Answers
Answer:
D) [tex]4x^2y^3\sqrt[3]{x^2y}[/tex]Step-by-step explanation:
Given expression:[tex](8x^4y^5)^{\frac{2}{3}[/tex]Simplify in steps, using below properties of exponents:
[tex]a^ba^c= a^{b+c}[/tex] Product of Powers Property[tex](a^b)^c=a^{bc}[/tex] Power of Power PropertySolution:[tex](8x^4y^5)^{\frac{2}{3} =[/tex][tex](2^3x^4y^5)^{\frac{2}{3} =[/tex][tex]2^{\frac{3*2}{3}} x^{\frac{4*2}{3}} y^{\frac{5*2}{3}} =[/tex][tex]2^2x^{\frac{8}{3}}y^{\frac{10}{3} =[/tex][tex]4x^{2\frac{2}{3}}y^{3{\frac{1}{3} =[/tex][tex]4x^2x^{\frac{2}{3}} y^3y^{\frac{1}{3}} =[/tex][tex]4x^2y^3(x^2y)^{\frac{1}{3}}=[/tex][tex]4x^2y^3\sqrt[3]{x^2y}[/tex]Correct choice is D
Answer:
[tex]4x^2y^3\sqrt[3]{x^2y}[/tex]
Step-by-step explanation:
Given expression:
[tex]\left(8x^4y^5\right)^{\frac{2}{3}}[/tex]
Rewrite 4 as (3 + 1) and 5 as (3 + 2):
[tex]\implies \left(8x^{(3+1)}y^{(3+2)}\right)^{\frac{2}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies \left(8x^3xy^3y^2}\right)^{\frac{2}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 8^{\left(\frac{2}{3}\right)}x^{\left(3 \times\frac{2}{3}\right)}x^{\left(\frac{2}{3}\right)}y^{\left(3 \times \frac{2}{3}\right)}y^{\left(2 \times \frac{2}{3}\right)}}[/tex]
[tex]\implies 4x^2x^{\frac{2}{3}}y^2y^{\frac{4}{3}}[/tex]
[tex]\implies 4x^2y^2x^{\frac{2}{3}}y^{\frac{4}{3}}[/tex]
Rewrite 4/3 as 1 + 1/3:
[tex]\implies 4x^2y^2x^{\frac{2}{3}}y^{\left(1+\frac{1}{3}\right)}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies 4x^2y^2x^{\frac{2}{3}}y^1y^{\frac{1}{3}}[/tex]
[tex]\implies 4x^2y^2y^1x^{\frac{2}{3}}y^{\frac{1}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 4x^2y^{(2+1)}x^{\frac{2}{3}}y^{\frac{1}{3}}[/tex]
[tex]\implies 4x^2y^3x^{\frac{2}{3}}y^{\frac{1}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies 4x^2y^3\left(x^2\right)^{\frac{1}{3}}y^{\frac{1}{3}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot c^b=ac^b:[/tex]
[tex]\implies 4x^2y^3\left(x^2y\right)^{\frac{1}{3}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]
[tex]\implies 4x^2y^3\sqrt[3]{x^2y}[/tex]
Related Questions
A car travelled a distance of 50km in an hour.what distance did it travel in 30min at the same speed?
Answers
Answer:
The car would have traveled 25 km.
Step-by-step explanation:
Set up the Proportion [tex]\frac{50}{60} = \frac{x}{30}[/tex]. Solving that proportion gets you an answer of 25, getting you the answer 25 km in 30 minutes. I hope this helps! :)
The points E(- 4, 6), F(- 6, - 2), G(2, - 4) , and H(4, 4) form quadrilateral EFGH. Plot the points then click the "Graph Quadrilateral " button.
Answers
The slope of EF, FG, GH, and HE is 4, -1/4, 4, and -1/4 respectively. And the length of sides EF, FG, GH, and HE will be √68, √68, √68, and √68 units respectively.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
The points E(-4, 6), F(-6, -2), G(2, -4) , and H(4, 4) form quadrilateral EFGH.
Then the slopes are calculated below.
Slope of EF = (6 + 2)/(-4 + 6)
Slope of EF = 8/2
Slope of EF = 4
Slope of FG = (-4 + 2)/(2 + 6)
Slope of FG = -2/8
Slope of FG = -1/4
Slope of GH = (4 + 4)/(4 - 2)
Slope of GH = 8/2
Slope of GH = 4
Slope of HE = (6 - 4)/(-4 - 4)
Slope of HE = -2/8
Slope of HE = -1/4
Then the distance between the point will be
EF² = (-6 + 4)² + (-2 - 6)²
EF² = (-2)² + (-8)²
EF² = 4 + 64
EF = √68
FG² = (2 + 6)² + (-4 + 2)²
FG² = (8)² + (-2)²
FG² = 64 + 4
FG = √68
GH² = (4 - 2)² + (4 + 4)²
GH² = (2)² + (8)²
GH² = 4 + 64
GH = √68
FG² = (4 + 4)² + (4 - 6)²
FG² = (8)² + (-2)²
FG² = 64 + 4
FG = √68
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!!20 POINTS AND BRAINLIEST!!! HELP ASAP!!!
How much ribbon would be needed to go around a package that had a length 2x^2+3x-5/x^2+x-3 centimeters and width x^2-x-5/x^2+x-3 centimeters?
(show work)
Answers
Answer:
23cm
Step-by-step explanation:
If you multiply like terms you will get the answers. Then you add last to get 23cm
The required length ribbon needed to go around the package is 2(3x^2 + 2x -10) / (x^2 + x - 3).
Given that,
Package that had a length of 2x^2+3x-5/x^2+x-3 centimeters and width x^2-x-5/x^2+x-3.
How much ribbon would be needed to go around the package in centimeters is to be determined.
Perimeter is the measure of the figure on its circumference.
The rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.
Quantity of ribbon = perimeter of the rectangular package
= 2 * length + 2* width
= 2 * (2x^2+3x-5/x^2+x-3) + 2(x^2-x-5/x^2+x-3)
= 2 (3x^2 + 2x -10) / (x^2 + x - 3)
Thus, the required length of ribbon needed to go around the package is 2(3x^2 + 2x -10) / (x^2 + x - 3).
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Using the segment addition postulate, which is true?
Answers
The complete question is
"Using the segment addition postulate, which is true?
AB + BC = AD
AB + BC = CD
BC + CD = AD
BC + CD = BD"
Using the segment addition postulate, the true option is D; BC + CD = BD.
What is a line segment?A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
We have been given the number line and four points A, B, C, and D on the line with coordinates -6, -1, 2, and 8 respectively.
(a) L.H.S. = AB + BC = 5 + 3 = 8,
R.H.S = AD = 14 ≠ 8.
So, this option is incorrect.
(b) L.H.S. = AB + BC = 5 + 3 = 8,
R.H.S = CD = 6 ≠ 8.
So, this option is incorrect.
(c) L.H.S. = BC + CD = 3 + 6 = 9,
R.H.S = AD = 14 ≠ 9.
So, this option is incorrect.
(d) L.H.S. = BC + CD = 3 + 6 = 9,
R.H.S = BD = 9.
So, this option is correct.
Hence, the correct option is (d).
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answer please image is below 35 points btw
Answers
Convert 5.6 times 10 to power of 4 to ordinary form
Answers
———-
5
3.3.1. Calculate the new cost per night of the standard and family standard chalets. Round of (4) your answer to the nearest hundred. 3.3.2. Calculate the percentage increase that Pule proposes for the Luxe suite. Use the following formula: Percentage Difference Original 1 x 100% (3) 3.4. Pule decides to run a special on the Family standard chalet. He will charge: R4 000 per night but will decrease the amount by R100 per person occupying the chalet. 3.4.1. Use the information above to complete the table below: Number of 1 2 3 4 5 8 9 10 people(c) 4 000 3 900 Cost per night (R) (n) (3) 3.4.2. Write an equation that shows the relationship between the cost per night C and the number of people staying in the chalet n. (3) 3.4.3. The graph below shows the cost of renting the family standard chalet at the usual rat On the same set of axes, draw the graph that represents renting the chalet at the spe rate. (Remember to include all missing graph elements). (4)
Answers
An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in math when you do not know the exact number in a calculation.
Given that:
Pules Rs 4000 per night but will decrease the amount by R100 per person occupying the chalet.
Number of People Cost per night
1 4000
2 3900
3 3800
4 3700
5 3600
6 3500
7 3400
8 3300
9 3200
10 3100
let C be cost per night and n be the number of people of staying in chalet.
equation: C= 4000-100(n-1)
for n=1: C= 4000- 0=4000
n=2, C= 4000-100(1)= 3900
The graph is attached below:
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Pleaseeee!
I need help evaluating this:
Tan 2 theta-(1-tan^ 2 )=?
Answers
Answer:
[tex]\tan \left(2\theta\right)-1+\tan ^2\left(\theta\right)[/tex]
Key:
• [tex]-\left(a-b\right)=-a+b[/tex]
Step-by-step explanation:
[tex]\tan \left(2\theta\right)-\left(1-\tan ^2\left(\theta\right)\right)[/tex]
[tex]-\left(1-\tan ^2\left(\theta\right)\right)=-1+\tan ^2\left(\theta\right)[/tex]
[tex]=\tan \left(2\theta\right)-1+\tan ^2\left(\theta\right)[/tex]
HELP ME AND ANSWER BOTH PARTS PLEASE!
Answers
2 is -15+2x
Glad I could help
Keith is working two jobs this summer as a lifeguard and a tutor. he earns $16 an hour as a lifeguard and $18 an hour as a tutor. he wants to earn at least $250 to put towards his car. what is one possible combination of hours he can work at each job to earn at least $250?
Answers
Answer:
He could work 10 hours as a lifeguard, and 5 hours as a tutor
Step-by-step explanation:
If he makes $16 an hour as a lifeguard
and $18 an hour as a tutor,
He could work 10 times $16, to make $160 for 10 hours.
Now we subtract this from $250, this makes $90.
We know need to find out how many times 18 goes into 90, 5 times.
So we know that he could work 10 hours as a lifeguard and 5 hours as a tutor.
I hope this is right.
I hope this helps too, have a nice day!
A square notepad has sides that are 10 centimeters long. What is the notepad's area?
Answers
Answer:
100cm²
Step-by-step explanation:
The notepad is square.
The area of a square = length X width.
All the sides of a square are the same length.
Therefore, the area of the notepad = 10 X 10 which equals 100.
Don't forget the units!
The units for area is cm².
The units for volume is cm³.
This is area so your answer is 100cm².
Hope this helped, have a nice day!
please answer the question below, will give brainliest to first answer :)
Answers
Answer:
None of these answers are correct
Step-by-step explanation:
neither of them are rays.
a ray goes from the center to the edge of a circle.
the amount (a) that principal (p) will be worth after t years at interest rate (r) compounded annually is
a = p(1 + r)^t
suppose $6,000 is invested at 5.5% and yields a total of $7,255. how many was it invested
Answers
The number of years the money was invested with annual compounding is 3.45 years.
How many years was it invested?When an amount earn interest compounded annually, it means that both the amount invested and the interest earned increases in value once a year.
Number of years = (In FV / PV) / r
Where:
FV = future valuePV = present valuer = interest rate(In 7255 / 6000) 0.055 = 3.45 years
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Factor: 5x2 – 15x – 20.
(a) 5(x-4)(x+1),
(b) -2(x-4)(x+5),
(c) -5(x+4)(x-1),
(d) 5(x+4)(x+1).
Answers
Answer:
[tex]a)~5(x-4)(x+1)[/tex]
Step-by-step explanation:
[tex]~~~5x^2 -15x -20\\\\=5(x^2 -3x -4)\\\\=5(x^2 -4x +x -4)\\\\=5\textbf{[}x(x-4) +(x-4)\textbf{]}\\\\=5(x-4)(x+1)[/tex]
Mr. Fishie bought a tank for $15 and 10 fish which cost $f each. If he gave the cashier two 20-dollar bills, what was his change in terms of f?
Answers
Answer:
$25 - $10f
Step-by-step explanation:
Fishie's name is fishy.
We know Mr. Fishie spent $15 on a tank. His 10 fish cost 10*$f. His total is:
Total =15 + 10*f
His change after 2 $20 would be:
$40 - ($15 - $10f), or
$25 - $10f
The mean of a set of 10 number is 56,
If the mean of the first nine is 55 find the 10th number
Answers
Answer:
65
Step-by-step explanation:
10*56=5609*55=495560-495=65=65The regular price of a tennis racquet is $79.99 and the sale price is $64.99. Find the percent of discount to the nearest whole percent.
Answers
Step-by-step explanation:
$79.99 - $64.99 = $15
(79.99 - 64.99)/|79.99| =15
15/79.99 =
15 ÷ 79.99 =
15 ÷ 79.99 × 100/100 =
(15 × 100 ÷ 79.99)/100 =
(1,500 ÷ 79.99)/100
≈18.752344043005/100 =
18.752344043005% ≈18.75%;
HELP ME PLEASE!!!
.................................................
Answers
Answer:
Step-by-step explanation:
Explanation: find the hypotenuse of the 1st triangle a^2 + b^2 = c^2 -> 9*9 + 5*5 = c^2
Which is 81+25 = c^2 -> 106 = c^2 now square root c = 10.3
Now you have the hypotenuse of the triangle on the left notice that the hypotenuse we just solved for is actually a leg for the triangle on the right. Now you can use the hypotenuse formula for x.
10.3^2 + 4^2 = x^2 -> 106.09 + 16 = x^2
Next, 122.09 = x^2 now we need to square root to isolate the square (2). x = 11.04 when rounded the closest radical is you answer x=11
Ninety members of a gym were asked whether or not they use a treadmill when they exercise and whether or not they lift weights when they exercise.
The results of the poll are as follows:
14 members do not use a treadmill or lift weights
31 members use a treadmill but do not lift weights
28 members lift weights but do not use a treadmill
17 members use a treadmill and lift weights
Which two-way table represents the information found in the poll?
Answers
The answer is Y
Step-by-step explanation:
You have to compare the numbers with conditions both in Rows and Columns.
Anyone know the answer?
James is using cement to make a new sidewalk and new steps.
He will make a new rectangular sidewalk that is 8 feet long, 4 feet wide, and 0.25 foot thick.
What is the volume, in cubic feet, of the cement used to make the sidewalk? Show or explain all of the steps you used to determine your answer.
Enter answer, including explanation, here
Answers
The volume, in cubic feet, of the cement used to make the sidewalk is 8 cu.ft.
What is a Cuboid ?A cuboid is a three dimensional figure with six rectangular faces .
The volume of the cuboid is given by
V = length * breadth * height
It is given in the question that
a new rectangular sidewalk that is 8 feet long, 4 feet wide, and 0.25 foot thick , this will be in the shape of a cuboid
The volume of cement required = 8 * 4 * 0.25
= 8 cu.ft
The volume, in cubic feet, of the cement used to make the sidewalk is 8 cu.ft.
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Paula walks 1/12 mile in 5/3 minutes. What rate is equivalent to the rate she walked?
Answers
The rate that is equivalent to the rate Paula walked is 1/20 mile/minute OR 0.05 mile/minute
Calculating RateFrom the question, we are to determine the rate which is equivalent to the rate Paula walked
Using the formula,
[tex]Rate = \frac{Distance}{Time}[/tex]
From the given information,
Distance = 1/12 mile
Time = 5/3 minutes
Putting the parameters into the formula, we get
[tex]Rate =\frac{\frac{1}{12} }{\frac{5}{3} }[/tex]
[tex]Rate = \frac{1}{12} \div \frac{5}{3}[/tex]
[tex]Rate = \frac{1}{12} \times \frac{3}{5}[/tex]
[tex]Rate = \frac{3}{60}[/tex]
[tex]Rate = \frac{1}{20}[/tex] mile/minute
Hence, the rate that is equivalent to the rate Paula walked is 1/20 mile/minute OR 0.05 mile/minute
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solve these algebraic fractions please with step by step explanation would be great
Answers
Answer:
first ans =x-7
second ans= x+y/x-y
Step-by-step explanation:
I think you would get it and it doesn't need explanation.
Factor completely AND solve for the solutions of the quadratic.
Answers
(WORK SHOWN BELOW)
The graphs of f(x) = -2x and g(x)=()* are shown.
What are the solutions to the equation -2x = ()*?
Select each correct answer.
0-2
0 -1
02
04
-10-8-6-4
10
8
6-
72
-4
6
in
8
10+
2 4 6 8 10
Answers
The solutions to the equation -2x = 2^x are (1,2) and (2,4)
How to determine the solutions?The attached graph represents the missing part of the question
The equations are given as:
f(x) = -2x
g(x) = 2^x
The solution to -2x = 2^x is the points where the graphs of f(x) and g(x) intersect
From the attached graph, the points of intersection are:
(1,2) and (2,4)
Hence, the solutions to the equation -2x = 2^x are (1,2) and (2,4)
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A physical therapist claims that 75% of people lose their balance if they close their eyes while standing on one foot. A gymnast feels that the rate is less than 75%. To test this, she randomly selects 100 people and finds that 80 of them lose their balance while standing on one foot. To determine if these data provide convincing evidence that the proportion of people who lose their balance while standing on one foot and closing their eyes is less than 75%, 150 trials of a simulation are conducted. The gymnast is testing the hypotheses: H0: p = 75% and Ha: p < 75%, where p = the true proportion of people who will lose their balance while standing on one foot and closing their eyes. Based on the results of the simulation, what is the estimate of the P-value of the test? A dotplot. A number line labeled simulated sample percentage of people who lose balance goes from 64 to 88 percent. 64, 3; 66, 3; 67, 4; 68, 8; 69, 5; 70, 7; 71, 8; 72, 11; 73, 15; 74, 12; 75, 11; 76, 8; 77, 18; 78, 10; 79, 10; 80, 5; 81, 4; 82, 2; 83, 2; 84, 1; 85, 2; 87, 1. 0.1133 0.17 0.887 0.92
Answers
Answer:
75
Step-by-step explanation:
becAUSE IF YOU TEST IT THATS UR ANSWER
Find each square (x+4)^2
Answers
Answer:
[tex]x^{2} +8x+16[/tex]
Step-by-step explanation:
There are 2 ways to find the square of a binomial. You can use FOIL or use a formula. Just remember that the square of a binomial will always be a trinomial.
FOIL
Since we are squaring a binomial we can rewrite the expression as (x+4) * (x+4). FOIL stands for First, Outside, Inside, Last. This explains how to multiply out 2 binomials. This method will give you 4 different terms that can then be combined to find the answer.
First - multiply the first terms of each binomial
x * x = [tex]x^{2}[/tex]Outside - multiply the terms on the outside of both binomials
x * 4 = 4xInside - multiply the terms on the inside of both binomials
4 * x = 4xLast - multiply the last terms of each binomial
4 * 4 = 16Now we can combine these terms to create the new polynomial [tex]x^{2} +4x+4x+16[/tex]. Then, combine like terms for the final answer: [tex]x^{2} +8x+16[/tex].
Shortcut
Another way to square binomials is to use the formula [tex]a^{2} +2ab+b^{2}[/tex], where a is the first term and b is the second term. So, for this formula, the binomial would look like (a+b).
So, we can apply this formula by plugging in x for a and 4 for b.
[tex]x^2+2*4*x+4^2[/tex]Then, multiply the middle term
[tex]x^{2} +8x+4^2[/tex]Finally, square 4
[tex]x^2+8x+16[/tex]This gives us the same final answer as the method above.
Step-by-step explanation:
(x+4)^2
you can also expand it
(x+4)(x+4)
x^2+4x+4x+16
x^2+8x+16
What is 6x-6x56 =?
Show all work.
Answers
Answer:
6x-6x56 =-2016
Step-by-step explanation:
You have to subtract, then multiply by 56 to get -2016, as it shows a negative.
Which polynomial is equal to the sum of polynomials 1 and 2?
Polynomials 1 and 2 are represented below with tiles.
Polynomial 1
X²X²
X²
Polynomial 2
A. 2x²+2x+1
OB. 5x² + 4x+6
OC. 7x² +6x+7
OD. 7x² +6x+5
SUBMIT
Answers
Polynomial are mathematical expressions involving variables raised with non-negative integers and coefficients. The correct option is C.
What is a polynomial?Polynomial are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Example:
x² + 3x + 5
As per the given tile diagram, the first polynomial is,
First polynomial = 5x² + 4x + 6
The second polynomial equal is,
Second polynomial = 2x² + 2x + 1
Now, the sum of the two polynomial can be written as,
Sum = 5x² + 4x + 6 + 2x² + 2x + 1
= 7x² + 6x + 7
Hence, the correct option is C.
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3.991 nearest one hundred answer
Answers
[tex]\huge\purple{hi!}[/tex]
3.991 nearest one hundred is 3.99
The answer wood be 3.99
Since 1 is closer to 0 you round down and it is 3.99
a water tap fills a tank within 4 hours, at the bottom of the tank
there is a hole for empty. the tank takes one hour to be empty. If the tap and the hole
are turning on together, the tank is fully filled. how long will the tank take to be completely
empty?
(70 min, 80 min, 90 min, 100 min)
Answers
Let V be the volume of the tank. The tap fills the tank at a rate of V/(4 hours), or V/4 per hour. The hole empties the tank at a rate of V per hour. If both the tap and hole work together, the net rate of water flow is V/4 - V or -3V/4 per hour.
Starting with a full tank, the volume v of water at time t is given by the function
v(t) = V + (-3V/4) t
Solve v(t) = 0 to find the time it takes to empty:
V - 3V/4 t = 0
V = 3V/4 t
t = V / (3V/4) = 4/3
So it takes 4/3 hours = 80 minutes to empty a full tank.