Answers
Answer:
A) 3
Step-by-step explanation:
Method 1)Ques: 30/(4√3 + 3√2) = 4√3 - a√2
Rationalise the denominator.
→ 30/(4√3 + 3√2) × (4√3 - 3√2)/(4√3 - 3√2) = 4√3 - a√2
→ (120√3 - 90√2)/(48 - 18) = 4√3 - a√2
→ (120√3 - 90√2)/30 = 4√3 - a√2
→ 120√3 - 90√2 = 120√3 - 30a√2
→ 90√2 = 30a√2
On solving we get,
→ a = 3
Method 2)Ques: 30/(4√3 + 3√2) = 4√3 - a√2
→ 30 = 4√3(4√3) + 4√3(-a√2) + 3√2(4√3) + 3√2(-a√2)
Solve the brackets,
→ 30 = 48 - 4a√6 + 12√6 - 6a
→ - 18 = - 4a√6 - 12√6 - 6a
Put like terms on one side,
→ - 18 + 6a = - 4√6 (a + 3)
Take the common,
→ 3(a - 3) = - 2√6 (a + 3)
→ 3 (a - 3) = 2√6 (-a - 3)
→ [3(a - 3)]/2√6 = - a - 3
Rationalise the denominator,
→ 2√6(3a - 9)/24 = - a - 3
→ (3a√6 - 9√6)/12 = - a - 3
→ √6(a - 3) = - 4a - 12
Do squaring on both sides,
→ [√6(a - 3)]² = - (4a + 12)²
→ 6(a² + 9 - 6a) = - (16a² + 144 + 96a)
Solve the brackets,
→ 6a² + 54 - 36a = - 16a² - 144 - 96a
→ 22a² - 132a + 198 = 0
→ 11a² - 66a + 99 = 0
→ a² - 6a + 9 = 0
Split the middle term,
→ a² - 3a - 3a + 9 = 0
→ a(a - 3) -3(a - 3) = 0
→ (a - 3)(a - 3) = 0
On comparing we get,
→ a = 3 (key to solve this and similar questions is rationalisation of the denominator)
Hence, the correct option is option A) 3.
Related Questions
What is the approximate length of minor arc XZ
Answers
Answer:
3.7
Step-by-step explanation:
2r(pi)(∅/360)
2*3*(pi)*(70/360)
6*(pi)*(0.19444...)
3.665191429188092
3.7
On a circle with radius 12 m, what angle would subtend an arc with a length of 7 m?
Answers
Answer:
33.42
Step-by-step explanation:
just trust me
33.42 angle would subtend an arc with a length of 7 m.
How do you find the angle of an arc?The angle formed by the arc at the center of the circle is the angle of the arc. Indicated by. m A B ^, A, and B are the endpoints of the arc. You can use the arc length equation to find a measure of the arc angle.
For a circle, the arc length equation is θ times the radius of the circle. The equation for arc length in radians can be expressed as Arc length = θ × r, where θ is in radians. Arc length = θ × (π / 180) × r, where θ is in degrees and L = arc length. θ = central angle of the arc.
Learn more about the angle of an arc here: https://brainly.com/question/2005046
#SPJ2
You don’t have ti explain just tell me if it’s true or not
Answers
Answer:
no its not true
Step-by-step explanation:
Use long division to convert the rational number 5/16 to its equivalent decimal form
Answers
Answer: the answer would be 0.3125
Just use a calculator and type in 5 divided by 16 :)
A friend asks to borrow $250 for 100 days and agrees to pay 36.5% annual simple interest. How much interest will you earn? Assume that one year has 365 days
Answers
Answer:
$25
Step-by-step explanation:
We express the interest rate r in decimal form, so we have r=36.5%=36.5100=0.365. We express the time t in years, so we have t=100365. The principal is P=250, so the interest is I=Prt=(250)(0.365)(100365)=$25. The interest earned is $25.
p- 6= -5 what is the answer (NEED HELP)
Answers
Answer:
P=1
Step-by-step explanation:
1-6=-5
the degree of non constant zero polynomial is
Answers
Answer:
it is zero . zero is the degree of zero polnomial
Find the slope of the line that passes between the points (4, 3/8) and (6, 7/8)
Answers
Answer:
1/4
Step-by-step explanation:
We have two points, so we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 7/8 - 3/8 ) / ( 6-4)
= ( 4/8) /2
= 1/2 / 2
= 1/4
Data were collected on two variables, x and y, to create a model to predict y from x. A scatterplot of the collected data revealed a curved pattern with a possible cubic relationship (y=ax^3, where a is a constant) between the variables. Which of the following transformations would be most appropriate for creating linearity between the variables?
A - Taking the cube of y
B - Taking the cube root of y
C - Taking the cube root of both y and x
D - Taking the log of y
E - Taking the log of both y and x
Answers
Answer:
B - Taking the cube root of y
Step-by-step explanation:
Data provided in the question
y = ax^3
Based on the above information
Now we take the cube root of y
So, it would be calculated below:
y1/3 = a1/3 × x
So
As it can seen by the above equation there is a linear relationship between the cube root of y and x
Therefore, the correct option is B.
Hence, all the other options are wrong
Linearity is the concept used to describe linear relationships between variables.
The appropriate method for creating linearity between the variables is: (e) Taking the log of both y and x
The function is given as:
[tex]\mathbf{y = ax^3}[/tex]
The function is a power function (i.e. cube of x)
To create linearity between power function, we simply take the logarithms of both variables
So, we have:
[tex]\mathbf{\log(y) = a\log(x^3)}[/tex]
Apply law of logarithm
[tex]\mathbf{\log(y) = 3a\log(x)}[/tex]
Hence, the appropriate method for creating linearity between the variables is: (e) Taking the log of both y and x
Read more about linearity between variables at:
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what is 390,000×600÷5?
Answers
Answer:
46,800,000 thats the answer
For the function h(x) = 9 + 6x , what is the domain of function h if the range is {-12, -3, 15, 24}? TIMED!WILL GIVE BRANLIEST!
A. {−3.5, −2, 1, 2.5}
B. {−3, 6, 24, 33}
C. {−63, −9, 99, 153}
D. {−0.5, 1, 4, 5.5}
Answers
Answer:
A. {−3.5, −2, 1, 2.5}
Step-by-step explanation:
Remember that the range is the possible values for Y in any given function, so in this case, we are given the Y values and we have to solve the function for x:
y=9+6x
6x=y-9
[tex]x=\frac{y-9}{6}[/tex]
So we just insert the values, the first one being -12.
[tex]x=\frac{y-9}{6}\\x=\frac{-21}{6}\\x=\frac{-12-9}{6}\\x=-3.5[/tex]
So since from the options only A has -3.5 as an option that's the correct answer.
a high school had 740 students at the start of the year but then some students left the school after , that the school had 726 students .
if s = the number of students who left the school which mathematical sentence expresses the information above?
Answers
Answer:
I believe it's 726=740-S
Answer:
s = 740 - 14
Hope it helps u
least common factor of 12 and 22
Answers
132 is the least common multiple
Answer:
Least common multiple (LCM) of 12 and 22 is 132.Step-by-step explanation:
Which graph represents the function y - 3= 3/2 (x - 4)?
Answers
Answer:
A
Step-by-step explanation:
Answer:
Step-by-step explanation:
Yes it is A i did it rn
A line of symmetry for the figure is shown in red. Find the coordinates of point A. (Photo attached)
Answers
Answer:
a. Coordinate of A (-4,-1)
b. Coordinate of A (4,4)
c. Coordinate of A (-2,2)
what is the slop between (2,7) and (10,22) on fraction form
Answers
Answer:
m=15/8
Step-by-step explanation:
Slope intercept form- Y=mx+b
Slope- 15/8x
Y- intercept- (0,13/4)
Solve r-x+2y = 1 for y
Answers
Answer:
y=(1-r+x)/2
Step-by-step explanation:
(r-x)+2*y=12*y=1-(r-x)y=(1-r+x)/2Latoya drove 335 miles in 5 hours.
At the same rate, how long would it take her to drive 603 miles?
Answers
Answer:
It would take her 9 hours because she would be going 67mph
Step-by-step explanation:
335mph divided by 5 hours is 67mph
to celebrate the end of the school year, Gabby and her friends go out for pizza. the total bill is $37.84. if the 4 people split the cost evenly, how much does each person pay?
Answers
Answer:
9.46, u get this by dividing 37.84 by 4
Step-by-step explanation:
Answer:
9.46
Step-by-step explanation:
m∠AXB = this is the question
Answers
Answer:
Need a figure or more information to answer this question
Grant is making muffins for a reunion. The recipe to makes 12 muffins. The recipe for bran muffins makes 18 muffins. He wants to make the same number of each kind of muffin using only recipes of each. A. What is the least number of each type of muffin Grant can make B. How many batches of each recipe will Grant make if he makes t number of each type of muffin possible? Blueberry: batches Bran: batches
Answers
Answer:
a 36
b 3 blueberry, 2 bran
PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((
Answers
Answer:
it is 25 percent
Step-by-step explanation:
in a decimal it is 0.25
Find X to complete the following ratio. 12:5 = 24:X
Answers
Answer:
x = 10
Step-by-step explanation:
This is the answer because:
1) 12:5 is equivalent to the ration 24:10
2) This is because to get 24 you have to multiply 12 and 2 which is 24
3) Next, you have to do the same to the other side to make everything equal. Therefore, you have to multiply 5 with 2 which is 10.
4) Finally, your answer should be 24:10
Hope this helps! :D
at the bank , mr smith changes a e5 note for 20p pieces . how many 20 pieces does he have
Answers
Answer:
it should be 25
Step-by-step explanation:
£500 = 500p
500 ÷ 20 = 25
1/x-x/6=2/3 how to answer this
Answers
Answer:
x = 0.1
Step-by-step explanation:
1/x - x/6 = 2/3
1/ x - 6/x = 2/3
6/x = 2/3
6x = 2/3
x = 0.1
Answer:
x = 0.2
Step-by-step explanation:
1/x - x/6 = 2/3
=> 1/x - x = 2/3 * 6
=> 1/x - x = 12/3
=> 1/x - x = 4
=> 1/x - x/1 = 4 (x = x/1 )
=> 1 - x/1 = 4 * x
=> -x/1 = 4x - 1
=> -x/1 -4x = -1
=> -5x/1 = -1
=> x = -1/-5
=> x = 0.2 (Because negative / negative = positive)
If I am wrong please tell me.
If my answer helped, kindly mark me as the brinliest!!
Thanks!!
The function C(x)=20x+4,000 represents the cost to produce x number of items. How many items should be produced so that the average cost is less than $40?
Answers
Answer:
More than 200 items must be produced to keep the average cost below $40 per item.
Step-by-step explanation:
Shana bought 6.2 pounds of pecans and paid $56.00. About how much per pound did the pecans cost?
$5.00
$6.00
$8.00
$10.00
Answers
$56/6.2=$9.032
Answer:
D
Step-by-step explanation:
Can you please solve? And if anyone can please explain how to do this, thank you so much!
Answers
Answer:
15
Step-by-step explanation:
Both angles can add up to 180, so what I did was 7t-6 plus 5t+6=180. From there, I combined both positive 6 and negative 6 to which they cancel out. All that leaves is 7t+5t, which is 12t. Finally leaving 12t=180, so divided both sides by 12 to remove the 12 from 12t. 180/12=15. I think this is correct, but I am not sure. Please do check
Answer:
15
Step-by-step explanation:
ig my question was deleted lol
HELP THIS IS MY LAST MATH QUESTION PLEASE HELP MEEEE!
Answers
Answer:
length =6 2/3 option 2.......
solve the following : -6x(-2) =
Answers
Answer:
12
Step-by-step explanation: Just do 6 x 2