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2 years ago

30 POINTS!!! Which choice is equivalent to the fraction below when x is greater than or equal to 3?

Mathematics

2 answers:

Bond [772]2 years ago

6 0

Answer:

the answer would be c

Step-by-step explanation:

like the hint says, rationalize the denominator by multiplying the numerator and denominator by the conjugate

( $\sqrt{x} + \sqrt{x-3}$ ), and then simplify after that...hope this helps :)

Mashcka [7]2 years ago

4 0

Answer: C.

$\frac{9}{\sqrt{x} -\sqrt{x-3} }=\frac{9(\sqrt{x} +\sqrt{x-3} )}{x-(x-3)}=\frac{9(\sqrt{x} +\sqrt{x-3} )}{3}=3(\sqrt{x} +\sqrt{x-3})$

Step-by-step explanation:

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Using principle of mathematical induction prove that 6^-1 divisble by 5 .

salantis [7]

I suppose the claim is $5 \mid 6^n - 1$ for $n\in\Bbb N$ .

When $n=1$ , we have $6^1 - 1 = 6 - 1 = 5$ , and of course 5 divides 5.

Assume the claim holds for $n=k$ , that $5 \mid 6^k - 1$ . We want to use this to show it holds for $n=k+1$ , that $5 \mid 6^{k+1} - 1$ .

We have

$6^{k+1} - 1 = \left(6^{k+1} - 6\right) + \left(6 - 1) = 6\left(6^k - 1\right) + 5$

Since $5 \mid 6^k - 1$ , we can write $6^k - 1 = 5\ell$ for some integer $\ell$ . Then

$6^{k+1} - 1 = 6\cdot5\ell + 5 = 5(6\ell + 1)$

which is clearly divisible by 5. QED

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1 year ago

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Vladimir79 [104]

Answer:

Step-by-step explanation:

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3 years ago

A certain car can travel on a highway for 350 miles on 15 gallons of gas and in a city for 280 miles on 18 gallons of gas. If th

user100 [1]

Answer:

The car's average 18 number of miles per gallon

Step-by-step explanation:

The car has different efficiencies depending if its used on highway or city streets.

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Then, we can calculate how many miles makes the car on average as:

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3 years ago

Write the equation of the line with an x-intercept at (0,2) and perpendicular to 3x+4y=12.

juin [17]

First you normalize 3x+4y=12 into y = -3/4 x + 3 (dividing by 4).

Then you observe that the slope of the line is -3/4 (it's always the factor with the x). A perpendicular line has the reciprocal slope. Reciprocal means inverted and negated. So -3/4 becomes +4/3.

The equation will thus look like y = 4/3 x + b. To find b, we fill in the given x intercept (0,2), (we get 2 = 4/3 * 0 + b). With x=0, b must be 2.

So the equation is: y = 4/3 x + 2

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