Answers
Answer:
Step-by-step explanation:
When you take the n-th root of a number, you can rewrite the expression by taking it to the 1/n-th power. For example:
[tex]\sqrt[n]{x} =x^\frac{1}{n}[/tex]
For the first expression, we can use this proprtery to get:
[tex]\sqrt[5]{a^x} =(a^x)^\frac{1}{5}[/tex]
Using exponent rules, you can combine the exponents by simply multiplying them to get:
[tex]a^\frac{x}{5}[/tex]
Moving on to the second expression. It is now the square root, or equivalently a 1/2 power. If we break up the terms under the radical into powers of 2, we can cancel a lot of the terms:
[tex]\frac{\sqrt{81a^3b^1^0} }{\sqrt{3}a } =\frac{\sqrt{81a^2*a*b^1^0} }{\sqrt{3}a }[/tex]
The a^2 and b^10 can be taken out of the radical because they have perfect roots:
[tex]\frac{\sqrt{81a^2*a*b^1^0} }{\sqrt{3}a }=ab^5\frac{\sqrt{81a} }{\sqrt{3}a }[/tex]
The square root of 81 has a perfect root of 9. We have:
[tex]ab^5\frac{\sqrt{81a} }{\sqrt{3}a }=9ab^5\frac{\sqrt{a} }{\sqrt{3}a }[/tex]
You can divide 9 and the square root of 3 by breaking up 9 into a product:
[tex]\frac{(3*3)ab^5}{\sqrt{3} } \frac{\sqrt{a} }{a }=3\sqrt{3} ab^5\frac{\sqrt{a} }{a }[/tex]
Simply by cancelling the 'a' terms to get:
[tex]3\sqrt{3} ab^5\frac{\sqrt{a} }{a }={3\sqrt{3}}\sqrt{a}b^5=3b^5\sqrt{3a}[/tex]
Related Questions
Help me actually,
What is the measure of angle R?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
m∠R=
°
Answers
Answer:
Step-by-step explanation:
Cos(R) = adjacent / hypotenuse
Adjacent is the side connected to the angle
Adjacent = 12
Hypotenuse = 13
Cos(R) = 12 / 13 = .9231
Now you find R by taking the inverse cos of (R). On most calculators it is 2nd function cos
R = cos-1(0.9231)
Answer: R = 22.62 degrees
[tex]\\ \rm\Rrightarrow sinR=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\\ \rm\Rrightarrow sinR=\dfrac{5}{13}[/tex]
[tex]\\ \rm\Rrightarrow sinR=0.38[/tex]
[tex]\\ \rm\Rrightarrow R=sin^{-1}(0.38)[/tex]
[tex]\\ \rm\Rrightarrow R=22.33°[/tex]
25 Points!! What is the volume of the prism 1 1/2ft 3 1/2ft 2 1/2 ft? Please answer when you have the time to.
Answers
Answer:
The first one: 13.125 ft³
The second one: 67.5 ft³
Step-by-step explanation:
For the first one:
The volume of a prism is length x width x height.
So, in this shape, the length is 3 1/2, the width is 2 1/2, and the height is 1 1/2.
However, you can conver 1/2 to .5, to make it easier to multiply.
So, 3.5 x 2.5 x 1.5 = 13.125
Make sure to add ft³, the ft is the unit, feet, and the ³ is used to denote volume, because volume is 3 dimensional.
For the second one, same formula:
Length = 6, width = 2 1/2, and height = 4 1/2
6 x 2.5 x 4.5 = 67.5
Again, make sure to add ft³, the ft is the unit, feet, and the ³ is used to denote volume, because volume is 3 dimensional.
Answer:
13.125 [tex]ft^{3}[/tex]
Step-by-step explanation:
Volume is base * length * height.
In this case, the dimensions are 1.5, 3.5, and 2.5.
Assuming these values are the base, length, and height,
1.5 * 3.5 * 2.5 = 13.125 [tex]ft^{3}[/tex].
Also, using the volume formula, the bottom shape's volume is 67.5 [tex]ft^{3}[/tex].
Hope this helps!
Also, please mark as brainliest!
Teachers are being trained to standardize the scores they give students essays. The results are shown in the tables
Calculate the MADs for the teachers scores. Did the teachers make progress in standardizing their scores?
____,(Yes or No) The MAD before the training was ______(MAD for the top chart) and the MAD at the end of the training is _______,(MAD for bottom chart) so _______ (progress or no progress)was made toward standardizing test scores
Answers
Answer:
yes
Step-by-step explanation:
yes
The first three terms of a geometric sequence are as follows.
-3, 15, -75
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
Answers
Here the common ratio is -5
next terms will be 375 and -1875
A bus makes 28 stop every 2 hours. How many stops does it make in 5 hours?
Answers
Answer:
70 stops
Step-by-step explanation:
To find the amount of stops it makes in an hour, do 28 stops ÷ 2 hours, which will give you 14 stops in one hour.
Then do 14 stops × 5 hours, which would give you 70 stops.
Here's the notation if you want to make it look pretty:
[tex]5(\frac{28}{2} )=70[/tex]
Henry begins a savings account with $500. The savings account accumulates 2.5% annual interest based on the
equation Vh= 500(1.025), where Vh is the value of the account after t years. Andres begins a savings account three
years later with the same initial amount of money at the same interest rate. Which equations represent the value of
Andres's account after t years?
A.
B.
C.
D.
Answers
Answer:
it’s B
Step-by-step explanation:
Answer: The answer to the question is option A
Step-by-step explanation:
What was the original cost of the jacket.
Answers
Answer:
(c) $80
Step-by-step explanation:
Each discounted price corresponds to the original price multiplied by a factor related to the discount. For a discount fraction of 'd', the multiplier is (1 -d).
This means you can use any of the lines in the table to find the original price.
5% disount: (1 -5%)·p = $76 . . . . where p is the original price
p = $76/0.95 = $80 . . . . . . . the original price
10% discount: (1 -10%)·p = $72
p = $72/0.90 = $80
25% discount: (1 -25%)·p = $60
p = $60/0.75 = $80
_____
Additional comment
The table values for 5% and 10% differ by 5% and $4. That means 5% of the original price is $4. There are two things you can do with this:
add back that 5% to the 5%-discounted price: $76 +4 = $80multiply that 5% by 20 to get 100% of the original price: 20(5%) = 20($4) ⇒ 100% = $80.if £2000 is placed into a bank account that pays 3% compound interest per year how much will be in the account after two years
Answers
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2\implies A=2121.8[/tex]
Answer:
2,121.8
Step-by-step explanation:
2000(1.03)^2
please rate and mark as brainlest.
ype the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
A science lab has several beakers containing different amounts of the same liquid, as shown in the line plot.
If all the liquid from the beakers is poured into one empty container that can hold exactly 4 liters, how much more liquid can the container hold?
liter(s)
Answers
Answer:
4/8 or 1/2
Step-by-step explanation:
Convert all size to x/8
1/4=2/8 and 1/2=4/8
Multiply size of beaker by how many there are filled
1/8 * 2= 2/8
2/8*7= 14/8
4/8*3 =12/8
then add all of them together = 28/8
convert 4 liters to 32/8
Subtract 32/8 - 28/8 = 4/8
Frank grows evergreen trees. He grew 535 trees for
the holiday season. In November he sold 215 trees
and in December he sold 275.
a. Write an expression. Then solve.
b. Frank replanted the left over trees with the
addition of 650 more trees. How many trees will
he have for next season?
Answers
Answer:
Frank grows 535 trees during holiday season in November sold 215 then dec sold 275535 minus 490 which gives a total of 45 trees left then to find out how many trees he will have next season 650 plus 45 gives 695I need help please this is very tricky to me
Answers
Answer:
273cm
Step-by-step explanation:
21 times 13 is 217. That is how you find out the area of parallelogram, (base times peperndicular heigh)
How to find the square root of complex numbers?? Find the square root of (6+8i) ??
Answers
Answer: NaN
Step-by-step explanation: The square root of a complex number can be determined using a formula. Just like the square root of a natural number comes in pairs (Square root of x2 is x and -x), the square root of complex number a + ib is given by √(a + ib) = ±(x + iy), where x and y are real numbers.
http://www.math.com/students/calculators/source/square-root.htm
that's the website I used
You can also maybe do it on a scientific calculator?
Hope that's helpful
What is the area of the given triangle?
Answers
Answer:
B 12
Step-by-step explanation:
4 x 6 = 24 divided by 2 = 12
To find the area of a triangle you need to use this formula. Length x base and then divide in half.
So 6x4=24 and half of 24 is 12
I hope this was helpful :)
Suppose the demand d, in units sold, for a company's jeans at price x, in dollars, is d(x)=800−4x.
A. If revenue=price×demand, write the rule for the function r(x), which represents the company's expected revenue in jean sales. Then state the domain of this function.
B. If the price is $30, how much revenue will the company earn?
A. The rule for the function r(x) is r(x)=
Answers
Answer:
Sorry let me try to understand the question
Step-by-step explanation:
The domain of the function r(x) is (0, 200).
The revenue earned when the price is $30 is $20400.
The rule for the function r(x) is x(800 - 4x).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Demand:
d(x) = 800 - 4x
Price = x
Revenue = Price x demand
Revenue = r(x)
A)
The rule for r(x).
r(x) = x d(x) = x(800 - 4x)
The domain of r(x) is 0 < x < 200 i.e (0, 200).
B)
x = 30
r(x) = 30(800 - 4 x 30)
r(x) = 30(800 - 120) = 30 x 680 = 20400
C)
r(x) = x(800 - 4x)
Thus,
The answers are given above.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ2
If there are fifty dimes in a roll of coins, then it is equal to________dollars
Answers
Answer:
$5
10 Dimes = $1 so If we have 50 dimes that = 5$
Please mark brainliest trying to level up :)
-5 1/2+6 3/4+(-4 1/4)=
Answers
Answer:
-3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
that the answer
calculate them
Assessment started: undefined.
Item 1
In this polygon, all angles are right angles.
What is the area of this polygon?
PLEASE HELP ME
Answers
Explanation: If you divide the polygon into two rectangles you can find each area and add them together. You can do this by taking the number on the bottom (21) and subtracting 12.
The measures of heights (in inches) of a class of students are shown. 60, 60,54, 62, 62, 57,58, 65, 54,67, 63,57, 62, 54, 72, 66, 54, 69, 55, 61 Find the mean, median, mode, range, and standard deviation of the heights.b. A new student who is 7 feet tall joins your class. How would you expect this student’s height to affect the measures in part (a)?
Answers
Answer:Compute the variance: 49+25+16+9+1+16+36+648=27.
The variance is a measure of the dispersion and its value is lower for tightly grouped data than for widely spread data. In the example above, the variance is 27. What does it mean to say that tightly grouped data will have a low variance? You can probably already imagine that the size of the variance also depends on the size of the data itself. Below we see ways that mathematicians have tried to standardize the variance.
Step-by-step explanation:
cuanto es 4{(-50+-5)÷3]+6}x[-4+-3÷1)÷3]
Answers
Answer:
-148/3 or -49.3
Step-by-step explanation:
Find the decimal approximations for these give your answers to 1 decimal place.
a)square root of 3
b)square root of 21
c)square root of 62
Answers
Answer:
A) 1.7
B) 4.5
C) 7.8
What is the equation of the line that passes through the point (-2,-1) and has a slope of 1/2? ?
Answers
equation of line will be
y+1=1/2(x+2)
Hello!
Let's write the equation of the line in both Point-Slope Form and Slope-Intercept Form.
First, point-slope form:
y-y1=m(x-x1)
y-(-1)=1/2(x-(-2) (Point-Slope Form)
Now, convert into Slope-Intercept form:
y+1=1/2(x+2)
y+1=1/2x+1
y=1/2x+1-1
y=1/2x
Hence, the equation of the line is
[tex]\boxed{\boxed{\bold{y=\frac{1}{2}}} }[/tex] (Slope-Intercept Form)
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
:-)
what is the solution of the system of equations 4x+2y=-1 and 3x+4y=3
Answers
Answer:
7x+6y=2
Step-by-step explanation:
All you have to do is add both of the equations together.
What’s 36 km=?m into a desmal
Answers
Explanation:
To go from km to meters, multiply by 1000
This is because 1 km = 1000 meters
Find the length of the third side. If necessary, round to the nearest tenth. 6 8 there also a right angle
Answers
Answer:
See below ↓
Step-by-step explanation:
Given side lengths :
68This question can be solved in two ways :
Taking the third side to be the hypotenuse (What you're probably looking for)Taking 8 to be the hypotenuse (Probably not needed, but good for understanding the various possiblities)Case 1
By Pythagorean Theorem, as right angle is mentioned :6² + 8² = x²x² = 100x = 10 [Your answer!]Case 2
6² + x² = 8²x² = 64 - 36x² = 28x = 2√7 [Just in case!]Hope it helps~
How much, in total, did Noel spend to cash her three most recent paychecks?
Answers
Based on the amount that Noel cashed in each of her most recent paychecks, the amount she spent in total is $10.99.
How much did Noel spend?The bank directory shows that you are charged 1.99% of the amount being cashed as well as a check processing fee of $1.39.
The amount Noel spent is therefore:
= (1.99% x 100.53) + (1.99% x 119.38) + (1.99% x 122.52) + (1.39 x 3 checks)
= 2.00 + 2.38 + 2.44 + 4.17
= $10.99
Find out more on bank charges at https://brainly.com/question/26494219.
When the vertex is the highest point it is called a:.
Answers
Answer:
Maximum
Step-by-step explanation:
At the vertex the function is at aits maximum value.
Bogart has 150 stamps. 30% of them are from Africa. How many stamps are from Africa?
Answers
Answer:
There are 45 stamps from Africa
Step-by-step explanation:
10% of 150 is 15
30% of 150 is 45
15*3 = 45
What is the value of x? (Do not put in the degree symbol)
Answers
Step-by-step explanation:
x+134=180(straight angle)
x=46
A community theater group produced 8 plays over the last two years. The
group's goal for the next two years is to produce at least 1 times as many
plays as they did in the two previous years. How many plays does the group
want to produce in the next two years?
Answers
Answer: 8 plays.
Step-by-step explanation: I might be missing something here, but it says at least 1 times as many plays?? 8 * 1 = 8, so I guess 8 plays?
What is the value of the discriminant for x2 + 5x = -7?
Answers
Answer:
x = -1
Step-by-step explanation:
2x + 5x = -7
7x = -7
x = -1