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aalyn [17]
3 years ago
9

√3 /√6 rationalise denominator and simplify

Mathematics
1 answer:
melomori [17]3 years ago
7 0

Answer:

\frac{ \sqrt{2} }{2}  \\

Step-by-step explanation:

\frac{ \sqrt{3} }{ \sqrt{6} }  \\  \frac{ \sqrt{3} }{ \sqrt{6} } \times \frac{ \sqrt{6} }{ \sqrt{6} }  \\   \frac{ \sqrt{3 \times 6} }{ \sqrt{ {6}^{2} } }  \\  \frac{ \sqrt{18} }{6}  \\  \frac{ \sqrt{2 \times 9} }{6}  \\  \frac{3 \sqrt{2} }{6}  \\  \frac{ \sqrt{2} }{2}

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What is the inverse of the function H(x)=3/4x+12
Mrac [35]

Answer:

h^{-1}(x) = \frac{4x-48}{3}

Step-by-step explanation:

let y = h(x) and rearrange making x the subject, that is

y = \frac{3}{4} x + 12 ( multiply through by 4 to clear the fraction )

4y = 3x + 48 ( subtract 48 from both sides )

4y - 48 = 3x ( divide both sides by 3 )

\frac{4y-48}{3} = x

Change y back into terms of x, thus

h^{-1} (x) = \frac{4x-48}{3}

3 0
4 years ago
A certain test preparation course is designed to help students improve their scores on the GMAT exam. A mock exam is given at th
Bogdan [553]

Answer:

95% confidence interval for the average net change is between a lower limit of 11.709 and an upper limit of 30.921.

The critical value that should be used in constructing the confidence interval is 4.303.

Step-by-step explanation:

Confidence interval is given as mean +/- margin of error (E)

mean = (17+20+26)/3 = 63/3 = 21

sd = sqrt[((17-21)^2 + (20-21)^2 + (26-21)^2) ÷ 3] = sqrt(42÷3) = sqrt(14) = 3.74

n = 3

degree of freedom = n-1 = 3-1 = 2

confidence level (C) = 95% = 0.95

significance level = 1 - C = 1 - 0.95 = 0.05 = 5%

critical value (t) corresponding to 2 degrees of freedom and 5% significance level is 4.303.

The critical value is 4.303

E = t×sd/√n = 4.303×3.74/√3 = 9.291

Lower limit of mean = mean - E = 21 - 9.291 = 11.709

Upper limit of mean = mean + E = 21 + 9.291 = 30.291

95% confidence interval is (11.709, 30.391)

8 0
3 years ago
A fence must be built to enclose a rectangular area of 20,000 ftsquared. fencing material costs $ 1 per foot for the two sides f
Simora [160]
The total cost of the least expensive fence would be $800.

To minimize perimeter and maximize area we take factors that are as close to equal as possible.  In this case, the closest whole number factors are 200 and 100.  Since the north and south faces cost less, we will make those 100 ft and make the more expensive east and west faces 200 ft.

100 ft × $2/ft = $200 per side × 2 sides = $400 for the north and south facing sides.

200 ft × $1/ft = $200 per side × 2 sides = $400 for the east and west facing sides

$400 + $400 = $800
6 0
3 years ago
Find the slope and the y-intercept of the line
Vinvika [58]

The slope is basically the coefficient of x and that is 1 since 1x=x. To find the y-intercept, you need to subtitute x=0 into y=x+5 because x is at 0 when you are looking at the y-intercept.

y=0+5=5

So the slope is 1 and the y-intercept is 5.

6 0
4 years ago
Answer 173.22÷4 and use long division to show work.
olga nikolaevna [1]
43.305 Hope this helps. 
8 0
3 years ago
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