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
[HELP, DUE TOMORROW. WILL GIVE BRAINLIST] What do exponential functions model in the real world? How does the standard equation form of the exponential equation change in each situation?
Answers
Step-by-step explanation:
write the function in module in real where how does standard it's easy how do you have to do is think in your mind and there's follow like if it had some if it have some notes or something like that you could actually read it and then you can get ideas in your head and complete answers and you will get it
In a city park, three walking paths form triangle ABC. The length AB is 800 meters, the length BC is 900 meters, and the length AC is 850 meters. Which angle of this triangle has the greatest measure?
Answers
Answer:
Step-by-step explanation:
angle c
The angle of the triangle with the greatest measure is ∠A
What is a triangle?A triangle is a polygon with three sides and three angles.
Analysis:
For the triangle, ABC the angle facing the side with the greatest measure is the angle with the greatest measure. From the given information side BC is the side with the greatest measure and the angle facing it is ∠A.
In conclusion, the angle with the greatest measure is ∠A
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4X+8<28
ayudenme por favor
Answers
Answer:
x < 5.
Step-by-step explanation:
Creo que esto es correcto. :')
When graphing f(x)=a sin(bx) you would determine the functions period using which of the following?
A. The period is 2pi/b
B. The period is a
C. The period is pi/b
Answers
Explanation:
The value of 'a' out front in y = a sin(bx) determines the amplitude.
The b term helps us compute the period, which is 2pi/b for sine, cosine, secant, and cosecant functions.
For example, y = 2sin(3x) has an amplitude of 2 and period of 2pi/3
For tangent and cotangent functions, the period would be pi/b.
If f(x) = |x| + 9 and g(x) = -6, which describes the range of (f+g)(x)
Answers
The range exist on all real values. This can be written as (-infty, infty)
Range of a functionThe range is the value of the dependent variable for which it exists. Given the following functions
f(x) = |x| + 9 and;
g(x) = -6
Determine the sum
(f+g)(x) = |x| + 9 + (-6)
(f+g)(x) = |x| + 9 -6
(f+g)(x) = |x| + 3
Determine the range of the function
The range exist on all real values. This can be written as (-infty, infty)
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Q). Express each of the following recurring decimal as a rational numbers . 1) 0.5 2) 0.13 3) 0.341
Answers
The following recurring decimal as a rational number are 1/2, 13/100 and 341 / 1000
What is rational number?A rational number is a number that is expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator such as;
3/4. where,
Numerator = 3Denominator = 4Therefore,
0.5
= 5/10
= 1/2
0.13
= 13/100
0.341
= 341 / 1000
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helppppppppppppppppppppppppp
Answers
Answer:
reason 1.) This is the original expression
reason 2.) you subtract 4 from both sides
reason 3.) you divide both sides by 2 to get x=5
The value of p in the equation 2p - 3 = p + 2 Is
Answers
Answer:
p = 5
Step-by-step explanation:
Given equation:
2p - 3 = p+2
To Find:
Value of pSoln:
2p - 3 = p + 2
Subtract p from both sides:
=>2p-3−p = p+2-p
=>p-3 = 2
Add 3 to both sides:
=>p−3+3 = 2+3
=>p = 5
Hence,the value of p would be 5.
We can plug the value we got to the original equation to verify:
=> 2p - 3 = p + 2
p = 5=> 2(5) -3 = 5 + 2
[Make sure to simplify using PEMDAS]=> 10 - 3 = 7
=> 7 = 7 [Proved]
Hence,this equation is true.
[tex]\rule{225pt}{2pt}[/tex]
Acronym PEMDAS rule means:
P:ParenthesesE:ExponentsM:MultiplicationD:DivisionA:AdditionS:SubtractionAnswer:
p = 5
Step-by-step explanation:
First we add 3 to both sides to make :
2p = p + 5
Now we subtract p from both sides :
p = 5
Hope this helped and brainliest please
Fill out the chart please!
The dot plot and the box plot shown both represent Manuel’s data. Determine which visual display is more useful for answering each of the questions listed in the table, and explain your reasons.
Answers
1. Mean of the data: 8
2. Median: 8
3. IQR = 4
4. Members that use the facility 10 days a month is: 2.
See reasons below.
What is the Mean, Median, and Interquartile Range of a Data?Mean = sum of all values ÷ number of data values (easily solved using a dot plot
Median = middle value (easily found using a box plot).
Interquartile range (IQR) = Q3 - Q1 (easily found using a box plot).
1. Mean of the data: use the dot plot.
Reasoning: (3 + 3 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 11 + 12 + 14)/15 = 8
2. Median of the data set: Using the box plot, it is the value indicated by the vertical line that divides the box.
Median = 8
3. IQR = Q3 - Q1 = 10 - 6
IQR = 4
4. Members that use the facility 10 days a month, using the dot plot is: 2. 10 has 2 dots.
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Brett draws the shape shown below.
He says the shape can be classified as a quadrilateral, parallelogram, rhombus, and square.
Is Brett correct? Explain.
Answers
The given figure is quadrilateral, parallelogram, and a rhombus but not a square. So brett is not correct.
What is a square?A square is a quadrilateral with all the sides equal and all the four sides are perpendicular to each other.
We know that it is a quadrilateral as a quadrilateral is having four sides and the sum of the angles is 180 degrees.
The given figure is a parallelogram as opposite sides of the figure are parallel and equal.
The given figure is a rhombus as all the sides are parallel and equal.
The given figure can not be a square as in the square all the four sides are perpendicular to each other.
Therefore given figure is quadrilateral, parallelogram, and a rhombus but not a square. So brett is not correct.
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From your observation : x⁰=
Answers
Answer:
=1
Step-by-step explanation:
Given that 2x³-5x² - 4x+8 = (Ax - 1)(x-B)(x + 1) + C for all values of x, find the
values of A, B and C.
Answers
Answer:
A=2, B=3, C=5
Step-by-step explanation:
Two polynomials are equal for all values of the variable if the corresponding coefficients are the same. The way to solve the problem is to multiply the RHS, rewrite it in a more orderly way
[tex](Ax-1)(x-B)(x+1)+C = \\Ax^3+(A-AB-1)x^2+(B-AB-1)x +B+C[/tex]
Now, for the two polynomials to be the same we need to have, at the same time
[tex]x^3: A=2\\x^2: A-AB-1= -5\\x:B-AB-1=-4\\1: B+C=8[/tex]
You might notice that we have more conditions than variables, but you can consider one of the two in the middle as a "check" option.
Now, grabbing the value from the first condition into the second we get B=3. Replacing both value in the third we see that the equality still holds, and replacing into the fourth we get C =5.
According to a survey, 48% of adults in the united states believe that unidentified flying objects (ufos) are observing our planet. you ask 8 randomly chosen adults whether they believe ufos are watching earth.
Answers
The expected number of adults that believe ufos are watching earth is 4
How to determine the number of adults?The given parameters are:
p = 48%
Sample size, n = 8
The expected number of adults that believe ufos are watching earth is calculated as:
E(x) = np
This gives
E(x) = 8 * 48%
Evaluate
E(x) = 3.84
Approximate
E(x) = 4
Hence, the expected number of adults that believe ufos are watching earth is 4
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True or false: f(x) represents a function.
A. True
B. False
Answers
Answer:
A.) True
Step-by-step explanation:
A set of outputs and inputs becomes a function when there is only one output per input. In this case, each "x" value only has one "y" value, making it a function.
What is a factor of X2–9 X +14
Answers
The factors of the expression x^2 - 9x + 14 are (x - 7) and (x - 2)
How to factor the expression?The expression is given as:
x^2 - 9x + 14
Expand
x^2 - 2x - 7x + 14
Factorize the expression
x(x - 2) - 7(x - 2)
Factor out x - 2 from the expression
(x - 7)(x - 2)'
Hence, the factorized expression of x^2 - 9x + 14 is (x - 7)(x - 2)'
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there is 1 litre of tea in a teapot, alex pours 275ml of the tea into a cup what percentage of the tea has alex poured
Answers
Answer:
27.5%
Step-by-step explanation:
Given:
1 Liter In TeapotAlex poured 275 milliliters of the tea into a cupReview:
1,000 Milliliters = 1 LiterConcepts:
A liter is a noun meaning a unit of capacity redefined in 1964 by a reduction of 28 parts in a million to be exactly equal to one cubic decimeter. It is equivalent to 1.0567 U.S. liquid quarts and is equal to the volume of 1 kilogram of distilled water at 4°C.A millimeter is a noun meaning a unit of capacity equal to one thousandth of a liter, and equivalent to 0.033815 fluid ounce, or 0.061025 cubic inch.Formula:
The mℓ to ℓ formula is [L] = [mL] / 1000.Now we must convert 275 milliliters to liters.
1. Divide the volume by 1,000.
275 ÷ 1000 = 0.275
2. Add the Unit Symbol for Liter.
0.275 ⇒ 0.275 L
Now we have to find how much of 1 liter- 0.275 liters as a percentage is.
To convert 0.275 to percent multiply 0.275 by 100. The result is 27.5 percent, or, using the percent sign, 27.5 %.
Please Help I Don't Understand!
Answers
Answer:
D) None of the choices are correct.
Explanation:
Given triangles AHL and NKG
Sides which are congruent:
AH and NKHL and KGAL and NGSo, AHL ≅ NKG. There are no such options.
The roots of the quadratic equation x²+bx+c = 0 are a and ß a) Evaluate i) a² + ß², ii) (a − ß)² b) Find the quadratic equation whose roots are (a² +ß²) and (a - 3)²
Answers
If ɑ and β are the roots of x² + bx + c = 0, then we can write
x² + bx + c = (x - ɑ) (x - β)
Expanding the right side gives
x² + bx + c = x² - (ɑ + β) x + ɑβ
so that ɑ + β = -b and ɑβ = c.
Recall that for all real numbers m and n,
(m + n)² = m² + 2mn + n²
a) It follows that
(i) ɑ² + β² = (ɑ + β)² - 2ɑβ = (-b)² + c = b² + c
(ii) (ɑ - β)² = ɑ² - 2ɑβ + β² = b² + c - 2c = b² - c
b) I assume you mean to find the quadratic whose roots are ɑ² + β² and (ɑ - β)² (and not (ɑ - 3)²). The simplest quadratic of this form is
(x - (ɑ² + β²)) (x - (ɑ - β)²)
Using the results from part (a), this becomes
(x - (b² + c)) (x - (b² - c))
and expanding, we get
x² - (b² + c + b² - c) x + (b² + c) (b² - c)
= x² - 2b² x + b⁴ - c²
Part 1: Come up with and describe two scenarios: one that models a direct variation situation and one that models an inverse variation situation. Do not state explicitly which scenario is which, but provide at least four data pairs for each situation. Your classmates will have to determine which of the scenarios is a direct variation and which is an inverse variation, and the value of k for each.
Answers
Answer:
1. I went to a store four days in a row and only bought chocolate bars each day. All chocolate bars were the same and cost the same. On the first day, I bought 2 chocolate bars for $2.38. On the second day I bought 1 chocolate bar for $1.19. On the third day, I bought 10 chocolate bars for $11.90. On the fourth day, I bough 4 chocolate bars for $4.76.
2. A sink is full. It contains 20 gallons of water. The stopper is removed and water starts draining out. One minute after the stopper is removed, the volume of water in the sink is 18 gallons. Two minutes after the stopper is removed, the volume of water in the sink is 16 gallons. Four minutes after the stopper is removed, the volume of water in the sink is 12 gallons. Ten minutes after the stopper is removed, the sink is empty.
simplify (x^3+2x-3)-(x^2-2x+4)
Answers
Answer:
x³ - ((x+1)(x+1))
Step-by-step explanation:
x³ + 2x -3 - x² - 2x + 4
x³ - x² + 1
x³ - ((x+1)(x+1))
Answer:
x^3−x^2+4x−7
Step-by-step explanation:
Hope this helps! Have a great day!!
Determine the marginal distribution of Gender. In paragraph form, how you calculated the marginal distribution. Include your calculations in your explanation.
Answers
The marginal distribution for gender tells you the probability that a randomly selected person taken from this sample is either male or female, regardless of their blood type.
In this case, we have total sample size of 714 people. Of these, 379 are male and 335 are female. Then the marginal probability mass function would be
[tex]\mathrm{Pr}[G = g] = \begin{cases} \dfrac{379}{714} \approx 0.5308 & \text{if }g = \text{male} \\\\ \dfrac{335}{714} \approx 0.4692 & \text{if } g = \text{female} \\\\ 0 & \text{otherwise} \end{cases}[/tex]
where G is a random variable taking on one of two values (male or female).
How many different sequences of 3 playing cards (from a single 52-card deck) exist?
22,100
140,608
132,600
24,804
Answers
There 1,32,600 possibilities to withdrawn 3 different sequence of playing cards from 52 cards.
What is Permutations?A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.
Here, total number of cards = 52
Number of Withdrawn cards = 3
Possibilities of different sequences of 3 playing cards = 52 X 51 X 50
= 132600
Thus, there 1,32,600 possibilities to withdrawn 3 different sequence of playing cards from 52 cards.
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Answer:
132,600
Step-by-step explanation:
To determine the number of different sequences of 3 playing cards from a 52-card deck, we can use the formula for permutations, which is given by:
P(n, k) = n! / (n-k)!
Where n is the total number of items (in this case, the number of cards in the deck) and k is the number of items chosen (in this case, 3 cards).
Plugging in the values:
n = 52 (total number of cards in the deck)
k = 3 (number of cards chosen)
P(52, 3) = 52! / (52-3)!
Calculating the factorial terms:
52! = 52 x 51 x 50 x ... x 3 x 2 x 1
(52-3)! = 49! = 49 x 48 x ... x 3 x 2 x 1
Simplifying the equation:
P(52, 3) = 52 x 51 x 50
P(52, 3) = 132,600
Therefore, there are 132,600 different sequences of 3 playing cards that can be formed from a single 52-card deck.
Select the correct answer. in which career would you most likely apply concepts from geometry? a. food critic b. social worker c. radio dj d. computer game designer
Answers
Answer:
Computer game designer.
Step-by-step explanation:
If you want to design a game, you need to have some basic shapes and stuff in it. I'm not sure what else needs to be explained here lol
what is the value of the digit 5in the number 734.95?
Answers
Answer:
0.05
explanation
value means total value
so it's 5*0.01
=0.05
Satoranaing
19100
Points C, D, and G lie on plane X. Points E and F lie on
plane Y.
X
B
A
Y
Intro
E
D
G
F
Which statements are true? Select three options.
There are exactly two planes that contain points A,
B, and F.
There is exactly one plane that contains points E, F,
and B.
The line that can be drawn through points C and G
would lie in plane X.
The line that can be drawn through points E and F
would lie in plane Y.
The only points that can lie on plane Y are points E
and F.
Done
Answers
The statements that are true about the given points on the line are; Options B, C and D
How to identify points on a Plane?
A plane is defined by a line and a point outside of it. Meanwhile, a line is defined by two points. Thus, whenever we have 3 non-collinear points, we can define a plane.
Let us check each of the given options;
A) There are exactly two planes that contain points A, B, and F;
If these points are collinear, they can't make a plane and If they are not collinear, they define a plane.
Since we can't make two planes with them, then the statement is false.
B) There is exactly one plane that contains points E, F, and B;
Due to the same reasoning in part A, the statement is true assuming the points are not collinear.
C) The line that can be drawn through points C and G would lie in plane X;
The statement is true because both points C and G lie on plane X, and as such the line that connects them also should lie on the same plane.
D) The line that can be drawn through points E and F would lie in plane Y; Similar to above, this statement is true.
E) The only points that can lie on plane Y are points E and F.
This statement is false because infinite points can lie on a plane.
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what is the slope of y=-9x-8?
Answers
The slope of the linear equation, y = -9x - 8 is determined as: -9.
How to Identify the Slope in an Equation?If the equation of a line is given in a slope-intercept form, y = mx + b, the slope value is represented as m.
Thus, given the equation y = -9x - 8, the slope in the linear equation is -9.
Therefore, slope of y = -9x - 8 is: -9.
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A group of students from your school is part of the audience for a TV game show. The total number of people in the audience is . What is the theoretical probability of students from your school being selected as contestants out of possible contestant spots?
Answers
A group of students from your school is part of the audience for a TV game show, the theoretical probability of students is mathematically given as
P=2.7%
What is the theoretical probability of students from your school being selected as contestants out of possible contestant spots?Generally, the equation for Probability is mathematically given as
[tex]P=\frac{Desired outcomes}{Total outcomes}[/tex]
Where Desired outcomes
D=40C5 *110C3
D=1420112865560
And Total outcomes
T=150C8 *
T=5.2572*10^10{12}
Hence, Probability
[tex]P=1420112865560/ 5.2572*10^10{12}[/tex]
P=0.0270
P=2.7%
In conclusion, the theoretical probability
P=2.7%
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what is the answer to −1.4+(−1.2)
Answers
Answer:
-2.6
Step-by-step explanation:
-1.4+(-1.2)
-1.4-1.2=-2.6
Hope this helps!
If not, I am sorry.
find the distance between the two points in simplest radical form.
(3,-8) and (8,4)
Answers
Answer:
13
Step-by-step explanation:
The way to find the distance between two points on the coordinate plane is to use the distance formula, which is basically a way of applying the Pythagorean Theorem.
The distance formula is [tex]\sqrt{(x_{1}- x_{2} )^2 + (y_{1}- y_{2})^2}[/tex]. Let's say the coordinate (3, -8) is (x1, y1) and the coordinate (8, 4) is (x2, y2). We can plug these values into the formula:
[tex]\sqrt{(3- 8 )^2 + (-8 - 4)^2}\\\sqrt{(-5)^{2} + (-12)^{2}} \\\sqrt{25+144} \\\sqrt{169} \\13[/tex]
So, the distance between the two points is 13.
Which system has no solutions? x < 3 x < 1 x > 3 x > 1 x < 3 x > 1 x > 3 x < 1
Answers
The system of inequalities with no solution is x > 3 x < 1
How to determine the system with no solutions?The systems of inequalities are given as:
x < 3 x < 1
x > 3 x > 1
x < 3 x > 1
x > 3 x < 1
As a general rule, it is impossible for a variable to be greater than a higher number and less than a smaller number.
This means that if x is greater than 3, then it must be greater than 1
Hence, the system of inequalities with no solution is x > 3 x < 1
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