Rationalise
[tex]{ \frac{1 + \sqrt{3} }{ \sqrt{12} } } [/tex]
Answers
Answer:
Step-by-step explanation:
![Rationalise [tex]{ \frac{1 + \sqrt{3} }{ \sqrt{12} } } [/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/2TghkhbV58UKvZUMFmIzx50LwzafXYm2.jpeg)
Answer:
[tex]\frac{2\sqrt{3} + 6}{12}[/tex]
Step-by-step explanation:
Simplify the denominator of [tex]\frac{1 + \sqrt{3} }{\sqrt{12} }[/tex] completely.
[tex]=> \frac{1 + \sqrt{3} }{ \sqrt{(4 \times 3)} } = \frac{1 + \sqrt{3} }{\sqrt{4} \times \sqrt{3} } = \frac{1 + \sqrt{3} }{2\sqrt{3} }[/tex]
Now, to rationalise it you need to make the denominator rational.
Multiply & divide [tex]\frac{1 + \sqrt{3} }{2\sqrt{3} }[/tex] by [tex]2\sqrt{3}[/tex].[tex]=> \frac{1 + \sqrt{3} }{2\sqrt{3} } \times \frac{2\sqrt{3} }{2\sqrt{3} }[/tex]
[tex]=> \frac{(1 + \sqrt{3})\times 2\sqrt{3} }{2\sqrt{3} \times 2\sqrt{3} }[/tex]
[tex]=> \frac{2\sqrt{3} + 6 }{12}[/tex]
Related Questions
Simplify. State any restrictions on the variables.
[tex]\frac{x^2+9x+18}{x+6}[/tex]
Answers
Answer: [tex]x+3, x \neq -6[/tex]
Step-by-step explanation:
The denominator cannot equal 0, so [tex]x \neq -6[/tex].
Simplfying,
[tex]\frac{x^2 +9x+18}{x+6}=\frac{(x+6)(x+3)}{x+6}=x+3[/tex]
A regression was run to determine if there is a relationship between hours of tv watched per day (x) and the number of situps a person can do (y).The results of the regression were:y=ax+ba=−1.077b=30.98r2=0.744769r=−0.863Use this to predict the number of situps a person who watches 13.5 hours of TV can do.
Answers
Answer:
The number of situps is: 16.4405
Step-by-step explanation:
Given
[tex]y = ax + b[/tex]
[tex]a =-1.077[/tex]
[tex]b=30.98[/tex]
[tex]r^2 = 0.74476[/tex]
Required
Predict y when [tex]x = 13.5[/tex]
In the result, we have:
[tex]y = ax + b[/tex]
[tex]a =-1.077[/tex]
[tex]b=30.98[/tex]
This implies that:
[tex]y = -1.077x + 30.98[/tex]
To make prediction when [tex]x = 13.5[/tex]
We have:
[tex]y = -1.077*13.5 + 30.98[/tex]
[tex]y = -14.5395 + 30.98[/tex]
[tex]y = 16.4405[/tex]
Money Neil has a total of twelve $5 and $10 bills in his wallet. He has 5 times as many $10 bills as $5 dollar bills. How many of each does he have?
Answers
Answer:
He has 2 $5 bills and 10 $10 bills
A man buys a marker at Rs. 40 and sells it at Rs. 50. What is the profit percentage?
Answers
Step-by-step explanation:
C.P of the marker= Rs. 40
S.P of the marker= Rs. 50
Profit= S.P- C.P
= 50- 40
= Rs. 10
Profit%= {[tex]\frac{Profit}{C.P}[/tex]×100}%
= {[tex]\frac{10}{40}[/tex]×100}%
= 25%
Hope it helps♡The route between the park and Josh's house is 81 meters. He walks this route 4 times on Saturday. How far does Josh walk between the park and his house on Saturday? Enter your answer in the box.
Answers
Answer:
648 m.
Step-by-step explanation:
Each walk = 2*81 = 162 m.
So total for 4 walks = 4 * 162
= 648 m.
Answer:
Josh walked 324 meters
Step-by-step explanation:
81×4= 324
PLEASE HELP !! I will give Brainly to whoever answers
Answers
Answer:
A
Step-by-step explanation:
In the triangle ABC shown below, DE is parallel to BC. Find the length of DB.
20
10
D
E
х
B
15
с
Answers
Answer:
i think it's 10 because if DE is 10 so BD is the same think it's 10
i need the measurement of angle a
Answers
Angle B = 90°
Angle C = 67°
To find:-Angle A.
Solution:-[tex]{\boxed{\mathcal{\red{Angle\: A \:=\: 23° \:}}}}[/tex]✅
Step-by-step explanation:-We know that,
[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]
➪ ∠ A + ∠ B + ∠ C = 180°
➪ ∠ A + 90° + 67° = 180°
➪ ∠ A + 157° = 180°
➪ ∠ A = 180° - 157°
➪ ∠ A = 23°
[tex]\sf\red{Therefore, \:the\: value \:of \:∠\: A\: is \:23°.}[/tex]
To verify:-∠ A + ∠ B + ∠ C = 180°
✒ 23° + 90° + 67° = 180°
✒ 180° = 180°
✒ L. H. S. = R. H. S.
[tex]\boxed{Hence\:verified.}[/tex]
Note:-
Please refer to the attached file.
[tex]\bold{ \green{ \star{ \orange{Hope\:it\:helps.}}}}⋆[/tex]
<3 Help! A teacher buys 8 packs of orange erasers
Answers
Answer:
360 total numbers of easers
Step-by-step explanation:
You first do
8 x 24
which equals
192
then do
6 x 28
which equals
168
then you take
168 + 192
then that will be
360
you are welcome
The living room in a new house has the dimensions shown. What is the volume of the room?
Answers
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 445 gram setting. Is there sufficient evidence at the 0.01 level that the bags are underfilled
Answers
Complete Question
A manufacturer of banana chips would like to know whether its bag filing machine works correctly at the 445 gram setting is there sufficient evidence at the 0.01 level that the bags are underfilled? Assume the population is normally distributed State the null and alternative hypotheses for the above scenario
Answer:
[tex]H_o=\mu=445g[/tex]
[tex]H_a=\mu<445g[/tex]
Step-by-step explanation:
From the question we are told that:
Mass [tex]M=445g[/tex]
Significance level [tex]\alpha=0.01[/tex]
Generally the Null and Alternative Hypothesis is
[tex]H_o=\mu=445g[/tex]
i.e The bags are not under filled
[tex]H_a=\mu<445g[/tex]
i.e The bags are under filled
On Tuesday, 4 out of every 10 people who entered a store purchased something. If 8,800 people entered the store on Tuesday, how many people purchased something?
Answers
Make a line plot of the measurements in the table. Then find the fair share.
Table:
Amount of Sports drink (gallons)
1 over 4
1 over 2
1 over 3
1 over 2
1 over 4
1 over 3
1 over 3
1 over 2
Answers
Answer:
its nothing 0
Step-by-step explanation:
Answer:
Step-by-step explanation:
3/8 or 1/3 if you round it.
composite figure help omg
Answers
Answer:
188 sq m
Step-by-step explanation:
for the top square its just 6 x 6 which is 36
then for the bottom you add 6 + 13 for the width (which is 19) and we've already been given 8 for the height so then you multiply 19 x 8 and get 152
you then add 152 and 36 to get 188 (and the unit is sq m or m^2)
Which does NOT have a value of 4 when
simplified?
1. 5.6x0.15 + (-3.16)
1. (-7x23) + (-43)
III. -5.6+4(3)
Answers
Answer:
3 beause when you dividend it -5.6+4(3) .
What is 90 inches converted into centimetres?
Answers
Answer:
228.9
Step-by-step explanation:
Answer:
228.6
Step-by-step explanation:
Multiply the inches by 2.54
90 x 2.54 = 228.6
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
pleace helppp meeeee
In ΔCDE, the measure of ∠E=90°, ED = 28, CE = 45, and DC = 53. What ratio represents the tangent of ∠C?
Answers
Answer:.
Step-by-step explanation:
Answer:
Step-by-step explanation:20/29
Enter the number that belongs in the green box
Answers
Answer:
m<B = 107°
Step-by-step explanation:
∆ADC is congruent to ∆ABC by the SSS Congruence Theorem.
<D corresponds to <B, therefore,
m<D = m<B
m<D = 180° - (41° + 32°)
m<D = 180° - 73°
m<D = 107°
m<D = m<B = 107°
m<B = 107°
Find the perimeter of a quadrilateral with vertices at C (-2, 1), D (2, 4), E (5.0), and F (1, -3).Round your answer to the nearest hundredth when necessary.
1) 12 units
2) 16 units
3) 20 units
4) 24 units
Answers
Answer:
16 units
Step-by-step explanation:
Find the measure of each angle in the isosceles trapezoid.
Answers
Answer:
Below in bold.
Step-by-step explanation:
m < C = m < D = 64 degrees
m <A + m < D = 180
m < A + 64 = 180
m<A = 180 - 64 = 116 degrees.
m < B = m< A = 116 degrees.
a. Find the probability of the normal curve between z = -2.50 and z = 1.50.
Answers
Answer:
[tex] = \phi( - 2.50) + \phi(1.50) \\ from \: calc : \\ = 0.4938 + 0.4332 \\ = 0.927[/tex]
Find the volume of the sphere.
r= 6 cm
Formulas for Spheres
S.A. = 4tr?
V = [?] cm3
Round to the nearest tenth.
V = Arr
Answers
Answer:
904.8cm^3
Step-by-step explanation:
[tex] \frac{4}{3} \pi{(6)}^{3} \\ \frac{4}{3} \pi(216) \\ \frac{864}{3} \pi \\ 288\pi \\ 904.8 {cm}^{3} [/tex]
The volume of the sphere will be 904.32 cubic cm.
What is the volume of the sphere?Let r be the radius of the sphere. Then the volume of the sphere will be given as,
V = 4/3 πr³ cubic units
The radius of the sphere is 6 cm. Then the volume of the sphere is calculated as,
V = 4/3 x 3.14 x 6³
V = 904.32 cubic cm
The volume of the sphere will be 904.32 cubic cm.
More about the volume of the sphere link is given below.
https://brainly.com/question/9994313
#SPJ7
My exam, does any one know the answer
Answers
Answer:
D) 7
Step-by-step explanation:
Five times a number=5x
added to 4= 5x+4
[tex]5x+4=39[/tex]
[tex]5x=35[/tex]
[tex]x=7[/tex]
So, the number is 7.
Ms. Jimenez surveyed 430 men and 200 women about their vehicles. Of those surveyed, 160 men and 85 women said that they own a white vehicle.
Answers
Answer:
3/7
Step-by-step explanation:
430 +200 = 630 (630 people in all)
430-160 =270 (270 men NO WHITE CAR)
270/630 = 3/7
What are the solutions of the equation
x2-1=15?
Answers
Answer:
x=4, -4
Step-by-step explanation:
hope this helps!
What combination of transformations is shown below?
Answers
Answer:
Correct answer is "reflection, then rotation".
Step-by-step explanation:
The figure shows the following two operations:
1) Reflection through central horizontal line. ([tex]1 \to 2[/tex])
2) Rotation with center at the upper left corner of the reflected figure. ([tex]2 \to 3[/tex])
Therefore, correct answer is "reflection, then rotation".
What is 4n + 3 ( n – 5 ) + 2 simplified? I suck At math sry
Answers
Answer:
[tex]7n−13[/tex]
Step-by-step explanation:
[tex]4n+3(n−5)+2[/tex]
[tex]4n+3n+3 \times (−5+2)[/tex]
[tex]4n+3n−15+2[/tex]
[tex]7n−15+27n-15+2[/tex]
[tex]7n−13[/tex]
Hope it is helpful....When filled to capacity, the water in the aquarium water tank reaches 32 feet. The water is currently reaching 24 feet. What percentage of the tank is full? A 70% C 75% B 25% D 80% 28
Answers
Answer:
75%
Step-by-step explanation:
24/32 * 100%
75%
TESTS OF
ADULT BASIC
EDUCATION
ABE
LOCATOR TEST
Answers
Answer:
Step-by-step explanation:
Wat lol
y = 1/2x + 1 and 2y - x = 6 How many solutions does this system have?(: -none, one, or ifinite?
Answers
Answer:
none
Step-by-step explanation:
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