By using exponent properties, we will get the simplified expression:
[tex]x^{-1}*y^{1/2}*z^2[/tex]
How to simplify the given expression?
Here we have the expression:
[tex](x^{1/2}*y^{-1/4}*z)^{-2}[/tex]
Remember the exponent properties:
[tex](a^n)^m = a^{n*m}[/tex]
And:
[tex](a*b)^n = (a^n)*(b^n)[/tex]
So using these two properties, we can rewrite:
[tex](x^{1/2})^{-2}*(y^{-1/4})^{-2}*(z)^{-2}\\\\(x^{-2*1/2})*(y^{-2*-1/4})*(z^{-2}})\\\\x^{-1}*y^{1/2}*z^2[/tex]
So we conclude that the completely simplified expression is:
[tex]x^{-1}*y^{1/2}*z^2[/tex]
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Answer:
C
Step-by-step explanation:
Distribute the -2 to the exponents of x, y, and z.
x: 1/2 * -2/1 = -2/2 = -1
y: -1/4 * -2/1 = 2/4 = 1/2
z: 1/1 * -2/1 = -2/1 = -2
Now to get a negative out of the exponents, you simply move them on the other side of the equation (If it is on top move, it to the bottom and vice versa.)
So, once you move all of the exponents you get C.
If set A contains four distinct numbers and set B contains seven distinct letters, how many elements are in (A U B)?
There are 11 elements are in (A U B)
How to determine the number of elements?The given parameters are:
n(A) = 4
n(B) = 7
The number of elements in (A U B) is calculated using:
n(A U B) = n(A) +n(B) - n(A U B)
Given that the sets have distincts elements, we have:
n(A U B) = 4 + 7 - 0
Evaluate
n(A U B) = 11
Hence, there are 11 elements are in (A U B)
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Answer: There are 11 elements are in (A U B)
Step-by-step explanation:
Which statements are true?
Select each correct answer.
All trapezoids are quadrilaterals.
All rhombuses are squares.
All rhombuses are parallelograms.
All quadrilaterals are parallelograms.
Answer:
all rhombuses are parallelograms, all trapezoids are quadrilaterals
Step-by-step explanation:
rhombuses have all equal sides, 2 sets of parallel lines and are a diamond shape. a quadrilateral is a shape with 4 sides (quad means 4) therefore, all rhombuses are parallelograms. we know that all trapezoids have 4 sides, so we can conclude that all trapezoids are quadrilaterals i hope this helped because i know that end of year tests are super hard.
Aisha has a piece of string that she cuts into smaller pieces. This line plot shows the length of each piece. Juan has a piece of string that is 12 as long as Aisha's seventh-longest piece. (Note: The problem states the seventh-longest piece, not the seventh-longest length.)
How long is Juan's piece of string?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
2 5/8 inches
Step-by-step explanation:
There are 2 pieces 5 3/4 inches long.
There is 1 piece 5 1/2 inches long.
There are 4 pieces 5 1/4 inches long.
The seventh longest piece is one of the pieces measuring 5 1/4 inches.
Juan's piece is 1/2 as long as 5 1/4 inches.
1/2 × 5 1/4 inches = 1/2 × 21/4 = 21/8 inches = (16/8 + 5/8) = 2 5/8 inches
Using the net below, find the surface area
of the triangular prism.
6 cm
8 cm
15 cm
15 cm
6 cm 8 cm
6 cm
Surface Area
[?] cm²
10 cm
Enter
Which of these is a recurring cost of car ownership?
A. Windshield replacement
B. Driver's license application fee
C. Gas
O D. Bumper replacement
Thank you for your help. The question is in the screenshot
Answer:
Hi,
Step-by-step explanation:
Using the pythagorean theorem , let's calculate the apothem of a side:
a²=26²-10²=57=24²
Area of a side: 24*10*2/2=240 (ft²)
Lateral area=240*4=960(ft²)
Area of the base: 20²=400 (ft²)
Total area=1360(ft²)
A convex hexagon has exterior angles of 39°, 47°, 42°, 59°, and 64°. What is the measure of an exterior angle at the
sixth vertex?
Answer: [tex]109^{\circ}[/tex]
Step-by-step explanation:
The exterior angles of a polygon add to 360 degrees, so the sixth angle measures [tex]360-39-47-42-59-64=\boxed{109^{\circ}}[/tex]
which of the following is located over the center of the base of a regular pyramid
A vertex
B slant height
C face
D edge
Answer:
vertex
Step-by-step explanation:
Which function has a vertex at (2, 6)?
f(x) = 2x21 - 6
f(x) = 2|x2| +6
f(x) = 2x + 2+ 6
f(x) = 2x + 2 - 6
The function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function that has vertex at (2, 6)
The options are:
f(x) = 2|x – 2| – 6
f(x) = 2|x – 2| + 6
f(x) = 2|x + 2| + 6
f(x) = 2|x + 2| – 6
As we know the vertex form of a quadratic function is given by:
f(x) = a(x - h)² + k
Similarly, mod function can be expressed as:
m(x) = a|x - h| + k
Here (h, k) is the vertex of a function.
In the function:
f(x) = 2|x – 2| + 6
The vertex of the function is (2, 6)
Thus, the function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.
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What is the range of function g if g(x) =-2f(x-3)
Answer:
If you entered the function correctly there is not a range
Step-by-step explanation:
Answer: {y|-♾<y<0}
Step-by-step explanation: i’m taking this summer school class
The diameter of a circle is m. What is the area
Answer:
[tex] (\frac{{m}^{2} }{4} )\pi[/tex]
Step-by-step explanation:
we can find the radius from the diameter by dividing the diameter by 2 (radius is half the diameter)
the formula for the area of a circle is r²π (with r being radius) but since we must use diameter we have to replace r with (m/2)
this gives us our new formula of (m/2)²π, which simplifies to (m²/4)π
that is the answer
- kan academy advance
A music company offers a loan to buy a drum set for $1800.
-15.25% simple interest
-Equal monthly payment for 4 years.
What is the monthly payment?
The monthly payment is $____
Using it's formula, it is found that the value of the monthly payment for the loan to buy the drum set is of $50.32.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.In this problem, the parameters are given as follows:
P = 1800, r = 0.1525, n = 4 x 12 = 48.
Hence:
r/12 = 0.1525/12 = 0.01270833.
Hence, the monthly payments will be of:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 1800\frac{0.01270833(1 + 0.01270833)^{48}}{(1 + 0.01270833)^{48} - 1}[/tex]
A = 50.32.
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Please answer quick. Will mark whoever is first brainliest. The x intercept of the line is either A. (5,0) or B. (10,0) and it’s Y intercept is either A. (0,1/20) or B (0,20)
Answer:#1 A, #2 B
Step-by-step explanation:
Heres the proof
Find the median of the following data : 9, 15, 17, 18,6, 20, 8, 5, 18, 18, 10, 5, 14, 12, 10, 7
Answer:
The median of the data is 12.
Step-by-step explanation:
The median is really just another word for the average. To find that, you add all of the numbers and divide that sum by the number of numbers there are.
9+15+17+18+6+20+8+5+18+18+10+5+14+12+10+7=192
There are 16 numbers in this data set. So, we will divide the sum by 16.
192÷16=12
I hope this helps!! :)
Use the long division method to find the result when 2 x 3 + 3 x 2 + 17 x + 8 2x 3 +3x 2 +17x+8 is divided by 2 x + 1 2x+1.
what is pemdas? algebra 1
Answer:
p=Parentheses
e=Exponents
m=Multiplication
d=Division
a=Addition
s=Subtraction
its an order of solving a equation
A pie has a diameter of 9 inches. each slice of the pie has a central angle of 45 degrees. What is the area of each slice of pie?
Area of sector
Ø/360×πr²45/360×π(4.5)²1/8×π(20.25)7.95in²option B
Answer:
b
Step-by-step explanation:
The area of a sector is (the angle) over 360 multiplied by pi (radius) squared
This would be 45/360 pi (4.5) squared, resulting in option b.
factorize
2x²-x²-x
Please help me fast to solve this problem.
Answer: x (x - 1)
Step-by-step explanation:
[tex]2x^{2} - x^{2} -x[/tex]
[tex]x^{2} -x[/tex]
x (x - 1)
The production supervisor at a particular office products company finds that it takes 3 hours to manufacture each table for one of its special dining room sets. Each
chair
takes 8 hours to manufacture. A total of 6000 hours is available to produce tables and chairs of this style. The linear equation that models this situation is
3x+8y=6000, where x represents the number of tables produced and y the number of chairs produced.
a. Complete the ordered pair solution (0.) of this equation. Describe the manufacturing situation that corresponds to this solution.
The ordered pair is (0…)
The ordered pairs of the equation are
0 tables, 750 chairs2000 tables. 0 chairsHow to find the ordered pairs of the equationThe equation is given as
3x + 8y = 6000
We have x = number of tables
y = number of chairs
When x = 0
3(0) + 8y = 6000
8y = 6000
y = 750
When y = 0
3x + 8(0) = 6000
3x = 6000
x = 2000
The ordered pairs of the products are:
0 table 750 chairs
200 tables, 0 chairs.
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Find the angle of depression
from point A to point C.
A
?
C
B
Angle of depression = [?]°
Enter
55°
350 m
The angle of depression is 35 degree in the right angle triangle if the angle BAC is 55 degree.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have shown a right-angle triangle in the picture.
In the right angle triangle, ABC
The angle BAC = 55 degree
Angle BAA' = 90 degree
In the figure, the angle of depression = CAA'
= BAA' - BAC
= 90 - 55
= 35 degree
Thus, the angle of depression is 35 degree in the right angle triangle if the angle BAC is 55 degree.
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Please help to prove parallelogram.
The question requests proof that WV = VR. See the definition of Mathematical proof and the explanation for the proof below.
What is a mathematical proof?Mathematical proof refers to the steps of logical arguments which are given to show that a mathematical statement is true or correct.
What is the proof that WV = VR?Note that SR ║ QT;Reason: This is given. The image is a parallelogram.
Hence, ∠PSR = ∠WVPTherefore if ΔSVR ≅ PVW;
Then WV = VR.
QED.
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What is the area of the trapezoid shown? The figure is not drawn to scale.
284.31 in.²
303.75 in.²
568.62 in.²
607.5 in.2
The area of the trapezoid is 284.31 square inches
How to determine the area?The area of a trapezoid is:
Area = 0.5 * (Sum of parallel sides) * height
Using the given figure, we have:
Area = 0.5 * (17 + 31.6) * 11.7
Evaluate
Area = 284.31
Hence, the area of the trapezoid is 284.31 square inches
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Solve question 11 for me please
Answer:
C
Step-by-step explanation:
-4x+2<6
-4x<4
x<-1
because the sign doesnt have a line under it, it is an open hole
Find the value of x and the measure of angleMNQ.
3x − 11°62°
The value of x is
90
° and the measure of angleMNQ is
180
°.
Answer:
180
Step-by-step explanation:
Find the value of x and the measure of angleMNQ.
3x − 11°62°
The value of x is
90
° and the measure of angleMNQ is
180
°.
which function is increasing on the interval (-∞, ∞)
Differentiating each function, we have for all x, unless otherwise indicated,
[tex]h(x) = 2^x - 1 \implies h'(x) = \ln(2) \, 2^x > 0[/tex]
[tex]g(x) = -4 (2^x) \implies g'(x) = -4 \ln(2) \, 2^x < 0[/tex]
[tex]f(x) = -3x+7 \implies f'(x) = -3 < 0[/tex]
[tex]j(x) = x^2 + 8x + 1 \implies j'(x) = 2x + 8 > 0 \text{ only when } x > -4[/tex]
and only h(x) has a strictly positive derivative. (A)
In the following exercises, translate into an equation and solve
Kindergarten Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. How many children will she put in each group?
Answer: 6 children
Step-by-step explanation:
Given:
Children - 24
Groups - 4
Number of children per group - x
Solve:
24 ÷ 4 = x
x = 6
Hope it helps!!! Please mark as brainliest. Thanks :D
p and q are complex numbers such that |p|=7√3 and |p+q|=12√2. On what interval must |q| fall on?
The interval where |q| will fall will be[ 12√2−7√3,∞ ).
What are complex numbers?A complex number is an element of a number system that contains the real numbers and a specific element.
In this case, p and q are complex numbers such that |p|=7√3 and |p+q|=12√2. The interval where |q| will fall will be[ 12√2−7√3,∞ ).
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The Pythagorean theorem can only be used with witch type of triangle
Answer:
Right Triangles
Step-by-step explanation:
In the discussion board, post the coordinates of the center point and the radius of a circle.
Step-by-step explanation:
coordinates of center is 0,0 there are no hints given to find radius
A rectangular patio has a length of 12 1\2 feet and an area of 103 1\8 square feet. What is the width of the patio?
Answer:
8.25 feet
Step-by-step explanation:
to find the width, you divide the area by the length
103 1/8 / 12 1/2 = 8.25
Give brainliest, please!
Hope this helps :)