2 3/4 divided by 3 =

An equivalent expression with a rational denominator is...

Whitepunk [10]

Given the expression,

$(8x-56x^2)/(\sqrt{14x-2})$

We will have to rationalize the denominator first. To rationalize the denominator we have to multiply the numerator and denominator both by the square root part of the denominator.

$[(8x-56x^2)(\sqrt{14x-2})]/[(\sqrt{14x-2})(\sqrt{14x-2})]$

If we have $(\sqrt{a})(\sqrt{a})$ , we will get $\sqrt{a^2}$ by multiplying them. And $\sqrt{a^2} = a$ .

So here in the problem, we will get,

$[(8x-56x^2)(\sqrt{14x-2})]/(14x-2)$

Now in the numerator we have $(8x-56x^2)$ . We can check 8x is common there. we will take out -8x from it, we will get,

$-8x(-1+7x)$

$-8x(7x-1)$

And in the denominator we have $14x-2$ . We can check 2 is common there. If we take out 2 from it we will get,

$2(7x-1)$

So we can write the expression as

$[(-8x)(7x-1)(\sqrt{14x-2})]/[2(7x-1)]$

$(7x-1)$ is common to the numerator and denominator both, if we cancel it we will get,

$(-8x)(\sqrt{14x-2})/2$

We can divide -8 by the denominator, as -8 os divisible by 2. By dividing them we will get,

$(-4x)(\sqrt{14x-2})$

$(-4x)(14x-2)^(1/2)$

So we have got the required answer here.

The correct option is the last one.

4 0

3 years ago

Find the mean, median, mode for the data set below. 32, 20, 45, 20, 14, 7, 20

Butoxors [25]

Answer:

mean-22

mode-20

median-20

7 0

3 years ago

Read 2 more answers

Solve 4(3x+3)=15x+7-3x+5

Flura [38]

Answer:

Infinite amount of solutions

Step-by-step explanation:

Step 1: Write equation

4(3x + 3) = 15x + 7 - 3x + 5

Step 2: Solve for x

Distribute 4: 12x + 12 = 15x + 7 - 3x + 5
Combine like terms: 12x + 12 = 12x + 12
Subtract 12 on both sides: 12x = 12x
Divide both sides by 12: x = x

Here, we can see that x would be infinite amount of solutions. We can plug in any number x and it would render the equation true.

4 0

3 years ago

The output is eight more than the input

d1i1m1o1n [39]

Answer:

x = input

y = output

y = 8 + x

7 0

3 years ago

48. Reading Rates The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute a

son4ous [18]

Answer:

The reading speed of a sixth-grader whose reading speed is at the 90th percentile is 155.72 words per minute.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 125, \sigma = 24$