Simplify $\frac{1+\sqrt{2}}{2+\sqrt{3}}$. Your solution can be converted to the form $A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})$, where $A$, $B$, $C$, and $D$ are positive integers. What is $A+B+C+D$?
Answers
Answer:
A+B+C+D = 13
Step-by-step explanation:
The given expression is:
\(\dfrac{1+\sqrt{2}}{2+\sqrt{3}}\)
We have to simply it and express it in the form of:
\(A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})\)
Multiply and divide the given expression with \(2-\sqrt 3\):
\(\dfrac{1+\sqrt{2}}{2+\sqrt{3}} \times \dfrac{2-\sqrt 3}{2-\sqrt 3}\\\Rightarrow \dfrac{(1+\sqrt{2}) \times (2-\sqrt 3)}{(2+\sqrt{3})\times (2-\sqrt 3)}\\\Rightarrow \dfrac{2+2\sqrt2-\sqrt3-\sqrt6}{2^2-(\sqrt{3})^2}\\\Rightarrow \dfrac{2+2\sqrt2-\sqrt3-\sqrt6}{4-3}\\\Rightarrow \dfrac{2(1+\sqrt2)-(\sqrt3+\sqrt6)}{1}\\\Rightarrow 2(1+\sqrt2)-(\sqrt3+\sqrt6)\)
It is the simplified form of given expression.
Formula used:
\((a+b)(a-b) = a^{2} -b^{2}\)
Comparing the simplified expression with \(A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})\)
\(2(1+\sqrt2)-(\sqrt3+\sqrt6)=A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})\\\Rightarrow A =2, B=2, C=3\ and\ D=6\)
So, value of
\(A+B+C+D = 2+2+3+6 = 13\)
Related Questions
PLEASE HELP! I need this answered ASAP ;-; (Question is shown below in the attachment)
Answers
Answer:
3.14 units²
Step-by-step explanation:
The key realization here is that this shape is one quarter of a circle.
Therefore, it's area will be \(\frac{1}{4}\) of the whole circle's area.
So, let's first find the area as if this were a whole circle.
The formula is \(\pi r^2\), and we know that the radius, r, is 2. So:
\(\pi\cdot2^2\\\\\pi\cdot4\\\\3.14\cdot4\\\\12.56\)
Now we need to find one fourth of this, we can do this by dividing by 4.
\(12.56\div4=3.14\)
Hope this helped!
Answer:
pi units squared
Step-by-step explanation:
(cant find pi sign)
(pi times r^2)/4
4pi/4
pi
The base of this pyramid is a rectangle. How many congruent faces does this pyramid have?
The pyramid has 4 congruent faces.
The pyramid has 5 congruent faces.
The pyramid has 1 pair of congruent faces.
The pyramid has 2 pairs of congruent faces.
Answers
Answer: The Pyramid has 2 pairs of congruent faces
Step-by-step explanation:
The explanation of congruent is the face has the same shape and same size. On rectangle pyramid, the height triangle are 2 same faces and 2 same faces, so it has 2 pairs of congruent faces
number 12 please!
12. A wall contains a rectangular window. The area (in square feet) of the window is represented by x ^ 2 - 14x + 48
a. Write a binomial that represents the height of the window.
b. Find the perimeter of the window when the height of the wall is 12 feet.
Answers
Answer :
a - binominal = an algebraic expression of the sum or the difference of two terms. So I put it in the perimter 12. 6+12=18. So the width would be 18. 18+12+18+12 = 30+30 = 60. just put that ig ??
Question : Is this RSM? Because if I knew the grade , advanced/normal/honors I would be able to help u more
Solve step by step : x=12 because it said the height is 12.
Inside, x-6, so therefor it would really be, 12-6. Which we know would be 6.
Perimeter : 60
now we know the inside is 6. The outside height is 12. 6+12=18. So the width would be 18. 18+12+18+12 = 30+30 = 60.
H O P E I H E L P E D ! ! !
giving brainlyest need anser Bud and his friends stopped at a local fast food restaurant after the football game Friday night. Bud ate a one-fourth pound cheeseburger and a large order of fries. The cheeseburger contained 30 grams of total fat. If the recommended daily allowance of total fat for a 2,000 calorie diet is 64 grams, what percent of the daily allowance did Bud have when he ate the cheeseburger? Show your work.
Answers
To find out what percentage of the daily allowance of total fat Bud had when he ate the cheeseburger, we first need to calculate how many grams of total fat he consumed, and then divide that by the recommended daily allowance, and finally multiply by 100 to get the percentage.
Bud ate a cheeseburger containing 30 grams of total fat. The recommended daily allowance of total fat for a 2,000 calorie diet is 64 grams. Therefore, we can calculate the percentage of the daily allowance that Bud had by dividing the amount of fat he consumed by the recommended daily allowance and then multiplying by 100:
Percentage of daily allowance = (30 / 64) x 100 = 46.875%
So, Bud had 46.875% of the recommended daily allowance of total fat when he ate the cheeseburger.
Answer:
46.875 %
Step-by-step explanation:
30 grams of fat out of 64 grams
30/64 =.46875
Change to percent form
46.875 %
A certain Small Factory employs 98 workers. of these 10 received, a wage of $350 per day, and the rest receive $255 per day. To the management, a week is equal to 6 working days. How much does the factory payout each day? How much does the factory payout in a week?
Answers
Answer:
155,640
Step-by-step explanation:
10*350+255*88=(25,940)6=155,640
Answer:
25940 per day
155640 per week
Step-by-step explanation:
If 9 3
2 (3
−
2 )– 27
3
3 2
3 =
1
27
then prove that m – n = 1
Answers
Imagine below explains, please help! This is my last question on my homework.
Answers
2 ⇒ 1
3 ⇒ 3
4 ⇒ 2
5 ⇒ 1
6 ⇒ 3
7 ⇒ 5
8 ⇒ 2
9 ⇒ 4
10 ⇒ 0
11 ⇒ 2
12 ⇒ 2
Hope my answer helps you✌️
Mark BRAINLIEST
Give you the brainlest if can just can with me
Answers
Answer:
Just can with you
Step-by-step explanation
Can just can can can just can can just just just just.
Yup need help again
Answers
Answer: the 2nd one
Step-by-step explanation:
Help pls. Also wdym this is to short yk why so long >:/
Answers
Answer:
Y= mx + b
so Y = 1/3x + 2
just substitute
Now, we shall use points (3,2) as the substitutes for the solution for b, which 3 would be the input and 2 would be y.
Therefore, 2 = 1/3(3) + b
2 = 1 + b, therefore, one would be subtracted from 2 which would give us the answer of b equaling to one. Thus, y = 1/3x + 1
I need help now please
Answers
Answer:
the tens place
Step-by-step explanation:
The tens place value would help you write 50/1,000 as 5/100 because to get 50 to 5, you would need to get rid of the tens place. In other words, you would need to divide by 10.
50 divided by 10 is 5
1,000 divided by 10 is 100
Help me pls. This is a grade
Answers
Answer: He should knit at least 25 scarfs.
Step-by-step explanation:
can you please mark me brainliest?
Pls help I will give u brainlest whoever is first and gets it right!
Answers
Answer:
the answer is D
Step-by-step explanation:
Can someone help with this Algebra? pls will mark Brainlist It's due in 7 mins
13 - 4x = 1 - x
Answers
x = 4
the answer will be x = 4
Answer x=4
Step-by-step explanation:
What is 4^15 or 4^3 x ^5??
Answers
Answer:
Step-by-step explanation
I hope this is the right answer but i'm pretty sure
4^3 x ^5=1073741824
4^3 = 13
^3 = 3
60 + 13 + 3 = 76
76 is the answer
An experiment involves rolling two dice simultaneously. The following table shows the possible outcomes using the format of (die 1,die 2).
What is the probability of rolling 2 even numbers?
Answers
To determine the probability of rolling two even numbers, we need to find the favorable outcomes (outcomes with two even numbers) and divide it by the total number of possible outcomes.
The possible outcomes when rolling two dice are:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
Out of these, the favorable outcomes (outcomes with two even numbers) are:
(2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), (6,6)
Thus, there are 9 favorable outcomes.
The total number of possible outcomes is 36 (since each die has 6 possible outcomes).
Therefore, the probability of rolling 2 even numbers is:
\(\text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{9}{36} = \frac{1}{4} = 0.25\)
Hence, the probability of rolling 2 even numbers is 0.25 or 1/4.
if a die cast rally car drove 75 centimeters per second, how long would it take to go 100cm?
Answers
At Leslie's school, the ratio of boys to girls is 7 to 11. At Mark's school, the ratio of boys to girls is 33 to 44. If both schools have the same total number of students, which statement about the number of boys at Mark's and Leslie's schools is true?
Answers
Answer:
umm it say "Which statement about the number of boys at Mark's and Leslie's schools is true?" so can you tell the statements
Step-by-step explanation:
Answer:
mm it say "Which statement about the number of boys at Mark's and Leslie's schools is true?" so can you tell the statements
Step-by-step explanation:
Step-by-step explanation:
A) 21 + 32 + 54 +(-54) + (-32) + (-21) = ______
B) -25 + 17 - 65 = _____
C) 5 + 9 - 16 = _____
D) -3 - 2 + 5 + 7 = ____
E) -12 - (-8) - 6 + 4 = _____
F) 25 + (-18) - (-14) = _____
G) -4.3 - 3.1+ 5.7 -(-4.3) =___
H) 1 2/3 + (-3 2/3) - 4 =__
I) -2 + 7 - 11 - (-15) + 6 = _____
Answers
B) = -73
C) = -2
D) = 7
E) = -6
F) = 21
G) = 13/5
H) = -6
I) =15
B) 73
C) 2
D) 7
E)-6
F) 21
G) 13 5
H) -6
I) =13 :)
The line graphed below has a slope of ____.
(A) 3
(B) 2
(C) 1/2
(D) 1/3
Answers
Answer:
D) 1/3
Step-by-step explanation:
rise over run
The line went up once while moving 3 to the right.
Answer: (D) - 1/3
Step-by-step explanation: The slope of a line is RISE OVER RUN. The graph shows up (rise) 1, over (run) 3.
Enter the missing numbers in the boxes to complete the table of equivalent ratios.
Answers
Answer:
1) 1
2) 5
3) 36
Answer:
1 ----> 3
6 ----> 9
5 ----> 15
12 ----> 36
Step-by-step explanation:
MULTIPLY BY 3
A line passes through the point (–2, 7) and has a slope of –5. What is the value of a if the point (a, 2) is also on the line?
–7
–1
1
7
Answers
Answer:
The answer is -1.
Step-by-step explanation:
Hope i helped
If xx and y vary directly and y is 21 when x is 7, find y when x is 5
Answers
Answer:
y = 15
Step-by-step explanation:
We need to solve for k
y = x
21 = 7k Divide both sides by 7 to solve for k
3 = k
y = xk
y = 5(3)
y = 15
Answer: y = 15
Step-by-step explanation:
What is the measurement of the longest line segment in a right rectangular prism that is 11.2 centimeters long, 6.6 centimeters wide, and 6 centimeters tall?
Answers
Answer:
Step-by-step explanation:
3.1313109
Answer: the answer should equal 3.131
Step-by-step explanation: as this is the measurement of the longest line in right rectangular prism.
Please got brainliest
(ANswer quickly please!) giving brainliest !!!
Last summer, a sports club had 380 members. This summer, due to some renovations, it has 30% more members. How many members are there now?
Answers
Answer:
494
Step-by-step explanation:
380 * 1.3 = 494
If Point B(-3, -6) is translated right 5 units, then rotated 180˚, what are the coordinates of B'?
Answers
Answer: (-2, 6)
Step-by-step explanation:
Step by step explanation:
Jess is making some fruit baskets each fruit basket weights 67 ounces right inside and equations using ex as the bourbon to represent one apple and get stuck try drawing a diagram each basket contains six identical wheat apples and 7 ounces of strawberries.
A. 6 + 7a = 67 a= 8.7
B. 6(a+7) = 67 a= 4.16
C. 6a+7=67 a= 10
Answers
Answer:
a
Step-by-step explanation:
that Is
answer
through the question
Find the area of the figure
Answers
Answer:
The answer is E
551.6ft²
Step-by-step explanation:
Area of shape =Area of rectangle +Area of circle
A=25×15+22/7×7.5²
A=375+176.8
A=551.7ft²
The model of an old wagon is 48 cm long. The scale of the model is 5 cm: 2 m. What is the actual length of the old wagon?
Answers
The scale of the model is 5 cm : 2 m. This means that for every 5 cm on the model, the actual length is 2 m.
If the length of the model is 48 cm, we can set up a proportion to find the actual length of the old wagon:
5 cm (actual length) / 2 m = 48 cm (model length) / x (actual length)
where x is the actual length of the old wagon.
To solve for x, we can cross-multiply and simplify:
5 cm * x = 2 m * 48 cm
5 cm * x = 96 cm
Dividing both sides by 5 cm, we get:
x = 96 cm / 5 cm
x ≈ 19.2 m
Therefore, the actual length of the old wagon is approximately 19.2 meters.
Write your question here. We can't read your mind. Yet.
Answers
Answer:
38 right-handed players
Step-by-step explanation:
first, let's find 10% of 95. 95 divided by 10 = 9.5. now, we multiply 9.5 times 4 because 9.5 is 10% and we need to find out 40%. 9.5*4=38.