MATHEMATICS HIGH SCHOOL

What is the simplest form of the expression? sqrt 2 - sqrt 6 / sqrt 2 + sqrt 6

Answers

Answer 1
Answer:

Answer:

-2+√(3)

Step-by-step explanation:

we have

(√(2)-√(6))/(√(2)+√(6))

Multiply the expression by the conjugate of denominator

(√(2)-√(6))/(√(2)+√(6))*(√(2)-√(6))/(√(2)-√(6))\n \n=-(√(2)-√(6))^(2)/4  

=-(1/4)*(2-4√(3)+6)\n \n=-(1/4)*(8-4√(3))\n \n=-2+√(3)
Answer 2
Answer:    
\displaystyle \n ( √(2) -√(6))/(√(2) +√(6)) = ( (√(2) -√(6))(√(2) -√(6)))/((√(2) +√(6))(√(2) -√(6))) = \n \n \n = ( (√(2) -√(6))^2)/((√(2))^2 -(√(6))^2) = ( 2-2√(2)√(6) + 6)/(2 -6) = \n \n \n = ( 8-2√(12) )/(-4) = ( 8-2√(4* 3) )/(-4) = ( 8-4√(3) )/(-4) = \boxed{-2+√(3)}

Related Questions

Math Help! 62 points for answer(s) Right answers only, and credible reasoning please. Question 1) Which interval on the graph could be described as linear increasing? A B C D Question 2) Which of the following best describes interval B on the graph shown? Linear constant Linear decreasing Linear increasing Nonlinear increasing Question 3) Keisha ran to swim practice but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour. Which graph best represents the scenario described? Which graph best represents the scenario described? A coordinate plane graph is shown. The axis is labeled time and the y-axis is labeled distance from home in blocks. A line begins at 0 comma 5, decreases to 0.25 comma 2, stays horizontal to 0.6 comma 2, then increases to 0.75 comma 9. The line is horizontal to 1.75 comma 9. A coordinate plane graph is shown. The axis is labeled time and the y-axis is labeled distance from home in blocks. A line begins at 0 comma 0, increases to 0.3 comma 2, increases to 0.5 comma 5, then increases to 0.75 comma 9. The line decreases to 1.75 comma 0, where it touches the axis. A coordinate plane graph is shown. The x-axis is labeled time and the y-axis is labeled distance from home in blocks. A line begins at 0 comma 0, increases to 0.25 comma 5, stays horizontal until 0.5 comma 5, then increases to 0.75 comma 9. The line is horizontal until 1.75 comma 9. A coordinate plane graph is shown. The axis is labeled time and the y-axis is labeled distance from home in blocks. A line begins at 0 comma 5, is horizontal to 0.3 comma 5, increases to 0.5 comma 6, is horizontal to 0.8 comma 6, then increases to 1.75 comma 9 Question 4) The graph shown represents the water level in Kayla’s bathtub as a function of time: Which description would best explain what was happening during Kayla’s bath during interval C on the graph? Kayla ran water to fill the bathtub. Kayla emptied the tub. Kayla got into the bathtub. Kayla soaked in the bathtub
Can someone solve this please
The regular price for a pair of shoes is $48. The store is having a buy one get one off sale. If you buy 2 pairs of shoes for that price, what percent discount is that?
Which statement best describes a solution to the system of equations 3x+Y=17 X+2y=49 A. It has no solution B. It has infinite solutions C. It has a single solution x=15 y=17 D. It has a single solution x=-3 y=26
Macy's department stores markup men's cologne 63% on cost for an 8 ounce bottle. A bottle of cologne costs Macy $23.00. What is the selling price for the 8 ounce bottle

Charlie saves 21.45 each month for 6 months in the seventh month he only saves 10.60 how much money will Charlie have saved in 7 months

Answers

If you would like to know how much money will Charlie have in 7 months, you can calculate this using the following steps:

21.45 each month for 6 months: 21.45 * 6 = 128.7
in the seventh month: 10.60

in 7 months: 128.7 + 10.6 = 139.3

The correct result would be 139.3.

PLEASE HELP The table below represents the distance of a car from its destination as a function of time.


Time
(hour)
x
Distance (miles)
y
0
900
1
850
2
800
3
750


Part A: What is the y-intercept of the function and what does this tell you about the car? (4 points)

Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3 and what does the average rate represent? (4 points)

Part C: What would be the domain of this function if the car traveled the same rate until it reached its destination? (2 points)

Answers

First we have to determine a linear equation. We will take two points (0,900) and (1,850):
y=mx+b
900=m*0+b,   b=900
850=m*1+900
m=-50
Linear equation is:
y=-50x+900
Part A: y-interception is y=900 or(0,900).
It means that a car has to travel a distance of 900 miles to reach a final destination.
Part B:Average rate of change:(y2-y1)/(x2-x1) = (750-850)/(3-1)= (-100)/(2)=-50. It represents how many miles per one hour changes the distance from a destination.
Part C: Domain of this function if the car traveled the same rate until it reached its destination:
0=-50x+900
50x=900
x=900/50=18
Domain: x∈ [0, 18].
 

Answer:

Step-by-step explanation:

First we have to determine a linear equation. We will take two points (0,900) and (1,850):

y=mx+b

900=m*0+b, b=900

850=m*1+900

m=-50

Linear equation is:

y=-50x+900

Part A: y-interception is y=900 or(0,900).

It means that a car has to travel a distance of 900 miles to reach a final destination.

Part B:Average rate of change:=-50. It represents how many miles per one hour changes the distance from a destination.

Part C: Domain of this function if the car traveled the same rate until it reached its destination:

0=-50x+900

50x=900

x=900/50=18

Domain: x∈ [0, 18

Luisa's restaurant and Bill comes to $75.50, and she leaves a 15% tip. What is Luisa's total restaurant bill?

Answers

The total amount is given by the equation A = $ 86.825

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount in the restaurant be represented as A

Now , the equation will be

The amount of bill from the restaurant = $ 75.50

The percentage of tip by Luisa = 15 %

So , the amount of tip by Luisa = ( 15/100 ) x amount of bill from the restaurant

Substituting the values in the equation , we get

The amount of tip by Luisa = 0.15 x 75.50

The amount of tip by Luisa = $ 11.325

So , the total amount in the restaurant A = amount of bill from the restaurant + amount of tip by Luisa

Substituting the values in the equation , we get

The total amount in the restaurant A = $ 75.50 + $ 11.325

The total amount in the restaurant A = $ 86.825

Hence , the equation is A = $ 86.825

To learn more about equations click :

brainly.com/question/19297665

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if she leaves a 15% tip then the total bill is $86.83 when rounded. multiply 75.50 by 1.15.

you are given two sequences tn=4+(n-1)7 and Sn=4(2)^n-1. Without calculating, which term is bigger t534 or S534? why?

Answers

2^534 would be an absolutely huge number.

4+533*7 wouldn't get near 4*(2^534)-1.

Please need help!!!!

Answers

it's is true because 4 and 5are closer

Write log8 3 as a logarithm of base 5.1) (log3)5/(log8)5
2) (log5)3/(log5)8
3) (log8)5/(log3)5
4) (log5)8/(log5)3 ...?

Answers

The answer is 2) (log5)3/(log5)8

We will use the change-of-base formula: log_a(x)= (log_b(x))/(log_b(a))

So, if we want to write log8 3 as a logarithm of base 5,  in these example a = 8, x = 3, b = 5:
log_8(3)= (log_5(3))/(log_5(8))
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