The simplified product of the ^3sqrt2x^5 x ^3sqrt64x^9 is [tex]24\sqrt{2} x^{17}[/tex]
Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.
For finding the simplified product we will first remove the squareroot possible and simplify the value in a simplest way as possible. In the given question, first we will simplifying [tex]\sqrt{64}[/tex] and after simplifying it we will then apply [tex]a^{n} . a^{m} = a^{n+m}[/tex], and lastly we will multiply the two numbers i.e., 3 and 8.
[tex]3\sqrt{2}x^5x^3\sqrt{64}x^9[/tex]
[tex]3\sqrt{2}x^5x^3\sqrt{8^{2} }x^9[/tex]
[tex]3.8\sqrt{2}x^{5+3+9}[/tex]
[tex]3.8\sqrt{2}x^{17}[/tex]
[tex]24\sqrt{2}x^{17}[/tex]
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if the quadrilateral is enlarged by a scale factor of 3, what will be the new perimeter?3.2 3.2 9.6 8 6.4 4.8
The new perimeter of the quadrilateral is 157.2 ft
Consider the following diagram.
We name the quadrilateral ABCD such that side AB = 12.2 ft, side BC = 16 ft, side AD = 12 ft
Let us assume that the perpendicular or height be DE = 12 ft
From figure we can observe that side AB = side CD
So, side CD = 12.2 ft
The quadrilateral is enlarged by a scale factor of 3
so, the dimensions of the new quadrilateral would be,
A'B' = 3 × AB
= 36.6 ft
So, C'D' = 36.6 ft ............(as AB = CD)
B'C' = 3 × BC
B'C' = 48 ft
And A'D' = 3 × AD
A'D' = 36 ft
We know that the perimeter of quadrilateral is the sum of all the four sides.
So, the perimeter of new quadrilateral A'B'C'D' would be,
A'B' + B'C' + C'D' + A'D'
= 36.6 + 48 + 36.6 + 36
= 157.2 ft
Therefore, the perimeter is 157.2 ft
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Find the complete question below.
A cylinder has a base diameter of 6m and a height of 12m what is the volume in cubic m, to the nearest tenths place
Answer:
339.3 cubic m
Step-by-step explanation:
r = Base radius
= [tex]\frac{Diameter}{2}[/tex]
= [tex]\frac{6}{2}[/tex] m
Base radius = 3 m
h = Perpendicular height
= 12 m
Volume of a cylinder: [tex]\pi r^{2} h[/tex]
= [tex]\pi (3 m)^{2} (12 m)[/tex]
= [tex]\pi (108)m^{3}[/tex]
= 339.3 cubic m (Rounded to the nearest tenths place)
Sage and Tom started the month with the same number of talk minutes on their cell phones. Sage talked for 7 minutes with her dad. Tom talked for 4 minutes with a friend and 3 more minutes with his mom. Do Sage and Tom have the same number of talk minutes left on their cell phone plans?
Question 1
Yes, Sage and Tom have the same number of talk minutes left in their cell phones. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The term "arithmetic operations" refers to the four basic mathematical operations that can be used to express any real number. Multiplication, division, addition, and subtraction are the four operations.
We are given that Sage and Tom both started the month with the same number of talk minutes on their cell phones.
So, let 'x' be the number of talk minutes on their cell phones.
Sage talked for 7 minutes with her dad.
So, talk minutes left in Sage's phone = x-7
Tom talked for 4 minutes with a friend and 3 more minutes with his mom.
So, talk minutes left in Tom's phone = x - (4 +3) = x -7
Hence, Sage and Tom have the same number of talk minutes left in their cell phones.
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which of the following continuous improvement tools is often used to initiate a root cause analysis effort? group of answer choices scatter plot. cause-and-effect (fishbone) diagram. pareto chart. swim lane process map.
Among the continuous improvement tools listed in the query, the cause-and-effect (fishbone) diagram is often used to initiate a root cause analysis effort. This tool helps identify potential causes of a problem by breaking down a complex issue into smaller and more manageable components.
The diagram is shaped like a fishbone, with the problem at the head and the potential causes in the "bones" of the fish. By examining the various factors that could contribute to a problem, a team can begin to isolate the most likely root causes and develop targeted solutions to address them. Other tools like scatter plot, Pareto chart, and swim lane process map can also be useful in continuous improvement efforts, but they may not be the best choice for initiating a root cause analysis
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What are the tests for parallel and perpendicular lines?
To determine if a line is parallel or perpendicular, we can place each line on a sloped intersection shape (y = mx + b) and observe the slope m of each line. Equal slopes result in parallel lines. If the slope is multiplied by -1, then the line is vertical.
Parallel Lines:
Two or more lines that lie in the same plane and do not intersect are called parallel lines. They are equidistant from each other and have the same slope. A straight line equation is usually written in the form of a slope intercept represented by the equation y = mx + b. where "m" is the slope and "b" is the y-intercept. The "m" value defines the slope and tells how steep the line is.
Perpendicular Lines:
A vertical line or perpendicular line is two separate lines that intersect at an angle of 90° to each other. These are straight lines known as perpendiculars that meet each other at certain angles (right angles).
We have already seen what a vertical line looks like. If a shape has an "L" shape, its vertex angles are right angles. Vertical lines always intersect each other, but not all intersecting lines are always perpendicular to each other.
Two main properties of vertical lines:
1. Perpendicular lines always intersect or intersect each other.
2. The angle between two vertical lines is always 90°.
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Lavonne sold 4 times as many raffle tickets as Kenneth. Lavonne sold 56 raffle tickets. Write an equation with a variable and solve the equation to find how many tickets Kenneth sold
Equation: 4x = 56
Answer: 14 tickets
Step-by-step explanation:
4x = 56
Lavonne's tickets sold 4 times as many as Kenneth's. This means we would need to multiply Kennneth's ticket by 4 to equal Lavonne's.
4x/4 = 56/4
Now you need to solve the equation by isolating x. Here you have to divide both sides by 4.
x = 14
Kenneth sold 14 tickets.
4(14) = 56
Let’s see who gets this right..
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If Y varies directly with X, how do you write the equation when Y=16 and X=4?
When Y directly varies with X, the direct variation equation is X = 2.
What is the direct variation formula?A direct variation is a relationship between two variables when their ratio is constant. One variable is said to vary in direct proportion to another. Y = kx, where k is the variational constant, is the formula for direct variation. If y varies in direct proportion to x and y = 6 when x = 2, the variational constant is k = = 3. Consequently, y = 3x is the equation that describes this direct variation.
If y directly correlates with x, we can apply the direct variation formula as follows:
y = kx
where k is the proportionality constant.
We may utilise the y and x values provided to find k:
y = kx
16 = k(4)
Solving for k, we get:
k = 16/4 = 4
Now we can use the value of k to find x when y = 8:
y = kx
8 = 4x
Dividing both sides by 4, we get:
x = 2
Therefore, when y = 8, x = 2.
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Question:
If y varies directly with x and y = 16 when x = 4, find x when y = 8.
Write and solve a direct variation equation to find the answer.
X =?
A newspaper randomly chooses 100 names from it's subscriber database and then survey's those subscribers to find if they read the restaurant review is this biased or non biased
Answer:
Non biased (kind of)
Step-by-step explanation:
It depends on how they randomly chose but if it was truly random it would be non biased as many people will read newspapers for things such as sports or catalogs
City A and City B had two different temperatures on a particular day. On that day, four times the temperature of City A was 8A C more than 3 times the temperature of City B. The temperature of City A minus twice the temperature of City B was _3A C. What was the temperature of City A and City B on that day?
City A was 5A C, and City B was 4A C. City A was 3A C, and City B was _1A C. City A was 8A C, and City B was _3A C. City A was 5A C, and City B was _5A C
So the temperature in City A was 8A C and the temperature in City B was y = x + 1 = 8 + 1 = 9A C.
The problem can be solved by setting up an equation using the information given. Let's call the temperature of City A "x" and the temperature of City B "y". We can then write two equations based on the information given:
4x = 3y + 8
x - 2y = -3
We can use substitution to solve for one of the variables and then use that information to solve for the other. For example, we can substitute 3y + 8 for 4x in the second equation:
x - 2y = -3
x - 2y = 3y + 8 - 3
x - 2y = 3y + 5
x - 5y = 5
We can then solve for y by multiplying both sides of the equation by -1/5:
-5x + 5y = -5
5y = 5x + 5
y = x + 1
We can then substitute this expression for y into one of the original equations and solve for x:
4x = 3(x + 1) + 8
4x = 3x + 3 + 8
x = 8
So the temperature in City A was 8A C and the temperature in City B was y = x + 1 = 8 + 1 = 9A C.
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From the set {7, 9, 36}, use substitution to determine which value of x makes the inequality true. 2x < 18
The only value of x from the set {7, 9, 36} that makes the inequality 2x < 18 true is x = 7.
We can use substitution to find which value of x makes the inequality 2x < 18 true by trying each value in the set {7, 9, 36} one by one.
Let's start with x = 7:
2x = 2(7) = 14
14 < 18 is true, so x = 7 satisfies the inequality.
Next, let's try x = 9:
2x = 2(9) = 18
18 < 18 is not true, so x = 9 does not satisfy the inequality.
Finally, let's try x = 36:
2x = 2(36) = 72
72 < 18 is not true, so x = 36 does not satisfy the inequality.
Therefore, the only value of x from the set {7, 9, 36} that makes the inequality 2x < 18 true is x = 7.
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Consider the system of equations -2x + 3y = -5 and 3x - 4y = 6.
-Describe two different ways to solve the system by elimination. Select ALL that apply.
A) Multiply the first equation by 4, the second equation by 3, and subtract to eliminate y,
B) Multiply the first equation by 3, the second equation by 2, and subtract to eliminate x
c) Multiply the first equation by 3, the second equation by 2, and add to eliminate x.
D) Multiply the first equation by 3, the second equation by -2, and add to eliminate x
E) Multiply the first equation by 4, the second equation by 3, and add to eliminate y
F) Multiply the first equation by -4, the second equation by 3, and add to eliminate y
(Write below which of the letter answer(s) it is)
Two ways of solving the system of equations are:
c) Multiply the first equation by 3, the second equation by 2, and add to eliminate x.E) Multiply the first equation by 4, the second equation by 3, and add to eliminate yWhich two ways can be used to solve the system of equations?Here we want to identify two ways of solving the system of equations:
-2x + 3y = -5
3x - 4y = 6
One way is using the elimination method, then the option E is true, if we multiply the first equation by 4 and the second by 3 and then we add the two equations, the variable y will be eliminated and we could solve the equation for x.
We also could eliminate the variable x, to do so, we need to multiply the first equation by 3 and the second by 2, and add the two equations.
Then option C is also true.
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Determine a relationship between the x- and y-values. Write an equation.
x 1:2,3,4
y -4,-3,-2,-1
Oy=x-8
O y = -5x+1
O y=-x-5
O y=x-5
The linear equation that shows the relationship between y and x is y = x - 5
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The slope intercept form of an equation is:
y = mx + b
where m is the rate of change and b is the y intercept.
From the values given, using (1, -4) and (2, -3):
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-4)=\frac{-3-(-4)}{2-1} (x-1)\\\\y=x - 1-4\\\\y=x-5[/tex]
The linear equation is y = x - 5
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does anybody know the answers for these question?
The functions are solved for the inverses and matched as follows
1. not inverse function
2. not inverse function
3. inverse functions
4. not inverse function
5. not inverse function
6. not inverse function
How to find the inverse of the functions1. g(n) = -1/n + 1 and f(n) = -1/(n - 1)
say y = g(n) = -1/n + 1
y - 1 = -1/n
-y + 1 = 1/n
n = -1/(y - 1)
interchanging the variables
y = -1/(n - 1)
2. The cube root of 4 not in the inverse hence this is not inverse function.
3. g(x) = (x + 2)³ - 3 and f(x) = ∛(x + 3) - 2
say y = g(x) = (x + 2)³ - 3
y + 3 = (x + 2)³
x + 2 = ∛(y + 3)
x = ∛(y + 3) - 2
interchanging the variables
y = f(x) = ∛(x + 3) - 2 this is inverse functions
4.f(n) = 4/(n - 1) - 3 and g(n) = -2/n + 1
say y = f(n) = 4/(n - 1) - 3
y + 3 = 4/(n - 1)
1 / (y + 3) = (n - 1) / 4
4 / (y + 3) = n - 1
4 / (y + 3) + 1 = n
interchanging the variables
y = 4/(n + 3) + 1 this is not inverse functions
5. g(x) = 4/(x - 3) - 2 and f(x) = -2/(x + 1)
say y = g(x) = 4/(x - 3) - 2
y + 2 = 4/(x - 3)
1 / (y + 2) = (x - 3) / 4
4 / (y + 2) = x - 3
4 / (y + 2) + 3 = x
interchanging the variables
y = 4/(x + 2) + 3 this is not inverse functions
6. f(x) = 2/(x - 3) - 1 and g(x) = -3(-x + 2) - 2
say y = f(x) = 2(x - 3) - 1
y + 1 = 2/(x - 3)
1 / (y + 1) = (x - 3) / 2
2 / (y + 1) = x - 3
2 / (y + 1) + 3 = x
interchanging the variables
y = 1/(x + 1) + 3 this is not inverse functions
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A board 50 inches long is to be cut into two parts so that one part will be 6 inches longer than the other. How long should each part be?
The board should be 28 inches long.
What is an expression?
An expression or mathematical expression in mathematics is a finite combination of symbols that is well-formed in accordance with context-dependent principles.
Let's call the length of the first part "x". Then, the length of the second part would be x + 6 inches. The total length of both parts is 50 inches, so we can set up an equation to solve for x:
x + (x + 6) = 50
Expanding and solving for x:
2x + 6 = 50
2x = 44
x = 22
So, the first part should be 22 inches long, and the second part should be 22 + 6 = 28 inches long.
The board should be 28 inches long
Given below is a sample of expression please refer the following
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if a, b, and c are boolean variables, then the value of !(a & !(b & !c)) is the same as which of these expressions: !a || (!b || c) !a || (b & !c) (!a || b) & !c
The value of the expression is the same as the second option: !a || (b & !c).
What are boolean variables?Boolean variables are variables that can have only one of two possible values: true or false. They are named after the 19th-century mathematician George Boole, who developed a system of logic based on binary values. In computer programming, boolean variables are commonly used to represent conditions or states that can be either true or false, such as whether a certain condition is met or whether a certain task has been completed.
The expression !(a & !(b & !c)) can be simplified using De Morgan's laws and distributive property to obtain:
!(a & !(b & !c)) = !a || (b & !c)
Therefore, the value of the expression is the same as the second option: !a || (b & !c).
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If you borrow $1,100 for 9 years at an annual interest rate of 4% , what is the total amount of money you will pay back?
Calculate the problem A sum of money was shared between Mario, Giana and Allan in the 2:3:7. If Allan received $640 more than Giana, find the total sum of money shared
The total amount of money Mario, Giana, and Allan split was $2160. Giana received $640 less than Allan did.
Let x represent the sum of money Mario got.
Giana got three times
Allan got seven times
Total: 2x, 3x, 7x, or 12x.
Allan received $640 more than Giana, therefore
7x = 640 + 3x
4x = 640
x = 160
Total amount split is 12x, or 12 * 160, or $2160.
The total amount of money Mario, Giana, and Allan split was $2160. To determine the overall amount, we must first determine how much money each person received. We know that Giana received three times as much as Mario did, while Allan received seven times as much. So, using 2x, 3x, and 7x, respectively, where x is the amount of money Mario received, we can express how much each person earned.
We may draw up an equation to determine how much money Mario received by taking into account the fact that Allan received $640 more than Giana. It goes like this: 7x = 640 + 3x. x = 160 is the result of solving this equation. Mario thus received $160 whereas Giana received $480 after multiplying 3x by 3 * 160. Allan received $1120 since he was paid $640 more than Giana (7x = 7 * 160). Mario, Giana, and Allan divided the total amount of money as follows: 2x + 3x + 7x = 12x = 12 * 160 = $2160.
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Line a is parallel to line b if the measure of <7 Is 114 what is the measure of <1
The measure of ∠1 is 114.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
∠7 = 114
From the figure,
Line a is parallel to line b.
So,
∠7 and ∠1 are alternate exterior angles.
And,
Alternate exterior angles are equal.
So,
∠7 = ∠1 = 114
Thus,
∠1 is 114.
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How do I find the roots of a cubic equation?
Answer:First, we need to find which number when substituted into the equation will give the answer zero. Therefore is a factor. Factorise the quadratic until the expression is factorised fully. Therefore the roots occur when = -3, -2 and 1.
Step-by-step explanation:
Answer:
by reducing it into a quadratic equation and then solving
Step-by-step explanation:
Savi and Suri had a total of 40.00 savi had 3 times as many as suri how much does each have? Show working
Suri has 10.00, and Savi has 3 times as much, or 30.00.
What is algebraic expression?
When we use numbers and words to solve a mathematical problem, we are using algebraic expressions.
Let's use algebra to solve the problem.
Let's say Suri has x amount of money. Then we know that Savi has 3 times as much money, or 3x. We also know that together they have 40.00. So we can write an equation:
x + 3x = 40
Simplifying this equation, we get:
4x = 40
Dividing both sides by 4, we get:
x = 10
So Suri has 10.00, and Savi has 3 times as much, or 30.00.
To check, we can verify that their total is 40.00:
10 + 30 = 40
So, the solution checks out.
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A math teacher has a number cube with faces numbered 1 through 6. He will roll the number cube 400 times. Which of the following ranges contains the best prediction for the number of times the number cube will land with a 1 or a 4 on the top face?
What is the answer and the steps to this question?
Answer:
The probability of rolling a 1 or a 4 on a single roll of the number cube is 2/6, or 1/3. So the expected number of times the number cube will land with a 1 or a 4 on the top face after 400 rolls is 400 * 1/3 = 133.33.
The range that contains this expected value is roughly between 130 and 140, so a good prediction for the number of times the number cube will land with a 1 or a 4 on the top face is between 130 and 140.
Step-by-step explanation:
20% of what number is 5
Answer: 25
Step-by-step explanation: 5x5 =25
Answer: 25
20% is one-fifth of a whole. This means we must multiply our known number times five.
5 x 5 is 25.
To make sure that our answer is correct, we can figure out the 20% of 25, which is 5.
This means that 25 is our correct answer.
I hope this helps & good luck <3 !!!
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $8,000, annual interest: 7%, interest periods: 4, number of years: 10
Please help
sahalin cellphone plan costs $30 a month.she used 12.5 hours in january
a.what was her cost per minute?
The cost per minute is $0.04.
What is Unit rate?Unit rates are defined as rates that are expressed as multiples of 1, such as 2 feet per second or 5 miles per hour.
Given:
Sahalin cellphone plan costs $30 a month.
In a month of may she used cellphone 12.5 hours.
First convert 12.5 hours in minute.
As we know 1 hour = 60 minutes
So, 12.5 hours = 12.5 x 60
= 750 minutes
and, the cost per minute
= 30/750
= 0.04
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The altitude y in feet of a hawk that is descending can be represented by the equation y=−20x+350, where x represents the time in minutes. The equation y=−10x+400 represents the altitude y in feet of an eagle after descending x minutes.
plsss help
By evaluating both equations in x = 8 we will see that the hawk will be closer to the ground.
Which bird is closer to the ground after 8 minutes?We know that the height of the hawk is modeled by:
y=−20x+350
And the height of the eagle is modeled by:
y=−10x+400
Now we need to evaluate both equations in x = 8.
hawk:
y = -20*8 + 350 = 190
For the Eagle:
y = -10*8 + 400 = 320
We can see that the hawk is closer to the ground.
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carrie went running for 22 minutes and then did a series of exercises for 3 mins
Answer: Her total exercise time was 25 minutes
Need help with this one?
The image of the point after the dilation of scale factor k = -1/2 is:
(-1, -1/3)
How to find the coordinates of the image?If we have a point (x, y), and we dilate it by a scale factor k with the center of dilation on the origin, then the new coordinates of the point are (k*x, k*y).
Here the original point is (3, 1)
And the scale factor is k = -1/3
Then the image of the point after the dilation is:
( -1/3*3, -1/3*1)
(-1, -1/3)
That is the image.
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NEED THIS DONE ASAP Please
The expression which represents the perimeter of the rectangle is 2x + 14
Area of the rectangle = 4x + 12Area of the rectangle if x = 7 is 40 square unitsThe following expressions represent the descriptions respectively;
6x
(x - 5)
(x + 2.99)
The total cost of membership of each gym is represented by;
Gym A total cost = 80 + 25m
Gym B total cost = 40m
What is the expression to represent the perimeter of a rectangle?Length= x + 3
Width = 4
Perimeter of a rectangle= 2(length + width)
= 2{(x + 3) + 4}
= 2(x + 3 + 4)
= 2(x + 7)
Perimeter of the rectangle = 2x + 14
Area of the rectangle= length × width
= (x + 3) × 4
Area of the rectangle = 4x + 12
If x = 7
Area of the rectangle = 4x + 12
= 4(7) + 12
= 28 + 12
= 40 square units
If x is the cost of each apple, the total cost of 6 apples = 6x
Adam is x years old. John is 5 years younger.
So, John's age = (x - 5) years
Ben spent x dollars on a book and $2.99 on a pack of pencil.
Ben spent a total of x + 2.99
Gym A total cost:
80 + 25m
Gym B total cost:
40m
Where,
number of months= m
If m = 6 months
Gym A total cost:
80 + 25m
= 80 + 25(6)
= 80 + 150
= $230
Gym B total cost:
40m
= 40(6)
= $240
Therefore, the gym which is the best deal for 6 months is gym A
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If 15−−√×a 15 × a is a rational number, what could be the value of a a ? Explain your reasoning
For the given rational number √15 × a = 15 × a the value of 'a' is equal to 0 or ( 1 / 15 ).
The expression is written as :
√15 × a = 15 × a
The above expression is a rational number :
Squaring both the side of the expression we get,
⇒ 15 × a = ( 15 × a )²
⇒ 15 × a = 225 × a²
Divide by 15 on the both the side of the equation we get,
⇒ a = 15 a²
⇒ 15a² - a = 0
⇒ a( 15a - 1 ) = 0
⇒ a = 0 or 15a - 1 =0
⇒ a = 0 or a = 1 / 15
Therefore, the value of a for the given rational number is equal to
0 or ( 1 / 15 ).
The above question is incomplete , the complete question is:
If √15 × a = 15 × a is a rational number, what could be the value of a ? Explain your reasoning.
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