Answers
Answer:
a = 49
b = - 20√2
Step-by-step explanation:
5 - 2√6 / 5 + 2√6
We can rationalise the denominator as follow:
5 - 2√6 / 5 + 2√6
Multiply the numerator and the denominator by the conjugate of
5 + 2√6. The conjugate of 5 + 2√6 is
5 - 2√6
(5 - 2√6 / 5 + 2√6) x (5 - 2√6 / 5 - 2√6)
(5 - 2√6) (5 - 2√6) /(5 + 2√6) (5 - 2√6)
Expand
(25 - 10√6 - 10√6 + 4×6) / (25 - 10√6 + 10√6 + 4×6)
25 - 20√6 + 24 / 25 - 24
25 + 24 - 20√6 / 1
49 - 20√6
Equating 49 - 20√6 with a + b√3, we can obtain the value of a and b as follow:
49 - 20√6 = a + b√3
From the above
a = 49
b√3 = - 20√6
Divide both side by √3
b = - 20√6/√3
Rationalise
b = - 20√6/√3 x √3/√3
b = - 20√(6×3)/ √3×√3
b = - 20√18 / 3
b = - 20√(9×2) / 3
b = - 20 × 3√2 / 3
b = - 20√2
Given info:- Rationalise the denominator and find out the value of "a" and "b"
Given expression: {(5-2√6)/(5+2√6)} = a+b√3
Explanation:-
{(5-2√6)/(5+2√6)} = a+b√3
We know that Rationalising factor of a+b√c is a-b√c.
Therefore, the rationalising factor of 5+2√6 is 5-2√6.
⇛{(5-2√6)/(5+2√6)} × {(5-2√6)/(5-2√6)} = a+b√3
⇛{(5-2√6)(5-2√6)}/{(5+2√6)/(5-2√6)} = a+b√3
⇛{(5-2√6)²}/{5+2√6)(5-2√6)} = a+b√3 [∵(a-b)(a-b)=(a-b)²]
⇛{(5-2√6)²}/{(5)²-(2√6)²} = a+b√3 [∵(a+b)(a-b)=a²-b²]
⇛{(5-2√6)²}/({5*5)-(2*2√6*6)} = a+b√3
⇛{(5-2√6)²}/(25 - 4√6) = a+b√3
⇛{(5-2√6)²}/(25-24) = a+b√3
⇛{(5-2√6)²}/1 = a+b√3
⇛(5-2√6)² = a+b√3
⇛(5)²-(2√6)²+2(5)(2√6) = a+b√3
⇛(5*5) - (2*2√6*6) - 10 - 2√6 = a+b√3
⇛25 - 10 - 4√6 - 2√6 = a+b√3
⇛15 - 4√6 - 2√6 = a+b√3
⇛15 + 6√6 = a+b√3
∴ 15 + 6√6 = a+b√3
On, comparing with both RHS we notice that:
The value of a = 15 and b = 6.
Hope this helps!!
If you have any doubt, then you can ask me in the comments.
Related Questions
f(x)=-x^2+7x-13 {Find }f(-3) it's not -25....so if that's ur answer..it's wrong
VERY IMPORTANT THAT U CAN ANSWER AS FAST AS POSSIBLE!!!!!!! IM ON A TIME CRUNCH!!!!!!
Answers
Answer:
-43
Step-b-y-step explanation:
f(x)= -x^2+7x-13 so
f(-3)= - (-3)^2 + 7(-3) - 13
= -9 - 21 - 13
= -43.
50 Points, thanks for the help :)
Each question is related to the first question. I don't get this stuff fsr
（＞人＜；）
Answers
Answer:
See bolded for each part below.
Step-by-step explanation:
Attachment 1. (a) The range is 400 dollars, as her greatest balance was 400 dollars, so her domain would be 3 weeks.
( b ) Remember that B(0) models the balance over the course of 0 days. As you can see that starting mark is about half of the greatest balance on the graph, 400 dollars. Therefore you can estimate B(0) to be $200.
(c) B(12) models the balance over the course of 12 days. It mentions that at B(12) the balance reaches $0, so in function notation that would be B(12) = 0.
(d) Segment 4 would represent that information. As you can see on the graph, the only time period with which the balance became 0 is represented by the fourth segment.
Attachment 2. (a) As you can see on the graph, Ebony reached $400 on day 4, and stayed as such throughout day 8 (modeled by line segment 2). Therefore B(5) = 400 = B(6) = B(7).
(b) We also know that B(0) = ( About ) 200, B(4) = 400. Therefore B(1) = 250, B(2) = 300, B(3) = 350. The slope changes by a rate of 50.
(c) Jade is incorrect. By looking at the graph you can see that the rate from day 8 to day 12 is greater than the rate from day 0 to day 4.
Attachment 3. (a) I would say the amounts she deposited were less than $100 per day. Remember that from day 0 to 4 the slope is about 50. The slope of the line segment that models this situation, line segment 6, has about the same slope, 50.
(b) On day 21 she had 300 dollars, as it seems that this marking is between the starting amount (200) and 400. There are 5 days between 16 and 21. On day 16 she deposited 100 dollars. From then on she apparently deposited 50 dollars,
100 + 50 * 4 = 100 + 200 = 300 ✓
plss help me!!
A navy ship observes an illigal boat 'd' miles away to it's West. If the boat travels at a 'u' velocity towards the south , and it's given that the maximum velocity of the ship's canon is λu ( λ<1)
and the max range they can be shot at is 'v',
show that if λ^2 +(v/d)^2 <1 ,
1) that the illigal boat can avoid any harm caused by the navy ship.
( use relative velocity triangles and geometry)
Answers
Step-by-step explanation:
The problem statement says λ<1. If this is true, then the cannonball is slower than the boat, and it will never reach the boat. So I assume it's actually λ>1.
If we say t is the amount of time, then the boat travels south a distance of ut, and the cannonball travels a distance of λut.
v = λut
ut = v/λ
Using Pythagorean theorem:
d² + (ut)² > v²
d² + (v/λ)² > v²
λ²d² + v² > λ²v²
λ²d² > (λ² − 1) v²
λ² / (λ² − 1) > (v/d)²
what is the measure of ∠ABC? chile I'm confused
Answers
I hope this helps! :)
The answer is 120 degree
Pls mark as brainliest
Answer:
Simple 1 part 120 degrees
Step-by-step explanation:
A quiz consists of 15 multiple choice questions, each with five possible answers, only one of which is correct. If a student guesses on each question, what is the mean and standard deviation of the number of correct answers
Answers
Answer:
The mean and standard deviation of the number of correct answers is 3 and 1.55 respectively.
Step-by-step explanation:
We are given that a quiz consists of 15 multiple choice questions, each with five possible answers, only one of which is correct.
Let X = the number of correct answers
The above situation can be represented through binomial distribution;
[tex]P(X = x) = \binom{n}{r}\times p^{r}\times (1-p)^{n-r}; x = 0,1,2,3,......[/tex]
where, n = number of samples (trials) taken = 15 multiple choice questions
r = number of success
p = probability of success which in our question is probability of
one correct answer out of 5, i.e; p = [tex]\frac{1}{5}[/tex] = 0.2
So, X ~ Binom(n = 15, p = 0.2)
Now, the mean of the number of correct answers is given by;
Mean of X, E(X) = [tex]n \times p[/tex]
= [tex]15 \times 0.2[/tex] = 3
And the standard deviation of the number of correct answers is given by;
Standard deviation, S.D.(X) = [tex]\sqrt{n \times p\times (1-p)}[/tex]
= [tex]\sqrt{15 \times 0.2\times (1-0.2)}[/tex] = 1.55
Write an expression to represent the sum of three times the square of a number and -7.
In your expression, what is the value of the constant?
Answers
Answer:
3x^2-7
-7 is the constant
3 is the coefficient
x is the variable
Step-by-step explanation:
(3x^2)+(-7)
If the volume of a cube is 27m3 find one of it's sides
Answers
Answer:
3
Step-by-step explanation:
Cube volume formular = Side^3
27 = x^3
[tex]\sqrt[3]{27} = 3\\[/tex]
Check = 3*3*3 = 27
3 is the answer
Which expression is equivalent to 6 minus (negative 8)? Negative 6 + 8 Negative 6 + (negative 8) 6 + (negative 8) 6 + 8
Answers
Answer:
6+8
a negative minus a negative equals a positive and x minus a negative is addition
Answer:
6+8
Step-by-step explanation:
6 minus (negative 8)
6 - (-8)
We know that subtracting a negative is like adding
6+8
A high school graduating class is made up of 505 students. There 175 more girls than boys. How many boys are in the class
Answers
Answer:
165
Step-by-step explanation:
let the number of boys be x and girls be y.
But there are 175 more girls than boys, so y = x + 175
sum of boys and girls is 505
x + y = 505
and y = x + 175
x + x + 175 = 505
2x = 330
x = 165
How can you represent real world situations using positive nubers, negative nubers, and zero?
Answers
Answer:Maybe ffor the positive numbers you could use like 1,2,3,4,5,6,7,8, and 9. For the negitive number could be like -1,-2,-3,-4,-5. And zero could repersent the middle. Get it or no?
Step-by-step explanation:
If the subspace of all solutions of Ax 0 has a basis consisting of vectors and if A is a matrix, what is the rank of A
Answers
Question: If the subspace of all solutions of
Ax = 0
has a basis consisting of vectors and if A is a matrix, what is the rank of A.
Note: The rank of A can only be determined if the dimension of the matrix A is given, and the number of vectors is known. Here in this question, neither the dimension, nor the number of vectors is given.
Assume: The number of vectors is 3, and the dimension is 5 × 8.
Answer:
The rank of the matrix A is 5.
Step-by-step explanation:
In the standard basis of the linear transformation:
f : R^8 → R^5, x↦Ax
the matrix A is a representation.
and the dimension of kernel of A, written as dim(kerA) is 3.
By the rank-nullity theorem, rank of matrix A is equal to the subtraction of the dimension of the kernel of A from the dimension of R^8.
That is:
rank(A) = dim(R^8) - dim(kerA)
= 8 - 3
= 5
One side of a rhombus is 20mm, and the longer diagonal is 32mm. Find the area of the rhombus.
Answers
Answer:
384 sq mm
Step-by-step explanation:
Remember that the diagonals of a rhombus are perpendicular bisectors of each other.
So, one side of the rhombus, half the longer diag and half the shorter diag form the 3 sides of a right triangle
with the rhombus side being the hypotenuse.
In this case, let the shorter diagnoal be x mm. In the right triangle,
Hypotenuse = 20
One side = 32/2 = 16
Other side = x/2
Applying Pythagoras principle,
[ check the file attatched ] (taking only the positive square root)
So the shorter diagonal = 12*2 = 24 mm
Area of the rhombus is given by the formula (1/2)*d1*d2 where d1, d2 are the 2 diagonals.
Here, the area = (1/2)*32*24 = 32*12 = 384 sq mm
Help needed ASAP will give brainliest
Answers
Answer:
-5
Step-by-step explanation:
counting is like backwards in negatives so a +5 is slow and a +25 is high but in negatives its the opposite because you are missing that many
I dont really know who to explain it but I hope this helps
35 divided by 4 = 8 R3
Answers
Answer:
[tex]\Large \boxed{8\frac{3}{4} }[/tex]
Step-by-step explanation:
35 ÷ 4 = 8 R3
The quotient is 8.
The remainder is 3.
The divisor is 4.
Rewrite as a mixed fraction.
[tex]\displaystyle \sf quotient \frac{remainder}{divisor}[/tex]
35 divided by 4 gives the mixed fraction 4 3/8.
We have,
35 divided by 4 = 8 R3
When we divide 35 by 4, the result is:
35 ÷ 4 = 8 with a remainder of 3.
Or, in the form of mixed fraction we can write as
Divisor x quotient / Remainder
Then, 4 3/8 is the mixed fraction.
Thus, 35 divided by 4 gives the mixed fraction 4 3/8.
Learn more about Mixed fraction here:
https://brainly.com/question/29019463
#SPJ6
i need an explainarion
Answers
Answer:
x=3
Step-by-step explanation:
The line of reflection would be at x=3. It’s like a mirror. The reflection is backward, but the same distance from the line of reflection, so the line needs to be halfway between the two shapes. Since C is at 4 and C’ is at 2, the line of reflection has to be at 3.
13+6y y=6 evaluate
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
49
▹ Step-by-Step Explanation
Substitute:
13 + 6(6)
Solve:
6 * 6 = 36
13 + 36 = 49
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer: 49
Step-by-step explanation: To evaluate 13 + 6y if y = 6,
we start by substituting 6 in for y.
So we have 13 + 6(6).
Remember to use parentheses when
substituting numbers in for variables.
Now, we use the order of operations to simplify from here.
Since multiplication comes before addition, our next step is
to multiply 6(6) to get 36, and we have 13 + 36, which is 49.
[tex]m. \: 2cos \: a = \sqrt{2 + \sqrt{2 + \sqrt{2 + 2cos \: 8a} } } [/tex]
please help me.....
I need full work!!
Answers
While this is with theta instead of A it still is the same thing. I hope this helps
Answer: see proof below
Step-by-step explanation:
Use the following Double Angle Identity:
cos 2A = 2 cos²A - 1
Proof RHS → LHS
Given: [tex]\sqrt{2+\sqrt{2+\sqrt{2+2cos8A}}}[/tex]
Factor: [tex]\sqrt{2+\sqrt{2+\sqrt{2(1+cos8A)}}}[/tex]
Let α = 4A: [tex]\sqrt{2+\sqrt{2+\sqrt{2(1+cos2\alpha)}}}[/tex]
Double Angle Identity: [tex]\sqrt{2+\sqrt{2+\sqrt{2(1+2cos^2\alpha-1)}}}[/tex]
Simplify: [tex]\sqrt{2+\sqrt{2+\sqrt{2(2cos^2\alpha)}}}[/tex]
[tex]\sqrt{2+\sqrt{2+2cos\alpha}}}[/tex]
Substitute (α = 4A): [tex]\sqrt{2+\sqrt{2+2cos4A}}}[/tex]
Factor: [tex]\sqrt{2+\sqrt{2(1+cos4A)}}}[/tex]
Let β = 2A [tex]\sqrt{2+\sqrt{2(1+cos2\beta)}}}[/tex]
Double Angle Identity: [tex]\sqrt{2+\sqrt{2(1+2cos^2\beta-1)}}}[/tex]
Simplify: [tex]\sqrt{2+\sqrt{2(2cos^2\beta)}}}[/tex]
[tex]\sqrt{2+2cos\beta}[/tex]
Substitute (β = 2A): [tex]\sqrt{2+2cos2\alpha}[/tex]
Factor: [tex]\sqrt{2(1+cos2\alpha)}[/tex]
Double Angle Identity: [tex]\sqrt{2(1+2cos^2\alpha-1)}[/tex]
Simplify: [tex]\sqrt{2(2cos^2A)}[/tex]
2 cos A
2cos A = 2cos A [tex]\checkmark[/tex]
What is the factored form of x2 + 12x – 64?
Answers
Answer:
The answer is
( x - 4)( x + 16)Step-by-step explanation:
x² + 12x - 64
To factorize the expression write 12x as a difference
That's
x² + 16x - 4x - 64
Factor out x from the expression
That's
x( x + 16) - 4x - 64
Factor out - 4 from the expression
That's
x( x + 16) - 4 ( x + 16)
Factor out (x + 16) from the expression
We have the final answer as
( x - 4)( x + 16)Hope this helps you
Simplify the expression
2(7n+5m-3m)
Answers
Answer:
2(7n+2m)
2(7n+(5m-3m))
answer: 2(7n+2m)
With work please!!!
f(x) = -x^4 + 5x - 4x^2
(f (2))^2
Answers
Answer: 484
===============================================
Work Shown:
First let's compute f(2). We replace every x with 2 and then use PEMDAS to simplify
f(x) = -x^4 + 5x - 4x^2
f(2) = -(2)^4 + 5(2) - 4(2)^2
f(2) = -16 + 5(2) - 4(4)
f(2) = -16 + 10 - 16
f(2) = -6 - 16
f(2) = -22
Then we square this result to find the value of [tex][ f(2) ]^2[/tex]
[tex]f(2) = -22\\\\\left[ f(2) \right]^2 = [ -22 ]^2\\\\\left[ f(2) \right]^2 = 484[/tex]
How to do this question plz answer
Answers
Volume of cuboid= 600cm3
Volume of milk= 8*5*12= 480cm3
Orange side facing down base area = 8*15= 120
480/120= 4 cm
P.s= could you please check if my answer is correct :)
Answer:
The way to solve the question is:
Depth = Volume/ (Width x Length)
Volume = Depth x Length x Width
=> Volume = 12 x 15 x 5
=> Volume = 12 x 75
=> Volume = 900
Depth= 900 / (Width x Length)
=> Depth = 900/ 5 x 15
=> Depth = 900/75
=> Depth = 12
Can you explain exponents
Answers
Answer:
Read Exp:
Step-by-step explanation:
Exponents are like a simpler way to multiply something by itself a certain amount of times.
So like if you were to see 7^4 on a test or assignment you would solve it like this:
- 7x7x7x7.
It just means 7 times itself 4 times. NOT 7 times 4.
Solve each problem. Round to the nearest tenth or tenth of a percent.
1) What percent of 29 is 3?
2) What percent of 33.5 is 21?
I
3) What percent of 55 is 34?
4) 41% of 78 is what?
5) 28% of 63 is what?
6) 58% of what is 63.4?
Answers
Answer:
See below.
Step-by-step explanation:
1) What percent of 29 is 3?
3/29 * 100% = 10.3
2) What percent of 33.5 is 21?
21/33.5 * 100% = 62.7%
3) What percent of 55 is 34?
34/55 * 100% = 61.8%
4) 41% of 78 is what?
41% * 78 = 0.41 * 78 = 32.0
5) 28% of 63 is what?
28% * 63 = 0.28 * 63 = 17.6
6) 58% of what is 63.4?
58% * x = 63.4
0.58x = 63.4
x = 63.4/0.58 = 109.3
Please help me it’s emergency please
Answers
Answer:
-17x
Step-by-step explanation:
(2x^3 - x^2) - (3x^3 - 2x^2)
(8x - 2x) - (27x - 4x)
6x - 23x
-17x
(I haven't seen many questions like this before, but I think that this may be the answer.)
Answer:
The other person is correct he should get brainliest!
Hope this helps!
Your teacher has 48 juice boxes and 64 candies for a Halloween party. Each student will receive the same amount of juice boxes / candies , and all juice boxes / candies must be used. What is the greatest number of students that can attend the party.
Answers
The greatest number of students —> 16
For 12 months,Janenne has belonged to a book-of-the-month-club.Janenne has spent 70.45 on the club.The first month, she payed a monthly fee and spent an additional 10.45 on books.She has only payed the monthly fee since then.What is the initial values of the rate of change of the function
Answers
Answer:
The rate of change of the function = 5
Step-by-step explanation:
From the given parameters, we have;
The number of months Janenne has belonged to the book-of-the-month-club = 12
The amount Janenne has spent on the club = 70.45
The amount she paid in the first month = Monthly fee + 10.45
Let the monthly fee = x
The total amount Janenne has spent on the club can be given by the following formula;
10.45 + 12×x = 70.45
12×x = 70.45 - 10.45 = 60
x = 60/12 = 5
The monthly due of the book club = 5
Therefore, the rate of change of the function × 5
The function of the amount spent on the club = Y = t×x
Where;
x = The rate of change of the function
t = The time in months
The rate of change of the function = 5.
Please help I will give out brainliest
Answers
Answer:
answer in attachment
Step-by-step explanation:
Zach is 4 years older than twice his sister Maya’s age. Zach is 28 years old. Let m represent Maya’s age. During the Strategize step of the five-step problem-solving plan, which expression would you use to represent Zach’s age?
Answers
Answer:
2m + 4 = 28
Step-by-step explanation:
Zach = 28 years old
2 times Maya's (m) age
2*m
4 years older plus twice Maya's age.
2 * m + 4 = 28
2m + 4 = 28
Hope it helps : )
2 multiplied by -1 divided by 2
Answers
Answer:
-1
Step-by-step explanation:
2 * -1 = -2
Then, -2 / 2 = 1
help find x out of these 4 questions i can’t find the answer anywheew
Answers
Answer:
Option D. 11√6/2
Step-by-step explanation:
We'll begin by calculating the side opposite to angle 60°.
This is illustrated below:
Angle θ = 60°
Opposite =?
Hypothenus = 11
Using the sine ratio, we can obtain the side opposite to angle 60° as follow:
Sine θ = Opposite/Hypothenus
Sine 60 = Opposite /11
Cross multiply
Opposite = 11 × Sine 60
Sine 60 = √3/2
Opposite = 11 × √3/2
Opposite = 11√3/2
Finally, we shall determine the value of x as follow:
Angle θ = 45°
Opposite = 11√3/2
Hypothenus = x
Using the sine ratio, we can obtain the value of x as shown below:
Sine θ = Opposite/Hypothenus
Sine 45° = 11√3/2 /x
Cross multiply
x × Sine 45° = 11√3/2
Sine 45° = 1/√2
x × 1/√2 = 11√3/2
x/√2 = 11√3/2
Multiply through by √2
x = √2 × 11√3/2
x = 11√6/2