Given the expression,

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})]](https://tex.z-dn.net/?f=%20%5B%288x-56x%5E2%29%28%5Csqrt%7B14x-2%7D%29%5D%2F%5B%28%5Csqrt%7B14x-2%7D%29%28%5Csqrt%7B14x-2%7D%29%5D%20)
If we have
, we will get
by multiplying them. And
.
So here in the problem, we will get,
![[(8x-56x^2)(\sqrt{14x-2})]/(14x-2)](https://tex.z-dn.net/?f=%20%5B%288x-56x%5E2%29%28%5Csqrt%7B14x-2%7D%29%5D%2F%2814x-2%29%20)
Now in the numerator we have
. We can check 8x is common there. we will take out -8x from it, we will get,


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

So we can write the expression as
![[(-8x)(7x-1)(\sqrt{14x-2})]/[2(7x-1)]](https://tex.z-dn.net/?f=%20%5B%28-8x%29%287x-1%29%28%5Csqrt%7B14x-2%7D%29%5D%2F%5B2%287x-1%29%5D%20)
is common to the numerator and denominator both, if we cancel it we will get,

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


So we have got the required answer here.
The correct option is the last one.
Answer:
Infinite amount of solutions
Step-by-step explanation:
Step 1: Write equation
4(3x + 3) = 15x + 7 - 3x + 5
Step 2: Solve for <em>x</em>
- 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 <em>x</em> would be infinite amount of solutions. We can plug in any number <em>x</em> and it would render the equation true.
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
and standard deviation
, the zscore of a measure X is given by:

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:

What is the reading speed of a sixth-grader whose reading speed is at the 90th percentile
This is the value of X when Z has a pvalue of 0.9. So it is X when Z = 1.28.




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