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3 years ago

To rationalize the denominator of (5-\sqrt(7))/(9-\sqrt(14)) , you should multiply the expression by which fraction?

2 answers:

4 0

You would multiply by

$\frac{9+\sqrt{14}}{9+\sqrt{14}}$ .

When you rationalize the denominator, you multiply by the conjugate of the denominator. The conjugate is the same numbers and radicals, but with the sign of the radical switched.

Tpy6a [65]3 years ago

3 0

Answer:

$\frac{9+\sqrt{14}}{9+\sqrt{14}}$

Step-by-step explanation:

we have

$\frac{5-\sqrt{7}}{9-\sqrt{14}}$

we know that

To rationalize the denominator, multiply by the conjugate of the denominator

$\frac{5-\sqrt{7}}{9-\sqrt{14}}*\frac{9+\sqrt{14}}{9+\sqrt{14}}=\frac{(5-\sqrt{7})(9+\sqrt{14})}{9^{2}-14}\\ \\=\frac{(5-\sqrt{7})(9+\sqrt{14})}{67}$

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Joe and his family are flying to Texas. Their plane flies 645 miles at 215 mph. How long does the trip take? Solve and explain

olya-2409 [2.1K]

You can use the distance equation.. d = rt
d = distance = 645
r = rate = 215 mph
t = time = ???? find the time
645 = 215t
645/215 = 215t / 215
3 = t
t = 3
It took 3 hours

7 0

3 years ago

A random sample of 64 students at a university showed an average age of 20 years and a sample standard deviation of 4 years. The

adelina 88 [10]

Answer:

The 90% confidence level is $19.15< L < 20.85$

Step-by-step explanation:

From the question we are told that

The sample size is $n = 64$

The mean age is $\= x = 20 \ years$

The standard deviation is $\sigma = 4 \ years$

Generally the degree of freedom for this data set is mathematically represented as

$df = n - 1$

substituting values

$df = 64 - 1$

$df = 63$

Given that the level of confidence is 90% the significance level is mathematically evaluated as

$\alpha = 100 - 90$

$\alpha =$ 10 %

$\alpha = 0.10$

Now $\frac{\alpha }{2} = \frac{0.10}{2} = 0.05$

Since we are considering a on tail experiment

The critical value for half of this significance level at the calculated degree of freedom is obtained from the critical value table as

$t_{df, \frac{ \alpha}{2} } = t_{63, 0.05 } = 1.669$

The margin for error is mathematically represented as

$MOE = t_{df , \frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

substituting values

$MOE = 1.699 * \frac{4 }{\sqrt{64} }$

$MOE = 0.85$

he 90% confidence interval for the true average age of all students in the university is evaluated as follows

$\= x - MOE < L < \= x + E$

substituting values

$20 - 0. 85 < L < 20 + 0.85$

$19.15< L < 20.85$

4 0

3 years ago

Find the centroid for an area defined by the equations y = x² + 3 and y = - (x – 2)² + 7

meriva

The points where the 2 graphs intersect is where x = 0 and x = 2.

- 2 2
x = INT x dA / INT dA
0 0

INT dA = INT -x^2 + 4x + 3 - (x^2 + 3 ) dx = INT -2x^2 + 4x
= -2 x^3/3 + 2x^2
= 2.667 between 0 and 2

xdA = -2x^3 + 4x^2 INT xdA = -x^4/2 + 4x^3/3 = 2.667

centroid = 2.667 / 2.667 = 1 (x = 1)

3 0

3 years ago

Read 2 more answers

Geometry number 11 only need help on

pogonyaev

Answer:

Good Luck!

Step-by-step explanation: