if you finish all of the work right u willget 100 points
Answers
The value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x and the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.
First, let us know some laws of exponent:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹We are given;
[tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] and [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex].
Now, we will solve one by one;
[tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex]
[tex]= \sqrt[5]{\frac{2^{10}(x^{-10})}{(2^5x^{-15})}}[/tex]
[tex]=[({2^{10}. 2^{-5}) (x^{-10}.x^{15})}]^\frac{1}{5}[/tex]
[tex]=[({2^{10-5}) (x^{-10+15})]^\frac{1}{5}[/tex]
[tex]=[({2^{5}) (x^{5})]^\frac{1}{5}[/tex]
= 2x
So, the value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x.
Now,
[tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex]
[tex]=\frac{(2^3x^6y^{-3})^\frac{1}{3} }{(2^3x^3y^3)}[/tex]
[tex]=\frac{(2x^26y^{-1})}{(2^3x^3y^3)}[/tex]
[tex]=\frac{1}{(2^{3-1}x^{3-2}y^{3+1})}[/tex]
[tex]=\frac{1}{(2^{2}x^{1}y^{4})}[/tex]
= 1 / 4xy^4
So, the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.
Thus, the value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x and the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.
Please find the figure for the questions below.
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Related Questions
Order these numbers from least to greatest.
2.8, 2.5081, 1.935, 2.58
2.8
<
2.5081
<
1.935
2.58
Answers
Answer:
Step-by-step explanation:
1.935<2.5081<2.58<2.8
∵1.9350<2.5081<2.5800<2.8000
An arithmetic sequence is shown below:
150, 100, 50, 0, -50, ....
Construct the explicit formula to represent the sequence above. (Rubric 1B)
ARITHMETIC SEQUENCE
an= a1 + (n−1)d
Answers
Answer:
an= -50n +200
Step-by-step explanation:
an = a1+(n-1)d=150-50n+50=-50n+200
The black graph is the graph of y = f(x).
Choose the equation for the red graph.
A. y - 1 = f(x)
B. = f(x)
C. y = f(x - 1)
D. y = f()
1
Answers
Answer:
It's A.
Step-by-step explanation:
If you subtract from y, the graph moves to the right. If you add, it moves to the left.
A stadium has 51,000 seats. Seats sell for $28 in Section A, $16 in Section B, and $12 in Section C. The number of seats in Section A equals the total number of seats in sections B and C. Suppose the stadium takes in $1,078,400 from each sold-out event. How many seats does each section hold?
Answers
Answer:
A: 25,500
B: 14,600
C: 10,900
Step-by-step explanation:
This is what we know:
a = b + c
a + b + c = 51,000 Substitute in a for b + c
a + a = 51000 Combine like terms.
2a = 51000 Divide both sides by 2
a = 25,500
28a + 16b + 12c = 1078400 Substitute in 25.600 for a
28(25500) + 16b + 12c = 1078400
714000 + 16b + 12c = 1078400 Subtract 714000 from both sides
16b + 12 c = 364400
25500 +b + c = 51000 Subtract 25500 from both sides
b + c + = 25500 Multiply this equation all the way through by -12 and add it to the bold equation above it.
-12b -12c = -306000
16b + 12c = 364400
4b = 58400 divide both sides by 4
b = 14600
a + b + c = 51000 Plug in what we know
25500 + 14600 + c = 51000
40100 + c = 51000 Subtract 40100 from both sides
c = 10900
Erica worked 14 hours last week and 20 hours this week. If she earns $9 per hour how much did she earn during these two weeks?
Answers
Answer: $306
Step-by-step explanation:
You can find the answer by multiplying 9 by each of the values.
14 * 9 = 126
20 * 9 = 180
Add these values together and you get 306 !
Find tα/2 for n = 18 and a 99% confidence interval.
Answers
The value of tα/2 of the t-test is 2.898
How to determine tα/2?A t-test is a statistical test that is used to compare the means of two groups. tα/2 refers to the t critical value from the t-distribution table that corresponds to α/2
Given: n = 18 and a 99% confidence interval
We have to find the critical t value for 99% confidence level and sample size of 18
Degrees of freedom = n - 1 = 17
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
In the t table (check the attached image), we have to check the value against the column 0.005 and for 17 degrees of freedom.
The value obtained from the table is 2.898
Therefore, tα/2 = 2.898
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The revenue for a business, as a function of units produced, x, is shown below
by R(x). C(x) represents the cost of producing x units. Calculate the profit function and then determine how many units must be produced for the business to break even.
R(x) = 12x
C(x) = x + 264
Answers
Profit function = P(x) = 11x - 264 and 24 Units must be produced for the business to break even.
What is a Profit function?
A mathematical link between a company's overall profit and output is called a profit function. It is greatest when the firm's marginal revenue and cost are equal. It is equal to total revenue minus total costs.
How to calculate the profit function?
Profit function = Revenue function - Cost function
P(x) = R(x) - C(x)
Here, we have
R(x) = 12x
C(x) = x + 264
by applying the Profit function formula, we get
P(x) = 12x - x - 264
P(x) = 11x - 264
At this point, there is no profit or loss.
so, at break-even P(x) = 0
11x - 264 = 0
x = 24
Hence, Profit function = P(x) = 11x - 264, and 24 Units must be produced for the business to break even.
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If the premier is 97 what is the square value of x
Answers
Answer: 21
Step-by-step explanation
if the premier is 97 the square value of x is 21
The cost in dollars y of producing x computer desks is given by y = 60x + 3000
Answers
The cost of producing 24 computer desks is $4440 .
In the question ,
it is given that ,
the equation representing the cost of producing "x" computer desks is
y = 60x + 3000 ,
we need to find the cost of producing 24 computer desks ,
substituting x = 24 in the cost equation for producing computer desks ,
we get ,
y = 60(24) + 3000
On further simplification ,
we get ,
= 1440 + 3000
Adding the numbers ,
we get ,
= 4440
the cost is $4440 .
Therefore , The cost of producing 24 computer desks is $4440 .
The given question is incomplete , the complete question is
The cost in dollars y of producing x computer desks is given by y = 60x + 3000 , Find the cost of producing 24 computer desks .
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2sin3x - sqrt3 = 0
express as: x = _____ + _____ pi n
Answers
The trigonometric equation 2sin3x - √3 = 0 is expressed as x = π/9 + 2πn/3, 2π/9 + 2πn/3
How to solve trigonometric equations?
A trigonometric equation is defined as an equation involving one or more trigonometric ratios of unknown angles
Given: 2sin3x - √3 = 0
2sin3x - √3 = 0
2sin3x = √3
sin3x = √3/2
3x = sin⁻¹√3/2 (Note: sin⁻¹√3/2 = 60° = π/3 in radian)
3x = π/3, π -3 (Note: sine is positive in 1st and 2nd quadrant)
3x = π/3, 2π/3
x = π/9, 2π/9
x = π/9 + 2πn/3, 2π/9 + 2πn/3
Therefore, 2sin3x - √3 = 0 can be expressed as x = π/9 + 2πn/3, 2π/9 + 2πn/3
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three rectangular prims have the same based area but different heights as the height of these prisms increase the volume increases what is the independent variable in this situation
Answers
The independent variable while calculating the volume of a rectangular prisms with equal base area and different height is the height
What is an independent variable?The input values for a specific function are represented by the independent variable (x).
During an experiment, the independent variables are kept under control. The outputs of the function are represented by the dependent variable (y). The quantities being measured are the dependent variables in an experiment.
As regard the problem, the base area is a constant, the volume calculated is the dependent variable while the height iis the independent variable.
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PLEASE I REALLY NEED THIS ANSWER!! Find the volume of a cube with the given side length.
1/5b^3
Answers
A cube is a three-dimensional solid object which has six square faces, facets or sides, and each meeting at a vertex.
How to find the Volume of a cube?
Volume is defined as the measurement of space occupied by the three-dimensional object.
Volume (V) = s³ where
V=volume
S=sides
V= (1/3b³)³
applying the power law of indices
V = (1/3b)∧9 cubic units
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Write an equation for the line in the following problems.
I NEED THIS ASAP
Answers
Answer:
Graph 1: y = (-3x/5) + 1
Graph 2: y = 4
Step-by-step explanation:
Both functions are linear, so we can use a linear equation to model these functions. Using slope-intercept form, "y=mx+b" will be easiest, since the graph is shown.
Graph 1:
(1 - (-2))/(0 - 5) = (1 + 2)/-5 = -3/5 = slope
y-intercept (0, 1)
y = (-3x/5) + 1
Graph 2:
(4 - 4)/(1 - 0) = 0 = slope
y-intercept (0, 4)
y = 0x + 4
y = 4
Answer:
First equation : [tex]y=-\frac{3}{5}x +1[/tex]
Second equation : y = 4
Step-by-step explanation:
We want to write equations for the two given lines in slope intercept form
y = mx + b
Where m = slope and b = y intercept
Identifying the y intercept
First lets find the y intercept.
The y intercepts is where the line passes the y axis.
By looking at the first line it appears that the line passes the y axis at (0,1) meaning the y intercept is 1 so b = 1
Identifying the slope
We can find the slope using the slope formula
slope = (y1-y2)/(x1-x2)
Where the values of x and y derive from any two points on the line. (x1,y1) and (x2,y2)
The points used may vary as there are many options however I have chosen (0,1) and (-5,4)
So (x1,y1) = (0,1) and (x2,y2) = (-5,4)
Meaning x1 = 0 , y1 = 1 , x2 = -5 and y2 = 4
( we now plug these into the slope formula )
Again recall slope = (y1-y2)/(x1-x2)
==> plug in x1 = 0 , y1 = 1 , x2 = -5 and y2 = 4
slope = (1-4)/(0-(-5))
==> reduce subtraction
slope = -3/5
so our slope(m) is -3/5
Plugging in slope and y intercept into slope intercept form
Finally we plug in the values of m and b into slope intercept form to get the equation
Again we have y = mx + b
m = -3/5 and b = 1
So our equation is y = -3/5x + 1
Identifying equation for second line
When we have a horizontal line our equation is going to be put in y = b form where b = the y value that the line crosses. (or y intercept)
Here the line goes through the y value of 4 so b = 4
Hence, the equation of the second line would be y = 4
integration of ∫x³+1/x³-x dx
Answers
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits \frac{x^3+1}{x^3-x} dx }} \end{gathered}$}[/tex]
We rewrite the integrand.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{x^3+1}{x^3+x}=1+\frac{1}{x-1}-\frac{1}{x} }} \end{gathered}$}[/tex]
We integrate terms by terms:
The integral of the constants have this constant multiplied by the variable of integration.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits 1 \ dx=x } } \end{gathered}$}[/tex]
That u = x -1. Then that du = dx and we put du.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\frac{1}{u} \ du }} \end{gathered}$}[/tex]
Integral 1/u is log(u). If you now substitute u further into:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{log(x-1) }} \end{gathered}$}[/tex]
The integral of the product of a function by a constant is the constant times the integral of this function:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\left(-\frac{1}{x}\right)dx=-\int\limits\frac{1}{x}dx }} \end{gathered}$}[/tex]
Integral 1/u is log(x). Therefore, the result is: -log(x).
The result is: x - log(x) + log(x - 1)
(-3y)^4 write the power as a product of powers
Answers
Answer: 81y^4
Step-by-step explanation:
expand then calculate, -3 to the power of 4+81 then 81 added to y ^4 81y^4 is your finally power.
How do you find Circumcenter of a triangle?
Answers
Answer:
The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of the triangle intersect.
Step-by-step explanation:
The process of calculation of circumcenter has been given below.
What is circumcenter of a triangle?
Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.
Let the coordinate of A, B, C [tex]\Delta[/tex] ABC be ([tex]x_1, y_1[/tex]), [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] respectively and let the coordinate of circumcenter of [tex]\Delta ABC[/tex] is (x, y)
We need to find the length of AB, BC and AC
The length will be obtained in terms of x and y
On solving the equations, we will obtain the value of x and y
The value of x and y is the required coordinate of the circumcenter.
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A net researched and found that 60% of students in his school ride the bus to school. Abner took a random sample of 50 students and found that 38 ride the bus to school. Which statement correctly describes the sample ratio?
Answers
Answer: 224 student ride the bus to school each day.
Step-by-step explanation:
In megan random sample of 60 students number of students preferred riding bus is found out to be 42 student.
Student riding the bus if the total number of students in the bus is 320
ratio of the student surveyed to the student ride bus =
=
Assuming the total number of student riding bus = x
now,
x = 224
hence, 224 student ride the bus to school each day.
Step-by-step explanation:
Can you solve these 2 problems please
Answers
Answer:
1) The top angle = 128°
Right angle = 52°
Bottom angle = 128°
Left angle = 52°
2) The top angle = 159°
Right angle = 21°
Left angle = 21°
Step-by-step explanation:
The left problem would involve verticle angles being congruent to each other.
[tex]5x + 2 = x + 42\\\\6y + 8 = 7y - 12[/tex]
Solve each equation:
[tex]5x + 2 = x + 42\\4x = 40\\x = 10[/tex]
[tex]6y + 8 = 7y - 12\\20 = y[/tex]
Substitute:
The top angle = 128°
Right angle = 52°
Bottom angle = 128°
Left angle = 52°
The right problem would involve supplementary angles.
[tex]\frac{1}{4}y - 1 + 27x + 24 = 180\\\\27x + 24 + 4x + 1 = 180[/tex]
Solve for second equation (for simplicity) :
[tex]27x + 24 + 4x + 1 = 180\\31x + 25 = 180\\31 = 155\\x = 5[/tex]
Substitute x = 5 into other equation :
[tex]\frac{1}{4}y - 1 + 27x + 24 = 180\\\frac{1}{4}y - 1 + 27(5) + 24 = 180\\\frac{1}{4}y = 22\\y = 88[/tex]
Substitute :
The top angle = 159°
Right angle = 21°
Left angle = 21°
Dave rented a limousine for his wife's birthday. The hourly rate is $70. They used the limousine for 3 hours, plus Dave gave the driver a 10% tip. How much did he spend in total for the hourly charges plus tip?
A.
$252
B.
$189
C.
$287
D.
$231
Answers
Answer:
$231
Step-by-step explanation:
3 hours for 70 dollars an hour we multiply 70 by 3
70x3
210
And then to get the 10 percent tip we multiply 210 by .10
210x.10
21
And now we add 210 and 21 to get 231
Hopes this helps please mark brainliest
Hey can someone please find the area of this shape? Thank you so much I’ll give brainly. Please explain
Answers
Answer:
44.63
Step-by-step explanation:
( The heart shape makes two half circles and a square )
1 ) The two half circles together make a whole, so we can first find the area of that circle!
2 ) We can see that the dynamiter is 5in. We can cut this in half to find the radius...
5 ÷ 2 = 2.5
3 ) The area of a circle is found with the equation ( A = πr2 ). We can plug in the radius ( 2.5 ) to find the area...
A = π( 2.5 )2 = 19.635in
4 ) Now that we know the area of the circle we can find the area of the square. To find this we can use the equation ( A = a2 ) where a represents the edge length in this case 5in.
A = ( 5 ) 2 = 25in
5 ) We can now add the area of the circle and the area of the square to get the area of the heart!
19.635 + 25 = 44.63
Hope this helps! :)
A standard die is rolled. Find the probability that the number rolled is greater than 1. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
As there are 6 numbers on a standard die the required probability is 5/6.
Complete the equation of the line through (-6, 5) and (-3, -3).
Use exact numbers.
y =
5
Answers
Answer:
(-6,5)(-3,-3)y
here is an equation I hope this helps :) <3
3. You are working as a computer programmer in a company that makes computer games. You are getting paid $50 per hour for your work. At the end of the day you earned $400. How many hours did you have to
work to earn that amount of money? Let h represent the number of hours you worked. Choose the equation below that does not represent this situation.
400-(h+h) x 50
400-hx 50
50h = 400
400 h+h+h+h+h+h+h+h
Answers
Answer: I think A? not fully sure
Step-by-step explanation:
Which expression is equivalent to 8 ^ -3
Answers
The expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.
First, let us understand the exponents or power:
A power, or index, is a little floating number that appears next to a number or letter.
It is denoted as a^m.
where a = base number
and m = power or index number.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹a⁻¹ = 1 / aWe are given:
8^-3
We can solve as;
8^-3 = 8^(3 * -1) = (8^3) ^ -1 = 1 / 8^3 [since a⁻¹ = 1 / a]
So, 8^-3 = 1 / 8^3.
Thus, the expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.
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Complete the equation for this model .
Answers
Answer:
Step-by-step explanation:
the anser is 3 + 5 =8
what is the factored form of the expression 2m^3 -26m^2+80m?
Who can team up with me ?
Answers
ANSWER 2m(m-8)(m-5)
EXPLANATION
Factor the expression: 2m(m²-13m+40)
Rewrite the term: 2m(m²-8m-5m+40)
Regroup terms into two proportional parts : 2m((m²-8m)+(-5m+40))
Factor the expression: 2m(m(m-8)-5(m-8))
Factor the expression: 2m(m-8)(m-5)
Answer: 2m(m-8)(m-5)
Humberto walks 3 miles due north then turns around and walks 5 miles due south how far is Humberto from his starting point
Answers
Humberto's displacement is 2 miles due south far from his starting point.
How is the displacement completed?We understand that displacement is a vector quantity with both magnitude and direction, while distance is a scalar quantity with only magnitude.
Displacement, unlike distance, shows the direction and position of an object from its original base. This means that displacement refers to how far an object has traveled out of its original position with the direction included.
In other words, displacement shows the object's overall change in position and the direction of the new position from the former.
Starting point = 0
Distance covered toward the north = 3 miles
Distance covered toward the south = 5 miles
Displacement = 2 (0 - 3 + 5) miles
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A rental car company charges $53 per day to rent a car and $0.08 for every mile driven. Rashaad wants to rent a car, knowing that: He plans to drive 475 miles. He has at most $250 to spend. Use the drop-down menu below to write an inequality representing dd, the total number of days Rashaad can rent the car while staying within his budget.
Answers
The inequality that can be used to represent the total number of days Rashaad can rent the car while staying within his budget is d ≤ 4 .
How to represent inequality?The rental car company charges $53 per day to rent a car and $0.08 for every mile driven.
Rashaad wants to rent a car, knowing that: He plans to drive 475 miles. He has at most $250 to spend.
Therefore, the inequality to represent the total number of days Rashaad can rent the car can be represented as follows:
Therefore,
53d + 0.08(475) ≤ 250
53d + 38 ≤ 250
53d ≤ 250 - 38
53d ≤ 212
divide both sides of the inequality by 53
53d / 53 ≤ 212 / 53
d ≤ 4
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(7 x 4) x 3 = 3 x (4 x 7)
which property is used
a) commutative
b) assositative
c) identity
d) distributive
Answers
Answer:
b) associative
Step-by-step explanation:
The associative property of multiplication was used to change the position of the parentheses
What is the curved surface area of a cylinder with the circumference of 4 and height of 6
Answers
The curved surface area of a cylinder is 24cm²
Given the following data;
Base circumference = 4 cm
Height = 6 cm
How to find the curved surface area of a cylinder?Suppose that:
Radius of the considered cylinder = 'r' units
Height of the considered cylinder = 'h' units
Then, the curved surface area of that cylinder is 2πr h
To find the curved surface area (CSA) of the cylinder we have;
CSA of a cylinder = 2πrh
But 2πr = 4 cm
Now Substituting the values into the equation, we have,
CSA of a cylinder = 6 x 4
CSA of a cylinder = 24 cm²
Hence, The curved surface area of a cylinder is 24cm²
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