The equation of the line that passes through the point (8, 5) and perpendicular to y = −12x +7 is y = (1/12)x + 13/3.
We know that,
The product of the slopes of two perpendicular lines is -1.
The slope intercept form of a line is given by :-
y = mx + c
Comparing it with y = -12x + 7
We get,
m = -12 (slope of the line)
c = 7 (y-intercept of the line)
Let the slope of the line perpendicular to the given line be n.
Hence, we can write,
(-12)*n = -1
n = 1/12
Also, the line passes through (8,5).
Hence, we can write,
5 = (1/12)(8) + c
5 = 2/3 + c
c = 5 - 2/3 = 13/3
Hence, the equation of the line is given by :-
y = (1/12)x + 13/3
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Determine the total surface area of each pyramid with a regular polygon base
The total surface area of the pyramid (a) is 624.32 cm² , and of pyramid (b) is 265.6 m² .
The Total Surface Area of the Pyramid with pentagon base can be calculated using the formula
TSA = 5/2*b(a+s) ,
where b is the base length (side of pentagon)
s is the slant height ,
a is the apothem
and the Total Surface Area of the Pyramid with square base can be calculated using the formula .
TSA = b² + 2bs
where , b is the base and
s is the slant height .
Pyramid (a)
we can see from the figure that ,the pyramid has a pentagon base ,
So, the TSA will be 5/2*b(a+s) ,
in the figure , given that height =12 cm , apothem = 7.8cm
we find the slant height by Pythagoras theorem
(slant height)²=(height)²+(apothem)²
(slant height)² = 12² + 7.8²
(slant height) = √(12² + 7.8²)
(slant height) = √(144+60.84)
(slant height) = 14.3 cm
Substituting in TSA formula , TSA = 5/2*b(a+s)
we get ,
TSA = 5/2*11.3(7.8+14.3)
= 2.5*11.3(22.1)
= 28.25*22.1
=624.32 cm²
Pyramid (b)
we can see from the figure that ,the pyramid has a square base ,
So, the TSA will be b² + 2bs,
in the figure , given that height =12 m , apothem = 4 m
we find the slant height by Pythagoras theorem
(slant height)²=(height)²+(apothem)²
(slant height)² = 12² + 4²
(slant height) = √(12² + 4²)
(slant height) = √(144+16)
(slant height) = 12.6 m
Substituting in TSA formula , TSA = b² + 2bs
we get ,
TSA = 8² + 2*8*12.6
= 64 + 16*12.6
= 64 + 201.6
= 265.6 m²
Therefore , the total surface area of the pyramid (a) is 624.32 cm² , and of pyramid (b) is 265.6 m² .
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A group of friends wants to go to the amusement park. They have no more than $195 to spend on parking and admission. Parking is $9.75, and tickets cost $17.75 per person, including tax. Which inequality can be used to determine xx, the maximum number of people who can go to the amusement park?
Answer:
7
Step-by-step explanation:
assuming everyone takes their own car, 9.75+17.75 * 7 = 192 I don’t know the state tax, because each state is different but 192 gives about $3 worth of room for tax. If the tax is higher in your state maybe I’d answer with 6 people. Hope this helped!
Vector v has initial point (-2, -1) and terminal point (8, -5). Write v as a linear combination of the standard unit vectors i and j.
Given vector v as a linear combination of the standard unit vectors i and j would be, vec v = 10 i -4 j
In this question, we have been given a vector whose initial point is (-2, -1) and the final point is (8, -5)
We need to write vector v as a linear combination of the standard unit vectors i and j.
Let (x1, y1) = (-2, -1) and (x2, y2) = (8, -5)
We know that for vector A having initial point (x1, y1) and terminal point (x2, y2), a linear combination of the standard unit vectors i and j is:
vec A = (x2 - x1)i + (y2 - y1)j
So, for given vector it would be,
vec v = (x2 - x1) i + (y2 - y1) j
vec v = (8 - (-2)) i + (-5 - (-1)) j
vec v = (8 + 2) i + (-5 + 1) j
vec v = 10 i -4 j
Therefore, given vector v as a linear combination of the standard unit vectors i and j would be, vec v = 10 i -4 j
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Answer:
Step-by-step explanation:
Joanne slices a large banana bread into pieces 16 There are 6 adults and 6 children who get a piece of banana bread. The rest of the pieces will be donated to the homeless. What fraction of the banana bread will be donated?
The most appropriate choice for fraction will be given by
Fraction of banana bread will be donated to the homeless is [tex]\frac{1}{4}[/tex]
What is a fraction?
Suppose there is a collection of objects and some part of the objects are taken from the collection. The part which has been taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.
Here,
Total number of banana breads 16
Number of adults who got banana bread = 6
Number of Children who got banana bread = 6
Total number of children and adult who got banana bread = 6 + 6 = 12
Number of banana breads given to the homeless = 16 - 12 = 4
Fraction of banana bread given to the homeless = [tex]\frac{4}{16}[/tex]
= [tex]\frac{1}{4}[/tex]
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9. Reflect in the y-axis.
B
C
a. A'(3, 3), B'(6, 3), C'(5, 6), D'(0, 6)
b. A'(-3, 3), B'(-6, 3), C'(-5, 6), D'(0, 6)
c. A'(3,-3), B'(6, -3), C'(5, -6), D'(0, -6)
d. A'(-3, -3), B'(-6, -3), C'(-5, -6), D'(0, -6)
C
The coordinates of the vertices of triangle A'B'C' after a reflection over the y-axis to triangle ABC are: C. A' = (3, -3), B' = (6, -3), C' = (5, -6), D' = (0, -6).
What is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (x, y).
By applying a reflection over the y-axis to triangle ABC, the coordinates of the vertices of the image triangle A'B'C' include the following:
(x, y) → (x, y)
Point A = (3, -3) → Point A' = (3, -3)
Point B = (6, -3) → Point B' = (6, -3)
Point C = (5, -6) → Point C' = (5, -6)
Point D = (0, -6) → Point D' = (0, -6)
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The four algebra classes at sanchez school are going on a field trip to a museum. each class contains s students. the museum charges $8 per student for admission. there is also a flat fee of $200 for the buses. a. write an expression for the total cost of the buses and the museum admission fees for all four classes. b. write a rational expression for the cost per student. simplify the expression as much as possible. c. use the expression you wrote in part (b) to find the cost per student if each class has 20 students.
a)The expression for the total cost for all four classes can be given as 32s + 200. b) the rational expression for the cost per student is 2(4s+25)/s c) if each class has 20 students then the cost per student is equal to $10.50.
a) Total cost expression can be determined as follows:
total fees of admission + fees of bus = total cost
total cost = (4s × 8) + 200
total cost = 32s + 200
b) A rational expression to determine the cost per student can be calculated as follows:
cost per student = total cost ÷ the total number of students
cost per student = 32s + 200 ÷ 4s
We now factor the numerator by using its GCF;
cost per student = 4 × 2 (4s + 25) / 4×s
cost per student =2 (4s + 25) / s
c) Now using this expression we can find the cost per student if each class has 20 students;
cost per student = 2 (4s + 25) / s
cost per student = 2 ( 4×20 + 25)/ 20
cost per student = 2 ( 80 + 25) / 20
cost per student = 2 (105) / 20
cost per student = 210 / 20 = $10.50
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Find the value of x(Options are included in the photo)
23
Explanation
Complementary angles are pair angles with the sum of 90 degrees, so we can say that
[tex]\begin{gathered} (3x-9)\text{ and }(x+7) \\ \end{gathered}[/tex]are complementary angles, therefore
[tex](3x-9)\text{ and }(x+7)[/tex]Step 1
so,we need to equals to 90 and solve for x
[tex]\begin{gathered} (3x-9)\text{ and }(x+7) \\ (3x-9)\text{ + }(x+7)=90 \\ 3x-9+x+7=90 \\ \text{add like terms} \\ 4x-2=180 \\ \text{add 2 in both sides} \\ 4x-2+2=90+2 \\ 4x=92 \\ \text{divide both sides by 4} \\ \frac{4x}{4}=\frac{92}{4} \\ x=23 \end{gathered}[/tex]so, the answer is
23
I hope this helps you
Match the following. Match the items in the left column to the items in the right column.
1. total to fish
2. starfish to fish
3. starfish to total
4. fish to starfish
The items matched in the left column to the items in the right column are
total to fish = 8 : 3starfish to fish = 5 : 3starfish to total = 5 : 8fish to starfish = 3 : 5Matching the items in the left column to the items in the right columnRatio is the number representing a comparison between two named things or quantities.
Total = 8Fish = 3Starfish = 51. total to fish
= 8 : 3
2. starfish to fish
= 5 : 3
3. starfish to total
= 5 : 8
4. fish to starfish
3 : 5
In conclusion, the ratio of the total to fish to starfish is 8 : 3 : 5
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what is 23/10 times 16/3
Given a triangle with coordinates at A(2, 3), B(8, 3), and
C(5, 6) classify the triangle as obtuse/acute/right and
scalene/isosceles/equilateral.
Use the sketch to show your thinking.
(Select all that apply.
Right
Acute
Obtuse
Isoceles
Equilateral
The triangle is Isosceles and Acute.
From the given data, the coordinates of the three points of the triangle are, A(2, 3), B(8, 3), and C(5, 6).
applying the distance formula, D = √((x2-x1)²+(y2-y1)²) the distance AC and BC are obtained as 3√2 and the distance AB as 2√3.
From this, it can be concluded that AC=BC≠AB.
thus since two of the sides, AC and BC are equal and the third side AB is not equal to AC and BC hence the given triangle is an isosceles triangle.
To check whether the given triangle is right, acute.
A right triangle is a triangle with one of its angles equal to 90 degrees.
An acute triangle is a triangle with all three of its angles less than 90 degrees.
An obtuse triangle is a triangle with at least one of its angles greater than 90 degrees.
To check whether the given triangle is right, acute, or obtuse we use the law of cosines.
To find the angle of a triangle given 3 of its sides, let the angle between the sides AB and AC be A then,
cos(A) = (AC² + AB² − BC²)÷(2×AB×AC).
cos(A) = (3√2² + 2√3² - 3√2²)÷(2×2√3×3√2) =2÷√6
[tex]cos^{-1}[/tex](2÷√6) = 39.182.
Let the angle between the sides AB and BC be B then,
cos(B) = (BC² + AB² − AC²)÷(2×AB×BC).
cos(B) = (3√2² + 2√3² - 3√2²)÷(2×2√3×3√2) =2÷√6
[tex]cos^{-1}[/tex](2÷√6) = 39.182.
Let the angle between the sides AC and BC be then,
cos(C) = (AC² + BC² − AB²)÷(2×AC×BC).
cos(C) = (3√2² + 3√2² - 2√3²)÷(2×3√2×3√2) =2÷3
[tex]cos^{-1}[/tex](2÷3) = 53.544.
Since all the angles A, B, and C is less than 90 degrees the triangle is acute.
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Coffee with sugar and milk added to it can contain up to
how many calories.
Answer:
The total of all calories in a coffee with milk and sugar, is somewhere between 120 and 180. A couple of cups per day could easily add a lot of calories to the 2 000 calories needed per day.
Step-by-step explanation:
Answer:
A standard coffee with whole milk and sugar contains around 140 calories. This number can increase depending on the type of milk used, as well as the amount of sugar added.
S is less then or equal to 18 ; s is greater or equal to -9. What is the value of s
Answer: 18>=S>=-9
Explanation:
in 3-5, suppose z is a relation which includes the point (-3, 5). what other point must be included in the relation of z has the stated property?
3. z is odd
4. z is even
Z is Odd.
What are relations in Math?In mathematics, a relation is a group of ordered pairs that expresses the relationship between two sets. In arithmetic, a relation is called a function if it connects each element of the domain to a single element of the codomain. A relation could be a function or it could not. Relations are all functions.Eg :- The Association between Height and Age
This is a relation since you would get various heights if you entered a specific age and checked all the persons of that age. Nevertheless, if you were to look at a person's height over time, it would depend on their age.
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piggy bank contains 2.65$ in nickles and dimes. If the number of nickles is 7 less that three times the number of dimes, how many of each are there?
There are 29 nickels and 12 dimes in the piggy bank.
In this question, we have been given a piggy bank contains 2.65$ in nickels and dimes.
We need to find the number of nickels and dimes if the number of nickels is 7 less than three times the number of dimes.
Let x be the number of nickels and y be the number of dimes.
We know that, 1 dollar = 20 nickels
and 1 dollar = 10 dimes
So, we get an equation
0.05x + 0.1y = 2.65 ...........(1)
Also the number of nickels is 7 less than three times the number of dimes.
x = 3y - 7 .................(2)
Substitute above value of x in equation (1)
0.05(3y - 7) + (0.1)y = 2.65
0.15y - 0.35 + 0.1y = 2.65
0.25y = 2.65 + 0.35
0.25 y = 3
y = 12
Substitute above value of y in equation (2)
x = 3(12) - 7
x = 29
Therefore, there are 29 nickels and 12 dimes in the piggy bank.
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I don’t understand how to solve
By using a translation rule, the coordinates of C' are (- 1, - 2). (Correct choice: E)
How to translate the vertices of a triangle in a accordance to a vector
Triangles are defined by the locations of its three vertices on Cartesian plane and we must find the locations of the images of the three vertices after applying a translation rule. In this case, we must translate each vertex 2 units upward and 4 units to the right. The general translation formula is described below:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Location of the vertex.T(x, y) - Translation vector.P'(x, y) - Location of the image of the vertex.If we know that C(x, y) = (- 5, - 4) and T(x, y) = (4, 2), then the location of the image of point C is:
C'(x, y) = (- 5, - 4) + (4, 2)
C'(x, y) = (- 1, - 2)
The coordinates of C' are (- 1, 2).
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Determine whether the ratios are equivalent.
1 : 4 and 2 : 6
Responses
The ratios, 1 : 4 and 2 :6 are not equivalent.
Are the ratios equivalent?
Ratio shows the relationship that exist between two or more numbers. Ratio is used to compare two or more numbers. It shows the number of times that one value is contained within other value(s).
In order to determine if the ratios are equivalent, express 2 : 6 in its simplest form. To do this, divide 2 and 6 by 2, a common multiple of both numbers.
2 :6 in its simplest form is 1 : 3
Since, 1 : 3 is different from 1 : 4, the ratios are not equivalent.
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find the next number in the sequence 128,64,32
Answer:
16!
Step-by-step explanation:
The sequence shows that from left to right, the numbers are being divided by two (or multiplied by 1/2). So, for that reason I think that the answer must be 16.
Solve 2(1-x)>2x
X<0.5
X<2
X>2
X>0.5
Answer:
x < 0.5
Step-by-step explanation:
2(1 - x) > 2x ( divide both sides by 2 )
1 - x > x ( add x to both sides )
1 > 2x ( divide both sides by 2 )
0.5 > x , that is
x < 0.5
the following data represent the number of grams of fat in breakfast meals offered at a local fast food restaurant. (a) construct an ordered stem-and-leaf plot and (b) describe the shape of the distribution.
An ordered stem-and-leaf plot has the following results:
0=4 counts
1=7 counts
2=6 counts
3=4 counts
4=1 count
The shape of the distribution is skewed to the right
Part 1
An ordered stem-and-leaf plot:
Total Counts
0 | 3 4 5 7 | 4
1 | 2 2 4 4 5 7 7 | 7
2 | 0 3 4 4 5 8 | 6
3 | 3 4 7 9 | 4
4 | 1 | 1
Part 2
Shape of distribution
When the data in the stem-and-leaf plot given above is plotted in graph, the tail of the plot will be on the right. Hence, the shape of the distribution is skewed to the right
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|PLSSSS SHELLPP URGENTTT
Triangle A is right angled triangle
Triangle B is right angled triangle
Triangle C is obtuse angled triangle
Triangle D is acute angled triangle
In right angled triangle one of the three angles in the triangle is 90 degrees
In acute angled triangle all the angels in the triangle is less than 90 degrees
In obtuse angled triangle one of the three angles in the triangle is greater than 90 degrees
In triangle A one of the angle is 90 degrees, then the triangles is right angled triangle
In triangle B one of the angle is 90 degrees, then the triangles is right angled triangle
In triangle C one of the angle is greater than 90 degrees, then the triangle is obtuse angled triangle
In triangle D all the angles are less than 90 degrees, then the triangle is acute angled triangle
Hence, Triangle A is right angled triangle
Triangle B is right angled triangle
Triangle C is obtuse angled triangle
Triangle D is acute angled triangle
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Given the polynomial below:
9m5 +3n³2q² + 1 +
State:
Degree:
Number of Terms:
Constant:
This polynomial have 5 degree , 4 terms and one connstant
What is polynomial ?Algebraic expressions called polynomials only have non-negative integer powers for their variables. A polynomial is, for instance, Expressions with one or more terms that have a non-zero coefficient are called polynomials. The terminology include constants, exponents, and variables. The "leading term" refers to the first term of the polynomial in standard form. A standard polynomial is one in which the first term, which has the highest degree, is followed by succeeding terms that are organized in descending order of the exponents or powers of the variables, then by constant values. A "coefficient" is a number that has been multiplied by a variable.
Given that : [tex]9m^{5}+3n^{2} +2q^{2} +1[/tex]
[tex]9m^{5}+3n^{2} +2q^{2} +1[/tex]
This polynomial have 5 degree , 4 terms and one connstant
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Solve for x :
5x+8=7x-72
Answer:
x = 40
Step-by-step explanation:
We just have to manipulate the terms, putting each term that has the variable "x" on one side of the equation like this:
5x + 8 = 7x - 72
5x - 7x = - 72 - 8
-2x = -80
x = -80/--2
x = 40
Answer:
x = 40
Step-by-step explanation:
Given equation:
[tex]5x+8=7x-72[/tex]
Add 72 to both sides:
[tex]\implies 5x+8+72=7x-72+72[/tex]
[tex]\implies 5x+80=7x[/tex]
Subtract 5x from both sides:
[tex]\implies 5x+80-5x=7x-5x[/tex]
[tex]\implies 80=2x[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{80}{2}=\dfrac{2x}{2}[/tex]
[tex]\implies 40=x[/tex]
Therefore, the solution to the given equation is x = 40.
Apply
15. The table shows the minimum and maximum
elevations, relative to sea level, of several
hiking trails. Which hiking trail has the least
change in elevation, related to sea level?
Explain how you solved.
The hiking trail that has the least change in elevation, related to sea level, is:
Southern Moon.
Which trail has the least change in altitude?The change in altitude of each trail is calculated as the subtraction of the highest altitude by the lowest altitude, that is:
Change in elevation = highest altitude - lowest altitude.
For Eastern Point, the change is given as follows:
Change = 78 - (-85) = 78 + 85 = 163 feet.
(subtracting by a negative is the same as adding to the positive of the number).
For Northern Star, the change is given as follows:
Change = 34 - (-150) = 34 + 150 = 184 feet.
For Southern Moon, the change is calculated as follows:
Change = 48 - (-62) = 48 + 62 = 110 feet.
The smallest amount is of 110, hence Southern Moon has the least change in elevation relative to sea level.
Missing InformationThe table is shown by the image at the end of the answer.
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What numbers are missing from the pattern below? Enter your answer, using
a comma to separate each number.
72, 3, 28, 42, ?, ?, ?, ?, 72, 3, 28, 42
Answer:
78, 3, 28, 42
Step-by-step explanation:
This appears to be a repeating sequence of four numbers:
72, 3, 28, 42
so the missing 4 numbers must be as above
Help pls with number 7
Answer:
-1.5 goes in between -2 and -1
3/2 goes in between 2 and 1 but closer to 1
-2/3 goes in between 0 and -1 but closer to 0
I’m not very sure about -4/3 but I think it goes in between -2 and -1 but closer to -1 than 3/2
Step-by-step explanation:
Out of 120 students, 80 passed in Science, 70 in Nepali, 10 failed in both subjects and 7 did not appear in an examination. Find the number of students who passed in both subjects by representing the above information in a Venn-diagram.
Step-by-step explanation:
we can find the number of students passed in both subject by following method.
Solution;
im struggling on this
The scale factor of figure A to figure B is 5/2
What is a scale factor?A scale factor can be defined as the ratio of the scale difference between a given original shape and a new shape.
It is seen as a number from which the size of a dimensional shape or figure can be transformed with respect to its original size or magnitude.
It is also described as the ratio between corresponding measurements of an object and a representation of that object.
The formula for scale factor is expressed as;
Scale factor = Dimension of the new shape ÷ Dimension of the original shape
This is so for the downgrading of a shape
Now, we have;
Scale factor = Adjacent of the triangle A/adjacent of triangle B
Scale factor = 10/ 4
Reduce to simply forms
Scale factor = 5/ 2
Hence, the scale factor is 5/2
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Please Help! :)
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:slope(m) = \dfrac{5}{2} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Slope (m) of a line can be calculated by using this formulae :
[tex]\qquad \tt \rightarrow \: m = \dfrac{rise}{run} [/tex]
Considering two points [ (60 , 0) and (80 , 50) ]
[tex]\qquad \tt \rightarrow \: m = \dfrac{y2 - y1}{x2 - x1} [/tex]
[tex]\qquad \tt \rightarrow \: m = \dfrac{50 - 0}{80 - 60} [/tex]
[tex]\qquad \tt \rightarrow \: m = \dfrac{50}{20} [/tex]
[tex]\qquad \tt \rightarrow \: m = \dfrac{5}{2} [/tex]
So, slope of given line is 5/2
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Pls Help asap for math
Answer:
A
Step-by-step explanation:
it reflects over the y axis
These are radical and complex number questions, i need to simplify both WITH WORK, please help
The values of the radical expressions are [tex]\frac{5x^4z^3}{7y}[/tex] and [tex]2x^2y\sqrt{5z}[/tex]
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the radical expression?Expression 1
Here, we have
[tex]\sqrt{\frac{25x^8z^6}{49y^2}}[/tex]
Take the square roots of 25 and 49
So, we have
[tex]\frac{5}{7}\sqrt{\frac{x^8z^6}{y^2}}[/tex]
Next, we apply the law of indices in simplifying the radical expressions
This gives
[tex]\frac{5}{7}\frac{x^{(8/2)}z^{(6/2)}}{y^{(2/2)}}[/tex]
Evaluate
[tex]\frac{5}{7}\frac{x^4z^3}{y}[/tex]
Rewrite as
[tex]\frac{5x^4z^3}{7y}[/tex]
Expression 2
Here, we have
[tex]\frac{\sqrt{100x^4y^2z}}{\sqrt 5}}[/tex]
Take the square roots of 100
So, we have
[tex]10\frac{\sqrt{x^4y^2z}}{\sqrt 5}}[/tex]
Rationalize
[tex]10\frac{\sqrt{5x^4y^2z}}{5}[/tex]
Next, we apply the law of indices in simplifying the radical expressions
This gives
[tex]10\frac{\sqrt{5z}x^{4/2}y^{2/2}}{5}[/tex]
Evaluate
[tex]2\sqrt{5z}x^2y[/tex]
Rewrite as
[tex]2x^2y\sqrt{5z}[/tex]
Hence, the solution is [tex]2x^2y\sqrt{5z}[/tex]
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