After the use of fractional exponents give us the value 8√(x²y⁴) is 2³(x²y⁴)¹/₂.
Exponent:
Exponent is refers the way of writing the words, "raised to the power". And it is used to show that a number has been raised to a certain power.
Given,
Here we have the expression 8√(x²y⁴).
Now, we need to simplify the fractional exponents.
When we rewritten the expression like the following,
=> 8√(x²y⁴)
While we looking at these expression we know that, the number 8 can be written as the multiple of 2,
So, it can be written as,
=> 8√(x²y⁴) = 2³√(x²y⁴).
So, in the simplified form it can be written as,
=>8√(x²y⁴) = 2³(x²y⁴)¹/₂.
Therefore, the simplified form is 2³(x²y⁴)¹/₂.
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Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y = 8x - 6
Step-by-step explanation:
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
We know that the y-intercept occurs when x = 0 so from the table, it's b = -6
We can use the slope formula to find the slope:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\\ \frac{2-(-6)}{1-0} \\\frac{2+6}{1-0} \\8=m[/tex]
can you guys help me with these?
the distance y (in miles) that train A travels in x amount of time is represented by the equality y=78x. The graph shows the distance that train B travels.
URGENT PLS ANSWER!!!
ty!
We can conclude that train A is moving faster than train B
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have the following problem -
The distance y (in miles) that train A travels in [x] amount of time is represented by the equality y = 78x. The graph shows the distance that train B travels.
Train A is moving with speed s[A] = 78 miles/hour {As slope of the equation is 78}. The train B will move with speed given by -
s[B] = (132 - 66)/(2 - 1) = 66 miles/hour
Therefore, we can conclude that train A is moving faster than train B
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[In the complete question it is asking to find which train is moving faster]
Charis invested 140. She earned a simple interest of 3% per year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charis received at the end of two years?
The amount received by Charis on Simple interest in 2 years will be $8.4
What is Simple Interest?
The process of figuring out how much interest will accrue on a given principal sum of money is known as simple interest (S.I.).
It's formula is given by S.I. = PRT/100 where P = principle amount
R= rate and T = time.
Main Body:
P= $140
R= 3%
T= 2 years
so S.I. = 140*2*3/100
S.I. = $ 8.4
Hence total amount received by Charis at the end of 2 years will be $8.4
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help me please ! correct answer gets brainliest
The expressions that show the distance between P and Q are option (d) |-6| + (-2) and option (e) 6 - 2
From the given number line
The distance between P and Q = 4 units
Now we have to solve each expression
Expression 1
|-6| + |-2| = 6 +2
Add the terms
= 8
Expression 2
|2-(-6)| = | 2 + 6|
= |8|
= 8
Expression 3
|-2| - (-6) = 2 + 6
Add the terms
= 8
Expression 4
|-6| + (-2) = 6 - 2
Subtract the term
= 4
Expression 5
6 - 2 = 4
Hence, the expressions that show the distance between -6 and -2 are option (d) |-6| + (-2) and option (e) 6 - 2
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There are 11,357 pets in a town that has a population of 47,500. What is the number of pets per capita?
Round your answer to 2 decimal places.
The number of pets per capita is 0.24
Given,
Number of pets in a town = 11,357
Population of the town = 47,500
We have to find the number of pets per capita;
Per capita;-
The Latin phrase "per capita" means "by head." It is used to calculate the average for each individual in a certain measurement. Per capita is frequently used, for instance, to calculate a population's per capita gross domestic product (GDP).
Here,
Number of pets per capita = Number of pets / Population
Number of pets per capita = 11,357 / 47,500
Number of pets per capita = 0.24
That is,
The number of pets per capita is 0.24
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Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window.
H
HH represents the height of the tree (in centimeters),
t
tt years since Renata moved in.
H
=
210
+
33
t
H=210+33tH, equals, 210, plus, 33, t
How fast does the tree grow?
The required increasement of height of tree is 33 centimeters annually
What is function of time?Function of time is defined as the change of abject or expression of variables with time. As the time increases, there is change in shape, height, etc. is called function of time.
According to given data in the question:we have given an expression of height of tree,
H = 210 + 33t
Where t represent the time and H is height of tree.
So, Changes in the height of the tree with years,
for t = 1 year
⇒ H = 210 + 33×1 = 210 + 33 = 243 centimeters
Thus, the height of tree in increases by 33 centimeters yearly.
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Which expression is equivalent to 4f^2
e
/
1
4f
Answer:
4f^2/3 divided 1/4f 16f^3/3 f/3 3/16f^3 3/f
✓ Lets use algebra and simplify:[tex]\frac{\frac{4f^{2}}{3}}{\frac{1}{4f}} \\=\frac{4f^{2}}{3}* \frac{4f}{1} \\=…
the population of a town increased from 3450 in 2006 to 5700 in 2012. find the absolute and relative (percent) increase. absolute increase: relative increase:
Answer:
The absolute difference is 1050
The relative percentage is 32.3076%
Step-by-step explanation:
We are given
The population of a town increased from 3,250 in 2008 to 4,300 in 2010
In 2008:
In 2010:
Absolute difference:
we know that
absolute difference =
absolute difference =
absolute difference is 1050
Relative increase:
we know that
Relative percentage is
now, we can plug values
=32.3076
So, the relative percentage is 32.3076%
2 3/5 times 3 1/3
NEED ASAP
Answer:
Answer is: 8 2/3 but improper is 26/3
the nth term of a gp 145800. if the fist term is 2 and the common ratio is 3. find the sum of the gp
The sum of the geometric progression with the features stated in the text is given as follows:
S = 2.62 x 10^(43).
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of a finite geometric sequence with n terms is given as follows:
[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
In this problem, the first term and the common ratio are given as follows:
[tex]a_1 = 2, n = 3[/tex]
Hence the equation is:
[tex]a_n = 2(3)^{n - 1}[/tex]
The nth term is of 1458000, hence the number of terms of the sequence is obtained as follows:
[tex]a_n = 2(3)^{n - 1}[/tex]
[tex]1458000 = 2(3)^{n - 1}[/tex]
[tex]3^{n - 1} = 729000[/tex]
[tex]3^{n - 1} = 3^{90}[/tex]
Then:
n - 1 = 90
n = 91.
Thus the sum of the sequence is given as follows:
[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
[tex]S_{91} = \frac{2(1 - 3^{91})}{1 - 3}[/tex]
S = 2.62 x 10^(43).
Typing mistakeThe problem is solvable with an nth term of 1,450,800, not 145,800, as 145,800/2 is not a root of 3.
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Given: DEFG is a trapezoid DE=FG, DF=a, m∠FDG=45° Find: Area of DEFG
Answer:
DEFG = (1/2)a^2
Step-by-step explanation:
tells us ∠FDG = 45° and ∠EGD = 45° and by corresponding angles related to parallel lines ∠FBD = 45°. Then ∠DFB = 90°!
So DFB- (1/2)(DF)(FB)=(1/2)a2
Express your answer as a polynomial in standard form.
f(x)= -3x+5
g(x)=x^2+2x+15
Find: (g∘f)(x)
Answer: [tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]
=====================================================
Explanation:
The notation (g∘f)(x) is the same as g(f(x))
We'll start with the outer function g(x). Then replace each x with f(x). Afterward plug in f(x) = -3x+5 for the right hand side only.
This is what the steps look like
[tex]g(\text{x})=\text{x}^2+2\text{x}+15\\\\g(f(\text{x}))=(f(\text{x}))^2+2f(\text{x})+15\\\\g(f(\text{x}))=(-3\text{x}+5)^2+2(-3\text{x}+5)+15\\\\g(f(\text{x}))=9\text{x}^2-30\text{x}+25-6\text{x}+10+15\\\\g(f(\text{x}))=9\text{x}^2-36\text{x}+50\\\\[/tex]
Therefore,
[tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]
You can use tools like WolframAlpha, GeoGebra, and Desmos as ways to confirm the answer.
hello please help
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A small park in the shape of a rectangle has dimensions 20m by 50m. a road through the park follows the diagonal of the rectangle. find the length of the road in simplest radical form.
The length of the road in the simplest radial form is 10[tex]\sqrt{29}[/tex].
Here a rectangle of dimensions is 20m by 50m. So the length of 50m and the breadth is 20m
As the road is diagonal of the rectangle.
So we have to find the length of the diagonal of the rectangle.
Formula to find the diagonal of rectangle:
Diagonal = [tex]\sqrt{l^{2} + b^{2} }[/tex]
length (l) = 50m
Breadth(b) = 20m
Diagonal = [tex]\sqrt{50^{2} + 20^{2} }[/tex]
= [tex]\sqrt{2500 + 400}[/tex]
= √2900
= 10√29
Therefore the length of the road is 10√29.
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Time taken for a 3 litre bowl at a rate of 2 litre per minute
Thus, it takes 1.5 minutes {30 seconds} for filling a 3-litre bowl
Find g(x) if g(x) is the resulting function from moving f(x) = (x + 2) right 1 unit and up 6 units.
g(x) = (x+2-3) + 4 = (x-1)+4
What is the ordered pair for the reflection of the point (2,-1) over the x~axis
Answer:
(2,1)
Step-by-step explanation:
The x-value stays the same since we are only moving up/down and the y-value becomes the opposite
(x,y)--> (x,-y)
So the point becomes (2,1)
Answer:
(2,-1) hope this helps you understand
Y intercept = -1 and goes through the point (3,8)
The equation of a line for y-intercept and the coordinate point is y=3x-1.
Given that, y-intercept is -1 and the line passes through the point (3, 8).
What is a y-intercept?In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
Put, c=-1 and (x, y)=(3, 8) in y = mx+c, we get
8=m(3)-1
⇒ 3m=9
⇒ m=3
Substitute c=-1 and m=3 in y = mx+c, we get
y=3x-1
Therefore, the equation of a line for y-intercept and the coordinate point is y=3x-1.
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Given g(x)=x-4 and h(x)=2x-8use the graph shown to evaluate the composition (f•g)(0)
Answer:
(f ￮ g)(0) = 3
Step-by-step explanation:
evaluate g(0) then substitute the value obtained into f(x)
g(0) means what is the value of g(x) when x = 0
from the graph g(0) = 2 , then
f(2) , that is what is the value of f(x) when x = 2
from the graph f(2) = 3
then
(f ￮ g)(0) = 3
in a tournament there are six teams that play each other twice. a team earns 3 points for a win, 1 point for a draw, and zero points for a loss. after all the games have been played it turns out that the top three teams earned the same number of total points. what is the greatest possible number of total points for each of the top three teams?
The greatest possible number of total points for each of the top three teams is 24.
Given;
Six teams compete against one another twice in a tournament. A team receives three points for a victory, one point for a tie, and no points for a defeat. The top three clubs ended up with the same total number of points when all the games were completed.
After fully understanding the problem, we immediately know that the three top teams, say team A, team B, and team C, must beat the other three teams D, E, F. Therefore, A, B, and C must each obtain (3 + 3 + 3 ) = 9 points. However, they play against each team twice, for a total of 18 points against D, E, and F. For games between A, B, and C, we have 2 cases. There is an equality of points between A, B, and C in the following cases.
Case (I): A team ties the two other teams. For a tie, we have 1 point, so we have (1 + 1) * 2 = 4 points (they play twice).
Therefore, this case brings a total of 4 + 18 = 22 points.
Case (II): A team beats one team while losing to another. This gives equality, as each team wins once and loses once as well. For a win, we have 3 points, so a team gets 3 * 2 = 6 points if they each win a game and lose a game.
This case brings a total of 18 + 6 = 24 points.
Therefore, we use case (II) since it brings the greater amount of points as 24.
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the table below lists probabilities for the corresponding number of girls in three live births. what is the random variable, what are its possible values, and are its values all numerical?
The random variable in given problem is "x" . The possible values of random variable x are 0,1,2 and 3..
All possible values of random variable is numrical in nature.
We have a table to right lists probabilities for the corresponding number of girls in three live births.
from the table we cleary see that the random variable is x which represents the number of girls in three live births.
Random variable is a variable whose value is unknown or a variable which assigns a numerical value to each trials in Sample Space.
Also, we can see in list that the number of girls in three live birth values are 0, 1 ,2 and 3 ( 3 live birth)
So, the possible values of random variable x is 4 i.e., 0, 1, 2 and 3..
From data we get a result that all possible values of random variable and it's probabilities are numrical in nature.
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Please help me please help me
Answer:
the answer Is 6 .........
What is wrong I need help
I don’t understand it
Answer:
Step 2 is incorrect
Step-by-step explanation:
Step 2 is where you are distributing out -5. Step 2 should be distribution rather than division property of equality.
Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest. What was her initial deposit
Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest then the initial deposit was $4700
Use the simple interest formula
I = P r t
where I = simple interest
P = principal
r= rate of interest
t= number of years
5922=Px6.3%x20
5922=Px1.26
P=5922/1.26
P=4700
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Which system of equations is represented by the graph ?
A. y=x^2+2x+1
2x+y=2
B. y=x^2-2x+1
2x+y=2
C. y=x^2+2x+1
2x+y=2
D. y=x^2-2x+1
2x-y=2
y = x²-2x+1, 2x-y=2 is the system of equations represented by the graph
How to determine the system of equations represented by the graph?
By examining the graph, you will notice that the straight and the curve meet at (3,4) and (1,0) as indicated. The x values of these points of intersection give the solution of the system. Thus:
We have x = 3 and x = 1
These values can be used to form the equation of the system. Thus:
(x-3)(x-1) = 0 (Clear the parenthesis)
x² -x-3x +3 = 0
x² -4x +3 = 0
Next, we are going to check for the option that gives the x² -4x +3 = 0
Given: y = x²-2x+1, 2x-y=2
Rewrite 2x-y=2 to be in form y: y =2x-2
We now have y = x²-2x+1 and y =2x-2
Equate the two y: x²-2x+1 =2x-2
x²-2x+1 -2x+2 = 0
x²- 4x+ 3 = 0
Since y = x²-2x+1, 2x-y=2 gives the same equation, therefore, the system of equations represented by the graph is y = x²-2x+1, 2x-y=2. So option D is the answer
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what do you add to 3and 3/8 to make 6
21/8 must be added to the terms to give the result as 6. The answer will be in a fraction.
What is a fraction?
In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. In ordinary English, a fraction refers to the number of parts of a specific size.
Main Body:
Let the term to be added be x.
3+3/8+x =6
on solving this we will get the value of x= 21/8
Hence the answer of this question is 21/8.
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An 80 kg jumper in flight accelerates at a rate of 8 m/s^2. What is the force of the long jumper? F = ma
By taking the product between the mass and the acceleration, we will see that the force is:
F = 640 N
What is the force of the long jumper?
By the second Newton's law, we know that a force can cause motion on a body by accelerating it, such that the force is equal to the product between the mass of the object and the acceleration.
F = m*a
F = forcem = massa = acceleration.Here we know that:
m = 80kg
a = 8 m/s^2
Replacing that we get:
F = (80 kg)*( 8 m/s^2) = 640 N
Where N is the unit Newton.
1 N = 1 kg*m/s^2
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Write the set A = {1, 2, 3, 4, 5, …} in set-builder form and descriptive form.
(please notice that it is an infinite set)
a. The set in set builder form A = {x : x ∈ N}
b. the set in descriptive form, A = {set of natural numbers}
What is a set?A set is a collection of well defined items.
What is set builder form?Set builder form is a way of enumerating a set by using a set of rules which define its elements.
What is descriptive form?Descriptive form is a way of enumerating the elements of a set in words.
a. How to write the elements of the set in set builder form?Since we have the set A = {1, 2, 3, 4, 5, …}, which is the set of natural numbers ,N, we identify each element of the set as x and give it a rule that x is an element of N. That is x ∈ N.
So, in set builder form A = {x : x ∈ N}
b. How to write the elements of the set in descriptive form?Since we have the set A = {1, 2, 3, 4, 5, …}, which is the set of natural numbers ,N.
In descriptive form, we write that A = {set of natural numbers}
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How can I evaluate P = 3n+2r+t -1 when n=3, r=2, and t=5?
Answer:
p=17
Step-by-step explanation:
P = 3n+2r+t -1
when n=3, r=2, and t=5?
we will just substitute for the values
p=3(3)+2(2)+5-1
p=9+4+4
p=9+8
p=17
;- The value for p is 17
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