rationalise the denominator of (6+root3)(6-root3) over root33
Answers
Answer:
√33
Step-by-step explanation:
In the image .
The expression (6 + √3) (6 - √3) / √33 upon rationalizing the denominator gives √33.
What is Square Root?Square root of a number is the value such that upon multiplying the value by itself twice gives the original number.
The given expression is (6 + √3) (6 - √3) / √33
We have the identity,
(a + b) (a - b) = a² - b²
∴ (6 + √3) (6 - √3) / 33 = 6² - (√3)² / √33
= (36 - 3) / √33
= 33 /√33
Multiplying numerator and denominator by √33,
(6 + √3) (6 - √3) / 33 = (33 × √33) / (√33 × √33)
= 33√33 / 33
= √33
Hence upon rationalizing the denominator in the expression (6 + √3) (6 - √3) / 33 yields √33.
To learn more about Square Roots, click on the link below:
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Related Questions
Line m contains the points (−3, 2) and (5 , 1). Line n contains the points (2 , 7) and (1, −1) . Which statement is TRUE about lines m and n?
A. The lines are parallel.
B. The lines are coincident.
C. Both lines intersect but are neither parallel nor perpendicular.
D. The lines are perpendicular.
Answers
9514 1404 393
Answer:
D. The lines are perpendicular
Step-by-step explanation:
The first line has a rise of (1-2) = -1 for a run of (5-(-3)) = 8.
The second line has a rise of (-1-7) = -8 for a run of (1-2) = -1.
Then the slopes are -1/8 and -8/-1 = 8, which are negative reciprocals of each other. Lines with slopes having that relationship are perpendicular.
I Need help please!!!
Answers
slope of (-3, 1), (1, 9) and slope of (-2, -9), (-1, -7)
Answers
Answer:
8/4 and 2/1(or just 2)
Step-by-step explanation:
slope formula- (y2-y1)/(x2-x1)
plug in the numbers-
(9-1)/(1+3) and (-7+9)/(-1+2)
Please help me I will really appreciate it!!!
Answers
Answer:
t = [tex]\sqrt{\frac{-2(h-1)}{a} }[/tex]
Step-by-step explanation:
solve for t
h = -[tex]\frac{1}{2}[/tex]a[tex]t^{2}[/tex] + 1; multiply both sides by -2
-2h = a[tex]t^{2}[/tex] - 2; add 2 to both sides
-2h + 2 = a[tex]t^{2}[/tex]; divide by a
(-2h + 2) / a = [tex]t^{2}[/tex] ; take the square root
t = [tex]\sqrt{\frac{-2(h-1)}{a} }[/tex]
what do you need to add to 2 4/7 to make 4
Answers
answer=0.58
Step-by-step explanation:
24/7= 3.42 ,so you subtract this from 4 to get 0.58
PLEASE HELP ME ASAP??!Which of the following are valid names for the triangle below? Check all that
apply.
Answers
Answer:
A, E
Step-by-step explanation:
Answer:
a,e
Step-by-step explanation:
What is 2M?
M=[3 5]
[-4 0]
Answers
Answer:
2M will be:
[tex]2\begin{pmatrix}3&5\\ -4&0\end{pmatrix}=\begin{pmatrix}6&10\\ -8&0\end{pmatrix}[/tex]
Therefore, the 2nd option is true.
Step-by-step explanation:
Given the matrix
[tex]M=\begin{pmatrix}3&5\\ -4&0\end{pmatrix}[/tex]
Multiplying by 2 will basically be a scalar multiplication.
Therefore, multiply each of the matrix elements by a scalar.
[tex]2M=2\begin{pmatrix}3&5\\ \:-4&0\end{pmatrix}[/tex]
[tex]=\begin{pmatrix}2\cdot \:3&2\cdot \:5\\ 2\left(-4\right)&2\cdot \:0\end{pmatrix}[/tex]
[tex]=\begin{pmatrix}6&10\\ -8&0\end{pmatrix}[/tex]
Hence, 2M will be:
[tex]2\begin{pmatrix}3&5\\ -4&0\end{pmatrix}=\begin{pmatrix}6&10\\ -8&0\end{pmatrix}[/tex]
Therefore, the 2nd option is true.
3.14 × 6.25..............
Answers
Answer:
calculator says 19.625
Answer:
19.625
Step-by-step explanation:
The volume of the large cube is 125 cubic inches. The volume of the small cube is 27 inches. What is the difference between the length of one side of the large cube and the length of one side of the small cube?
Answers
Answer:
2cmStep-by-step explanation:
Step one:
given data
for the large cube
the volume= 125cm^3
we know that volume = l*l*l
volume=l^3
we want to find l, so we have to cube both sides
125=l^3
l=∛125
l=5cm
Step two:
given data
for the large cube
the volume= 27cm^3
we know that volume = l*l*l
volume=l^3
we want to find l, so we have to cube both sides
27=l^3
l=∛27
l=3cm
The difference between the length of one side of the large cube and the length of one side of the small cube=5-3= 2cmHelp!!!!
Given log73≈0.5646 and log716≈1.4248, evaluate the expressions.
Answers
Answer:
a) 0.356
b) 1.1397
Step-by-step explanation:
a) log₇2
log(2) / log(7) 0.356b) log₇ (¹⁴⁷/₁₆)
log (¹⁴⁷/₁₆)log (7)
1.1397Simplify the expression
Answers
Answer:
f(y) = y g(y) = y - 6Step-by-step explanation:
[tex]\dfrac{y^2+6y}{y^2-36}\qquad\qquad\qquad\qquad y\ne6\,,y\ne-6 \\\\ \\\dfrac{y^2+6y}{y^2-36}=\dfrac{y\cdot y+6\cdot y}{y^2-6^2}=\dfrac{y(y+6)}{(y+6)(y-6)}=\dfrac{y}{(y-6)}\\\\\\f(y)=y\\\\g(y)=y-6[/tex]
(19 -16), (-7 -15) find the slope
Answers
-15-16=-31
-7-19=-26
Hope this helps
Nov 06, 7:43:52 PM
Which equation represents a line which is parallel to the line y =
= -x - 8?
O 8x + 3y = -6
O 8x – 3y = 3
Submit Answer
8y - 3x = -48
3x + 8y = 48
O
Answers
Answer:
8x-3y=3
Step-by-step explanation:
Its the only one that would give you a negative x
Which pairs of expressions are equivalent? Select all that apply.
A
-4 - 7 and -4 + (-7)
B
16 - 7 and -16 + 7
C
-7 - (-12) and -7 + 12
D
-2 - 3 and 2 + 3
E
10 - 2 and 10 - (-2)
Answers
Answer:
A & C
-4-7=-11 and -4+(-)=-11
-7-(-12) and -7+12
Step-by-step explanation:
-4-7= -11, -4+ (-7)= -11
-7-(-12) turns into -7+12=5
the second equation is the same as the first (after using PEDMAS), resulting in the answering being -7+12=5
The pairs of expressions that are equivalent will be -4 - 7 & -4 + (-7) and -7 - (-12) & -7 + 12. Then the correct options are A and C.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Check all the options, then we have
A. -4 - 7 and -4 + (-7), then we have
-4 - 7 = - 4 + (-7)
B. 16 - 7 and -16 + 7, then we have
16 - 7 ≠ - 16 + 7
C. -7 - (-12) and -7 + 12, then we have
- 7 - (-12) = - 7 + 12
D. -2 - 3 and 2 + 3, then we have
- 2 - 3 ≠ 2 + 3
E. 10 - 2 and 10 - (-2), then we have
10 - 2 ≠ 10 - (-2)
The pairs of expressions that are equivalent will be -4 - 7 & -4 + (-7) and -7 - (-12) & -7 + 12. Then the correct options are A and C.
More about the equivalent link is given below.
https://brainly.com/question/889935
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Give the domain and range of the relation.
Answers
Answer:
The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range. Domain: all x-values that are to be used (independent values).
Step-by-step explanation:
it c
Can someone plzz answer this!!?
Answers
Answer: B Angle Side Angle
Step-by-step explanation:
Since line AB and CD are parallel angles D and A are congruent by the alternate interior theorem and both angles AOB and DOC are congruent by the vertical angle theorem and it already shows line OC and line OB are congruent.
15. The diameter of a circle is given as 10 cm, correct to the nearest cm. Calculate:
a) the maximum possible circumference
b) the minimum possible area of the circle consistent with this data
Answers
Answer:
10cm correct to nearest cm" means the diameter could be arbitrarily close to (but less than) 10.5 cm. So the maximum possible circumference is 10.5π cm.
"10cm correct to nearest cm" also means that the diameter could be arbitrarily close to (but greater than) 9.5 cm. So the minimum possible area is π(9.5)²/4 cm²
The graph shows that the distance a dog runs is proportional to the time the dog is running. You want to use only one plotted point to find the unit rate. Which of the three plotted points could you choose? Select all that apply.
(0,0)
(1,9.7)
(4,38.8)
Question 2
The unit rate is
feet per second.
Answers
Answer:
2
Step-by-step explanation:
2
Are the triangles congruent?
1. If they are congruent tell me the how you determined congruence, AND tell me the rigid transformations
needed to match the triangles over each other.
2. If they are not congruent then answer "not congruent" or "not enough information" and explain why.
Answers
Answer:
yes they are congruent because they are the same size
Step-by-step explanation:
theyre the same size so yes
Parents will kill me if I don't get this done in an hour (BRAINLIEST IF ANSWER IS CORRECT AND WORK IS SHOWN)
Answers
Answer: -3 1/2 and -6
Will mark brainliest!! Please answer ASAP
Will give extra points!!!
Please let me know if the picture above answer is correct or not and tell me the right answer!
Second question-
Which linear equation can be used to represent a line parallel to the x axis that passes through the point (8,5)
1) y=5
2) y=x+8
3) y=x+5
Answers
Answer:
y=5
Step-by-step explanation:
y= 5 is always parallel to x axis
Write the expression in simplest form.
(11 + 3) – 2(- 4 1 - 1) =
NIO
Answers
Answer:
11+3=14
-41-1=-42
14-2(-42)
-2(-42)
14+84
98
I hope this is good enough:
mr. and Mrs . Coronado took a bus to belmopan . they left at 7:15 a.m. and arrived at 8:00 a.m . How long was the trip show ur working out and thank u once again
Answers
Answer:
The trip was 45 minutes
Step-by-step explanation:
you take 60 minutes which is an hour and subtract 15 to get 45 minutes
f(x) = 3x + 5
g(x) = 4x^2 – 2
h(x) = x^2 – 3x + 1
Find f(x) – g(x) – h(x).
Answers
Answer:
f(x) – g(x) – h(x) = -5x^2 + 6x + 6
Step-by-step explanation:
Copy f(x) as is: f(x) = 3x + 5
Negate g(x): -g(x) = -4x^2 + 2
Negate h(x): -h(x) = -x^2 + 3x - 1
Now combine like terms:
f(x) – g(x) – h(x) = -5x^2 + 6x + 6
Which of the following mathematical properties is described by the statement, “whatever is done on one side of the equation must also be done on the other side of the equation”?
Identity Property of Addition
Associative Property
Communitive Property
Property of Equality
today guys please
Answers
Answer:
Property of Equality
Step-by-step explanation:
Answer:Property of Equality
STEP BY STEP EXPLANATION HAS BEEN CANCELED ITS EASY:
PLEB
Use the dropdown to complete the following inequality.
Answers
Answer:
>
Step-by-step explanation:
b is clearly negative
- - = +
so therefore, subtracting the negative will result in a larger answer than adding a small positive to a negative
Extremely easy question marking Brainliest answer
Answers
Answer:
It is hard to tell from this image, but I believe the word you are looking for is Integer. Integers are any positive or negative whole number.
Find three consecutive odd integers such that the sum of 7 times the smallest and twice the largest is -91.
Answers
(1,-19),(-2 -7) finnd the slope to this equation
Answers
Answer:
slope is 4
Step-by-step explanation:
a science teacher has 12 g of marble chips. Each lab station needs 0.5 g of marbles chips. How many lab station can she supply?
Answers
Answer:
24
Step-by-step explanation:
Since each lab station needs 0.5 grams of chips, we have to divide 0.5 from 12.
12/0.5 = 24