Express (8 - 3sqrt(2))/(4 + 3sqrt(2)) in the form of a + b * sqrt(2) where a and b are integers.
Answer: [tex]\boldsymbol{-25+18\sqrt{2}}[/tex]
The expression is in the form [tex]a+b\sqrt{2}[/tex] where a = -25 and b = 18
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Work Shown:
Let [tex]x = 3\sqrt{2}[/tex] and then square both sides
[tex]x = 3\sqrt{2}\\\\x^2 = \left(3\sqrt{2}\right)^2\\\\x^2 = \left(3\right)^2*\left(\sqrt{2}\right)^2\\\\x^2 = 9*2\\\\x^2 = 18\\\\[/tex]
We'll use both x and x^2 later on.
---------------------
The denominator is in the form 4+x. We'll multiply top and bottom by 4-x to then use the difference of squares rule. This will allow us to eliminate the square root in the denominator.
[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}}\\\\\frac{8-x}{4+x}\\\\\frac{(8-x)(4-x)}{(4+x)(4-x)}\\\\\frac{32-8x-4x+x^2}{16-x^2} \ \text{ difference of squares rule}\\\\\frac{32-12x+x^2}{16-x^2}\\\\[/tex]
[tex]\frac{32-12*3\sqrt{2}+18}{16-18} \ \text{ plug in } x = 3\sqrt{2} \text{ and } x^2 = 18\\\\\frac{50-36\sqrt{2}}{-2}\\\\\frac{-2(-25+18\sqrt{2})}{-2}\\\\\boldsymbol{-25+18\sqrt{2}}[/tex]
Therefore,
[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}}=\boldsymbol{-25+18\sqrt{2}}[/tex]
-------------------------------------
Checking the answer:
Use a calculator to find that,
[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}} \approx 0.45584412271571 \\\\-25+18\sqrt{2} \approx 0.45584412271571[/tex]
We get the same decimal approximation, which helps confirm the correct answer.
Or you could use the idea that if M = N, then M-N = 0 to subtract the original expression M and the final result N. You should get 0 or very close to it.
Solve for x.
8x - 5 = 6x + 8x + 10
Therefore, we found that x = -5/2.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
How do you pass 10th grade geometry
Answer:
Study hard and stay determined
Find simple steps to help you remember and "wrap you head" around it better.
If you ask for help and try your best you should be able to get enough passing grades to pass 10th grade geometry. If I did, that means you can too.
How do you pass any course?
Study and study some more.
There is no easy road to success.
Math is not easy. If math were easy, everybody would get an A. What specific geometry topic are you stuck on? I am not that smart. I passed geometry at FDR HIGH SCHOOL back in the 1980s. We had no internet back then. At least you have YOU TUBE. If I passed, so can you.
What is the percent decrease from 95 to 68 round to the nearest percent
The decrease is (95-68) = 27 .
As a fraction, the decrease is 27/95 of the original amount.
To change any fraction to a decimal, do the division:
(27) divided by (95) = 0.2842...
To change any decimal to a percentage, move the
decimal point two places that ==> way:
0.2842... = 28.42... %Answer:
Step-by-step explanation:
[tex]\qquad[/tex]☀️ At first we need to find out the difference between 95 and 68.
[tex]\qquad[/tex][tex] \sf \longrightarrow 68 -95 \\[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow -27[/tex]
[tex]\qquad[/tex]☀️ Now, divide the number by "the starting number.
[tex]\qquad[/tex][tex] \sf \longrightarrow \dfrac{-27 }{97}[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow -0.2842[/tex]
[tex]\qquad[/tex]☀️ And finally, we have to multiply the result by 100 to get it in terms of percent.
[tex]\qquad[/tex][tex] \sf \longrightarrow -0.2842 \times 100[/tex]
[tex]\qquad[/tex][tex] \red{\bf \longrightarrow -28.42℅}[/tex]
Hence, The answer will be -28.42℅[tex]\qquad[/tex]_________________________
x-5y=16 , 4x-2y=-8 solve using elimination method
Answer:
x = -4
y = -4
Step-by-step explanation:
L1 x - 5y = 16
L2 4x - 2y = -8
4*L1 - L2
4x - 20y = 64
-4x + 2y = 8
-----------------------
-18y = 72
y = 72 / -18
y = -4
x - 5y = 16
x = 16 + 5y
x = 16 + 5(-4)
x = 16 - 20
x = -4
Jordan made this design from three pieces of square shaped cloth. What is the total area of design Jordan made? EXPLAIN how u found your answer
Applying the area of a square, the total area of the design is: 116 cm²
Area of SquareA square has equal side lengths, s, this, the area of a square is given as: A = s².
The three pieces of square shaped cloth that Jordan made the design from is shown in the image attached below.
To find the total area of the design, find the area of each square shaped cloth and add all together.
Thus, applying the area of a square, the total area would be:
Total Area = 4² + 6² + 8²
Total Area = 116 cm²
Learn more about area of square on:
https://brainly.com/question/16758129
Karma took a 50 question math test, but only 40 questions were correct. What was the percentage of correct answers?
Answer:
85 percent
Step-by-step explanation:
Evaluate the expression 2-8 × 2-7=
Answer:
-21
Step-by-step explanation:
2-8 × 2-7 = 2-(8×2)-7
= 2-16-7
=-14-7
=-21
Help help math math
Answer:
5/1
Step-by-step explanation:
the y is 5units and the x is 1unit
Answer:
7/4
Step-by-step explanation:
Use rise over run to solve
4-(-3) 7
-------- = -
6-2 4
In the New York marathon there were 45 360 runners. 7 /10 of the runners were women. How many of the runners were men?
Answer:
13,608
Step-by-step explanation:
If 7/10 of the runners were women, than 3/10 of the runners were men. 3/10 of 45,360 runners is 13,608.
Hope this helps! Pls give brainliest! Also, plz sub to kgirl633 on yt.
Brandon just got a job at a restaurant. He worked 7 hours and got paid $63. He earns the same amount each hour. How much did Brandon make each hour. In complete Sentence
Answer:
Brandon will make 9 dollars an hour while he works at the resturant
Step-by-step explanation:
63/7=9
Hi!
If he got paid $63 an hour, and he worked 7 hours, we just have to simply divide 63 by 7.
7 goes into 63 nine times, therefore he makes $9 per hour.
Hope this helps and let me know if you need any other help! :D
A bicycle has a listed price of $643.95 before tax. If the sales tax rate is 6.75%, find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
$687.42
Step-by-step explanation:
The total with tax is ...
(price) + (tax rate)×(price)
= price(1 +tax rate)
= $643.95×1.0675 ≈ $687.42 . . . price with tax
It took Erika 8 games to score 30 points. At that rate, how many games will it take her to score 45 points?
Answer : 12 games
Step - by - step explanation :
In - order to find out how many games it will take Erika to get 45 points we need to find out how many points she normally gets in 1 game . . .
What is 30 divided by 8 ? 3.75 ( So Erika gets 3.75 points per game ! )
What is 45 divided by 3.75 ? 12 ( So Erika had to play 12 games in - order to get 45 points ! )
Fill in the blank f(x)=2x+1, then f(___)=13
Answer:
if f(x)=2x+1 then insert 6 in x
f(6)=2*6+1
f(6)=13
so the answer is 13
Solve. 6 Everyone at a park was either hiking or riding a bike. There were 24 more hikers than bike riders. If there were a total of 100 people at the park, how many were hiking?
b r = 178 + h;
b r + h = 676;
then, 178 + 2h = 676 => h = 498/2 = 249 => b r = 178 + 249 = 427
Answer:
676
Step-by-step explanation:
h=b+178=427
b=b=249
-------------
(b+178)+b=676
2b+178=676
2b=498
b=249
-------------
249+427=676
Kaneppeleqw and 2 more u
Determine whether or not the given value is a solution. 1. -5x + 4 = -1; x = -1 2.4x3 = -7; x = -1 3. 3y -4 = 5; y = // 4.-2y + 7 = 12; y = -1/2 5.3a-6 = 18 - a; a = -3 6. 5(2t - 1) = 2 = t; t = 2 7. ax = b = 0; x = b/a 8. ax + b = 2b; x = b/a
#1
[tex]\\ \sf\hookrightarrow -5x+4=-1[/tex]
[tex]\\ \sf\hookrightarrow -5x=-5[/tex]
[tex]\\ \sf\hookrightarrow x=1[/tex]
Incorrect
#2
[tex]\\ \sf\hookrightarrow 4x-3=-7[/tex]
[tex]\\ \sf\hookrightarrow 4x=-4[/tex]
[tex]\\ \sf\hookrightarrow x=-1[/tex]
Correct
#3
[tex]\\ \sf\hookrightarrow 3y-4=5[/tex]
[tex]\\ \sf\hookrightarrow 3y=9[/tex]
[tex]\\ \sf\hookrightarrow y=3[/tex]
Ans not given
#4
[tex]\\ \sf\hookrightarrow -2y+7=12[/tex]
[tex]\\ \sf\hookrightarrow -2y=5[/tex]
[tex]\\ \sf\hookrightarrow y=-5/2[/tex]
Incorrect
#5
[tex]\\ \sf\hookrightarrow 3a-6=18-a[/tex]
[tex]\\ \sf\hookrightarrow 4a=24[/tex]
[tex]\\ \sf\hookrightarrow a=6[/tex]
Incorrect
#6
[tex]\\ \sf\hookrightarrow 5(2t-1)=2[/tex]
[tex]\\ \sf\hookrightarrow 10t=7[/tex]
[tex]\\ \sf\hookrightarrow t=7/10[/tex]
Incorrect
#7
[tex]\\ \sf\hookrightarrow ax-b=0[/tex]
[tex]\\ \sf\hookrightarrow x=\dfrac{b}{a}[/tex]
Correct
Done
3. Chris rode his bike along the same route every day for 60 days. He logged that he had gone exactly 127.8 miles.How many miles did he bike over the course of two weeks
Step-by-step explanation:
2wks = 24 days
If he spent 60days going 127.8 miles
He will spend 14 days going X miles
60/14 =127.8/X cross multiply
60X= 14×127.8
X=( 14×127.8)÷60
X= 29.82 miles
Determine if the two triangles are congruent. If they are, state how you know
Giving 100 points for this and Brainliest!!
Well I ask this question for 100 points: I don't know how much it will give you
Please give me an explanation, no link please:
Write a few sentences to end Sarah’s story. How many shark teeth did she find? How many shark teeth did John find? How much money did they earn?
Answer: Sarah found 10 shark teeth(3 + 7 = 10).
John found 5 shark teeth(10/2 = 5).
The total money they earned was $5 x 15 = $75.
Explanation;
Given that:
$5 per shark tooth15 total collected shark teeth5 x 15 = 75, therefore the total money Sarah and John earned was $75.
The few sentences to end Sarah's story are: Sarah found 10 shark teeth for $50. John found 5 shark teeth for $25. They got $75 from their neighbor in total.
Answer:
Sarah’s neighbor offers to pay her $5 for every shark tooth she finds on the beach. After collecting only three shark’s teeth, Sarah decides to share the opportunity with her friend John. Sarah can find shark teeth twice as fast as John, but she can earn even more money with his help.
Sarah can use the expression 5(2j + 3 + j) to represent the amount of money they can earn.
Part 1: Writing Expressions
Q1. Write an expression that looks like Sarah’s expression: 5(2j + 3 + j). Replace the coefficients so that your expression is not equivalent. You may use any number that you choose to replace the coefficients. Be sure to leave the variables the same. For example, 8(3j + 7 + 3j) looks like Sarah’s expression but is not equivalent.
25(10j + 18 + 5j)
Step-by-step explanation:
Solve for equation for x: 5x^2 – 10x – 6 = 0
Correct me if im wrong po
Pls help as soon as possible thank you
Answer:
answer is b
Step-by-step explanation:
6x+10
6*-3+10=-8
4x+4
4*-3+4=-8
8. The exact lengths of the segments
connecting corresponding vertices
are:
BK = 2.2 units KB' = 2.2 units
AJ = 5.6 units JA' = 5.6 units
CL = 3.8 units LC' = 3.8 units
Which segments have equal
lengths?
no segments
all segments
corresponding segments
Answer:
corresponding segments
Step-by-step explanation:
BK = KB'
AJ - JA'
CL = LC'
a coffee mug collection includes four red mugs, eight yellow mugs and two white mugs. What is the probability of selecting two white mugs one after another?
Assuming that the selection process was done without replacement, the probability of selecting two white mugs without replacement is 1/28
Given dataSample Space
Red mugs = 4
yellow mugs = 8
white mugs = 2
Sample Size = 4+8+2 = 14
We are going to assume the selection was done with out replacement
Hence the probability of selecting the first white mug is
Pr(W1) = 2/8 = 1/4
The probability of selecting the second white mug is
Pr(W2) = 1/7
Hence the probability of selecting two white mugs one after another
= 1/4*1/7
=1/28
Learn more about probability at:
https://brainly.com/question/25839839
Please help!! Best answer gets brainliest<3
A family of 6 used 5400l of water in 7 days. Each member of the family used the same amount of water each day. How many litres of water did each person use in a day?
Answer:
Hello! The answer for this is 900 liters a day
Step-by-step explanation:
After a storm damages the community center, Shanika and her friends hold fundraising events to help pay for repairs. After the first event, they raise $240, which is 10% of the total amount that they want to raise
Answer:
Step-by-step explanation:
The total they want to raise is $2,400 if that is what you're asking?
I need help with math
51+60= 111 Answers fast rights
1/8+1/4=? do you know what it could be!?
Answer:0.375
Step-by-step explanation:
1/8 + 1/4 = 3/ 8=0.375
What is the missing number in the table
Am i blind or does this just not make any sense? Pls help!
Answer:
0.4
Step-by-step explanation:
2/5 converted into hundredths is 40/100.
40/100 as a decimal is 0.40, or 0.4
-hope it helps