Expression which is equivalent to [tex]$\sqrt{8 x^{7} y^{8}}[/tex] is [tex]$=2 \sqrt{2} x^{3} y^{4} \sqrt{x}$[/tex].
What are equivalent expressions?
Expressions that function identically despite having distinct appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).
Solution of the given equation [tex]$\sqrt{8 x^{7} y^{8}}[/tex].
[tex]$\sqrt{8 x^{7} y^{8}}=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]
[tex]$=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]
Simplify [tex]$\sqrt{x^{7}}: x^{3} \sqrt{x}$[/tex]
[tex]$=\sqrt{8} x^{3} \sqrt{x} \sqrt{y^{8}}$[/tex]
Simplify [tex]$\sqrt{y^{8}}: y^{4}$[/tex]
[tex]$=\sqrt{8} x^{3} \sqrt{x} y^{4}$[/tex]
[tex]$\sqrt{8}=2 \sqrt{2}$[/tex]
[tex]$=2 \sqrt{2} x^{3} \sqrt{x} y^{4}$[/tex]
To know more about equivalent expressions visit:
https://brainly.com/question/17102319
#SPJ4
The complete question is :
Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0. x y squared StartRoot 8 x cubed EndRoot 2 x cubed y cubed StartRoot x y squared EndRoot 2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot 4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
Identify the recursive formula for the sequence -3, 9, -27, 81, ....
Answer:
A
Step-by-step explanation:
there is a common ratio between consecutive terms , that is
9 ÷ - 3 = - 27 ÷ 9 = 81 ÷ - 27 = - 3
this indicates the sequence is geometric.
the recursive formula allows a term in the sequence to be found by multiplying the previous term by the common ratio r , that is
f(n) = - 3f(n - 1) if n > 1 : f(1) = - 3
given points (8,6) and ( 8, 0) as the endpoints of a radius ,what is the equation of the circle with center ( 8,6)
The general equation of a circle is written like [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the centre and r is the radius.
Solving the QuestionFirstly, we're given that the centre is (8,6).
Plug this into the general equation:
[tex](x-h)^2+(y-k)^2=r^2\\(x-8)^2+(y-6)^2=r^2[/tex]
We're given this other point on the circumference of the circle, (8,0), which is 6 units away from the center.
Therefore, the radius is 6 units. Plug this into the general equation too:
[tex](x-8)^2+(y-6)^2=r^2\\(x-8)^2+(y-6)^2=6^2\\(x-8)^2+(y-6)^2=36[/tex]
Answer[tex](x-8)^2+(y-6)^2=36[/tex]
A rectangular field is to be enclosed by 400m of fencing. Use quadratic to
determine what dimensions will result in the maximum area inside the fence. Show
all your work.
Work:
First it's a rectangle so its area is equal to the product (multiplication) of both sides of the rectangle (dimensions). A = a x b = ab
NOW: knowing the the circumference or perimeter is equal to 400m, we can say that P = 400 = 2(a+b) = 2a + 2b since the given polynom is rectangle. 2a + 2b = 400 <==> 2a = 400 - 2b <==> a = 200 - b.
We gave an expression of a in function of b. Now we can replace the variable a by 200 - b in the first expression of the area.
A = ab = (200-b)b = 200b-b^2 = -b^2 + 200b
A is now a quadratic equation. We note A(b) the epression -b^2 +200b so:
A(b) = -b^2 +200b
We can already see that A is a quadratic equation of the form:
ax^2 + b + c. The a coefficient is negative which will lead to closed parabola when looking from the top. Now we need to find the maximum of the function by using the derivatives:
A(b) = -b^2 +200b <==> A'(b) = -2b + 200b
and -2b + 200b = 0 <==> b = 100;
So the derivative function crosses the x-axis at (100; 0).
So is increasing over ]-∞; 100] and decreasing over [100; ∞[.
We obtain a maxima on (100; x) with A. To find it we need to replace 100 by b in the function A.
A(b) = -b^2 + 200b
<==> A(100) = -100^2 + 200 x 100 = - 10000 + 20000 = 10000
Now let's find a: if b = 100 what equals a ?
We know that ab = 10000 <==> 100a = 10000 <==> a = 100;
And we verify that ab = 100 x 100 = 10000.
The rectangle needs to be a square to reach the maximum area of 10000m^2 or also 0.01 km^2.
Q.E.D.
If t is the midpoint of segment rs then, segment rt is congruent to segment ts..
help please!!!!
It is the definition of Midpoint
Disclaimer!!!
The question is incomplete and the correct question is shown below
What definition would justify the following statement?
If T is the midpoint of segment RS then, Segment RT is congruent to segment TS..
Definition of Angle BisectorDefinition of CongruenceDefinition of MidpointDefinition of Segment BisectorIf t is the midpoint of segment rs then, segment rt is congruent to segment ts. is the definition of the midpoint
The line segment of a triangle connecting the midpoint of two sides of the triangle is said to be parallel to its third side and is also half the length of the third side, according to the midpoint theorem.
Hence It is the definition of the midpoint
Learn more about Midpoint here
brainly.com/question/5127660
#SPJ4
Answer: C: Definition of Midpoint
Step-by-step explanation: Hope that helped!
Which measure represents the standard deviation of the sample means and is used in place of the population standard deviation when
the population parameters are unknown?
The measure represents the standard deviation of the sample means and is used in place of the population standard deviation when the population parameters are unknown is; t-test.
Which measure is used when the population parameters are unknown?A hypothesis test for a population mean when In the case that the population standard deviation, σ, is unknown, carrying out a hypothesis test for the population mean is done in similarly like the population standard deviation is known. A major distinctive property is that unlike the standard normal distribution, the t-test is invoked.
Read more on t-test;
https://brainly.com/question/6501190
#SPJ1
Answer:
standard error of the mean
Step-by-step explanation:
Plato/Edmentum
How many two digit numbers have on odd digit and one evan digit?
Answer: There are only 90 two-digit numbers. It shouldn’t take long to write them out and count them
Step-by-step explanation:
Answer:
45 numbers
Step-by-step explanation:
The 10-digit numbers are 10-99. We can manually write them out to start and see if we can find a pattern.
We can start 10-19: The numbers that have one odd digit and one even digit at 10, 12, 14, 16, 18 (since 1 is odd, we can only pick the numbers that have an even unit digit)
Next, we move on to 20-29: The numbers that follow the property are 21, 23, 25, 27, 29
Both of these examples have 5 numbers that follow the property. We can notice that all of the subsequent clusters (30-39, 40-49, 50-59, 60-69, 70-79, 80-89, 90-99) will also have 5 each. The numbers that start with an odd number will have the same unit digits as the 10-19 cluster, and the numbers that start with an even number will have the same unit digits as the 20-29 cluster. Observe:
30-39: 30, 32, 34, 36, 38
40-49: 41, 43, 45, 47, 49
50-59: 50, 52, 54, 56, 58
60-69: 61, 63, 65, 67, 69
70-79: 70, 72, 74, 76, 78
80-89: 81, 83, 85, 87, 89
90-99: 90, 92, 94, 96, 98
In all, there are 9 clusters of numbers, and each one has 5 numbers that follow the property. Therefore, the total is 9*5 or 45 numbers
Solve the quadratic equation 2x2-1 = 7 x. write your answer correct to two decimal places
Answer:
Step-by-step explanation:
You have 2 x's. I think the first one is for multiplication and the second one is a variable.
2x2 -1 = 7x
4-1 = 7x (first multiple 2x2)
3=7x (second 4-1)
0.428571429 = x (Divide both sides by 7. On the left side, 3/7 is 0.428571429 and 7x/7 is just x because the 7s cancel out.
Since the answer needs to be to two decimal places, I have to decide if 0.428571429 is closer to 0.42 or 0.43 Since the digit after the 2 in the answer is 8, that makes the number closer to 0.43 than 0.42. So, the final answer is 0.43
EXTRA POINTS HELP ASAP!
x + x/3 = 4/9
solve for x
Answer:
x=1
Step-by-step explanation:
1 + 1/3 = 4/9
1/3 also equals 3/9
hope this helped :)
Answer :
Value of x is 1 / 3Step-by-step explanation :
>> (3 × x + x / 3) = 4 / 9
>> (3x + x / 3) = 4 / 9
>> (4x / 3) = 4 / 9
>> 4x × 9 = 3 × 4
>> 36x = 12
>> x = 12 / 36
>> x = 6 / 18
>> x = 3 / 9
>> x = 1 / 3
Vertical plane R intersects horizontal plane P. Points A, D, and B are on the line of the intersecting planes. Point F is on the top half of plane R. Point G is on the bottom half of plane G. Point C is on the left half of plane P. Point E is on the right half of plane P. Point H is above and to the right of the planes. Point J is below and to the left of the planes. Which statements are true based on the diagram? Check all that apply. Points A, B, and D are on both planes. Point H is not on plane R. Plane P contains point F. Points C, D, and A are noncollinear. The line containing points F and G is on plane R. The line containing points F and H is on plane R.
The true statements are:
Points A, B, and D are on both planes. Point H is not on plane R. Points C, D, and A are noncollinear. The line containing points F and G is on plane R. What is the intersection of 2 planes?If two planes are said to have intersect each other, the intersection will be regarded as a line.
Hence, looking at the image attached, you will see that Points C, D, and A are noncollinear and the line containing points F and G is on plane R.
Note that when a line and a plane are said to intersect each other , the intersection will be a single point, or say a line. So Points A, B, and D are on both planes.
Therefore, option 1, 2, 4 and 5 are correct.
Learn more about Vertical plane from
https://brainly.com/question/7150882
#SPJ1
Answer: option 1 , 2 , 4 , 5
Step-by-step explanation: edge 2022
Prove or disprove the following. In any group of two or more people, there are always at least two people who have the same number of friends. Assume that if a person p is a friend of a person q then q is also a friend of p.
Yes we can prove that in the group of more than two people that there are at least two people that have the same number friends given the condition here.
How to go about this proofLet us create a variable P. P is an individual called Joe. Now Joes seems to know all at this party. This tells us that all at this party should at least know him.
We have the set {1,2,...n-1} , given that the minimum number of persons that one person knows is 1.
Let us assume we have Harry. Harry is a party crasher who came to the party. Hence it is possible that someone like Joe that knows all at the party may not even know him. Hence the maximum persons that a person would know is given to be n. The set would then be {0, 1,...,n-2}.
There are n elements in the 2 sets that we have above. Given that n people are at this function, and there are n possibilities for the number that one person can know of the participants, then we can say that at least two people can then know equal number of persons at the party.
Read more on word problems here
https://brainly.com/question/21405634
#SPJ1
ucscout word problem define the variables. (see screenshot) please help
Integrated math 3
The exponential equation for the number of Bacterian Camels in Mongolia is:
[tex]P(t) = 600(0.982)^t[/tex]
The parameters can be described as follows:
P is the population after t years.A is the initial population.r is the decay rate, as a decimal.t is the time in years.What is an exponential function?A decaying exponential function is modeled by:
[tex]P(t) = A(1 - r)^t[/tex]
In which:
P is the population after t years.A is the initial population.r is the decay rate, as a decimal.t is the time in years.For this problem, the values of the parameters are given as follows:
A = 600, r = 0.018.
Then the equation is:
[tex]P(t) = A(1 - r)^t[/tex]
[tex]P(t) = 600(0.982)^t[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
Determine the missing information in the paragraph proof.
Given: Line PQ contains points (w, v) and (x, z) and line P'Q' contains points (w + a, v + b) and (x + a, z + b). Lines PQ and P'Q' are parallel.
Prove: Parallel lines have the same slope.
On a coordinate plane, 2 lines are shown. Line Q P goes through (w, v) and (x, z). Line Q prime P prime goes through (w + a, v + b) and (x + a, z + b).
Since slope is calculated using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction, the slope of both lines is equivalent to ________. It is given that the lines are parallel, and we calculated that the slopes are the same. Therefore, parallel lines have the same slopes.
The slope of both lines is mathematically equivalent to
[tex]Slope=\frac{(z - v)}{ (x - w)}[/tex]i
What is the slope of both lines is equivalent to?Generally, the equation for Slope is mathematically given as
[tex]S= dy / dx[/tex]
Therefore
[tex]Slope of PQ = \frac{(z - v)}{(x - w)}[/tex]
[tex]S of P'Q' =\frac{ (z + b - (v + b))}{((x + a) - (w + a))}\\\\S of P'Q' =\frac{ (z - v)}{(x - w)}[/tex]
The slopes of both lines are equivalent to
[tex]Slope=\frac{(z - v)}{ (x - w)}[/tex]
In conclusion, The slope of both lines is equivalent to
[tex]Slope=\frac{(z - v)}{ (x - w)}[/tex]
Read more about slope
https://brainly.com/question/3605446
#SPJ1
Answer:
A: z - v | x - w
Step-by-step explanation:
In the triangle below, what is the measure (in degrees) of angle X?
66°
55°
X
Answer:
59
Step-by-step explanation:
Angle degrees in a triangle add up to 180
66+55+x=180
121+x=180
x=59
Answer
59°
Step-by-step explanation:
A triangle's angles add up to 180°.
So to find the last angle of the shape, you need to add the given angles and then subtract the answer from 180° looking like this:
66° + 55° = 121°
180° - 121° = 59°
14. Kathy lives directly east of the park. The football field is directly south of the park. The library (1 point) sits on the line formed between Kathy's home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 9 miles from her home. The football field is 12 miles from the library.
Park
Home
9 miles
Library
12 miles
Football field
a. How far is the library from the park?
b. How far is the park from the football field?
6.√3 miles; 6.7 miles
6.7 miles: 6.3 miles
√33 miles. √21 miles
√21 miles, √33 miles
Answer:
(a) 6√3, 6√7
Step-by-step explanation:
The right triangles shown are all similar, so corresponding sides are proportional. This gives rise to three "geometric mean" relations between the various lengths.
Geometric mean relationsUsing P, F, L, and H to represent the points marked Park, Football field, Library, and Home, the relations are ...
PF/FH = FL/PF ⇒ PF = √(FH·FL)
PL/FL = HL/PL ⇒ PL = √(FL·HL)
PH/HL = HF/PH ⇒ PH = √(HL·HF)
Application(a) The distance from the park to the library is ...
PL = √(FL·HL) = √(12·9) = 6√3 . . . miles
(b) The distance from the football field to the park is ...
PF = √(FH·FL) = √(21·12) = 6√7 . . . miles
what formula would i need to use to graph the relationship of volume of surface area of a cylinder?
The formula is illustrated below:
Volume of cylinder = πr²hSurface area = 2πrh + 2πr²How to illustrate the information?It should be noted that a cylinder simply means a three dimensional solid which holds two parallel bases that are joined by a curved surface.
In this case, it can be seen that the formula that can be used to calculate the volume and the surface area of the cylinder is illustrated above.
Learn more about cylinder on:
brainly.com/question/76387
#SPJ1
Allen is 5 feet 9 inches tall, terrel is 6 feet 2 inches tall. what is the average height
The average height is [tex]5feet[/tex] and [tex]11.5[/tex] inches if Allen is [tex]5 feet 9 inches[/tex] tall and Terrel is [tex]6 feet 2 inches[/tex] tall.
How to find the average height ?
Allen height is [tex]5feet ,9inches[/tex]
Terrel height is [tex]6feet,2inches[/tex]
And we know that [tex]1feet=12inches[/tex]
So Allen height is
[tex]=5*12+9\\=60+9\\=69 inches[/tex]
And Terrel height is
[tex]=6*12+2\\=72+2\\=74inches[/tex]
Average of the Allen and Terrel height is
[tex]\frac{69+74}{2\\} \\=143/2\\=71.5inches[/tex]
And average height in feet is [tex]5feet,11.5inches[/tex]
Learn more about the average height is here:
https://brainly.com/question/28048854
#SPJ4
i’ll give brainliest
Answer:
5
Step-by-step explanation:
-2x - y = -3
y = -3x + 2
-2x - (-3x + 2) = -3
-2x + 3x - 2 = -3
x = -1
y = -3*-1 + 2 = 5
Need help understanding how to find the answer to problem
Answer:
3.Tan(45)=n/2
1=n/2
n=2
Cos(45)=2/m
1/√2=2/m
m=2√2
5.Sin(60)=x/14
√3/2=x/14
14√3/2=x
x=7√3
Cos(60)=y/14
1/2=y/14
y=7
1. What is the domain and range of the
graph shown?
-10 S
2799
-24
Answer:
D: (-∞,∞)
R: (0,∞)
Step-by-step explanation:
This is a parabola, so the domain of this function is always:
D:(-∞,∞)
The y-values of this parabola do not go any lower than 0, and it goes upwards in the positive y-direction. So, the range for this function is:
R:(0,∞)
A $6$-sided die is weighted so that the probability of any number being rolled is proportional to the value of the roll. (So, for example, the probability of a $2$ being rolled is twice that of a $1$ being rolled.) What is the expected value of a roll of this weighted die
The expected value of a roll of this weighted die is; 13/3 or 4.33
How to find the Expected Value?We are given that;
A $6 sided die is weighted.
Probability of any number being rolled is proportional to the value of the roll.
Probability of a $2 being rolled is twice that of a $1 being rolled.
Thus, the expected Value is;
E(x) = (1*1 + 2*2 + 3*3 + 4*4 + 5*5 + 6*6)/(1 + 2 + 3 + 4 + 5 + 6)
E(x) = 13/3 = 4.33
Read more about Expected Values at; https://brainly.com/question/24855677
#SPJ1
Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
Answer: no, it's not similar because we cannot multiply it by any factor that the ratio will be the
Step-by-step explanation:
11 points
please help me
Answer:
40%
8%
15%
37%
Step-by-step explanation:
The solutions are in the image
How is 6.3 written in scientific notation? 6.3 times. 100 63 times. 10–1 6.3 times. 101 63 times. 100
The scientific notation of 6.3 is written as 6.3 × 10^0; option A
Scientific notationThe decimal points should be moved between the first digit and the next digit.When moving decimal point to the left in scientific notation; it is negative, that is, -When moving decimal point to the right in scientific notation; it is positive, that is, +Therefore, since there are only two significant number in 6.3, the decimal point can not be moved.
6.3 in scientific notation
= 6.3 × 10^0
Learn more about scientific notation:
https://brainly.com/question/5756316
#SPJ1
Answer: A
Explanation: 6.3 x 10^0
WILL VOTE BRAINLIEST FOR THE FIRST RIGHT ANSWER
Answer:
last choice
Step-by-step explanation:
The domain is the set of x values: from -3 to 3.
The range is the set of y values: from 1 to 10.
Answer: last choice
A variable that can only take on specific numeric values is called a _____. Group of answer choices categorical variable discrete random variable continuous random variable categorical variable
A variable that can only take on specific numeric values is called A discrete random variable.
According to the statement
A variable which is used to select a specific numeric value and we have to find a those variable
A discrete random variable is one which may take on only a countable number of distinct values.
So, A variable that can only take on specific numeric values is called A discrete random variable.
Learn more about VARIABLES here https://brainly.com/question/5030068
#SPJ4
Josie has 16 coins. Each of her coins is either a quarter or a dime. If she has 6 more dimes than quarters, and the total value is $2.35, how many quarters does Josie have?
Josie has a total of 5 quarters.
How to find the number of quarters using equation?Josie has 16 coins. Each of her coins is either a quarter or a dime.
Let
x = number of quarters
y = number of dime
she has 6 more dimes than quarters.
Therefore,
y = 6 + x
x + y = 16
-x + y = 6
2y = 22
y = 11
11 = 6 + x
x = 11 - 6
x = 5
learn more on equation here: https://brainly.com/question/26404595
#SPJ1
How many triangles are there?
Answer:
15 triangles.
Step-by-step explanation:
just count them eventually you will reach there.
Given the right triangle below, for the Pythagorean theorem, in which a 2 + b 2 = c 2, which side would represent the side "c." Hint: look at this triangle and the names of the angles.
Answer:
line segment AC (hypotenuse)
Step-by-step explanation:
The Pythagorean Theorem states that the sum of squares of the base/height of the triangle will equal the hypotenuse squared which is what c is equal to. So the c would represent the hypotenuse which is the side from the points A to C in the diagram.
The function f(x) = 200(0.5)x/50 models the amount in pounds of a particular
radioactive material stored in a concrete vault, where x is the number of years since
the material was put into the vault. Find the amount of radioactive material in the
vault after 140 years. Round to the nearest whole number.
Answer:
29 years
Step-by-step explanation:
Given the function [tex]f(x)= 200(0.5)^{\frac{x}{50} }[/tex], where x stands for the number of years since the material was put into the vault, we can plug 140 into x to find the amount leftover.Another way of doing this is to change the function to [tex]f(x)=200(0.5^{\frac{1}{50} })^{x}[/tex] which are equivalent functions, and then plug 140 into x. This function is helpful if you also needed to find the rate. I'll use the 1st function because the question doesn't ask for the rate[tex]f(x)= 200(0.5)^\frac{140}{50}}[/tex]
From here I'll just use a calculator & get 28.7, or 29 years.
Several different roadways are in the same region as the railroad.
Part A: A highway's path can be found using the equation 2x+3y=21. Use the graphs of the functions to determine the number of intersections there will be between the railroad and the
highway, and explain completely. (5 points)
Part B: A turnpike's route is determined by the equation y=x2 Prove algebraically how many intersections there will be between the railroad and the turnpike, showing all necessary
work. (5 points)
There are 0 intersections between the railroad and the highway and there are 2 intersections between the railroad and the turnpike
The number of intersections there will be between the railroad and the highwayFrom the graph, we have the following points on the railroad
(x, y) = (3, 3) and (0, 5)
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
This gives
m = (5 -3)/(0 - 3)
Evaluate
m = -2/3
The equation is then calculated as:
y = mx + b
This gives
y = -2/3x + b
Substitute (0, 5)
5 = -2/3 * 0 + b
This gives
b = 5
Substitute b = 5 in y = -2/3x + b
y = -2/3x + 5
Multiply through by 3
3y = -2x + 15
Rewrite as:
2x + 3y = 15
The equation of the highway's path is
2x+3y=21
So, we have:
2x+3y=21
2x + 3y = 15
Subtract the equations
2x - 2x + 3y - 3y = 21 - 15
Evaluate
0 = 6
The above equation is false because 0 and 6 are not equal.
This means that the system of equations have no solution
Hence, there are 0 intersections between the railroad and the highway.
How many intersections there will be between the railroad and the turnpike?Here, we have
y = x^2 and 2x + 3y = 15
Substitute y = x^2 in 2x + 3y = 15
2x + 3x^2 = 15
Rewrite as:
3x^2 + 2x - 15 = 0
Calculate the discriminant using
d =b^2 - 4ac
This gives
d = 2^2 - 4 * 3 * -15
Evaluate
d = 184
The discriminant d is greater than 0.
This means that the equation has 2 real solutions
Hence, there are 2 intersections between the railroad and the turnpike
Read more about linear and quadratic functions at:
https://brainly.com/question/13594844
#SPJ1