Simplify the equation and write the answer without negative exponents

Answers

Answer 1

[tex] \sqrt{200} - \sqrt{32} = \sqrt{2 \times 100} - \sqrt{2 \times 16} = 10 \sqrt{2} - 4 \sqrt{2} = 6 \sqrt{2} [/tex]

Answer 2

[tex]\bf \sqrt{200}-\sqrt{32}\quad \begin{cases} 200=2\cdot 2\cdot 2\cdot 5\cdot 5\\ \qquad 2^2\cdot 2\cdot 5^2\\ \qquad (2\cdot 5)^2\cdot 2\\ \qquad (10)^2\cdot 2\\ 32=2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^2\cdot 2^2\cdot 2\\ \qquad (2\cdot 2)^2\cdot 2\\ \qquad (4)^2\cdot 2 \end{cases}\implies \sqrt{10^2\cdot 2}-\sqrt{4^2\cdot 2} \\\\\\ 10\sqrt{2}-4\sqrt{2}\implies 6\sqrt{2}\implies 6\cdot 2^{\frac{1}{2}}[/tex]

Related Questions

The s/n ration for a set of 50 measurements is 10. what number of measurements would make the s/n ratio 5

Answers

5 to 1 the process is quite simple

which expression has a value of 15 when p=12 18/p 3p. 18-p p+3

Answers

p+3 because p=12 and you need the answer to be 15 so...12+3=15

The required expression that has a value of 15 is given as P + 3.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Substitute the value of p in the expression,
= P + 3
= 12 + 3
= 15

When the value of p is put on another expression there output value is not 15.

Thus, the required expression that has a value of 15 is given as P + 3.

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Find three consecutive even integers such that the sum of the least integer and the middle integer is 30 more than the greatest integer

Answers

Let the first integer be represented by: 2k

the second integer by: 2(k+1)

and the third by: 2(k+2)

Then, 2k + 2(k+1) = 2(k+2) + 30

2k + 2k + 2 = 2k + 4 + 30

4k + 2 = 2k + 34

2k = 32

k = 16

first integer: 2k = 2(16) = 32

second integer: 2(k+1) = 2(16+1) = 2(17) = 34

third integer: 2(k+2) = 2(16+2) = 2(18) = 36

Answer: 32, 34, 36

chase drew the number line below to show -4 + (-3). Is his model accurate? If not, tell what is wrong with his model.

Answers

Chase's model is only accurate if it shows starting at -4 on a number line and moving 3 units left to land at -7. Otherwise, the model requires correction to accurately portray the sum of -4 and -3.

The student's question relates to the operation of adding two negative numbers on a number line. When adding -4 and -3, you start at -4 on the number line and move 3 units to the left because you're adding another negative number. If Chase's model does not show starting at -4 and moving 3 units left to end at -7, then his model is inaccurate. To correct the model, ensure that the number line accurately reflects this movement and resulting position on the number line.

How do you write 15 cubed in exponential notation

Answers

15^3
expanded form 15x15x15

what is 5/6 divided by 1/12

Answers

5/6 / 1/12

5/6 * 12

10

Hope this helps!

You have to make 5/6 have a common denominator (bottom number) of 1/12, so 5/6 would become 10/12 (5/6 multiplied by 2 is 10/12), and so you would get 10/12 divided by 1/12 equals 10.

One number exceeds another by 1 the sum of the numbers is 29 what are the numbers

Answers

For this question, we know that the first number is x, and the second number is x+1. Thus x+x+1(sum of the numbers)=29. 2x+1=29. If you do the calculations, you will find out that one number is 14, and the other number is 15.
To check, you add the numbers together and get 29, their difference is 1.
Thus, it is the correct answer.

Final answer:

To find the two numbers, we set up two equations, solve for one variable, and find the other. The numbers that satisfy the condition of one exceeding the other by 1 with their sum being 29 are 14 and 15.

Explanation:

The student's question involves finding two numbers where one number exceeds the other by 1 and their sum is 29. To solve this, let's set up a system of equations. We'll call the first number x and the second number y. Based on the question:

x = y + 1 (one number exceeds the other by 1)

x + y = 29 (the sum of the numbers is 29)

Substituting the first equation into the second gives us:

(y + 1) + y = 29

2y + 1 = 29

2y = 28

y = 14

Now that we have the value of y, we can find x:

x = y + 1

x = 14 + 1

x = 15

Therefore, the two numbers are 14 and 15.

Write the number with the same value as 32 tens

Answers

The answer is 320
Hope i helped

The answer for this is 320

The product of 6 and the sum of 5 and k

Answers

product means multiply, sum means add

so add 5+k = (5+k)

now multiply that by 6 to get

6(5+k)

The Des Plaines River Bridge is 2.1 km long. Engineers are considering re-lighting the bridge with a pole placed every 100 feet of the bridge length starting from the south end. Each pole will support four light globes. How many globes will be required for the re-lighting project?

Answers

228
hope this helped!

now, there are 3280.84 feet in 1 kilometer, so, how many feet are there in 2.1km? well, 2.1 * 3280.84 or 6889.764 feet.

now, they're putting globes on intervals of 100ft, however, how many times does 100 go into 6889.764? well 6889.764/100 which is rounded up 68.9.

so, that means roughly 69 poles, however, the division excludes the starting point, so if we include that, because is lighting and thus it needs to include the starting point of the bridge, so that'd be 70 poles then.

each pole with 4 globes, 70 * 4 globes then.

Tony says that 4,400 is halfway between 4,000 and 5,000.is he correct?why or why not?

Answers

Final answer:

Tony is not correct. The midway point between 4,000 and 5,000 is found by calculating the average of the two numbers, which is 4,500. Therefore, the halfway point is 4,500, not 4,400.

Explanation:

Tony states that 4,400 is halfway between 4,000 and 5,000. To determine if Tony is correct, we need to find the midpoint between the two numbers. The midpoint can be found by adding the two numbers together and dividing by 2:

(4,000 + 5,000) / 2 = 9,000 / 2 = 4,500.

Therefore, the exact halfway point between 4,000 and 5,000 is 4,500. This means that Tony's assertion that 4,400 is halfway between these two numbers is not correct; the correct halfway point is actually 4,500.

Final answer:

No, Tony is not correct. Halfway between 4,000 and 5,000 would be the average of the two numbers, which is 4,500.

Explanation:

No, Tony is not correct. Halfway between 4,000 and 5,000 would be the average of the two numbers. To find the average, we add the two numbers together and divide by 2. In this case, the average of 4,000 and 5,000 would be (4,000 + 5,000) / 2 = 9,000 / 2 = 4,500. Therefore, 4,400 is not halfway between 4,000 and 5,000.

solve the following problem correctly 6+6²÷(3+6) x 3

Answers

6 + 6ˆ2 / (3 + 6) X 3
= 6 + 36 / 9 X 3
= 6 + 4 X 3
= 6 + 12
= 18

6 + 36/9 x 3

6 + 4 x 3

6 + 12

18 is your answer

first do the parethesis, squares, multiplication and division (From left to right) and then the addition

hope this helps

The minimum sustained wind speed of a category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Let V represent the wind speed.

Answers

Final answer:

The absolute value equation that represents the range of a category 1 hurricane's wind speed is |V - 84.5| ≤ 10.5. 84.5 is the average of the range and 10.5 is the difference from the range's center to the end.

Explanation:

The absolute value equation that represents the minimum and maximum sustained wind speeds of a category 1 hurricane can be written as |V - 84.5| ≤ 10.5. Here, V stands for the wind speed. The middle value of 74 and 95 is 84.5 (the average of 74 and 95). And the distance from 84.5 to either end of the range (74 or 95) is 10.5. So, the range of speeds is represented by the absolute difference from the center of the range is less than or equal to 10.5.

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find the value of x so that f( x ) = 7

Answers

The value for x so that f(x) = 7 is at x = -3.

Using the equation of slope-intercept form (y = mx + b), where m is the gradient and b is the constant, we can find the value of x at which f(x) is equal to 7 as follows:

By observation on the graph, when x = 1, y = 3 and when x = 2, y = 2.

3 = m + b...(1)

2 = 2m + b...(2)

we multiply equation (1) by 2 and subtract equation (2) from the result;

6 - 2 = 2m - 2m + 2b - b

4 = b

putting 4 for b in equation (1) gives;

m = -1

Thus we have the equation for f(x) as

f(x) = (-1)x + 4

For f(x) = 7;

-x + 4 = 7

x = 4 - 7

x = -3.

Therefore, for f(x) to be equal to 7, the value of x is equal to -3.

A school has two pathways through the math program. At this school,
two-sevenths of students follow the first path, and the rest take the second path. During one semester, 35% of the students who follow the first path pass the program, while 70% of the students who follow the second path pass it. Find the fraction of students who take the first path and pass.

Answers

This would be a multiplication of fractions equation. To find this answer, write both percentages as fractions. In this case, the first path held two-sevenths (2/7) of the overall students, and of those, 35% (35/100) passed the exam. Setting these together as a multiplication problem leads to a result of 70/700. Reducing this gives a final fraction of 1/10 of the overall students taking the math program passed the first path this semester.

What is the equation of the circle shown in the graph

Answers

the answer is x² + (y + 3)² = 4 C. i just did the problem

Answer: its the third option

Is this better? Its all.. There is no book to read it over so its confusing

Answers

Part A)

Focus on the first column where it says "test finds student lying" since it asks "what percentage..were found to be lying". We can ignore the second column completely.

We have 282 people found to be lying based on the test (bottom of the first column). Of this total, 200 have not cheated meaning that the student isn't lying. This is based on the overall premise given at the top that states "All of them denied having cheated"

Simply divide the two values: 200/282 = 0.70921985815602 which rounds to roughly 0.7092 if you round to four decimal places

Now move the decimal over 2 spots to the right to convert to a percentage
0.7092 ---> 70.92%

Answer: 70.92%
==============================================================
Part B)

We'll use the result from part A. Subtract it from 100%

100% - 70.92% = (100 - 70.92)% = 29.08%

Answer: 29.08%

Note: another way to get this answer is to divide the values 82 over 282 to get 82/282 = 0.29078014184398 and we get the same answer roughly (after rounding)
==============================================================
Part C)

Now we focus on the second column only. We have 1718 people total and of this total, 12 have cheated. Since they initially deny cheating but they really did cheat, this is a lie they tell.

So 12/1718 = 0.0069848661234 which rounds to 0.0070 and that converts to 0.7%

Note: this isn't 7% or 70%, its point 7 percent

Answer: 0.7%

A drinking glass has height of 4 inches in height,in a length of 2 inches and 2 inches in width,while a baking pan has a width of 4 inches lenght of 8 inches and a depth of 2 inches.if the baking pan is filled of water up to its half depth using the drinking glass,how many glasses of full water would be needed?

Answers

2.
2 x 2 x 4 = 16
2 x 4 x 8 = 64
64 / 16 = 4
4 x 1/2 = 2.

There are 2 glasses of full water would be needed to fill the baking pan.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A drinking glass has height of 4 inches ,in a length of 2 inches and 2 inches in width.

And, A baking pan has a width of 4 inches length of 8 inches and a depth of 2 inches.

Now,

The volume of drinking water = 4 x 2 x 2

= 16 inches³

And, The volume of baking pan = 4 x 8 x 2

= 64 inches³

So, Half depth of baking pan = 64 / 2

= 32 inches³

Here, The volume of drinking water = 16 inches³

Thus, Number of glass of full water would be needed to fill the baking pan = 32 / 16 = 2

Therefore, There are 2 glasses of full water would be needed to fill the baking pan.

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Every 3 days Seth goes to the grocery store. His best friend Brian goes every 5 days. On what day will they both go to the store on the same day???

Answers

They will both go on Thursday Friday Saturday Sunday Monday

they would never meet.

A random sample of 50 units is drawn from a production process every half hour. the fraction of nonconforming product manufactured is 0.02. what is the probability that ????̂0.04 if the fraction nonconforming really is 0.02

Answers

Final answer:

The probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02 can be calculated using the normal approximation to the binomial distribution.

Explanation:

To find the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02, we can use the normal approximation to the binomial distribution.

1. Calculate the mean of the sampling distribution using the formula:

μ = np = 50 * 0.02 = 1

2. Calculate the standard deviation using the formula:

σ = sqrt(npq)

where q = 1 - p = 1 - 0.02 = 0.98

σ = sqrt(50 * 0.02 * 0.98) ≈ 0.99

3. Convert p(hat) to a z-score using the formula:

z = (p(hat) - μ) / σ

z = (0.04 - 1) / 0.99 ≈ -0.96

4. Look up the z-score in the standard normal distribution table to find the corresponding probability.

P(z < -0.96) ≈ 0.166

Therefore, the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02 is approximately 0.166.

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Complete question:

A random sample of 50 units is drawn from a production process every half hour. The fraction of non-conforming product manufactured is 0.02. What is the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02?

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Solve (1-sin(x))(1+sin(x))

Answers

Since these are conjugates (a conjugate is when we have anything a - anything b multiplied by anything a + anything b for the most part - this excludes things such as infinity) Since sin(x) and 1 both fit under 'anything', we have a special way of multiplying these - it's a^2-b^2, or
1^2-sin^2x=1-sin^2x=cos^2x using trigonometric properties

Describe the pattern you see when you move from a lesser place-value position to the next greater place-value position.

Answers

The underlying concept applied here is the place values. Each digit of a number holds its own value. The digit increases in value by 10 as it goes from the rightmost to the leftmost digit. Take for example, the number is 111. It contains the same digit of 1. But the ones digit has a value of 1, the tens value has a value of 10, and the hundreds digit has a value of 100. Hence, as you go from the lesser-value digit to the greater-value digit, the value increases by 10.

meg knows that it takes 16 minutes for her to read 7/x of a chapter. How long will it take her to read the entire chapter?

Answers

18 2/7 minutes
bru get yo facts right

in that case, if you're looking for x

since 16 = 7/x
x = 7/16
= .4375

Given CA=3x-4, AT=4x+1, and CT=32, find AT

Answers

Hello, I assume that CT is of course a line formed by lines CA and AT.

If you add CA and AT you get CT.

3x - 4 + 4x + 1 = 32

3x + 4x = 32 + 4 - 1

7x = 35

7x/7 = 35/7

x = 5

Plug in the value of 5

AT = 4(5)+1 = 20+1 = 21

Your answer is 21

It takes 23 minutes for 6 people to paint 6 walls. How many minutes does it take 9 people to paint 9 walls?

Answers

Since the proportion is the same, it is also 23 minutes.

Answer:

Step-by-step explanation:

Imagine that each person is assigned one wall, and all 6 people begin painting at the same time.

Since everyone will finish painting their assigned wall after 23 minutes, it takes one person 23 minutes to paint one wall.

If we have 9 people and 9 walls, we can again assign one wall to each person.

Everyone will take 23 minutes to paint their assigned wall.

In other words, it takes 23 minutes for 9 people to paint 9 walls.

Fifteen people volunteer for a park cleanup. The number of volunteers increases by 7 people each month for several months. After how many months will there be 50 volunteers

Answers

It will take 5 months

The answer and how to get it correctly on my own

Answers

The domain means the allowed values for x. In this example, you can work your way backwards through the equation.

On the outside, there is a square root. You know that the argument for the square root has to be zero or positive (>=0), so

-4x + 20 >= 0. This simplifies to x <= 5. The domain therefore is

(-∞, 5]

If you have trouble following this, please say which part needs clarification.

what does a negative net worth indicate

Answers

A negative net worth indicates that someone has lost some money. It could indicate that they borrowed more money or spent more money than they made. Regardless on the circumstances, a negative net worth is not a good thing, not is it something to be proud of. It means that your company could go out of business or you may have to file for bankruptcy, which is not fun at all.

A negative net worth indicates that your liabilities exceed your assets.

Theo mom bought an 8 pack of juice boxes at the store for four dollars. Find the unit rate for the juice boxes

Answers

4/8= 0.50

Each juice box cost 0.50 cents.

Hope this helps!

your local gas stations are having a price war during the past seven days they have lowered the price of regular gas by $0.2 each day define a variable then write and solve an equation to find the total change in gas price show your work

Answers

Answer with explanation:

Let x denotes the number of days and y denotes the total change in gas price ( in dollars).

Given : During the past seven days the price of regular gas is decreased by $0.2 each day.

Rate of decrease =$0.2 per day

Then , Total change in gas price = Rate of decrease x Number of days

i.e.[tex]y= 0.2 \times x[/tex]

i.e. [tex]y=0.2x[/tex] (1)

To find the total change in gas price in 7 days , we put x= 7 in (1) , we get

[tex]y=0.2(7)=1.4[/tex]

Hence, the total change in gas price in 7 days = $1.4

Answer:

0.14

Step-by-step explanation:

Let t be the total reduction. Then ...

t = daily change * number of days

t = 7 * 0.02

t = $0.14!

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