The equation of an ellipse with center, (h, k) that is elongated in the x-direction is: (x - h)²/a² + (y - k)²/b² = 1.
What is defined as the ellipse?In aspects of locus, an ellipse is the collection of every point on an XY-plane with whom the distance from 2 fixed points (called foci) adds up to the a constant value.
Ellipse does have two focal points, which are also known as foci.A fixed distance is referred to as a directrix.The eccentricity of an ellipse ranges from 0 to 1.The total sum of every distance from an ellipse's locus to its two focal points is constant.Ellipse contains a single major and one minor axis, as well as a center.The standard form of equation of ellipse with centres (h, k) that is elongated in the x-direction is given as;
(x - h)²/a² + (y - k)²/b² = 1
Now, when the centre of the ellipse coincides with the origin of coordinates axis, the becomes;
x²/a² + y²/b² = 1
Thus, the equation of ellipse of obtained.
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someone help me please!
The y intercept of the function f(x) = 2^2−4 is 0
The x intercept of the function f(x) = 2^2−4 is 0 or 2
The zeros of the function f(x) = 2^2−4 is 0 or 2
When f(x) = f(-4) then the function f(-4) = 48
When f(x) = 2 then x = -0.4142 or 2.142
How to fine the intercepts and the zeros
given data
f(x) = 2^2 − 4
The y intercept
f(x) = 2^2−4
y = 2^2−4
at x = 0
y = 2 ( 0 ) ^2 - 4 ( 0 )
y = 0 - 0
y = 0
The x intercept
f(x) = 2^2 − 4
y = 2^2− 4
at y = 0
0 = 2^2− 4
0 = 2x( x - 2 )
2x = 0 OR x - 2 = 0
x = 0 OR x = 2
The zeros
This same as the x intercept
f(-4)
f(x) = 2^2− 4
f(-4) = 2 (-4)^2 - 4 * -4
f(-4) = 2 * 16 + 16
f(-4) = 48
f(x) = 2 when x =
f(x) = 2^2− 4
2 = 2x( x - 2 )
1 = x^2 - 2x
0 = x^2 - 2x - 1
x = -0.4142 or 2.142
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If x= -12 and y=8 then what is the value of 2/x-3/ - /2y/ over /x+y/
If x= -12 and y=8 then the value of 2/x-3/ - /2y/ over /x+y/ is: 7/2. See the explanation below.
First, recall that the numbers enclosed in | | are absolute values. That is they remain in the positive domain regardless of their polarity. Recall that the absolute value is the distance between a number and Zero.
Since we know:
x = -12; and
y = 8
Hence,
[2|x-3| - |2y|] / |x+y|
= [2|-12-3| - |2 * 8| ]/ (|-12+8|)
= [2|-15| - | 16|] / |-4|
= ((2*15) - (16))/4 [Using the absolute values]
= (30 -16)/4
= 14/4
= 7/2
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What is the value of the expression −42 − 19 − (−24)?
−85
−61
−47
−37
Answer:
–37
Step-by-step explanation:
–42 – 19 – (–24)
–42 – 19 + 24
–61 + 24
= –37
help me im having trouble solving this
Step-by-step explanation:
[tex]sa = 2\pi \: r {}^{2} + 2\pi \: rh \\ = 2 \times 3.14 \times 3 { }^{2} + 2 \times 3.14 \times 11[/tex]
a motar racing circuit has length 5 5/6 miles. A straight section of the circuit has a length 1 1/4 miles. what fraction of the circuit is the straight section. give your answer in the simplest form
The fraction of straight section of motor racing circuit is 3/14 miles.
To find the fraction of circuit which is straight, we will perform division. The fraction will be found as - Fraction = length of straight section ÷ total length of motor racing circuit
Keep the values in mentioned relation to find the fraction of circuit which is straight.
Converting the mentioned lengths from mixed fraction to fraction.
Length of motor racing circuit = (6×5 + 5)/6
Length of motor racing circuit = 35/6
Length of straight section of circuit = (4×1 + 1)/4
Length of straight section of circuit = 5/4
Fraction of straight circuit = (5/4)/(35/6)
Simplifying the fraction
Fraction of straight circuit = (5×6)/(35×4)
Performing multiplication in numerator and denominator
Fraction of straight circuit = 30/140
Performing division
Fraction of straight circuit = 3/14 miles
Thus, the straight section is 3/14 miles.
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x = ____ (look at the photo)
Use the given information to determine which lines if any, I'm the figure to the right are parallel. Justify each conclusion with a theorem or postulate.
The complete statement would be 'Because it is given that ∠2 is supplementary to ∠3, lines a and b are parallel by Same-Side Interior Angles Postulate'
In this question, we have been given some information about lines a, b, k and m.
We need use this information and determine which lines in the figure are parallel.
We have been given angle 2 is supplementary to angle 3.
We know that, the sum of the angles on the same side of the transversal which are inside the two parallel lines is always 180°
Also, supplementary angles are the angles whose sum is 180°
i.e., ∠2 + ∠3 = 180°
From above we conclude that, the lines and b are parallel and line k would be the transversal.
Therefore, the complete statement would be 'Because it is given that ∠2 is supplementary to ∠3, lines a and b are parallel by Same-Side Interior Angles Postulate'
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Solve the inequality. (NESTED absolute value inequality)
[tex]||x-5| -4| \leq 1[/tex]
The result of the Nested absolute inequality when resolved gives:
x = -10, 0. See the solution below.
It is to be noted that when one absolute-value expression is inside another one, this is called a "nested" expression. Absolute expressions are expressions that values that can NEVER be negative.
The solution hence is given as follows:
Given: ||x-5|4|≤1
One absolute-value expression is stacked inside another in this equation. I'll work from the outside in, sorting items into their respective cases. Assume the argument of the outer bars is negative (do the "minus" case):
Step 1 - first splitting:
|x-5| -4 ≤ -1
|x-5| ≤ 3
I have to stop here since the last statement above states that an absolute value equals a negative number. Absolute values, on the other hand, are never negative! As a result, this step is invalid; it yields no viable solutions to the original problem.
Now I'll look at the scenario where the argument of the outside bars is positive (the "plus" case):
|x-5| -4 ≤ 1
|x-5| ≤ 1 + 4
Recall that absolute values are never negative. This equation is correct, and I've isolated the leftover absolute value, so I'll go over the two situations again.
Step 2 - First, consider the "minus" case:
x+5 ≤ -5
x ≤ -5-5
x≤ -10
The variable can have a "minus" value; the sole constraint is that an absolute-value expression cannot have a "minus" value. Now consider the "plus" case:
⇒ x + 5 ≤ 5 again recall that this is an absolute expression hence the laws of polarity while cross the inequality sign is suspended.
x ≤ 5-5
x≤0
Hence the answer which is complete is:
x = -10, 0
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what is the percent of 10 of 20 please give me a better understanding
We need to calculate the 10% of 20. By definition, a% is:
[tex]a\text{ \%}=\frac{a}{100}[/tex]Where a can be any positive number. In this case a = 10, then:
[tex]10\text{ \%}=\frac{10}{100}=\frac{1}{10}[/tex]In mathematics, the word "of" is reserved for the product. Then 10% of 20 is just:
[tex]10\text{ \% of }20=\frac{1}{10}\cdot20[/tex]Solving this leads to 2.
Answer:
50 percent.
Step-by-step explanation:
10 of 20 as a fraction is
10/20
- divide top and bottom by 10 and this simplifies to
1/2.
To convert to a percentage we multiply by 100:
= 1/2 * 100
= 50%.
Which of the equations are true identities?
\begin{aligned} \text{A. }&(5b-2)^2+4=25b^2-20b \\\\ \text{B. }&(2x^2+y^2)(2x^2-y^2)=4x^2-y^2 \end{aligned}
A.
B.
(5b−2)
2
+4=25b
2
−20b
(2x
2
+y
2
)(2x
2
−y
2
)=4x
2
−y
2
The given equations (5b - 2)² + 4 = 25b²– 20b and (2x² + y²)(2x² - y²) = 4x² – y have been found not to be true identities
What is the True Identity of the Algebra Expression?A) We want to check if (5b - 2)² + 4 = 25b²– 20b is a true identity.
A true identity is an equality that holds true regardless of the values chosen for its variables. They are used in simplifying or rearranging algebra expressions. By definition, the two sides of an identity are interchangeable, so we can replace one with the other at any time.
(5b - 2)² + 4 when expanded gives;
25b² - 20b + 4 + 4 = 25b² - 20b + 8
That is not equal to the right hand side and as such, we can say that both equations are not true identities
B) (2x² + y²)(2x² - y²) = 4x² – y
Expand the left side to get;
4x⁴ - y⁴
This result is not equal to the right hand side and as such, we can say that both equations are not true identities.
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Correct question is;
Which of the equations are true identities?
A. (5b - 2)² + 4 = 25b²– 20b
B. (2x² + y²)(2x² - y²) = 4x² – y
a/-8= - a+10/3
solve for A
Step-by-step explanation:
you can ask questions for clarification
Determine which integer will make the inequality x − 4 < 16 true.
S:{16}
S:{20}
S:{21}
S:{32}
Answer:
it's S:21
i had this same question lol
NP and QS areparallellines. M N O P Q R S T Which angles are supplementary angles? NOM and NOR NOM and QRO NOM and POR NOM and SRT Submit
The angles that are supplementary angles are: ∠SRT and ∠SRO
What are Supplementary Angles?Angles that are supplementary will give us a sum of 180 degrees when we add the two angles together. One is the supplement of the other.
Some examples of angles that are supplementary angles that are formed when two parallel lines are intersected by a transversal include:
Same-side interior anglesSame-side exterior anglesLinear pair angles formed on a straight line and are adjacent to each other.Angle SRT and angle SRO are angles that are adjacent to each other because they share a common side SR and a common vertex R. They line on the straight line OT.
Therefore, angle SRT and angle SRO are two angles that are supplementary angles as shown in the diagram attached below where lines NP and QS are parallel lines. The supplementary angles are therefore angle SRT and angle SRO.
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Chris designs a flag.
20% of the flag is white and the rest is pink.
What is the ratio of white to pink?
A polygon is shown on the graph: A polygon is shown on a coordinate plane. The vertices are A at negative 6 comma 5, B at negative 6 comma 2, C at negative 2 comma 2, and D at negative 2 comma 6. If the polygon is translated 4 units down and 5 units right, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates. (5 points)HELP ASAP
The coordinates of the image of polygon A'B'C'D' would be A' (-1, 1), B' (-1, -2), C' (3, -2), D' (3, 2).
What is a translation?A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.
Since the pre-image of polygon ABCD is translated (shifted) vertically downward by 4 units and right 5 units, the coordinates of the image of polygon A'B'C'D' would be given by:
(x, y) → (x + 5, y - 4)
Coordinate A = (-6, 5) → Coordinate A' (-6 + 5, 5 - 4) = (-1, 1)
Coordinate B = (-6, 2) → Coordinate B' = (-6 + 5, 2 - 4) = (-1, -2)
Coordinate C = (-2, 2) → Coordinate C' = (-2 + 5, 2 - 4) = (3, -2)
Coordinate D = (-2, 6) → Coordinate D' = (-2 + 5, 6 - 4) = (3, 2)
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A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 12 cm can be placed in the given cuboid?
56 small cubes can be placed in the given cuboid that has the given dimensions.
What is the Volume of a Cuboid?A cuboid's volume can be calculated using the formula below:
Volume of a cuboid = (length)(width)(height).
How to Find the Volume of a Cube?A cube has equal height, length, and width. Therefore, the volume of a cube is calculated as:
Volume of a cube = (side length)³.
The number of small cubes that can be placed in the given cuboid = volume of the cuboid/volume of one small cube.
Find the volume of the cuboid:
Length = 60 cm
Height = 54 cm
Width = 30 cm
Volume of the cuboid = (60)(54)(30)
Volume of the cuboid = 97,200 cm³
Find the volume of one cube:
Side length of one small cube = 12 cm
Volume of one small cube = (12)³
Volume of one small cube = 1,728 cm³.
Number of small cubes that will be placed in the cuboid = 97,200/1,728 ≈ 56 cubes.
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help please I rlly need help
Answer:
9. 160/2
10. 270/9
Step-by-step explanation:
To find unit rates, divide the top number (numerator) by the bottom number (denominator).
9.
160/2 = 80 mph
210/3 = 70 mph
10.
270/9 = 30 ft/min
180/9 = 20 ft/min
Each morning Martina attempts a
crossword and a Sudoku.
The probability that Martina successfully
completes the crossword is 0.3.
The probability that Martina successfully
completes the Sudoku is 0.6
a) Show this information on a tree
diagram in your books
b) What is the probability she
successfully completes both puzzles?
c) What is the probability that she
successfully completes at least one
puzzle?
Using the probability concept, it is found that:
a) The tree diagram is given by the image at the end of the answer.
b) The probability is of 0.18 = 18%.
c) The probability is of 0.72 = 72%.
What is a probability?A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.
For item a in this problem, we have two independent events, hence the tree diagram will contain two nodes, one with each event and it's probabilities.
For item b, since the events are independent, to find the probability of both, we multiply the probability of each, hence:
0.3 x 0.6 = 0.18.
For item c, first we find the probability of none being completed, hence:
(1 - 0.3) x (1 - 0.6) = 0.7 x 0.4 = 0.28.
At least one is complementary to none, hence the probability is given as follows:
p = 1 - 0.28 = 0.72 = 72%.
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Write an algebraic expression for each verbal expression
22. x more than 7
24. 5 times a number
26. f divided by 10
28. three times a number plus 16
30. k squared minus 11
32. the sum of a number and 10
34. the product of 18 and q
23. a number less 35
25. one third of a number
27. the quotient of 45 and r
29. 18 decreased by 3 times d
31. 20 divided by t to the fifth power
33. 15 less than the sum of k and 2
35. 6 more than twice m
Step-by-step explanation:
22. 7 + x
24. 5x
26. f/10
28. 3x + 16
30. k² - 11
32. x + 10
34. 18q
23. x - 35
25. x/3
27. 45/r
29. 18 - 3d
31. 20/t⁵
(although, if being superficial, it could mean (20/t)⁵)
33. (k + 2) - 15
35. 2m + 6
Using the figure below, Maggie used the definition of vertical angles to help her solve for x. Since vertical angles are congruent, she set the two given expressions equal to each other. After solving for x, her teacher said she got the wrong value for x. Explain where Maggie made her mistake when solving for x.
Using vertical angles, Maggie made her mistake when combining the like terms of x, which has a result of -3x and not 3x, hence the correct result is of x = 9.
What are vertical angles?Vertical angles are two angles that are opposite by the same vertex when two lines cross each other, and they are congruent, that is, they have the same measure.
For this problem, the vertical angles are given as follows:
4x + 2.7x - 25.Since they are congruent, we can solve for the variable x as follows:
4x + 2 = 7x - 25.
Moving all the terms with x to the left side of the equality and all the constant terms to the right side, with opposite signal, we have that:
4x - 7x = -25 - 2
Combining the like terms, it is found that:
-3x = -27.
Here happened Maggie's mistake, as 4x - 7x = -3x, hence the correct solution is given by:
3x = 27
x = 27/3
x = 9.
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Suppose line m passes through the points (6, 10) and (1, 6) & line n passes through the points (2, -1) and (8, 5).
PLA HELP URGENT NOWWWWWWW
WHAT ARE LINES M AND N PERPENDICULAR, PARALLEL OR NEITHER!!!!!
Line m passes through the points (6, 10) and (1, 6) & line n passes through the points (2, -1) and (8, 5) , both the lines are neither parallel nor perpendicular.
As given in the question,
Given two lines 'm' and 'n'
Line m passes through the points
(x₁ ,y₁) =(6,10)
(x₂ ,y₂)=(1,6)
Slope of the line m 'm₁'
= (y₂ -y₁)/ (x₂ -x₁)
= (6 -10) / (1 - 6)
=-4 / -5
=4 / 5
Line n passes through the points 'm₂'
(x₁ ,y₁) =(2,-1)
(x₂ ,y₂)=(8 ,5)
Slope of the line m
= (y₂ -y₁)/ (x₂ -x₁)
= (5 - (-1)) / (8 - 2)
= 6 / 6
= 1
m₁ ≠ m₂
m₁ × m₂ ≠-1
Therefore, line m passes through the points (6, 10) and (1, 6) & line n passes through the points (2, -1) and (8, 5) , both the lines are neither parallel nor perpendicular.
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Please help!! I’ve been stuck on this for days
Answer
Step 1: 6,3
Step 2: x1 -1 y2- 2
Step 3: 1, 7
Step-by-step explanation:
Ron is renting an apartment and his landlord just raised his rent.he now pays 1500 and his rent will go up 10%.what will be the new payment
Answer:
it would be 150 more, so 1650
Step-by-step explanation:
divide 1500 by 10 to get 10%
Identify the correct justification for each step, given that m∠1+m∠2=90° and m∠2+m∠3=90°.
The two column proof to justify the complementary angles are;
Statement 1. ∠1 and ∠2 are complementary
∠2 and ∠3 are complementary
Reason 1: Given
Statement 2: m∠1 + m∠2 = 90°
Reason 2: Definition of Complementary Angles
Statement 3. m∠2 + m∠3 = 90°
Reason 3: Definition of Complementary Angles
Statement 4: m∠1 + m∠2 = m∠2 + m∠3
Reason 4: Transitive property of equality
Statement 5: m∠1 = m∠3
Reason 5: Substitution Property of Equality
What are the Complementary angles?
Complementary angles are defined as angles that sum up to 90 degrees.
Now, from the question, we are given that;
∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.
From the image attached, we can get a two column proof based on the given questions as;
Statement 1. ∠1 and ∠2 are complementary
∠2 and ∠3 are complementary
Reason 1: Given
Statement 2: m∠1 + m∠2 = 90°
Reason 2: Definition of Complementary Angles
Statement 3. m∠2 + m∠3 = 90°
Reason 3: Definition of Complementary Angles
Statement 4: m∠1 + m∠2 = m∠2 + m∠3
Reason 4: Transitive property of equality
Statement 5: m∠1 = m∠3
Reason 5: Substitution Property of Equality
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Complete Question is;
Identify the correct justification for each step, given that ∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.
1. ∠1 and ∠2 are complementary
∠2 and ∠3 are complementary
2. m∠1 + m∠2 = 90°
3. m∠2 + m∠3 = 90°
4. m∠1 + m∠2 = m∠2 + m∠3
5. m∠1 = m∠3
20 points
Help………please
The coordinates of the point X are (1 + 2, 6 - 1.25) = (3,4.75).
The segments, PX and XQ, have lengths in a ratio of 1: 2.
What is meant by partition segment?A line segment is partitioned when it is divided into equal parts according to a specified ratio. The total number of partitions of the line segment must be equal to the sum of the two values in the ratio.
Suppose you have a line segment PQ on the coordinate plane, and you need to estimate the point on the segment 1/3 of the way from P to Q.
Where P exists at the origin and line segment is a horizontal one.
The length of the line exists 6 units and the point on the segment 1/3 of the way from P to Q would be 2 units away from P, 4 units away from Q and would be at (2, 0).
The segment exists not a horizontal or vertical line:
The components of the directed segment PQ exists (6, 3) and we require to estimate the point, say X on the segment 1/3 of the way from P to Q. Then, the components of the segment PX exists [tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(3)\right\rangle=\langle 2,1\rangle$[/tex].
Since the initial point of the segment exists at origin, the coordinates of the point X exists given by (0+2, 0+1) = (2, 1).
where neither P nor Q exists at the origin.
Use the end points of the segment PQ to estimate the components of the directed segment.
[tex]$\left\langle\left(x_2-x_1\right),\left(y_2-y_1\right)\right\rangle=\langle(7-1),(2-6)\rangle \\[/tex]
= (6, -4)
The components of the segment PX where X exists a point on the segment 1/3 of the way from P to Q are
[tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(-4)\right\rangle[/tex]= (2, -1.25)
To estimate the coordinates of the point X add the components of the segment PX to the coordinates of the initial point P.
Therefore, the coordinates of the point X exists (1 + 2, 6 - 1.25) = (3,4.75).
The segments, PX and XQ, have lengths in a ratio of 1: 2.
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what is the expression for t-3
The mathematical statement of the expression t - 3 is the difference between t and 3
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the expression?The algebraic expression is given as
t - 3
The above mathematical representation is an algebraic expression that is already in its most simplified form
This means that the algebraic expression cannot be further simplified
However, the algebraic expression can be rewritten as a mathematical statement
Recall that, we have
t - 3
The pronunciation of the above expression is:
t minus 3
In expressions, minus represents difference
So, we have
t minus 3 can be represented as the difference between t and 3
Hence, the representation of the algebraic expression given as t - 3 is the difference between t and 3
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6. three different distributions there are 559 full-service restaurants in delaware. the mean number of seats per restaurant is 99.2. [source: data based on the 2002 economic census from the us census bureau.] suppose that the true population mean µ
The standard deviation of the distribution of sample means (that is, the standard error, sigma_m) is; 2.9698
How to find the standard error of mean?From the complete question written below, we are given that;
Mean Number; M = 103.4
Standard deviation; σ = 21
Sample size; n = 50
Now, in statistics, the formula for the standard error of mean is;
σM = σ/√n
Plugging in the relevant values gives us;
σM = 21/√50
σM = 2.9698
The z score typical average difference between the mean number of seats is;
z = (103.4 - 99.2)/( 2.9698 )
z = 1.41
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Complete Question is;
There are 559 full-service restaurants in Delaware. The mean number of seats per restaurant is 99.2. [Source: Data based on the 2002 Economic Census from U.S. Census Bureau.]
Suppose that the true population mean mu = 99.2 and standard deviation sigma = 21 are unknown to the Delaware tourism board. They select a simple random sample of 50 full-service restaurants located within the state to estimate mu. The mean number of seats per restaurant in the sample is M = 103.4, with a sample standard deviation of s = 18.2. The standard deviation of the distribution of sample means (that is, the standard error, sigma_m) is_.
Find the value of the variables
Answer:
x = 3y
y + x = 4y = 180
y = 45
x = 135
I keep getting 0.33... but it says it wrong i need it as a fraction
Answer:
1/3
Step-by-step explanation:
0.3333...=1/3
What is the radical form of the expression? (5x3y4)37
The Radical Form is [tex]185x^3y^4[/tex].
What is the Radical Form?
If n is a positive integer that is greater than 1 and 'a' is a real number then,
[tex]n\sqrt{a} = a1n[/tex] where n is called the index, a is called the radicand, and the symbol [tex]\sqrt{}[/tex] is called the radical. The left side of this equation is often called The radical form and the right side is often called the exponent form.
Now, The question is :
The Expression is : (5x3y4)37
Convert to Radical form by using the formula :
[tex]a^\frac{x}{n} = \sqrt[n]{a^x}[/tex]
(5x3y4)37 = [tex]185x^3y^4[/tex]
Therefore, The Radical Form is [tex]185x^3y^4[/tex]
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