Answers
Answer:
[tex]B=\sqrt{2}[/tex]
Step-by-step explanation:
Original equation:
[tex]B = \sqrt{2+\sqrt{3}} - \sqrt{2 - \sqrt{3}}\\[/tex]
Square both sides:
[tex]B^2=(\sqrt{2+\sqrt{3}})^2 + 2(\sqrt{2+\sqrt{3}} * (-\sqrt{2 - \sqrt{3}}) + (-\sqrt{2-\sqrt{3}})^2[/tex]
Cancel out the square roots and squares:
[tex]B^2=2+\sqrt{3}}+ 2(\sqrt{2+\sqrt{3}} * (-\sqrt{2 - \sqrt{3}}) + 2-\sqrt{3}[/tex]
Add the sqrt(3) and -sqrt(3) as well as 2 and 2
[tex]B^2=4 + 2(\sqrt{2+\sqrt{3}} * (-\sqrt{2 - \sqrt{3}})[/tex]
Use the identity: [tex]\sqrt{a} * \sqrt{b} = \sqrt{a * b}[/tex] to rewrite the two square roots being multiplied:
[tex]B^2=4 + 2(-\sqrt{(2+\sqrt{3}) * (2 - \sqrt{3}}))[/tex]
Use difference of squares: [tex](a-b)(a+b) = a^2-b^2[/tex]
[tex]B^2=4 + 2(-\sqrt{2^2-\sqrt{3}^2})[/tex]
Square both sides
[tex]B^2=4 + 2(-\sqrt{4-3})[/tex]
Subtract:
[tex]B^2=4 + 2(-\sqrt{1})[/tex]
Evaluate square root of 1:
[tex]B^2=4 + 2(-1)[/tex]
Multiply
[tex]B^2=4 -2[/tex]
Subtract
[tex]B^2=2[/tex]
Take square root of both sides:
[tex]B=\sqrt{2}[/tex]
Related Questions
NEED QUICK HELP 20 POINTS
Answers
Answer:
Hello!
[tex]2^{3} +3^{2} -3[/tex]×[tex]4-5^{2}[/tex]÷[tex]5+(7[/tex]×[tex]4)[/tex]
The simplified value of the expression is 28
Hope this helped!
Answer:
The answer is 28
15. The cost of one yard of fabric is $7.99. What is the cost of 0.51 yd of fabric correct to 2 decimal places?
Answers
Answer:
Step-by-step explanation:
1 yard = $7.99
0.51 yard = x
cross multiply
1 (x) = ($7.99 × 0.51)
1 (x)/1 = 4.0749/1
x = 4.07
PLEASE HELP!!!!!
One of the angles in a right triangle is 20°. A median, an angle bisector, and a height are all drawn from the right angle.
a)Find the angle measure between the median and angle bisector.
b)Find the angle measure between the angle bisector and the height.
Answers
Answer: B. Find the angle measure between the anle bisetor and the height step-by-step explanation:
I my self dont really want to learn mysef i just get awnsers from here i know most of yall do the same so no step by step
please help!!! Evaluate the following expression.
10 x (-9 x (-6))
Answers
Answer: 540
Step-by-step explanation:
To solve this expression, we use PEMDAS to solve it.
-9*-6= 54
54*10=540
Answer:
540
Step-by-step explanation:
first, evaluate parenthesis and [tex]-9*-6=54[/tex] because the negatives cancel out, and multiply by 10 so you get 540
Show all work.
10. If ab + 2c= c, then c =
(A) 2ab+c
(B) 4abc
(C) 3abc + 4c
(D) c+ 2ab
Answers
Answer:
Step-by-step explanation:
6.) Write an addition expression to describe skateboarding
situation. Then determine the sum.
Hank starts at the bottom of a half pipe 6 feet below street
level. He rises 14 feet at the top of his kickturn.
Answers
first it was 6 feet and then he rises 14 more. pretty simple :)
Answer:
-6 + 14 = 8
Step-by-step explanation:
Hank starts at 6 feet below street level. He rises 14 feet at the top of his kickturn.
Rewrite the fraction as a decimal.
13/10 = ?
Answers
Answer:
13/10 as a decimal is 1.3
Step-by-step explanation:
Literally all you have to do is solve the fraction.
What is 13 divided by 10?
The answer is pretty obvious and you will get 1.3
So 13/10 into a decimal is 1.3
Hope this helped! :D
PLEASE HELP ASAP REALLY EASY
79.04/___=9.5
3.6 + 5.7 + __=17.024
56.89 - ___=2.001
8.7 x __ =16.2
356/__=3.56
5.0168+___=25
3.90800 - ___=0.15
___+0589=14
Answers
2. 7.724
3. 54.889
4. 1.862068965517241
5. 100
6. 19.9832
7. 3.758
8. 13.9411
7.724
54.889
1.862068965517241
100
19.9832
3.758
13.9411
A camera usually sells for $68. Because it was slightly damaged, it sold for $59.90, what was the rate of the discount to the NEAREST PERCENT?
Answers
I need help with this question
Answers
Answer:
x=12
Step-by-step explanation:
[tex]16+20+2x=60\\36+2x=60\\2x=24\\x=12[/tex]
the perimeter is the side lengths added together meaning it is
[tex]16+20+x+x=60[/tex]. x+x can be simplified to 2x. now solve for x
Answer:
x = 12 ft
Step-by-step explanation:
We know that by adding up all of the values of the sides, we will get the value of the perimeter. Using this information, we can set up an equation and simplify to find the variable.
16 + 20 + x + x = 60 <----- The sum of the sides is the perimeter
16 + 20 + 2x = 60 <------ Combine variables (x + x = 2x)
36 + 2x = 60 <----- Add 16 and 20
2x = 24 <----- Subtract 36 from both sides
x = 12 <----- Divide both sides by 2
8.37 Sale prices at the Ajax Outlet Store are 50% below original prices. On Saturdays, an additional discount of 20% off the sale price is given. What is the Saturday price of a coat whose original price is $180?
Answers
Answer:
Given:
Sale prices at the Ajax Outlet Store are 50% below the original prices. On Saturdays, an additional discount of 20% off the sale price is given.To find:
The Saturday price of a coat whose original price is $180.The formula used to calculate the percentage is (value/total value)*100%.
Step-by-step explanation:
Step 1 of 2
The original price of coat = $180
Ajax always sells at 50% discount
So their sale price = $90
Step 2 of 2
On Saturdays they sell 20% less
Which implies-
1/5*90 = 18
90-18=72
They sell at $72 on Saturday.
9000/100=90
90*20=1800
1800/100=18
90-18=72
The Saturday sale price of the coat would be $72.
50 points please help asap
Answers
Answer: 5 blue marbles than 3 green marbles. Than 3 green on top/5 red on bottom.
Step-by-step explanation:
For every 3 green marbles there are 5 blue marbles.
Answer:
For every 3 green marble there are 5 blue marbles.
Step-by-step explanation:
help 20 points added
Answers
Pt 2: 1 ladybug 4 butterflies
Pt 3: 5 Ladybugs 3 Ladybugs
2) 1 ladybug 4 butterflies
3) 3 butterflies 8 ladybugs
A computer prints out 1,000 characters every 3 seconds. If there are approximately 3,300 characters on a page the how many seconds will it take to print 5 pages?
Answers
3300 x 5 = 16,500
16,500 / 1000 = 16. 5
16.5 x 3 = 49.5
It takes to print 5 pages in 49.5 seconds
We have given that,
A computer prints out 1,000 characters every 3 seconds. If there are approximately 3,300 characters on a page the.
We have to determine how many seconds will it take to print 5 pages.
What is the time in the second?
The second (s or sec) is the International System of Units (SI) unit of time measurement. One second is the time.
3300 x 5 = 16,500
16,500 / 1000 = 16. 5
16.5 x 3 = 49.5
To learn more about the time visit:
https://brainly.com/question/10428039
#SPJ5
Help!! I have no clue what to do. I’m struggling and stuck on this whole problem. Can you please explain how you got the answers? Thank you!
Answers
Explanation 5x-3x will leave you with 2x on one side and only 7 on the other side of the equal sign
Second one: Multiply each side by 1/3
Explanation: Multiplying by a fraction is the equivalent to dividing. If you divide each number by 3 you are left with
4x + 1 = 2
Third one: Add -3 to each side
Explanation: Since -3 has no variable you can only subtract from the real numbers giving you 7 - 6x = 1 + 5x
Fourth: Multiple each side by -3
Explanation: Multiplication reverses division so multiplying 5x/-3 by -3 eliminates the -3 leaving you with 5x. the other side is just 12, and 12 • -3 = -36
Last one: Multiply by -1/3
Explanation: Like I said earlier, multiplication and division eliminate each other so on the first side it eliminates -3 and on the other side you just preform normal division.
Hope this helps! :)
2. mult. each side by 1/3
3. add -3 to each side
4. mult. each side by -3
5. mult. each side by -1/3
Circle the correct option: A, B, C, or D.
3. A box of 24 churros cost $25.50. What is the cost of one churro correct to 2 decimal places?
A $1.04
B $1.06
C $1.07
D $1.05
Answers
Answer:
B
Step-by-step explanation:
24 = $25.50
1 = x
cross multiply
$25.50/24 = 24x/24
$1.0625 = x
2 decimal places = $1.06
2 ACTIVITY: Estimating a Whole
Work with a partner. Use a model to estimate the answer to each question.
c. 110 is 20% of what number?
Answers
Answer: 550
15. The total mass of 6 similar bags of salt is 4.5 kg. What is the mass of each bag of salt rounded to 1 decimal place? Give the answer in kilograms.
Answers
Answer:
0.7kgStep-by-step explanation:
Total mass of the bags of salt = 4.5kgnumber of bags of salt = 6To find the mass of each bag of salt, we divide the total mass by the number of salt bags we have which is 6Therefore 4.5 ÷ 6 = 0.75 KgMass of each bag of salt = 0.75 Kg0.75Kg rounded to ONE decimal place = 0.7 KgHope this helps.Good luck ✅.6 divided by 4.5 is 0.7 kg
HELPPPPPPPP: A car stero that regularly sells for $109 is in sale at a 15% discount. How much is the discount?
Answers
Answer:
Step-by-step explanation:
the discount is $16.35
Answer:
15% = $16.35
Step-by-step explanation:
To find the amount, lets find 10% first. To do so, move the decimal one place to the left.
10%= $10.90
Now, lets find half of 10% value to add it up to deal, 15% off.
10.90/2= 5.45
5%= 5.45
Now, we must add the values of 10% and 5% to find the discount off of the stereo.
10.90 + 5.45 = 16.35
15% = $16.35
Your discounted amount will be $16.35.
What expression is equivalent to the algebraic expression 3(-2x-1)?
Answers
Answer:
-6x-3
Step-by-step explanation:
distribute the 3 by multiplying it with the -2x and the -1
i got this for mine and it was right!!
have a blessed day
send help asap 20 points
(if your confident please go answer the other questions im going to post after this each one will be 20 pointed added)
Answers
Essentially, we are being asked to find the unit rate. We want to figure out how many dollars it costs to buy 1 yard of fabric.
$10 : 8 yards
---Divide both values by 8
$1.25 : 1 yard
Hope this helps!
Jeremy earns extra money selling concessions during school sports events. On Thursday, he spent $126.78 at the local whole sale store for concession supplies. His concession sales at two weekend games were $345.26 and $248.24. After taking into account his expenses, how much money did Jeremy earn?
I need your help, thank you in advance!
Answers
Answer:
I think Jeremy earned $609.118 because you have to add
$126.78+$248.24+$345.26=$609.118
Step-by-step explanation:
hope this helps if it is wrong let me know have a blessed day
Jeremy earns $466.488extra money.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
Jeremy spent for concession supplies $126.78
Jeremy sales at two weekend games were $345.26 and $248.24
Jeremy earns extra money :
⇒ $248.24+$345.26 - $126.78
⇒ $466.48
Hence, Jeremy earns $466.488 extra money.
Learn more about Arithmetic operations here:
https://brainly.com/question/25834626
#SPJ5
using a mathematical table evalutate the square root of 0.792
Answers
Find the answers for the frequency and relative frequency tables below.
PLEASE ANSWER ALL 3 QUESTION, thank you
Answers
please helpp me asap i asked before and their answers were wrong \
2nd pic is the hint
Answers
Answer:
Step-by-step explanation:
In the first box, there should be 3 green marbles and 5 blue marbles. 3 for every 5.
In the second box, there should be 5 green marbles and 3 blue marbles. 5:3 would mean 5 against 3.
In the third box, there should be 3 green marbles and 2 blue marbles. This is because out of 5, there are 3 green, and 2 blue are left.
18. LOGIC A person surveys residents of a town to determine whether a skateboarding ban should be overturned.
a. Describe how the person could conduct the survey so that the sample is biased toward overturning the ban.
Answers
Answer:
go to a skatepark
Step-by-step explanation:
Answer:
Thus, conducting the survey so that the sample is biased toward overturning the ban is to increase the number of people not favoring the skateboarding ban in comparison to people who are favoring the ban.
Step-by-step explanation:
Given:
A survey regarding the decision on banning skateboarding
To find:
how the poll may be conducted in such a way that the sample is skewed in favor of reversing the prohibition
Explanation:
A reasonable sample is
● selected at random,
● representative of the population, and
● large enough to provide accurate data.
While taking the sample, the number of people who are not favoring the ban on skateboarding should be increased in comparison to the number of people who are in favor of the ban. Doing so will result in a biased sample indicating that majoring of people do not want to ban skateboarding as the sample is projecting a majority who are against the ban instead of favor the ban.
23. You want to estimate the number of students in your school whose favorite subject is biology. You survey the first 10 students who arrive at biology club. Determine whether the sample is biased or unbiased. Explain.
Answers
1. In an experiment, how can you determine the number of possible results?
Answers
8.3.4 Karl bought five folders from Pay-A-Lot at a cost of $2.50 each. Pay-A-Lot had a 20% -off sale the following day. How much could Karl have saved on the purchase by waiting a day?
Answers
Answer:
Karl could have saved $2.50
Step-by-step explanation:
Cost of folders without the sale: 2.5*5 = $12.50
Cost of folders with the sale: 0.8*2.5 = $2 per folder * 5 folders = $10.00
Difference between prices: 12.5-10 = $2.50
Answer:
2.50$ Karl could have saved on the purchase by waiting a day.
Step-by-step explanation:
Given: total number of folders Karl bought is 5 .
The cost of each folder is 2.50$.
20% off sale the following day at Pay-A-Lot.
we have to find the 20% of each folder and then add them to get the final saving of Karl if he had waited for a day.
Step 1 of 2
20% of 2.50$ is equal to
[tex]$$\begin{aligned}&=2.50 \cdot 20 \% \\&=2.50 \cdot \frac{20}{100} \\&=0.50 \$\end{aligned}$$[/tex]
this is the amount Karl would save on each folder if waited for a day or this is the discount on the amount of 2.50$ that the shopkeeper will give the next day on each
Step 2 of 2
Karl bought 5 folders
so, total savings would be equal to
[tex]$$\begin{aligned}&=5 \cdot 0.50 \\&=2.50 \$\end{aligned}$$[/tex]
What fraction does the red dot represent?
Answers
Hello,
There are ten dashes between the 0 and the 1. The red is located at the 4th dash so 4/10 = (2 × 2)/(2 × 5) = 2/5
The red dot represent 2/5.
Answer:
Step-by-step explanation:
The red dot is at 0.4 unit from the origin. Each division on the number line shown represents 0.1 unit.