20 is 40% of 50
because 50 x .40 = 20
Hope this helps!
Answer:
30
Step-by-step explanation:
40%/2=20%
20/2=10
100%-40%=60%
60%/3=20%
10x3=30
Triangle ABC is similar to triangle DEF. Find the measure of side DE. Round your
answer to the nearest tenth if necessary.
8
B
F
31
E
Ď
13-7
D
Answers
Answer:
53.1
Step-by-step explanation:
They're equal, so 8 = 31 and 13.7 = x
8/31 = 13.7/x
31(13.7) / 8 = 53.0875
Round your answer to nearest tenth to get 53.1
The rounded length of DE is 53.1.
What is similar triangles?
Similar triangles are triangles that have the same shape, but their sizes may vary.
What is the measure of DE?The both the triangles are similar, so the side length CB will be equal to FE and the side length AB will be equal to DE. Hence, the equation formed will be,
[tex]\frac{8}{31}=\frac{13.7}{DE}[/tex]
On solving this equation, we have DE=53.0875.
Therefore, the rounded length of DE is 53.1.
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find x
help please, asap.
Answers
Answer: x = 110 degrees
Step-by-step explanation:
35 and its vertical angle inside the triangle both = 35 deg
43 and 32 add to 75 deg
The total degree measure inside a triangle is 180
180-75-35 = 70 deg
70 degrees is the supplementary angle of x
180-70 = x
x = 110 degrees
Select the interval where g is positive.
Choose 1 answer:
A
1 < x < 2
B
3 < 3 < 4
4 < x < 5
Answers
Answer: it’s a
Step-by-step explanation:
Ans: 720cm
2
The ratio of the number of Malay students to the number of Indian students to the
number of Chinese students in a school is 5:4:8.
There are a total of 468 Indian and Chinese students.
What is the total number of students?
Ans:
Answers
Answer:
663
Step-by-step explanation:
ratio of Malay = 5
ratio of Indian= 4
ratio of Chinese= 8
Total number of Indian + Chinese= 468
Total ratio= 5+4+8= 17
Let the total number of students= X
Ratio of India= 4/17 × X=
Ratio of Chinese= 8/17 × X=
Addition of ratio of both India and Chinese=
4X/17 + 8X/17= 468
(4X +8X)/17 = 468
12X/17= 468
X= 663
Hence, total number of students is 663
Name the song that goes with these lyrics
1. I was rocking off white tryna have a fun time she gone eat like lunch time molly got her on time
2. Im a first class baby u in last baby im a 90's baby but i cook that shi from the 80's
3. I know i have a purpose but ion see the purpose they tell me the death of me gone be the perkys i know the lace the ills i bought them on purpose lifes unreal when deaths uncertain
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Answer:
1. I'll Be Fine - Juice Wrld
2. ON GOD - Juice Wrld
3. Rich and Blind - Juice Wrld
(x^2)+8x+12=0
i need help with this one
Answers
Answer:
x1=-6, x2=-2
Step-by-step explanation:
Answer:
this is the answer hope it helps
2 1/6* 2 5/6 IN SIMPLEST FORM
Answers
Answer:
6 5/36
Step-by-step explanation:
MARK ME BRAINLIEST?
Identify whether the following equation has a unique solution, no solution, or infinitely many solutions.
2( − 4) = 10 − 8 − 8
A
unique solution
B
no solution
C
infinite solutions
Answers
What is the probability of being born on a day that does not begin with the letter T?
Answers
Monday,Tuesday,Wednesday,Thursday,Friday,Saturday,Sunday
Only two start with a t so your answer would be
5/7
Solve each system.
3x – y = 5
4x – 2y = 4
Answers
Answer:
x = 3
y = 4
Step-by-step explanation:
y = 3x -5
4x - 2(3x-5) = 4
4x - 6x + 10 = 4
-2x = -6
x = 3
y = 4
Please help photos for my math
Answers
Answer:
1. Surface Area = 122 Volume = 84
2. Surface Area = 1632 Volume = 2880
3. Surface area = 168 Volume = 144
4. Volume = 1350[tex]\pi[/tex]
Step-by-step explanation:
1. This is a rectangular prism. To find the surface area it is the same thing. Find the area of all sides and add them together. Because this is a rectangular prism most of the sides are equal so we will only need to find the area of three sides. To find the area of the right side, just do 4*3=12. That would be the same for the opposite side. Then to find the front side, do 7*4= 28. That would also be the same for the opposite side. Then to find the top side, do 7*3= 21. That is the same for the bottom side. Add them all together and you will get your answer. 28+28+21+21+12+12 = 122.
To find the volume of a rectangular prism the formula is V = l*w*h.
Plug in: V = 7*3*4 and then you will get 84.
2. This is a triangular prism. First find the area of the the triangular surface by multiplying the base x height and dividing by 2. (16*12)/2 = 96. That is the same for the opposite side. Then find the area of the bottom rectangular surface. 12*30 = 360. Then find the area of the back rectangular surface. 16*30 = 480. Then find the area of the final base rectangle. 30*20 = 600. Add them together and you will get 1632. Basically, find the area of all sides and then add them together.
To find volume the formula is, V = (1/2)a*c*h
Fill that in: V = (1/2)16*12*30 and then you will get 2880.
3. This is a trapezoidal prism. To find the surface area you would find the area of all sides then add them together. To find the are of a trapezoid, the formula is: A = [tex]\frac{a+b}{2}[/tex]h
Fill that in: A = [tex]\frac{4+12}{2}[/tex](6) and then you will get 48.
That is the same for the opposite side. Then you need to find the area of the rectangular side of the trapezoidal prism. 3*4= 12. This is also the same as the opposite side. The bottom side is 12*3= 36. The top side is 3*4= 12.
Add all of them together and you get 168.
1/2(4+12)*6
To find volume, V = [tex]\frac{1}{2}[/tex]h(b₁+b₂)h.
Fill in: V = [tex]\frac{1}{2}[/tex]6(12+4)3 and then you will get 144.
4. This is a cylinder. The formula to find the volume is A=[tex]\pi[/tex]r²h. Because you are leaving the answer in terms of pi, do not multiply pi into the equation.
So you would do r²h. 15² = 225. 225*6= 1350. So your answer would be 1350[tex]\pi[/tex].
2. Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of . One day, her sink clogged. She has to use one of two conical cups to scoop the water out of the sink. The sink is completely full when Carissa begins scooping.
(a) One cup has a diameter of 4 in. and a height of 8 in. How many cups of water must Carissa scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.
(b) One cup has a diameter of 8 in. and a height of 8 in. How many cups of water must she scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.
Answers
Yes, your answers are correct.
The volume of a cone is given by V = 1/3πr²h. Since the diameter of the first cone is 4, the radius is 2; therefore the volume is
V = 1/3π(2²)(8) = 32π/3
We divide the volume of the sink, 2000π/3, by the volume of the cone:
2000π/3 ÷ 32π/3 = 2000π/3 × 3/32π = 6000π/96π = 62.5 ≈ 63.
The diameter of the second conical cup is 8, so the radius is 4. The volume then is:
V = 1/3π(4²)(8) = 128π/3
Dividing the volume of the sink, 2000π/3, by 128π/3:
2000π/3 ÷ 128π/3 = 2000π/3 × 3/128π = 6000π/384π = 15.625 ≈ 16
The requried,
(a) Carissa scoop out 63 cups.
(b) Carissa scoop out 16 cups
Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
The problem requires us to find out how many cups of water Carissa needs to scoop out of the sink to empty it, given the volume of the sink and the dimensions of the two cups. We can solve this problem by using the formula for the volume of a cone:
V = (1/3) * π * r² * h
First, simplify the volume formula for a cone to make it easier to manipulate:
V = 1/3πr²h
Next, plug in the given values for the first cone:
V = 1/3π(2²)(8) = 32π/3
Then, divide the volume of the sink by the volume of the first cone:
2000π/3 ÷ 32π/3 = (2000π/3) * (3/32π) = 2000/32 = 62.5 ≈ 63.
Now, calculate the volume of the second cone using the same formula:
V = 1/3π(4²)(8) = 128π/3
Finally, divide the volume of the sink by the volume of the second cone:
2000π/3 ÷ 128π/3 = (2000π/3) * (3/128π) = 2000/128 = 15.625 ≈ 16.
Divide the volume of the sink by the volume of the first cone to get the number of first cones that can fit into the sink:
2000π/3 ÷ 32π/3 = (2000π/3) * (3/32π) = 2000/32 = 62.5 ≈ 63.
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2. the sum of x and 9
Answers
Answer:
x + 9
Step-by-step explanation:
The sum of x and 9,
x + 9
What is the mode of the data set ?
3,3,5,5,5,7,7,8,15,15
Answers
Answer:
5
Step-by-step explanation:
the mode is the number that appears most frequently on a data set.
Answer:
5
Step-by-step explanation:
josie is looking at buying a new phone for $800. If she does not want to pay the entire $800 she has the option of buying a phone $150 deposit and making 12 monthly payment of $75 each. If josie Chooses the payment plan what will be the percent increase on the original cost of the phone? No links
Answers
Answer:
maybe its b
Step-by-step explanation:
What is the volume of the cylinder shown below? A. 12157 units B. 3617 units C. 647 units D. 152 T units
1215 Units 3
Answers
Answer:
D
Step-by-step explanation: the answer is D
two companies working together can clear a parcel of land in 9 hours. working alone,it would take company A 3 hours longer to clear the land than it would company B. How long would it take company B to clear the parcel of land alone ( round your answer to the nearest tenth.)
Answers
Answer:
.33
Step-by-step explanation:
The admission prices for a small fair are $1.50 for children and $4.00 for adults. In one day there was $5050 collected. If we know that 2100 children paid admission, find the number of adults that paid admission.
Answers
Answer: 475 adults paid admission
Step-by-step explanation:
1.50c+4a=5050 (1.50 per child and 4 per adult)
1.50(2100)+4c=5050 (2100 children times 1.5 each)
3130+4a=5050
4a=1900
a=475
Sam is making a picture frame. He is gluing craft sticks end-to-end to a piece of cardboard. The sticks do not overlap. The top of the frame is 18 and one-third inches long. Each craft stick is 3 and one-third inches long.
How many craft sticks will Sam glue to the cardboard to make the top of the frame?
Answers
Answer: 5 1/2
Step-by-step explanation:
I took the test ig, but im not 100% sure
Pam went to the mall one day, below shows what she bought and how much those items cost.
2 shirts - $31.45
Jeans - $18.50
Dress - $14.95
How much money did Pam spend in all?
Answers
Answer:
$96.35
Step-by-step explanation:
31.45 x 2 = 62.90
62.90 + 18.50 + 14.95 = $96.35
SIMPLE QUESTION! Multiply 3x^2(5x^3)
Answers
Answer:
15x^5
Step-by-step explanation:
That's the answer I got im pretty sure it correct
Juan has four ties, three shirts and four pairs of pants. How many different outfits can he wear if he chooses one Tie, one shirt, one pair of pants of each outfit?
Answers
Answer:
48 outfits
Step-by-step explanation:
Using Fundamental Principal of counting
number of outfits that Juan can wear
=number of ties * number of pants * numberof pants
=4*3*4
=48 outfits
The number of different outfits can he wear if he chooses one Tie, one shirt, one pair of pants for each outfit is 48 outfits.
What is the combination?The arrangement of different things or numbers in a number of ways is called a combination.
A permutation is an orderly arrangement of things or numbers. Combinations are a way to choose items or numbers from a collection or group of items without worrying about the items' chronological order.
Given that Juan has four ties, three shirts, and four pairs of pants.
Using the Fundamental Principle of counting,
Number of outfits that Juan can wear
N =number of ties x number of pants x number of pants
N =4 x 3 x 4
N =48 outfits
Therefore, the number of different outfits can he wear if he chooses one Tie, one shirt, one pair of pants for each outfit is 48 outfits.
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What is the gross earnings for a person who has $26,480 in total sales,
$1250 in Returns and Allowances, and a rate of commission of 7%?
Answers
Answer:
$3103.6
Step-by-step explanation:
Given data
Total sales= $26,480
Returns and Allowances=$1250
Commission = 7%
Let us find the amount in commission earned
=7/100*26,480
=0.07*26480
=$1853.6
Hence the gross earnings
=1853.6+1250
=$3103.6
round to nearest 10 place
318
4271
18293
Answers
Answer:
318-320
4271-4270
18293-18290
For each value of y, determine whether it is a solution to 7y - 9 = -58
Answers
Answer:
The answer is -7.
Step-by-Step explanation:
1. Discriminate the solutions of the following quadratic equations.
(1) [tex]x^2+5x+3+a=0[/tex]
(2) [tex]x^2+(a+b)x+ab=0[/tex]
(Please show the steps if possible)
Answers
Mrs.beck shops from the clearance rack of dresses.The stem and leaf plot represents the sale prices of dresses in Mrs.becks size.What statement is true?
F: 20 percent of the dresses cost more than $50
G:one-fifth of the dresses range in price from $30 to $40
C:Fifteen percent of the dresses cost less than $20
D:Four percent of the dresses cost $65
Answers
Answer:
The answer is F
Step-by-step explanation: