Answer:
Step-by-step explanation:
because we know 1 hour is 60 min so 3 hours would be 60x3=180 then you do 3x23.7=71 12x11.2=134 so in total he has 23.7 per hour and 11.2 for 3 hours
Find the equation of the line that passes through the given point and has the given slope. ( Use x as your variable.) (- 9, - 9), m = 0
An equation of the line that passes through the given point and has the given slope is y = -9.
What is the point-slope form?In Mathematics, the point-slope form of any straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represent the points.At data point (9, -9) and slope, m = 0, a linear equation of this line can be calculated in slope-intercept form as follows:
y - y₁ = m(x - x₁)
y - (-9) = 0(x - 9)
y + 9 = 0
y = -9
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Coach Walker has a cooler that can hold 5 1/2 gallons of a sports drink. He fills 3/4 of
the cooler with the sports drink to bring to football practice.
A. How many gallons of the sports drink did Coach Walker put into the cooler? Each
player on the football team fills his water bottle with the sports drink from the
cooler. Each water bottle can hold 1 1/2 pints of the sports drink. (1 gallon = 8 pints)
Show your work or explain how you know.
The gallons of the sports drink that Coach Walker put in the cooler is 4 1/8 gallons.
How many gallons were put in the cooler?In order to determine the gallons of the sports drink that was put into the cooler, multiply 5 1/2 by 3/4.
Multiplication is the process of determining the product of two or more numbers. The sign that is used to denote multiplication is x.
Gallons of sports drink that was put into the cooler = 5 1/2 x 3/4
= 11/2 x 3/4 = 33 / 8 = 4 1/8 gallons
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Need help, thanks!!!!!
When interpreted, the figures of the delivery times of the pizza shops shows that D. The means are nearly equal, but the variation is significantly greater for the second shop than for the first.
What do the delivery times mean ?This means that, on average, the second pizza shop delivers pizzas slightly faster than the first shop. However, the delivery times for the first shop are more consistent (less variable) than the second shop.
The standard deviation for the first shop (4 minutes) is much lower than the second shop (21 minutes), indicating that the delivery times for the first shop are clustered closely around the mean delivery time, whereas the delivery times for the second shop are more spread out. If delivery time is the only consideration, one may prefer the first shop as it has more consistent delivery times.
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what is the meaning of the following statement?
The proposition states that if the multiplication operation in a set is commutative and associative, then the product of any sequence of elements in the set, arranged according to any permutation of the sequence, will be the same as the product of the elements arranged in their original sequence.
What is associative multiplication and permutation?Associative multiplication refers to a property of multiplication where the order of performing the multiplication does not affect the final result. In other words, if we have three elements a, b, and c, then (a x b) x c is equal to a x (b x c).
Permutation refers to the rearrangement of a set of elements in a specific order. In mathematics, a permutation of a set of n elements is a bijective function from the set of integers {1,2, ..., n} to itself. In other words, a permutation is a way of rearranging the elements of a set in a specific order by swapping them around.
In the context of the given proposition, the associative property of multiplication ensures that the order of multiplication of elements in the product Xσ(1) Xσ(2) ... Xσ(n) can be rearranged without changing the final result. The proposition states that no matter how we permute the order of multiplication of elements, the final product will be the same, provided that the multiplication operation is both commutative and associative.
In other words, if we have a set of elements X1, X2, ..., Xn, and we multiply them together using a commutative and associative multiplication operation, then no matter how we permute the elements (i.e., rearrange them in a different order), the result of the multiplication will be the same.
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NEED THIS DESPERATELY !! PLEASE HELP
Answer:222
Step-by-step explanation:The arithmetic series is given by:
a1 = 2, d=3, n = 12
where a1 is the first term, d is the common difference, and n is the number of terms.
To evaluate this series, we can use the formula for the sum of an arithmetic series:
Sn = n/2 * [2a1 + (n-1)d]
where Sn is the sum of the first n terms.
Substituting the given values, we get:
S12 = 12/2 * [2(2) + (12-1)(3)]
= 6 * [4 + 33]
= 6 * 37
= 222
Therefore, the sum of the first 12 terms of the arithmetic series with a1 = 2, d=3 is 222.
If the December 1 balance in the Direct Materials Inventory account was $31,000, the December 31 balance was $38,500, and $185,000 of direct materials were issued to production during December, what was the amount of direct materials purchased during the month?
Answer:
We can use the following formula to calculate the amount of direct materials purchased during the month:
Direct Materials Purchased = Ending Direct Materials Inventory Balance - Beginning Direct Materials Inventory Balance + Direct Materials Issued to Production
Substituting the given values, we get:
Direct Materials Purchased = $38,500 - $31,000 + $185,000
Direct Materials Purchased = $192,500
Therefore, the amount of direct materials purchased during the month was $192,500.
help please. Geometry N.10 IXL. will mark brainliest
The value of y is given as follows:
y = 35.
How to obtain the value of y?A diagonal trapezoid, also known as a trapezium, is a quadrilateral with two parallel sides that are of different lengths. In a diagonal trapezoid, the non-parallel sides are not perpendicular to the parallel sides. This means that the two non-parallel sides are slanted or tilted, forming a diagonal line that connects them.
In a diagonal trapezoid, the diagonals are congruent, meaning that they have the same length.
The diagonals are HJ and IK, hence the value of y is obtained as follows:
5y - 1 = 4y + 34
y = 35.
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An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the linear regression line for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
The linear regression equation for the relationship between the number of times the commercial is run on TV in each city and the number of car sales is given as follows:
y = 0.44x + 0.27.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are usually given in a scatter plot or in a table.
From the image given at the end of the answer, the points are given as follows:
(4, 3), (8, 2), (12, 7), (15,5), (17,9).
Inserting these points into a linear regression calculator, the line of best fit is given as follows:
y = 0.44x + 0.27.
Missing InformationThe table is given by the image presented at the end of the answer.
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george is building a fence he builds at a constant rate of 1/3 section of the ffence every 1/2 hour at this rate what fraction represents the section of fence george can build per hours
George can build a section of fence per hour, thus 2/3 is the fraction that indicates that.
In math, what is a fraction?A fraction is a component of a whole. Mathematically, the number is expressed as a fraction, where the both the numerator and the denominator are divided. In a simple fraction, both are integers. A complex fraction has a fraction in both the numerator and denominator. A correct fraction has a lower denominator than its numerator.
George builds 1/3 of the fence every 1/2 hour.
We need to understand how many sections the fence he can construct in an hour in order to calculate the percentage of fence he can construct each hour.
George may construct 2 × (1/3) or 2/3 of the fence in an hour because 1 hour as equal to 2 of a 1/2-hour periods.
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A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,460 ft Determine the flag's width and length if the length is 250 ft greater than the width.
The flag's width is ___ ft. Its length is ___ ft.
Given:-
Perimeter of the flag is 2460 ft .length is 250 greater than the width .To find:-
length and breadth of the flag .Answer:-
Since a flag is of rectangular shape, its perimeter would be;
P = 2( l + b )
where ,
l is lengthb is breadth.Now let us assume the breadth to be " x " , then its length will be " x + 250 " . Now substitute the respective values in the given formula as ;
2460 = 2 ( x + x + 250)
2460/2 = 2x + 250
1230 = 2x + 250
2x = 1230 - 250
2x = 980
x = 980/2
x = 490
Hence,
length = x + 250 = 490 + 250 = 740ftbreadth = x = 490ftHence the flag's width is 490ft. Its length is 740ft.
and we are done!
_
6thMarch , 3:57 pm
Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
length = width + 250
2×length + 2× width = 2460
now we use the first equation in the second equation abd get
2×(width + 250) + 2×width = 2460
2×width + 500 + 2×width = 2460
4×width = 1960
width = 1960/4 = 490 ft
length = width + 250 = 490 + 250 = 740 ft
3x + 2y =4 complete the table
[tex] \mathbb{ANSWER:}[/tex]
[tex] \sf 3x + 2y = 4[/tex]
[tex] \sf x = 0 \\ \sf \cancel{3(0) }+ 2y = 4 \\ \sf \frac{2y}{2} = \frac{4}{2} \\ \sf y = \boxed{ \sf 2}[/tex]
[tex] \sf x = - 2 \\ \sf 3( - 2)+ 2y = 4 \\ \sf - 6 + 2y = 4 \\ \sf \cancel{- 6 + 6} + 2y = 4 + 6 \\ \sf \frac{2y}{2} = \frac{10}{2} \\ \sf y = \boxed{ \sf 5}[/tex]
[tex] \sf x = 1 \\ \sf 3(1)+ 2y = 4 \\ \sf 3 + 2y = 4 \\ \sf \cancel{3 - 3} + 2y = 4 - 3 \\ \sf \frac{2y}{2} = \frac{1}{2} \\ \sf y = \boxed{ \sf \frac{1}{2} }[/tex]
[tex] \sf x = 4 \\ \sf 3(4)+ 2y = 4 \\ \sf 12 + 2y = 4 \\ \sf \cancel{- 12 - 12} + 2y = 4 - 12 \\ \sf \frac{2y}{2} = \frac{ - 8}{2} \\ \sf y = \boxed{ \sf - 4}[/tex]
I will mark you brainiest!
Which quadrilaterals have diagonals that are perpendicular?
A) Kite,Rhombus, and square
B) Trapezoid, rhombus, and square
C) kites trapezoid, and parallelogram
D) rectangle, square, and parallelogram
The quadrilaterals which have diagonals that are perpendicular are Kite, Rhombus, Square.(option A)
What is Diagonal?Diagonals are the part of a shape, in geometry. In Mathematics , a diagonal is a line that connects two vertices of a polygon or a solid, whose vertices are not on the same edge. in general, a diagonal is defined as a sloping line or the slant line , that connects to the vertices of a shape. diagonals are defined as lateral shapes that have sides/ edges and corners.
Kite
Rhombus
Square
these are the quadrilaterals that have diagonals that are perpendicular.
hence the answer is option A.
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What is the following product? Assume d≥ 0.
3 root d *3 root d*3 root d
To simplify the given product, we can use the properties of radicals. By assuming d ≥ 0 the product is [tex]3^{(3/2)} \times d^{(3/2)}.[/tex]
Specifically, the product of radicals with the same index can be expressed as a single radical by multiplying their radicands.
In this case, we have:
3√d × 3√d × 3√d
We can write this as a single radical by multiplying the radicands:
[tex]3 \sqrt{d} \times 3\sqrt{d} \times 3\sqrt{d} = (3 \sqrt{d})^3[/tex]
To evaluate this expression, we can use the property of exponents that states that the cube of a number is equal to that number raised to the third power.
Thus:
[tex](3 \sqrt{d})^3 = 3 \sqrt{d} \times 3\sqrt{d} \times 3 \sqrt{d}[/tex]
[tex]= 3^{(3/2)} \times d^{(3/2)}[/tex]
Therefore, the simplified product is [tex]3^{(3/2)} \times d^{(3/2)}.[/tex]
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A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t)=−4.9t2+19t+19. How many seconds does it take to reach maximum height? Enter the answer with at least 3 decimal places.
t=
This answer can be derived from the equation h(t)=-4.9t²+19t+19.
What is Equation?An equation is a mathematical statement that two expressions are equal. Equations are used to describe relationships between numbers, variables, and constants. They are typically written in the form of an expression on the left of an equal sign and the result of the expression on the right. For example, 2 + 3 = 5 is an equation that states that the sum of two and three is five. Equations can be used to solve problems and express relationships in science, engineering, economics, and many other fields.
The equation represents a parabola, so the maximum height is found at the vertex of the parabola. The x-coordinate of the vertex can be found by setting the derivative of the equation equal to zero, which gives us the equation -4.9×2t + 19 = 0. Solving this equation for t gives us the answer of t = 1.914 seconds.
This is happening because of the kinematic equation which describes the motion of objects in terms of their displacement, velocity, and acceleration. In this equation, h(t) is the displacement of the ball as a function of time. The derivative of the displacement equation with respect to time gives us the equation for the velocity of the ball, which identifies the point at which the ball reaches its maximum height. Since velocity is equal to zero at the highest point of the ball's trajectory, this equation can be used to find the time it takes for the ball to reach its maximum height.
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A payday loan is made for four weeks, where the amount of interest owed per $100
borrowed is $10
. If you borrow $800
for four weeks, how much do you owe at the end of the four weeks?
What is it? 1/2(4x + 8)
Answer: (2x+4)
Step-by-step explanation:
The term (4x+8) is in brackets. That means whatever you do to it will affect every term in the bracket.
This time, you are dividing by 2
Thus, (4x+8)/2 = 4x/2+8/2
=2x+4
Hope this helps! :)
Find the equation of the line that passes through the given point and has the given slope. (Use x as your variable.) (- 9, - 9), m = 0
Answer:kwbebrhdjejhehe
Step-by-step explanation:
Can someone please help
The value of the variable x is 8. 25
How to determine the value of the variableIt is important to know the properties of a kite. They are;
It has two pairs of adjacent equal sidesIt has one pair of opposite angles that are equal to each otherThe shorter diagonal forms two isosceles trianglesThe longer diagonal forms two congruent trianglesAlso, the diagonals are perpendicular to each otherNote that the sum of the interior angles of a triangle is equal to 180 degrees
So,
m<R + m< V + m< S = 180
substitute the values
9x + 1 + 90 + 23x - 7 = 180
collect like terms
32x = 180 + 84
32x = 264
x = 8. 25
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What is the volume of this rectangular prism?
A)40 cu in
B)120 cu in
C)22cu in
D)84 cu in
Answer: B (120 in^3)
Step-by-step explanation: W * L *H = V
Length * Width * Height = Volume
You can multiply the LWH in any order.
Height = 4
Length = 10
Width = 3
Remember, anything multiplied by ten is just the product (answer) with a zero added to the end. Example: 4 * 3 = 12; 12 * 10 = 120
Another Example: 15 * 2 = 30; 30 * 10 = 300
4 * 10 = 40
40 * 3 = 120
Therefore, 120 is your answer.
Hope this helps!
Answer:
The answer to your problem is, 120 cu in
Step-by-step explanation:
In order to find the volume of the cube there is only one thing that you need to do which is pretty simple just follow these steps:
Multiply, l * w * h ( * = multiply )
By following the formula up above you can find the volume of a rectagular prism which is:
4 x 10 = 40
3 x 40 = 120.
Thus the answer to you problem is, 120 cu in
help!! A containers when 3/8 full holds 15 litres of gasoline. how many litres of gasoline would be needed to fill 5 similar containers?
The number of litres of gasoline that would be needed to fill 5 similar containers is 200 litres.
What is a litre?A litre is a measure of volume
Since a containers when 3/8 full holds 15 litres of gasoline. We need to find how many litres of gasoline would be needed to fill 5 similar containers.
Let x be the volume of the container.
Since a containers when 3/8 full holds 15 litres of gasoline, we have that
3x/8 = 15
Solving for x, we have that
3x/8 = 15
Multiplying through by 8, we have that
3x = 15 × 8
Dividing through by 3, we have that
x = 15 × 8/3
x = 5 × 8
x = 40 litres.
Since one container contains 40 litres, then 5 containers would contain V = 5 × 40 litres
= 200 litres.
So, 5 containers would contain 200 litres
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An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the linear regression line for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
Number of TV commercials, x 4
6
12
14
17
Car sales, y (in hundreds) 2
5
2
8
9
Answer:
the linear regression line for the given data is: y = 0.24x + 2.49
Step-by-step explanation:
To find the linear regression line for the given data, we need to first calculate the mean of x, the mean of y, the sum of squares of x, the sum of squares of y, and the sum of cross-products of x and y.
Using these values, we can then calculate the slope and y-intercept of the regression line.
First, we calculate the mean of x and y:
mean of x = (4 + 6 + 12 + 14 + 17) / 5 = 10.6
mean of y = (2 + 5 + 2 + 8 + 9) / 5 = 5.2
Next, we calculate the sum of squares of x and y:
sum of squares of x = (4 - 10.6)^2 + (6 - 10.6)^2 + (12 - 10.6)^2 + (14 - 10.6)^2 + (17 - 10.6)^2 = 240.4
sum of squares of y = (2 - 5.2)^2 + (5 - 5.2)^2 + (2 - 5.2)^2 + (8 - 5.2)^2 + (9 - 5.2)^2 = 44.8
Finally, we calculate the sum of cross-products of x and y:
sum of cross-products of x and y = (4 - 10.6)(2 - 5.2) + (6 - 10.6)(5 - 5.2) + (12 - 10.6)(2 - 5.2) + (14 - 10.6)(8 - 5.2) + (17 - 10.6)(9 - 5.2) = 56.8
Using these values, we can calculate the slope of the regression line:
slope = sum of cross-products of x and y / sum of squares of x = 56.8 / 240.4 = 0.236
Next, we can calculate the y-intercept of the regression line:
y-intercept = mean of y - slope * mean of x = 5.2 - 0.236 * 10.6 = 2.488
Therefore, the linear regression line for the given data is:
y = 0.24x + 2.49
Note: The slope and y-intercept have been rounded to two decimal places, as per the instructions.
203,433 rounded to the nearest ten thousand
Step-by-step explanation:
203,433 rounded to the nearest ten thousand is 200,000.
Please answer the question in the picture, I will mark brainliest. Show all work pls!!!
Arc length= 2pir * zero with a circle through it/360
Just for clarification 2pir is 2 then pi then r together
.72 radians is the answer.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
According to our question-
The relation of the arc length of a circle subtended by an angle to the radius of the circle is the definition of an angle in radians.
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A bakery sells chocolate cupcakes and mocha cupcakes. One day it sold 162 chocolate and 138 mocha. What percent of the cupcakes sold that day were chocolate?
Answer:
54%Step-by-step explanation:
TOTAL CUPCAKES
162+138=300
[tex] \frac{162}{300} \times 100\% \\ = 54\%[/tex]
please help me..........................
In response to the given question, we can state that So the entire function factored expression is: 8x + 96y = 8(x + 12y)
what is function?Mathematicians examine numbers and complex variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "functioning" signifies the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and results in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used this to denote functions (x). The symbol for admission is an x. The four primary types of usable functions are on operations, one-to-one capabilities, so multiple functionality, in capabilities, and then on functions.
To factor 8x + 96y, we can first factor out the greatest common factor, which is 8.
8x + 96y = 8(x + 12y)
So the entire factored expression is:
8x + 96y = 8(x + 12y)
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What is the solution to the inequality -6+12p+31 > 7?
O p<-8 or p>5
O-8
The solution to the inequality is p > -2 and p < -1, expressed in interval notation as -2>p>-1.
What is interval notation?Interval notation is a mathematical notation for expressing ranges of values between two numbers. It is used to describe the set of real numbers that are bounded between two specified numbers, such as [x, y]. The interval notation is composed of two numbers (x and y) separated by a comma and enclosed in square brackets. The notation is used to represent the entire set of values that lie between the two boundaries.
This is expressed in interval notation as -2>p>-1. This can be solved by isolating the variable p, first by subtracting 31 from both sides of the equation. This leaves -6 + 12p > -24. Then, divide both sides by 12, which gives p > -2. To check the solution, the original equation can be substituted with the value of p. If the equation is true, the solution is correct.
To solve the inequality -6+12p+31 > 7, first subtract 31 from both sides of the equation to isolate the variable. This leaves -6 + 12p > -24. Then, divide both sides by 12 to get p > -2. Finally, check the solution by substituting the value of p in the original equation. If the equation is true, the solution is correct. The solution to the inequality is p > -2 and p < -1, expressed in interval notation as -2>p>-1.
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2. Angle POQ is halfway between 0 radians and angle POR. What is the measure in RADIANS of angle POQ?
The measure in radians of angle POQ is given as follows:
π/4 radians.
How to obtain the measure of angle POQ?The measure of angle POQ is obtained applying the proportions in the context of the problem.
Angle POR is one fourth of the unit circle, which is of 360º, hence it's measure is given as follows:
POR = 0.25 x 360
POR = 90º.
Angle POQ is halfway between 0 radians and angle POR, hence it's measure is given as follows:
POQ = (0 + 90)/2 = 45º.
180º is equivalent to π radians, and 180/45 = 4, hence the measure in radians of angle POQ is given as follows:
π/4 radians.
Missing InformationThe diagram is given by the image presented at the end of the answer.
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Classifying a Parallelagram
The coordinates of the fourth vertex are (-3, -1).
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Substituting the given parameters into the midpoint of a line segment formula, the midpoint of the diagonal is given by;
Midpoint = [(5 - 5)/2, (-3 - 5)/2]
Midpoint = [0/2, -8/2]
Midpoint = (0, -4).
For the fourth vertex, we have:
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
(0, -4) = [(3 + x₂)/2, (-7 + y₂)/2]
3 + x₂ = 2(0)
x₂ = -3
-7 + y₂ = 2(-4)
-7 + y₂ = -8
y₂ = -8 + 7
y₂ = -1.
Therefore, the fourth vertex = (-3, -1).
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Ed wants to borrow $20,000 from a bank to open a small gym. Three banks charge different interest rates. To help decide the best loan option, Ed wants to know the percent profit he will make each month.
Part A
The cost to run the gym each month is $5,000. Find Ed’s total monthly expenses for each loan option.
Answer:
Step-by-step explanation:
it will take 4 days to pay of the loan
Simplify the given expression, and most importantly show the steps, please.
Answer:
[tex]\frac{3\sqrt{2} }{2}[/tex]
Step-by-step explanation:
[tex]\frac{6}{\sqrt{8} } =\frac{6}{\sqrt{4*2} } =\frac{6}{\sqrt{4}*\sqrt{2} }=\frac{6}{2*\sqrt{2} }= \frac{3}{\sqrt{2} }[/tex]
I simplified it leaving 3/sqrt(2).
We can not leave the denominator sqrt(2) for some reason due to a rule that i forgot.
[tex]\frac{3}{\sqrt{2} }*\frac{\sqrt{2} }{\sqrt{2} } =\frac{3*\sqrt{2} }{\sqrt{2}* \sqrt{2} } =\frac{3\sqrt{2} }{(\sqrt{2})^2 } =\frac{3\sqrt{2} }{2}[/tex]
Answer:
[tex]\dfrac{3\sqrt{2}}{2}[/tex]
Step-by-step explanation:
To simplify the given rational expression, first rewrite 8 as a product of prime numbers.
[tex]\implies \sf 8 = 2 \cdot 2 \cdot 2[/tex]
As we know that [tex]\sqrt{a^2}=a[/tex], rewrite 8 as 2² · 2:
[tex]\implies \dfrac{6}{\sqrt{2^2 \cdot 2}}[/tex]
[tex]\textsf{Apply radical the rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]
[tex]\implies \dfrac{6}{\sqrt{2^2} \sqrt{2}}[/tex]
[tex]\textsf{Apply radical the rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]\implies \dfrac{6}{2\sqrt{2}}[/tex]
Rewrite 6 as a product of prime numbers:
[tex]\implies \dfrac{2 \cdot 3}{2\sqrt{2}}[/tex]
Cancel the common factor 2:
[tex]\implies \dfrac{\diagup\!\!\!\!2 \cdot 3}{\diagup\!\!\!\!2\sqrt{2}}=\dfrac{3}{\sqrt{2}}[/tex]
For a fraction to be in simplest form, the denominator should not be irrational.
To rationalize the denominator (get rid of the radical in the denominator), multiply the numerator and denominator by the radical of the denominator:
[tex]\implies \dfrac{3}{\sqrt{2}} \cdot \dfrac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]\implies \dfrac{3\sqrt{2}}{\sqrt{2}\sqrt{2}}[/tex]
[tex]\textsf{Apply radical the rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}[/tex]
[tex]\implies \dfrac{3\sqrt{2}}{\sqrt{2 \cdot 2}}[/tex]
[tex]\implies \dfrac{3\sqrt{2}}{\sqrt{2^2}}[/tex]
[tex]\textsf{Apply radical the rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]\implies \dfrac{3\sqrt{2}}{2}[/tex]