Given that: √{11 + 4√(7)}
Let √{11 + 4√(7)} = √(x) + √(y)
Squaring on both sides then
= [√{11 + 4√(7)}]² = {√(x) + √(y)}²
= 11 + 4√(7) = x + y + 2√(xy)
= 11 + 2√(7 * 2²) = x + y + 2√(xy)
= 11 + 2√(7 * 2*2) = x + y + 2√(xy)
= 11 + 2√(7 * 4) = x + y + 2√(xy)
= 11 + 2√(28) = x + y + 2√(xy)
On comparing with both sides, we notice that:
⇛x + y = 11 →→→→Eqn(1)⇛2√(xy) = 2√(28)
⇛ xy = 28
We know that
(x-y)² = (x+y)² - 4xy
(x-y)² = (11)² - 4(28)
(x-y)² = (11*11) - 112
(x-y)² = 121 - 112
(x-y)² = 9
x - y = √(9)
x - y = √(3*3)
Therefore, x - y = 3 →→→→Eqn(2)On adding equation (1) and equation (2), we get
x + y = 11
(+) x - y = 3
_______
2x = 14
Shift the number 2 from LHS to RHS, changing it's sign.
⇛x = 14/2
⇛x = 7/1
Simplify the fraction to get the value of x.
Therefore, x = 7Now, substitute the value of x in equation (1) then
x + y = 11
⇛7 + y = 11
Shift the number 7 from LHS to RHS, changing it's sign.
⇛y = 11 - 7
Therefore, y = 4Now, we have: x = 7 and y = 4
So,
√(x) + √(y) = √(7) + √(4) = √(7) + √(2*2) √(7) + 2
(Or)
Short Method:√{11 + 4√(7)}
= √{11 + 2√(7*4)}
= √{11 + 2√(7)√(4)}
= √[{√(7)²} + {√(4)}² + 2√(7)√(4)
[since, (a+b)² = a² + 2ab + b²]
= √[{√(7) + √(4)}²]
= √(7) + √(4)
= √(7) + √(2*2)
Therefore, √{11 + 4√(7)} = √(7) + 2
Answer: Hence, the simplified form of √{11 + 4√(7)} is √(7) + 2
also read similar questions: Simplify: 3√4 508/1331 I am new in brainly. This is one of my homework assignment maths question.
https://brainly.com/question/26352309?/referrer
Please let me know if you have any other questions.
The solution √(11 +4 √7) is mathematically given as
x=4.64575131
What is the solution to the equation √(11 +4 √7)?Question Parameters:
√(11 +4 √7)
The question requires resolving the above expression and deciphering the solution
Generally, the equation is mathematically given as
x=√(11 +4 √7)
Hence
x=√(11 +4*2.64575131)
In conclusion, The resolution of the expression x=√(11 +4 √7) is
x=4.64575131
Read more about Arithmetic
https://brainly.com/question/22568180
ABC is a straight line where BC = 3AB. OA = a, AB = b Express OC in terms of a and b.
Pls help me and thanks rounding
Answer:
Step-by-step explanation:
1399 rounds to 1400 so A is not the answer
1449 rounds to 1400 so B is not the answer
1589 rounds to 1600 so D is not the answer
The hundreds place is second from the left. Third from the left determines what happens to second from the left. 5 and over round up. Less than 5 just use the first 2 digits left and 2 zeros.
The answer is C
1457 rounds to 1500
1547 rounds to 1500
Help please with explanations
The length of the segment AC is 4√3, so the correct option is E.
How to get the length of AC?
In the image, you can see a right triangle.
We do know that AB = 8 units, and BC is equal to the radius of the circle.
We also know that the area of the circle is 16pi, and the area of a circle of radius R is:
A = pi*R^2
Replacing our area, we get:
16pi = pi*R^2
16 = R^2
√16 = R = 4.
So the radius of the circle is 4, which means that BC = 4.
Now we can use the Pythagorean theorem, that says that the sum of the squares of the cathetus is equal to the square of the hypotenuse, this can be written as:
AB^2 = BC^2 + AC^2
8^2 = 4^2 + AC^2
64 - 16 = AC^2
√48 = AC
√(3*16) = AC
4√3 = AC
So the correct option is E.
If you want to learn more about right triangles, you can read:
https://brainly.com/question/2217700
What’s the correct answer for this question?
Answer:
Absolute change: $1,700
Relative change: 7.6577%
Step-by-step explanation:
Absolute change: $22,200 - $20,500 = $1,700
Relative change: (100 × $1,700) : $22,200 ≈ 7.6577%
There are 90 kids in the band. 20% of the kids own their own instruments, and the rest rent them.How many kids own their own instruments?
Answer:
18 kids
Step-by-step explanation:
because you multiply 0.2 by 90 and it equals 18
3. How many y-values are there
for each x-value in the function
represented by the graph?
(A) 0
(C) 2
(B) 1
0 infinitely many
Which equation has the same solution as x^2 - 6x - 14 = 0?
A (x + 3)^2 = 23
B (x - 3)^2 = 23
C(x + 3)^2 = 5
D (x-3)^2 = 5
Answer: B
Step-by-step explanation:
[tex]x^{2}-6x-14=(x-3)^{2}-14-9=(x-3)^{2}-23[/tex]
Madison is buying a laptop for $586. He paid for the laptop
using four $100 bills, fifteen $10 bills and forty-six $1 bills. How
much did Madison pay?
Repost of the last question.. Sorry it wasn't full.
someobe please help me here
Answer:
[tex]y < -\frac{4}{5} x+4[/tex]
Step-by-step explanation:
To graph the equation, draw the line [tex]y = -\frac{4}{5} x+4[/tex] and shade in the lower left part of the graph under the line to illustrate the inequality
Then pick two points to test
1. what is the y-intercept of this line?
2. what is the slope of this line?
3. what is the equation for this line?
Step-by-step explanation:
1. The y-intercept is the value for y when x = 0.
When x = 0, y equals 7.
Represented as:
(0, 7)
2. How to find the Slope?
Find 2 points on the graph then use the slope formula.
[tex] \frac{y2}{x2} - \frac{y1}{x1} = m[/tex]
m = slope
2 points:
(0, 7)
(2, 3)
Substitute the points into the formula:
[tex] \frac{3}{2} - \frac{7}{0} = m[/tex]
Subtract:
[tex] \frac{ - 4}{2} = m[/tex]
[tex] \frac{ - 4}{2} = m[/tex]Simplify:
[tex] \frac{ - 4 \div 2}{2 \div 2} = - \frac{2}{1} [/tex]
The slope is -2.
Forming an equation:
Use the slope-intercept format.
[tex]y = mx + b[/tex]
m = slope
b = y-intercept
Substitute 7 for b, and -2 for m.
[tex]y = - 2x + 7[/tex]
Solve the follow inequality. ∣3x−4∣≥8
Hello.
Let's solve the absolute value inequality.
In order to do that, let's imagine that |3x-4| is positive.
Since the absolute value of |3x-4| is 3x-4, we write 3x-4 and solve:
[tex]\mathrm{3x-4\geq 8}[/tex]
Now, move -4 to the right, using the opposite operation:
[tex]\mathrm{3x\geq 8+4}[/tex]
Add:
[tex]\mathrm{3x\geq 12}[/tex]
Divide both sides by 3:
[tex]\mathrm{x\geq 4}[/tex]
However, this is only 1 solution.
Let's imagine that |3x-4| is a negative number.
So, the inequality looks like so:
[tex]\mathrm{-3x+4\geq 8}[/tex]
Move 4 to the right:
[tex]\mathrm{-3x\geq 8-4}[/tex]
[tex]\mathrm{-3x\geq 4}[/tex]
Divide both sides by -3:
[tex]\mathrm{x\leq \displaystyle-\frac{4}{3} }[/tex]
Therefore, the solutions are
[tex]\mathrm{x\geq 4}\\\mathrm{x\leq \displaystyle-\frac{4}{3} }[/tex]
[tex]\bigstar[/tex] Note:
If we divide both sides of an inequality by a negative number, we flip the inequality sign.
I hope this helps you.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
x/3 = 2,how to calculate x?
please help me
Answer:
[tex]\displaystyle{ \frac{x}{3} = 2}[/tex]
[tex]x = 2 \times 3[/tex]
[tex]x = 6[/tex]
Let's check:-[tex]\displaystyle{ \frac{x}{3} = 2 }[/tex]
[tex]\displaystyle{ \frac{6}{3} = 2 } [/tex]
[tex] = > 2 = 2[/tex]
(57x2:3)+32x450-[39-(4+2):2[+8=
Answer:
57×2/3+32×450-[39-4+2]/2+8
57×2/3+32×450-(39-6/2)+8
57×2/3+32×450-36+8
57×2/3+14400-28
57×2/3+14372
38+14372
14410
what are the zeros of f(x)=x^2+2x-80
Answer:
The zeros are 8 and -10, all u have to do is substitute x for those values, factor it, or graph it.
Step-by-step explanation:
what is the hardest part of math
Answer:
Trying to learn it math isint about learning a eqution. its about expanding your mind and making you think.
Step-by-step explanation:
Hope it helps:)
Tony needs to buy hotdogs and hotdog buns for his cookout
Answer:
then what happened next so I can answer your questions
Answer:
Do you have any more information on this question so we can answer it for you?
How many solutions does the nonlinear system of equations graphed below
have?
A. Two
B. Zero
C. One
D. Four
The solutions of a system of equations is also the intersection of the two lines. In this case the red parabola and the blue linear equation intersects at One point and there fore the answer is C.) One
I hope it helped, if you need more explanation just comment and I will try to explain better!
For any real number c, sqrt c^2 =
A. I
B. ?
C. c
D. 1
Answer:
option A. |c| is the answer.
because sqrt of any number is always positive. that's why we add the modulas symbol around the interger.
What is the missing numbers in the synthetic division problem below?
Answer:
A. 9
Explanation:
2×4=8 and 8+1=9 so that's it.
Type the single exponent that would appear on the 7: *
7^5 (exponent 5) x 7^6 (exponent 6) x 7^2 (exponent 2)
7^5 x 7^6 x 7^2
Do I add the exponent or multiply?
You add the exponent. You never multiply it.
Hope this helps!
Say, mind doing me a favor and clicking the brainliest button for me? It would help me tons.
~~~PicklePoppers~~~
evauluate the equation r/15 = (-3)
A. r=45
B. r = 18
C. r = -18
D. r = -45
Answer:
The choice D. r= - 45
Step-by-step explanation:
[tex] \frac{r}{15} = ( - 3) \\ \\ r = ( - 3) \times 15 \\ \\ r = - 45[/tex]
-7 < 3x + 2 < 5.
Solve for x
Answer:
-3 < x < 1, This is the domain
The length of the sides of a polygon are in the ratio of 3: 4: 2: 5. If the perimeter is 84 cm, find the N length of the shortest side
Answer:
12 cm
Step-by-step explanation:
First, divide the perimeter by the sum of ratios.
=> 84 / (3 + 4 + 2 + 5)
=> 84 / 14
=> 6
Shortest side
= 2x
= 2(6)
= 12 cm
4
3
С
2
1
In the similarity
transformation of AABC
to ADEF, AABC was dilated by
a scale factor of [?], reflected
across the [ ], and moved
through the translation [ ].
B.
A
-7
-6
-5
-4
-2
-1 0
1
2
3
+
E
D
-2
-3
F
A. 2
B. 1/2
C. 3
D. 1/3
Answer: A
Step-by-step explanation:
Since DE=4 and AB=2, we know the scale factor of the dilation was 4/2 = 2.
2 When you multiply a a number by 7 and add 8 to the answer, you get 50. What is the number?
Answer:6
Step-by-step explanation:
the correct answer would be 6. Step-by-step explanation: when 7 is multiplied by 6 it gives 42 ,then we have to add 8 to the product and it gives 50
An employee works as a teacher at an online school making $38,900 per year. However, the school is hiring a principal at a salary of $59,500 per year.
The employee went back to school to become a principal.
How much more money could the employee make working as a principal instead of a teacher over 5 years?
Enter your answer in the box
Answer:
$103,000
Step-by-step explanation:
teacher : 38,900 x 5 = 194,500
principal : 59,500 x 5 = 297,500
$297,500 - $194,500 = $103,000 more
please help with this
Answer:
1. 120[tex]m^{2}[/tex]
2. 192[tex]ft^{2}[/tex]
3. 48[tex]cm^{2}[/tex]
Step-by-step explanation:
First triangle:
1. Find out the height
[tex]h^{2} +8^{2} =17^{2}[/tex]
[tex]h^2+64=289[/tex]
-64 -64
[tex]h^2=225[/tex]
h=15
2. Find the area
A=1/2 x 16 x 15
A=120[tex]m^{2}[/tex]
Second triangle:
1. Find out the height
[tex]h^2+16^{2} =20^{2}[/tex]
[tex]h^2+256=400[/tex]
-256 -256
[tex]h^{2} =144[/tex]
h=12
2. Find the area
A=1/2 x 32 x 12
A=192[tex]ft^{2}[/tex]
Third triangle:
1. Find out the height
[tex]h^2+6^2=10^{2}[/tex]
[tex]h^2+36=100\\[/tex]
-36 -36
[tex]h^2=64[/tex]
h=8
2. Find the area
A=1/2 x 12 x 8
A=48[tex]cm^{2}[/tex]
Find the probability of a couple having at least one boy when a couple has three children
Answer:
7/8
Step-by-step explanation:
assuming the probability of getting a boy and girl is 50 50,
(1/2)^3=1/8
1-1/8=7/8
new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed.
a Find the probability that the employee is idle.
The probability that the employee is idle in the shopping mall based on the information given will be 0.33.
How to calculate probability?From the information given, it is believed that people will arrive at the desk at a rate of 20 per hour and that it takes an average of 2 minutes to answer a question.
Therefore, the probability that the employee is idle will be:
= 1 - (20/30)
= 1 - 0.67
= 0.33
Therefore, probability that the employee is idle is 0.33.
Learn more about probability on:
https://brainly.com/question/24756209
Hank is painting houses this summer. He can paint 7 houses in 5 weeks. At this rate, how many houses did he paint in 18 weeks?
[tex]\begin{array}{ccll} houses&weeks\\ \cline{1-2} 7&5\\ x&18 \end{array}\implies \cfrac{7}{x}=\cfrac{5}{18}\implies 126=5x \\\\\\ \cfrac{126}{5}=x\implies 25\frac{1}{5}=x[/tex]
