Simplify the expression and rationalize the demonimator when appropriate, please show steps : >
Answers
Answer:
[tex]=-3tv^2[/tex]
Step-by-step explanation:
So we have the expression:
[tex]\sqrt[3]{3t^4v^2}\sqrt[3]{-9t^{-1}v^4}[/tex]
To simplify, combine the two radicals. Since they have the same index, we can combine them. Thus:
[tex]=\sqrt[3]{(3t^4v^2)(-9t^{-1}v^4)}[/tex]
Combine like terms:
[tex]=\sqrt[3]{(3\cdot -9)(t^4\cdot t^{-1})(v^2\cdot v^4)}[/tex]
Multiply. When multiplying the exponents, simply add the exponents:
[tex]=\sqrt[3]{-27t^3v^6}[/tex]
Now, simplify. Note that -27 can be written as (-3)^3. t^3 can be written as (t)^3 and v^6 can be written as (v^2)^3. Thus:
[tex]=\sqrt[3]{(-3)^3(t)^3(z^2)^3}[/tex]
Combine them all under one exponent:
[tex]=\sqrt[3]{(-3tv^2)^3}[/tex]
Cancel out the cube root:
[tex]=-3tv^2[/tex]
And this is the simplest it can get.
And we are done :)
Edit: Typo
Answer:
-3v²t
Step-by-step explanation:
[tex]\sqrt[3]{3t^4v^2} \sqrt[3]{-9t^-1v^4}[/tex]
= [tex]\sqrt[3]{3t} \sqrt[3]{v^2t} \sqrt[3]{-9v^4t^-1}[/tex]
= [tex]\sqrt[3]{3t} (-\sqrt[3]{9v^4/t)} \sqrt[3]{v^2t}[/tex]
= - [tex]\sqrt[3]{3t} \sqrt[3]{v^2 9v^4/t}t[/tex]
= - [tex]\sqrt[3]{3} \sqrt[3]{9t} \sqrt[3]{v^6}[/tex]
= - [tex]\sqrt[3]{3*9}v^2t[/tex]
= - [tex]\sqrt[3]{27} v^2t[/tex]
= -3v²t
Related Questions
hello to whoever is reading this, I have a question. my scan and solve feature is no longer working and it says that I have connection issues. but I have 4 bars of mobile data and my wifi is fine. is there any way to fix this?
Answers
claili has 35 flowers and 7 vases she wants to put the same number of flowers in each vase which question can calli use ro find the number of flowers to put in each vase
A. what number equals 7 subtracted from 35
B. what number added to 7 equals 35
C. what numbers multiplied by 7 equals 35
E. what number multiplied by 35 equals 7
Answers
1. Point P is between points F and G. The distance between points F and P
is 1/4 of FG. What is the coordinate of point P?
Answers
Answer:
Point P is in between points F and G.
Now, here we do not have the actual locations of F and G, so i will answer this in a general way.
Suppose that F is located at 0 and G is located at some value A.
Then the distance FG = A - 0 = A.
Now, the distance between F and P is:
Distance = (1/4)*FG = A/4
Then the location of P is equal to the location of F plus A/4
P = 0 + A/4
Now, writing this in a more general way:
P = F + FG/4
two times the sum of a number and 9 is half the number
Write an equation to represent the phrase
Answers
Answer:
Equation:
2(a+9) = a/2
Solve:
The umber is:
-12
Step-by-step explanation:
Equation:
2(a+9) = a/2
Solve:
2*a + 2*9 = a/2
2a + 18 = a/2
2a - a/2 = -18
4a/2 - a/2 = -18
3a/2 = -18
a = -18*2/3
a = -12
Check:
2(-12+9) = -12/2
2(-3) = -12/2 = -6
The Equation for the phrase is 2(x + 9) = x/2.
What is the equation?A mathematical statement with two algebraic expressions on either side of an "equal to (=)" sign is called an equation. It demonstrates the equality of the relationship between the expression written on the left and right sides. If there is no "equal to" symbol in the statement of any mathematical equation, it is not one. It will be taken into account as a phrase.
Given a phrase two times the sum of a number and 9 is half the number,
the first part of the phrase says two times the number and 9,
let the number be x, the equation will be
2(x + 9)
the second part of the phrase is half the number
x/2
final equation is
2(x + 9) = x/2
Therefore, the equation is 2(x + 9) = x/2.
Learn more about equation;
https://brainly.com/question/29657983
#SPJ2
when you have a multiplication problem, what do you do to the exponents?
Answers
Answer:
When you multiply two numbers or variables with the same base, you simply add the exponents. When you multiply expressions with the same exponent but different bases, you multiply the bases and use the same exponent.
Step-by-step explanation:
y = - |x+3| - 4
It needs to be graphed, please help!
Answers
Answer:
Step-by-step explanation:
Answer:
Hope this helps!! :)
If you need to know about how exactly to graph it, you can tell me
Angie and kenny play online video games. Angie biys 1 software package and 4 months of game play. Kenny buys 1 software package and 1 month of game play. Each software costs $35. If their total cost is $130 what is thr cost of one month of game play
Answers
Answer:
1 month of game play will cost $12
Step-by-step explanation:
Here in this question, we are interested in calculating the cost of one month of game play.
From the question, we know the following;
Angie bought 1 software package and 4 months of game play
while
Kenny bought 1 software package and 1 month of game play.
The total packages and months bought will be;
2 packages and 5 months of game play
From the question, we are told that 1 month of game play is $35, so 2 months of game play will be 2 * $35 = $70
So the amount remaining for the 5 months will be; $130 - $70 = $60
So if 5 months cost $60, it means one month will be $60/5 = $12
Given the equation p = s Subscript 1 Baseline t minus 2 Subscript 2 Baseline t, which equation is solved for t?
Answers
Answer:
[tex]t=\dfrac{p}{(s_1-s_2)}[/tex]
Step-by-step explanation:
It is given that, p = s Subscript 1 Baseline t minus 2 Subscript 2 Baseline t. It can also written as :
[tex]p=s_1t-s_2t[/tex]
We need to solve the above equation for t.
Taking t common on RHS of the equation :
[tex]p=(s_1-s_2)t[/tex]
Now dividing both sides by [tex](s_1-s_2)[/tex], so,
[tex]\dfrac{p}{(s_1-s_2)}=\dfrac{(s_1-s_2)}{(s_1-s_2)}t\\\\t=\dfrac{p}{(s_1-s_2)}[/tex]
So, the equation for t is : [tex]t=\dfrac{p}{(s_1-s_2)}[/tex]
Answer:
Option C- t= p/s1-s2
___________________
If you have the same test I had the answers will be: (I got 100% proof is in the image below.)
1. C- t= p/s1-s2
2. B- y-mx=b
3. D- c= (10b-10)^2/25
4. C- L/pr=t
5. C- x=3 (y-2/3)
6. C- Using the multiplication property of equality to multiply both sides of the equation by 10
7. C- V^2-V^2/2s=a
8. D- a=2A/p
9. B- h=S/pie r^2
10. A- m=s-c/c
Step-by-step explanation:
Edge 2021. Happy to Help!
What is the solution to this system of equations using the linear combination method?
5x+y=2
4x+y=5
(im really bad at math so an explanation would be helpful so i can understand better)
Answers
Answer:
[tex]\huge \boxed{x=-3 \ \mathrm{and} \ y=17}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
Subtracting both equations:
5x + y = 2
- (4x + y = 5)
————————
1x + 0y = -3
x = -3
Substituting x = -3 for the second equation:
4(-3) + y = 5
Solving for y.
-12 + y = 5
y = 17
[tex]\rule[225]{225}{2}[/tex]
An air conditioner repair service charges $60 for a service call plus $30 per hour for labor, from 1 to 6 hours. The total
amount charged to the customer m, for any number of service hours, h can be represented by the function
m=30h+60 where h is an integer. What is the range?
Answers
Answer:
[90, 240]
Step-by-step explanation:
Here, the range can be found by considering the values of m at the extremes of the domain.
for 1 hour, m = 30(1) +60 = 90
for 6 hours, m = 30(6) +60 = 240
The range of m is [90, 240].
What percentage of the data values falls between the values of 27 and 45 in the data set shown?
25
30
35
40
45
50
O 25%
o 5096
75%
100%
Answers
The answer is 75% this is because 4/6 numbers are between 27 and 45
PLEASE HELP!!
A. Beef uses significantly more land than plants to produce 100 grams of protein
B. Meat production is more efficient than farming protein from fish and prawns
C. Lamb and mutton produce more protein per square meters than pig meat and poultry
D. Nuts and grains produce less protein per square meter than milk and cheese
Answers
Answer:
the answer is correct 2 one
Answer:
A. Beef uses significantly more land than plants to produce 100 grams of protein
Step-by-step explanation:
Let's examine each answer choice.
A. Beef uses significantly more land than plants to produce 100 grams of protein
This is true. Beef uses 163.6 square meters of land, while peas only use 3.4 square meters.
B. Meat production is more efficient than farming protein from fish and prawns
This is not true. Meat production is less efficient, because it uses more land than fish and prawns.
C. Lamb and mutton produce more protein per square meters than pig meat and poultry
This is false. Lamb produces less protein per square meter, because it takes 184.8 square meters to produce 100 grams of protein, while pig meat only takes 10.7 square meters to make the same amount.
D. Nuts and grains produce less protein per square meter than milk and cheese
This is false. Milk and cheese require more square meters per 100 grams of protein/ Therefore they produce less protein per square meter, not the nuts and grains.
So, the best answer choice is A. Beef uses significantly more land than plants to produce 100 grams of protein
Diameter of Earth is 12756000m. In 1996, a new planet was discovered whose diameter is 5/86 of the diameter of Earth. Find the diameter of this planet in km.
Answers
Answer:
741.63km
Step-by-step explanation:
From the above question, we know the following things:
Diameter of the Earth = 12756000m
Diameter of the new planet = 5/86 of the Diameter of the Earth
Diameter of the new planet =
5/86 × 12756000m
= 741627.90698m
The diameter of the new planet = 741627.90698m
We were asked to find the diameter of the new planet in km, hence we convert from meters to kilometers
1m = 0.001km
741627.90698m =
741627.90698 × 0.001km
= 741.62790698km
Approximately = 741.63km
Therefore, the diameter of the new planet = 741.63km
Find the product of (x + (3+5i))^2
Answers
Answer:
x^2 +6x +10xi -16 +30i
Step-by-step explanation:
(x + (3+5i))^2
Rewriting as
(x + (3+5i)) (x + (3+5i))
Let 3+5i = m
(x + m) (x + m)
FOILing
x^2 + xm+xm+m^2
x^2 +2xm + m^2
Replacing m with 3+5i
x^2 +2x (3+5i) +(3+5i)^2
Distribute
x^2 +6x +10xi +(3+5i)^2
Now FOIL (3+5i)^2
( 3+5i) ( 3+5i)
3*3+ 3*5i + 3*5i+ 25i^2
= 9 +15i+15i +25(-1)
9+30i -25
-16 +30 i
Replacing that in the equation
x^2 +6x +10xi -16 +30i
Answer:
x² + 6x + 10xi -16 + 30i
Step-by-step explanation:
(x + (3 + 5i) )²
use the binomial theorem:
(a + b)² = a² + 2ab + b² to expand (x + (3 + 5i) )²
substitute the values,
x² + (6 + 10i)x + (-16 + 30i)
therefore
x² + 6x + 10xi -16 + 30i
A deli has a special one-day event to celebrate its anniversary. On the day of the event, every eighth customer receives a free drink. Every twenty-eighth customer receives a free sandwich. If 200 customers show up for the event, how many of the customers will receive both a free drink and a free sandwich?
Answers
Answer:
the number of common customers are 8 in number
Answer: The answer is just 3 people will get BOTH the free drink and free sandwich.
Step-by-step explanation:
Every 8th = 1 free drink
Every 28th = 1 free sandwich
200 costumers showed
Add 28 to 28 until you reach the closest to 200 so: 28,56,84,112,140,168,196
Then add 8 to 8 until 200, every number that match the 28th sequence is 1 costumer that receives 1 drink and 1 sandwich
The match numbers are 56,112,168
How many pairs of parallel lines are in the flipped shape
Answers
Answer: 5
Step-by-step explanation:
how to do this question plz answer me step by step plzz
Answers
Answer:
120 degrees. Hope this helps
<3
Step-by-step explanation:
We know the sum of all the angles in a quadilateral is equal to 360. so,
it would be: 360 - (55+65+120)
= 360 - 240
= 120 degrees
As part of this month's customer appreciation,
iSongs is offering every fifth customer a free song
download. Every twelfth customer gets a free video
download. How many customers in the first 200 will
receive both the free song and free video -
downloads?
Answers
Answer:
Hey there!
LCM of 12 and 5= 60
Thus, in 200 customers, 3 will get both free song and video downloads.
Let me know if this helps :)
Answer: HELLO
Step-by-step explanation:
5) 20 out 50 rolls of a number cube resulted in a 2 being rolled. Based on this information, if the cube was rolled 220 times, how many rolls of a 2 could be expected? A) 37 B) 66 C) 88 D) 99
Answers
Answer:
C) 88
Step-by-step explanation:
20 out of 50 is same ratio as:
20/50 = 2/5Applied to the number 220 we get:
220*2/5 =88So expected number is 88
Correct answer choice is C
Please answer area of this triangle
Answers
Answer:
[tex]A=2\text{ units}^2[/tex]
Step-by-step explanation:
The area for a triangle is given by:
[tex]A=\frac{1}{2}bh[/tex]
Where b is the base length and h is the height.
The base is 2 and height is also 2. Therefore:
[tex]A=\frac{1}{2}(2)(2)[/tex]
Simplify:
[tex]A=\frac{1}{2}(4)[/tex]
Multiply:
[tex]A=2\text{ units}^2[/tex]
What is a reasonable domain for the data below?
Answers
Answer:
[8,30]
Step-by-step explanation:
Domain means X. So you look for the smallest X value in your data and the largest X value in your data.
7 is a prime number. No multiple of 7, except 7 itself, can be a prime number. Explain why not.
Answers
Answer: Answer is in the steps.
Step-by-step explanation:
No multiple of 7 can be a prime number because then it will have more than two factors.7 is a prime number because it has only two factors 1 and itself. For example, 14 is a multiple of 7 because 7 times 2 is 14. But now it 14 itself will not be a prime number because it has more than two factors which is 1,2,7 and 14.
Answer:
yes, 7 is prime
Step-by-step explanation:
It has only2 factors: 1 and itself:)
solve the following equation for B be sure to take into account whether a letter is capitalized or not.
d - 3f^2 = 5BM
Answers
Answer:
B = d - 3f²
5M
Step-by-step explanation:
d -3f² = 5 B B
5 BM = d - 3f²
B = d - 3f²
5M
Answer:
[tex]\huge \boxed{B=\frac{d - 3f^2}{5M}}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex]d - 3f^2 = 5BM[/tex]
Dividing both sides by 5M.
[tex]\displaystyle \frac{d - 3f^2}{5M} =\frac{5BM}{5M}[/tex]
[tex]\displaystyle \frac{d - 3f^2}{5M} =B[/tex]
[tex]\rule[225]{225}{2}[/tex]
The state of Kansas has a population of about 2.85 million people. Find the population density
in the people per square mile.
Answers
Answer:
In the state of Kansas, the density of people per square mile is 34.3
Step-by-step explanation:
According to US topographers, the state of Kansas has an area of 213 096 km².
If 1 km² is equal to 0.39 mi², then how much is 213 096 km².
If 1 km² : 0.39 mi².
213,096 km² : 83,107.44 mi²
If the state of Kansas has a population of 2.85 million people, then:
2.85 x10^6 people / 83 107.44 mi² =
34.3 people per square mile.
What is the value of x in the parallelogram given . 5x-5 130 degrees
Answers
Answer:
Upload the parallelogram or let me know if 5x-5 = 130 degrees and if it is one of the angles of the parallelogram.
If you vertically compress the absolute value patent function, f(x)=|x|, by a factor of 5, what is the equation of the new function?
Answers
A vertical compression implies a reduction in the y-values of the absolute value function. Therefore, the term that we use to accomplish the reduction cannot be attached to the x in the equation. If so, we would end up with a horizontal stretch, not a vertical compression.
Compression implies a reduction, or dividing, so our term will be 1/5. This should be placed outside of the absolute value bars so that the compression affects only the y-values.
Correct answer: B. g(x) = 1/5|x|
Hope this helps! :)
what is the divisibility rule for 11
Answers
Answer:
Here an easy way to test for divisibility by 11. Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number. So, for instance, 2728 has alternating sum of digits 2 – 7 + 2 – 8 = -11
Step-by-step explanation:
Which statement is true about the parentheses in this expression? 10 ÷ (8 − 6) − 2 A) The parentheses indicate that 6 − 2 should be evaluated first. B) The parentheses indicate that 8 − 6 should be evaluated first. C) The parentheses indicate that 10 − 2 should be evaluated first. D) The parentheses indicate that 10 ÷ 8 should be evaluated first.
Answers
Answer:B
Step-by-step explanation: When solving expressions with parentheses it’s important to always solve what’s in parentheses first. And when there’s parentheses in parentheses, solve the parentheses that are in the parenthesis. Whew...I hope this helps :)
what is the mean for 50 and 51
Answers
Answer: 50.5
Step-by-step explanation:
CONCEPT TO KNOW
The mean of any numbers= The sum of all numbers/ The total amount of numbers.
---------------------------------------------------
The sum of all numbers: 50+51=101
The total amount of numbers: 50 and 51=2 numbers
The sum of all numbers/ The total amount of numbers
=101/ 2
=50.5
Hope this helps!! :)
Please let me know if you have any question
If the figure above shows the graph of the function F, where f(x) = x^2 + 1, if the graph Gis the same as the reflection of about the x axis which of the following is g(x)?
Answers
Answer:
B, g(x)=-x^2-1
Step-by-step explanation:
-g(x)=x^2+1 is the reflection of g(x)=x^2+1 over the x-axis. Therefore, g(x)=-x^2-1.
Hope this helps :)