Answers
The algebraic expression [tex]x^{10/3}[/tex] is equivalent to the algebraic expression [tex]x^{3}\cdot \sqrt[3]{x}[/tex]. Thus, the right choice is option D.
How to apply power and root properties to rewrite a given expression
In this question we must apply the following set of algebraic properties to simplify a given expression:
[tex]x^{m/n} = \sqrt[n]{x^{m}} = \left(\sqrt[n]{x}\right)^{m}[/tex] (1)
[tex]x^{m+n} = x^{m}\cdot x^{n}[/tex] (2)
[tex]x^{m\cdot n} = \left(x^{m}\right)^{n} = \left(x^{n}\right)^{m}[/tex] (3)
Where:
m, n - Exponentsx - BaseAnd also by apply the definition of power.
If we know that the given expression is [tex]x^{10/3}[/tex], then the equivalent expression is:
[tex]x^{10/3} = \sqrt[3]{x^{10}} = \sqrt[3]{x^{9}\cdot x} = \sqrt[3]{x^{9}}\cdot \sqrt[3]{x} = x^{3}\cdot \sqrt[3]{x}[/tex]
The algebraic expression [tex]x^{10/3}[/tex] is equivalent to the algebraic expression [tex]x^{3}\cdot \sqrt[3]{x}[/tex]. Thus, the right choice is option D.
To learn more on roots, we kindly invite to check this verified question: https://brainly.com/question/1527773
Related Questions
A cylinder and its dimensions are shown in the diagram. Which equation can be used to find V, the volume of the cylinder in cubic centimeter? I think A. is the answer :)
Answers
Answer: it’s simply a
Step-by-step explanation: X =bsquare
What is the greatest common factor of 21 and 64?
Answers
Answer:
1
Step-by-step explanation:
Factors of 21: 1, 3, 7, and 21
Factors of 64: 1, 2, 4, 8, 16, 32, and 64
These numbers do not share any other factors other than 1
A right angle is divided into 3 equal angles. What is the measure of
each smaller angle in degrees?
Answers
Answer: 30 degrees
Step-by-step explanation:
90 degrees / 3 angles = 30 degrees
Help please! Again this is the last question
Answers
5/6 = 25/30
3/5 = 18/30
5/6 is greater than 3/5.
15 + 1 = 16
The answer is D: 16
what is the perimeter of a rectangular playground 30 m long and 24 m wide
Answers
Answer:
108m
Step-by-step explanation:
2 sides are 30m long and 2 sides are 24m long.
Add all 4 sides of the playground to find the perimeter.
30m + 24m + 30m + 24m = 108 m
What’s life about and why are we here on this earth
Answers
Many out there got different opinions on this especially with the influence of religion and science.
LIFE is about learning the best in you and others. Its about loving, being kind and to be someone of great worth who at the the end of the day makes a mark of positivity in every life encountered. Its about living a life of meaning and that's all that matters. Every religion holds it's own perspectives and it's most important that you choose to believe in a religion that helps better Express your faith.
remember that there'll be a day you sit back and look at the life you "lived"
make sure that the choices you make now don't bring ANY regrets.
Find the slope of the line that passes through 4, −6 and −3, 1 . Write your answer in simplest form. Select "Undefined" if applicable.
The slope is ______ .
Answers
To find the slope between two points:
⇒ must know the slope's formula
[tex]\frac{y2-y1}{x2-x1}[/tex]
(x1, y1) --> any point on the line (x2, y2) --> any point on the line but (x1, y1)Let's consider the information given
⇒ given two points ⇒ (4, -6) and (-3,1)
Let's set: (you can interchange the two values of (x1,y1) and (x2,y2), it doesn't change the answer in any way)(x1, y) --> (4, -6)
(x2, y2) --> (-3, 1)
Let's calculate the slope:
[tex]slope = \frac{1--6}{-3-4} =\frac{7}{-7} =-1[/tex]
Thus the slope is -1
Hope that helps!
Help help help help math math
Answers
Equation of the graph: x = 3
Since the graph is a vertical line, the equation must be 'x ='
You will get the 3 by seeing its horizontal position on the x-axis
Hope that helps!
Please help me understand the question
Answers
Answer:
180 units^2
Step-by-step explanation:
The formula to find the area of a sphere is:
A=4(pi)(r)^2
A sphere with radius 2r has an area = 4π(2r)² = 4π.4r² = 16πr²
The ratio of the larger sphere to the smaller = 16πr² : 4πr² = 4 : 1
If the area of the smaller sphere is 45 units then the area of the larger sphere is 45 x 4 = 180 units^2.
hope this helps :)
Distance between athe and moon written in scientific notation
Answers
Answer:
here
Step-by-step explanation:
The distance between the earth and the moon is approximately 384000 km. To Do: Express the distance in meters in exponential notation. Therefore the answer is 3.84 × 10 8 m.
Which choice is equivalent to the expression below?
√-125
A. 5i√5
B. -5i
C. 5i√-5
D. 5i
E. √125
Answers
Answer:
5i√5
Step-by-step explanation:
Remark
125 factors
It is factored into 5*5*5
The rule for √5*5*5 is that two can be taken outside the square root sign. I is placed in front of the root sign like 5√ and the other 5 is thrown away.
The remaining 5 is left under the root sign
As usual
√-1 is i is taken outside the root sign
Solution
5i √5 is what you get.
which of the following is an algebraic equation. a. 10+5=15. b. 10x+5=15. c. 10x+5. d. 10+5
Answers
A store is having a sale to celebrate President's Day. Every item in the store is advertised as one-fifth
off the original price. If an item is marked with a sale price of $140.00, what is the original price?
Answers
I think this is how u do it
Hope this helps:)
Зу - 10 < 11
How to solve
Answers
Answer:
y<7
Step-by-step explanation:
3y-10 < 11 add 10 to both sides of the equation
3y < 21 divide by 3
y < 7
There are people fishing at Lake Connor: 4 have fishing licenses, and 4 do not. An inspector chooses two of the people at random. What is the probability that
the first person chosen does not have a license and the second one does? Write your answer as a fraction in simplest form
Answers
every other person has one
Find the product of the following by writing one of numbers as the sum or difference of two numbers -
785*105
1006*95
3096*91
Answers
Answer:
Step-by-step explanation:
Use distributive property: a*(b+c) =a*b +a*c
1) 785 * 105 = 785 * (100 + 5)
= 785*100 + 785*5
= 78500 + 3925
= 82425
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2) 1006 * 95 = (1000 + 6) *95
= 1000*95 + 6*95
= 95000 + 570
= 95570
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3) 3096*91 = 3096 * (100 - 9)
= 3096*100 - 3096*9
= 309600 - 27864
= 281736
Someone help pls tysmmm
Answers
Answer:
29
Step-by-step explanation:
Substitute v = 15 into 14 + v
14 + 15 = 29
Hope this helps :)
Use the point-slope formula to write an equation of the line that passes through 4, 5 and −6, −4 . Write the answer in slope-intercept form (if possible).
The equation of the line is _________ .
Answers
Answer:
y-5=9/10⋅(x−4)
Step-by-step explanation:
I NEED HELP WITH NUMBER 7
Answers
Answer:
c po
because that is the answer in the bakc of my module hope its help
I hope this helps you :)
find the average rate of change of f(x) = 3x - 7 over the interval 1 ≤ x ≤ 5
Answers
Answer:
If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.
Step-by-step explanation:
If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.
A teacher asks her class of 22 students, "What is your age?" Their responses are shown below.
19, 19, 14, 14, 16, 19, 19, 16, 16, 15, 17, 16, 17, 16, 15, 14, 15, 15, 17, 14, 16, 15
Find the mean, median, and mode for the data. If necessary, round to the nearest tenth.
O A 16.5; 17; 17
OB. 16.1: 16; 16
C. 16.1; 17; 16
o
D. 16.5; 16; 17
Answers
Answer:
B.
Mean: 16.1
Median: 16
Mode: 16
Step-by-step explanation:
First, order the numbers in the data set from least to greatest:
[tex]14 , 14 , 14 , 14 , 15 , 15 , 15 , 15 , 15 , 16 , 16 , 16 , 16 , 16 , 16 , 17 , 17 , 17 , 19 , 19 , 19 , 19[/tex]
First, find the mean. The mean of a data set can be found by adding all the numbers together and dividing by the amount of numbers in the set:
[tex]\frac{14 + 14 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 16 + 16 + 16 + 17 + 17 + 17 + 19 + 19 + 19 + 19}{22} = \frac{354}{22}[/tex]
Next, simplify by dividing:
[tex]\frac{354}{22} = \frac{177}{11} = 16 \frac{1}{11} or ~16.1[/tex]
Mean: 16.1
Next, find the median. The median is the number(s) directly in the middle. If there is a even amount of number in the data set, find the mean of the two median numbers:
Median: 16 , 16
Median = [tex]\frac{16 + 16}{2} = \frac{32}{2} = 16[/tex]
Median = 16
Next, find the mode. The median is the number that shows up the most. In this case, it is 16, which appears 6 times, 1 more time then the next number that appears the most 15, which appears 5 times.
Mode: 16
~
If you are asked about range, range would be the greatest digit value subtracted by the least digit value. In this case, it would be 14 & 19:
19 - 14 = 5
Range: 5
~
What integer best represents
a withdrawal of $85?
Answers
Answer:
the answer is -85 good luck on your test or honework :)
Find the sum of the first 150 positive even integers.
Answers
Answer:
Sum of first 150 positive even integers is 22650Step-by-step explanation:
We know that first 150 postive even Integers are 2,4,6,8,10... 300.
Here,
First term (a) = 2 Comman difference (d) = 4 - 2 = 2 Total terms (n) = 150Last term (aₙ) = 300[tex]\\[/tex]
Substituting values in the formula:
[tex] \\ :\implies \sf \: \: S_{n} = \dfrac{n}{2} (a + a_{n}) \\ \\[/tex]
[tex] :\implies \sf \: \: S_{n} = \dfrac{150}{2} (2 + 300) \\ \\ [/tex]
[tex] :\implies \sf \: \: S_{n} = 75(302) \\ \\ [/tex]
[tex] :\implies \: \:{ \underline{ \boxed{ \pmb{ \pink { \rm{S_{n} = 22650 }}}}}} \\ \\[/tex]
Sum of first 150 positive even integers is 22650Answer:
The number series 2, 4, 6 , 8. . . . , 150.The first term (a) = 1The common difference (d) = 4 – 2 = 2Total number of terms (n) = 150last term (an) = 300Formula for finding sum of nth terms =
n/2 × (a + an)
putting the known values ,
Sum = 150/2 × ( 2+300)
Sum = 75 × 302
Sum of first 150 positive even integers = 22650
FIND THE RADIUS OF THE SHPERE WITH THE GIVEN VOLUME?
562.5π in.³
Answers
Answer:
Radius = 7.5 inStep-by-step explanation:
In the question we have given volume of Sphere that is 562.5 π in³ and we have asked to find the radius of given sphere. We know that the volume of sphere ,
[tex] \blue{ \boxed{ \rm{Volume \: of \: Sphere = \frac{4}{3} \pi r {}^{3} }}}[/tex]
So equating it with given volume for finding the radius of sphere :
[tex] \longmapsto \: \frac{4}{3} \pi r{}^{3} = 562.5\pi[/tex]
Step 1 : Cancelling π as it was present in both side :
[tex]\longmapsto\:\frac{4}{3} \cancel{\pi }r{}^{3} = 562.5 \cancel{\pi}[/tex]
Step 2 : Transposing 4/3 to right hand side :
[tex]\longmapsto \: r {}^{3} = 562.5 \times \frac{3}{4} [/tex]
Step 3 : Multiplying 562.5 with 3 :
[tex]\longmapsto \:r {}^{3} = \frac{1687.5}{4} [/tex]
Step 4 : Dividing 1687.5 by 4 :
[tex]\longmapsto \:r {}^{3} = 421.875[/tex]
Step 5 : Finding cube root of 421.875
[tex]\longmapsto \:r = \sqrt[3]{421.875} [/tex]
Step 6 : We get :
[tex]\longmapsto \: \red{ \boxed{r = 7.5}}[/tex]
Therefore , radius of sphere is 7.5 inches .#Keep LearningSolve This Quadratic:
7x²-26x-45
Answers
Answer:
(7x+9)(x-5)
Hope this helps!
Help! please last question
Answers
Step-by-step explanation:
The centroid O cuts every median in the ratio 2:1. The distance between a vertex and the centroid is twice the distance between the centroid and the midpoint of the opposite side.
Therefore: |OD| = 2|OCI
3x-2=2(5x)
3x-2=10x
7x=-2
x=(-2/7)
Find the area of the circle shown.
Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
radius is 1.5 cm
Answers
Answer:
7.1 cm^2
Step-by-step explanation:
Area = pie * radius^2
Area = pie * 1.5^2
= 7.0685
Answer: 7.1 cm ^2
Step-by-step explanation:
Mr. Smith has 847 gallons of paint. If he uses 1/3 of his paint to paint his fence, how much paint did use to paint his fence?
Answers
Answer:
282.3 gallons
Step-by-step explanation:
if needed you can round to 282
When building a house, the number of days required to build varies inversely with with the number of workers. One house was built in 10 days by 40 workers. How many days would it take to build a similar house with 25 workers?
Answers
Answer:
16 days
Step-by-step explanation:
NO LINKS!!!
Three statements were made about each problem. Two are true and one is false. Mark each statement as true or false and rewrite the false statement to make it true.
Answers
Answer:
Step-by-step explanation:
Answer:
1) True, True, False
Rewritten statement: 46,013.86 cm³ of water was used to fill 40 balloons
2) False, True, True
Rewritten statement: The formula [tex]\sf V= \sf \dfrac43 \pi (2.4)^3[/tex] can be used to find the volume of the model of Earth.
3) True, False, True
Rewritten statement: The volume of all the basketballs is 13,467.62 in³
Step-by-step explanation:
Question 1[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3 \quad \textsf{(where r is the radius)}[/tex]
Given:
r = 6.5 cmSubstituting the given radius into the formula:
[tex]\begin{aligned}\implies \sf V & = \sf \dfrac43 \pi (6.5)^3\\\\& =\sf \dfrac{2197}{6} \pi \\\\& = \sf 1150.35\: cm^3 \:(nearest\:hundredth)\end{aligned}[/tex]
[tex]\textsf{Volume of 40 balloons}=\sf 40 \times \dfrac{2197}{6} \pi=46013.86\:cm^3\:(nearest\:hundredth)[/tex]
Rewritten statement: 46,013.86 cm³ of water was used to fill 40 balloons
-------------------------------------------------------------------------------------------------------
Question 2[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3 \quad \textsf{(where r is the radius)}[/tex]
Earth
Given:
diameter = 4.8 cm ⇒ r = 2.4 cmSubstituting the given radius into the formula:
[tex]\implies \sf V= \sf \dfrac43 \pi (2.4)^3[/tex]
[tex]\implies \sf V=57.91\:cm^3\:(nearest\:hundredth)[/tex]
Rewritten statement:
The formula [tex]\sf V= \sf \dfrac43 \pi (2.4)^3[/tex] can be used to find the volume of the model of Earth.
Saturn
Given:
diameter = 45.6 cm ⇒ r = 22.8 cmSubstituting the given radius into the formula:
[tex]\implies \sf V= \sf \dfrac43 \pi (22.8)^3[/tex]
[tex]\implies \sf V=49647.02\:cm^3\:(nearest\:hundredth)[/tex]
Difference between models= 49,647.02 - 57.91 = 49,589.11 cm³
-------------------------------------------------------------------------------------------------------
Question 3[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 21 inh = 54 inSubstituting the given values into the formula:
[tex]\implies \sf V=\pi (21)^2(54)[/tex]
[tex]\implies \sf V=23814\pi[/tex]
[tex]\implies \sf V=74813.89\:in^3\:(nearest\:hundredth)[/tex]
[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3 \quad \textsf{(where r is the radius)}[/tex]
Given:
diameter = 9.5 in ⇒ r = 4.75 in30 basketballs[tex]\begin{aligned}\textsf{Volume of all 30 basketballs} &=\sf 30 \times \dfrac{4}{3}\pi (4.75)^3\\ & =\sf 13467.62\:in^3\:(nearest\:hundredth)\end{aligned}[/tex]
Rewritten statement: The volume of all the basketballs is 13,467.62 in³
Empty space in the container = volume of container - volume of basketballs
⇒ 74813.89 - 13467.62 = 61,346.27 in³