Answers
We are given that ,
[tex]{:\implies \quad \sf \dfrac{12+\sqrt{128}}{1-\sqrt{2}}=a+b\sqrt{2}}[/tex]
Consider LHS;
[tex]{:\implies \quad \sf \dfrac{12+\sqrt{128}}{1-\sqrt{2}}}[/tex]
Can be further written as ;
[tex]{:\implies \quad \sf \dfrac{12+8\sqrt{2}}{1-\sqrt{2}}}[/tex]
Rationalizing the denominator we have ;
[tex]{:\implies \quad \sf \dfrac{12+8\sqrt{2}}{1-\sqrt{2}}\times \dfrac{1+\sqrt{2}}{1+\sqrt{2}}}[/tex]
[tex]{:\implies \quad \sf \dfrac{(12+8\sqrt{2})(1+\sqrt{2})}{(1-\sqrt{2})(1+\sqrt{2})}}[/tex]
[tex]{:\implies \quad \sf \dfrac{12(1+\sqrt{2})+8\sqrt{2}(1+\sqrt{2})}{1-2}}[/tex]
[tex]{:\implies \quad \sf \dfrac{12+12\sqrt{2}+8\sqrt{2}+16}{-1}}[/tex]
[tex]{:\implies \quad \sf \dfrac{28+20\sqrt{2}}{-1}}[/tex]
[tex]{:\implies \quad \sf -28-20\sqrt{2}}[/tex]
Hence, we can conclude that ;
[tex]{\bf a=-28}[/tex] [tex]{\bf b=-20}[/tex]Related Questions
PLEASE HELP!!!!! Will award brainliest need help asap
Answers
[tex]\\ \rm\rightarrowtail 2-sin^2x=2cos^2\left(\dfrac{x}{2}\right)[/tex]
[tex]\\ \rm\rightarrowtail 1+1-sin^2x=2cos^2\left(\dfrac{x}{2}\right)[/tex]
1-sin^2x=cos^2x[tex]\\ \rm\rightarrowtail 1+cos^2x=2cos^2\left(\dfrac{x}{2}\right)[/tex]
[tex]\\ \rm\rightarrowtail cos^2x=2cos^2\left(\dfrac{x}{2}\right)-1[/tex]
[tex]\\ \rm\rightarrowtail cos^2x=cosx[/tex]
[tex]\\ \rm\rightarrowtail cosx=1[/tex]
[tex]\\ \rm\rightarrowtail x=n\pi[/tex]
As x lies in between 0 and 2π
The answers are 0,2πAnswer:
[tex]x=0,\dfrac{\pi}{2}, \dfrac{3\pi}{2},2\pi[/tex]
Step-by-step explanation:
Given equation:
[tex]2-\sin^2x=2 \cos^2(\frac{x}{2})[/tex]
Subtract [tex]2 \cos^2(\frac{x}{2})[/tex] from both sides:
[tex]\implies 2-\sin^2x-2 \cos^2(\frac{x}{2})=0[/tex]
Pythagorean identity
[tex]\sin^2x+\cos^2x =1[/tex]
[tex]\implies \sin^2x =1-\cos^2x[/tex]
Substituting into the equation:
[tex]\implies 2-(1-\cos^2x)-2 \cos^2(\frac{x}{2})=0[/tex]
[tex]\implies 1+\cos^2x-2 \cos^2(\frac{x}{2})=0[/tex]
Cosine double angle identity:
[tex]\cos(2x)=2 \cos^2x-1[/tex]
[tex]\implies 2 \cos^2x=\cos(2x)+1[/tex]
Substituting [tex]\frac{x}{2}[/tex] for [tex]x[/tex]:
[tex]\implies 2 \cos^2(\frac{x}{2})=\cos(2\cdot\frac{x}{2})+1[/tex]
[tex]\implies 2 \cos^2(\frac{x}{2})=\cos x+1[/tex]
Substituting into the equation:
[tex]\implies 1+\cos^2x- (\cos x +1)=0[/tex]
[tex]\implies \cos^2x- \cos x =0[/tex]
Factoring:
[tex]\implies \cos x(\cos x- 1)=0[/tex]
Therefore,
[tex]\cos x=0[/tex]
[tex]\implies x=\dfrac{\pi}{2}, \dfrac{3\pi}{2}[/tex]
and [tex]\cos x-1=0[/tex]
[tex]\implies \cos x=1[/tex]
[tex]\implies x=0, 2\pi[/tex]
Need help with question 7- TYSM!
Answers
x = 4
Because the area is 20cm^2, and area = length x width, we just need to divide 20 by the number we have already, which is 5
20/5 = 4
To check this answer, we do 5 x 4 = 20
Hope this helps :)
Answer:
A=½bh
20=5x(½)
multiply by reciprocal both sides
40=5x
divide
8=x
f(x) = 3x + k
f(4) = 10
easy equation but I just need a confirmation that the answer is actually -2 lol
Answers
Answer:
-2
Step-by-step explanation:
f(x) = 3x + k
f(4) = 10
f(4) = 3×4+k
10 = 12 + k
10-12 = k
k = -2
Jenny wants to serve fruit punch at her party. She plans to buy a punch bowl that costs 5$ and fruit punch that costs 1.40$ per liter. If p represents the number of liters of fruit punch that she buys, which expression can be used to find how much it will cost Jenny to serve punch at her party?
Answers
Find the degree of the monomial.
-39^4rs^6
The degree is
Answers
Answer:
The answer to your question would be 20
Hope this helps!
please help fhgdsafghjk,
Answers
Answer:
b
Step-by-step explanation:
Pattern A: 3, 10, 17, 24, 31
Pattern B: 3, 7, 11, 15, 19
Which number is not a perfect square?
(A) 1
(B) 25
(C) 30
(D) 36
Answers
Answer:
Hello! :) I hope I’m correct!!
Step-by-step explanation:
I think (C) 30 is not a perfect square.
(A) 1 = perfect square
(B) 25 = perfect square
(C) 30 = NOT a perfect square
(D) 36= perfect square
{Note: The square root of 30 is not an integer, so therefore 30 is not a square number}
Since the question is asking to find a number that is NOT a perfect square...
The answer would be (C) 30
Hope this helps! If you have any questions about this, feel free to ask! Have a wonderful day! ^-^
~By, BrainlyAnime~ <3
what is 3 1/4 - (-5/8)
Answers
Answer:
3.875
Step-By-Step-Explanation
3 2/8 + 5/8
a = , b = , c = , d = , e = .
- To people who need this for Edge "Modeling a Bicycle Wheel" it's 6, 8, 6, 7, 7.
Answers
Answer:
Thanks! I was doing this lesson now and was getting ready to ask a question, but I saw this, and it helped me a lot. Thank you!
Step-by-step explanation:
Even though I technically didn't answer anything, can I have brainliest? I really want to level up
Have a blessed day and remember to keep smiling! :)
What is y+2=-7(x-4) in slope intercept form
Answers
Answer:
y= -7x+26
Step-by-step explanation:
not sure how to explain... just followed order of operations
*I NEED THIS ASAP*
5. number of terms
6. degree
7. leading coefficient
8. end behavior
9. turning point(s)
10. x-intercept(s)
11. relative minimum(s)
12. relative maximum(s)
Answers
Answer:
5 terms
to the fourth degree
leading coeff of 1
3 turning points
end behavior (when x -> inf, y -> inf. When x -> - inf, y -> -inf)
x intercepts are (0,-4) (0,-2) (0,1) (0,3)
Relative min: (-3.193, -25) (2.193, 25)
Relative max: (-0.5, 27.563)
Step-by-step explanation:
The terms can be counted, seperated by the + and - in the equation given.
The highest exponent is your degree.
The number before the highest term is your leading coeff, if there is no number it is 1.
The turning points are where the graph goes from falling to increasing or vice versa.
End behaviour you have to look at what why does when x goes to -inf and inf.
X int are the points at which the graph crosses the x-axis.
The relative min and max are findable if you plug in the graph on desmos or a graphing calculator.
Which is not a cubic number?a.1 b.9 c.27 d.64
Answers
Answer:
9
Step-by-step explanation:
1= 1x1x1 cubic
27=3x3x3 cubic
64=4x4x4 cubic
9 is not cubic
Answer:
Step-by-step explanation:
1x1x1=1³
3x3x3=27=3³
4x4x4=64=4³
PLEASE PLEASE ANSWER I WILL MARK AS BRAINLIST
Answers
Answer:
hey! ill do it but first do 3/4 x 8/15 for me PLSSSSSSSSSSS
Step-by-step explanation:
Q7: What is the slope of the line represented by the equation 2x + 6y = 5
Answers
Answer:
-1/3
Step-by-step explanation:
2x + 6y = 5
6y = -2x + 5
y = -1/3x + 5/6
Representing the equation in slope intercept form, the slope of the line represented by the equation is - 1/3
Given the equation :
2x + 6y = 5Slope intercept format :
y = bx + c ; b = slope2x + 6y = 5
6y = - 2x + 5
Divide both sides by 6 to isolate y
y = - 1/3x + 5/6
Hence, the value of slope, b in the equation is - 1/3
Learn more : https://brainly.com/question/18106342
Mary decreased her time for the mile walk from 30 minutes to 24 minutes. What was the percent of decrease?
A. 32%
B. 20% increase
C. 20% decrease
D 88%
Answers
(24-30/ 30) *100
= - 20
So we will be stating (-) as 20% decrease .
Hope it helps
The graph of g(x) = x2 + 2 is a translation of the
4
graph of f(x)
by
units.
2
DONE
-4
-2
-2
-4
y=x²
Answers
Answer:
up and 2; down and 3
Step-by-step explanation:
hope this helps!! have an amazing day <3
The equation the function after the transformation is g(x) = -4x² - 16
What is transformation?Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.
here, we have,
to determine the transformation of the function:
The equation of the function is given as
f(x) = x²+2
The sequence of transformations is given as follows:
Translate up by 2 units
Reflection across the x-axis
Vertically stretched by a factor of 4
When the above transformations are combined, we have:
Translate up by 2 units: g(x) = f(x) + 2
Reflection across the x-axis: g(x) = -(f(x) + 2)
Vertically stretched by a factor of 4: g(x) = -4(f(x) + 2)
So, we have
g(x) = -4(x²+2 + 2)
Expand
g(x) = -4x² - 16
Hence, the function g(x) is g(x) = -4x² - 16
Read more about transformation at
brainly.com/question/27224272
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This figure represents a small brick that is to be covered on all sides with a striped fabric. How much fabric is needed to cover the brick? Enter your answer as a decimal in the box.
Answers
The amount of fabric needed = surface area of the rectangular prism (brick) = 146.5 cm²
What is the Surface Area of a Rectangular Prism?The surface area of a rectangular prism is given as, A=2(wl+hl+hw).
The brick is a rectangular prism. Therefore, the amount of fabric needed to cover the brick would equal the surface area of the brick.
Given the following:
l = 6 cmw = 3.5 cmh = 5.5 cmPlug in the values into the formula:
The surface area of the rectangular prism (brick) = 2(3.5 × 6 + 5.5 × 6 + 5.5 × 3.5) = 146.5 cm²
Learn more about surface area of rectangular prism on:
https://brainly.com/question/1310421
Answer:
The Answer Is : 146.5
Step-by-step explanation:
I Just Took The Test And I Have Proof
Select the best estimate that would help you check the answer to 778×23
.
A.
700×30
B.
700×20
C.
800×20
D.
800×30
Answers
Answer:
C: 800 x 20
Step-by-step explanation:
Basically, when you round 778 you see that the 7 and 8 are above 5, which means you round upwards. Therefore it would be best to round up to 800.
Then the 3 in 23 is below 5, meaning you round downwards. 20 Is the closest and best option.
So, C: 800 x 20 is best to do!
Answer:
Answer-C
Step-by-step explanation:
MARK ME BRAINLEST PLZ
if y=10 when x=4, find y when x=12.
Answers
Answer:
If both numbers have to stay equivalent, then y equals 30 if x = 12. My reasoning is 12/4 = 3. 3 times 10 = 30.
Simplify. 5 2+20
5
30
45
72
(The 5 2 is an exponent.)
Answers
Answer:C.45
Step-by-step explanation:
[tex]\Huge\boxed{Your\;answer\;is\;45.}[/tex]
___________________________________________________________
[tex]\boxed{Explanation}[/tex]
So, we have the following equation...
[tex]5^2+20=(?)[/tex]
Remember, 5² also means 5x5.
Therefore, [tex]5x5=25\\25+20=45[/tex]
This means your final answer is 45.
___________________________________________________________
Glad to help!
Could i possibly get brainliest?
[tex]\huge\boxed{Thanks,\;Plip.}[/tex]
a population of 120000 grows 5% per year for 16 years
Answers
6000*16=96000+120000=216000
Evaluate 3x + 12 for x=5
Hurry!!! ASAP!
Answers
Answer:
27
Step-by-step explanation:
3*5=15+12=27]
Evaluation of 3x + 12 for x = 5 is 27.
What is an expression?Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.
Given expression,
3x + 12
And to solve for x= 5,
we substitute the value of x in given expression,
3(5)+ 12 = 15 + 12
= 27
Therefore, evaluation of expression 3x + 12 for x = 5 is 27.
To learn more about the expression;
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The eqaution R=10A-20 represents the revenue R (in dollars) you make by spending Adollars on advertising. Your revenue totaled $110. How much did you spend on advertising.
Answers
Add 20 to both sides
130=10A
Divide by 10
13=A
You spent $13
Two times a number decreased by 7
Answers
Answer:
result is 35
Step-by-step explanation:
If 9-2k/3=k-2 what is the value of k
Answers
Answer:
[tex]k=3[/tex]
Step-by-step explanation:
Given the following question:
[tex]\frac{9-2k}{3} =k-2[/tex]
To find the answer we need to isolate k, in order to do that we need to use inverse of operations to cancel out integers on each side of the expression.
[tex]\frac{9-2k}{3} =k-2[/tex]
[tex]3\times0=0[/tex]
[tex]2\times3=6[/tex]
[tex]9-2k=k\times3-6[/tex]
[tex]9-9=0[/tex]
[tex]-6-9=15[/tex]
[tex]k\times3=3k[/tex]
[tex]-2k=3k-15[/tex]
[tex]-2k-2k=0[/tex]
[tex]3k+-3k=-5k[/tex]
[tex]-5k=-15[/tex]
[tex]-5k\div-5=k[/tex]
[tex]-15\div-5=3[/tex]
[tex]k=3[/tex]
Your answer is "k =3."
Hope this helps.
Last year at science camp there were 140 people sleeping in cabins. There were 18 students for every 2 chaperones. How many students were sleeping in
cabins?
Answers
Answer:
126 students
Step-by-step explanation:
18+2=20
140 divided by 20=7
7x18=126
140-126=14 chaperones
50 POINTS FOR CORRECT AWNSER
Answers
Answer:
[tex]y\leq \frac{1}{2} x+3[/tex]
Step-by-step explanation:
slope intercept form is [tex]y=mx+b[/tex] where [tex]m[/tex] is the gradient and [tex]b[/tex] is the y-intercept (the number at which it crosses the y axis)
firstly find the equation for this line:
the gradient can be found with the formula [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
so the gradient is [tex]\frac{4-3}{2-0}=\frac{1}{2} =0.5[/tex]
the y intercept is where it crosses the y axis so it is simply 3
our equation for the line is now [tex]y=\frac{1}{2} x+3[/tex] but the question is asking for an equality where the shaded area is BELOW the line.
so the inequality is [tex]y\leq \frac{1}{2} x+3[/tex]
Answer:
y ≤ [tex]\frac{1}{2}[/tex] x + 3
Step-by-step explanation:
the equation of the line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0-(-6)}[/tex] = [tex]\frac{3}{0+6}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = [tex]\frac{1}{2}[/tex] x + 3 ← is the equation of the line
the solution lies below the line and on the line.
as line is solid use ≤
y ≤ [tex]\frac{1}{2}[/tex] x + 3
Pls help me on this problem I’m confused
Answers
Answer:
1 yard = 3 feet
40 × 3 = 120 feet
1 foot per 2 seconds
120 × 2 = 240
240 ÷ 60 = 4 minutes
it takes her 4 minutes to reach the surface
Answer:
6 minutes and 65 seconds
Step-by-step explanation:
The unit rate is: 1/2.
1/2 x 40 = 40/80
80/60 = 1.33
1.33 x 3 (Because every foot is a meter)
3.99 / .60
6.65.
Hope this helps! Have a good day.
(Also, nice Sans PFP, mine is Sans too ;>)
someone help answer the bottom 4 pls I'll brainlist u !!
Answers
(-15)2 equals ? This has got me stuck for a few minutes.
Answers
Answer:
225
Step-by-step explanation:
(- 15)² = - 15 × - 15 = 225