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3 years ago

What is the simplified form of 3 over 4x plus 3 + 21 over 8 x squared plus 26x plus 15 ?

Mathematics

2 answers:

Sladkaya [172]3 years ago

6 0

3 over 4x plus 3 + 21 over 8 x squared plus 26x plus 15 $\frac{3}{4x+3} +\frac{21}{8x^2 +26x+15}$

factor the quadratic expression

⇒ $\frac{3}{4x+3} +\frac{21}{8x^2 +20x+6x+15}= \frac{3}{4x+3} +\frac{21}{4x(2x+5)+3(2x+5)}$

= $\frac{3}{4x+3} +\frac{21}{(2x+5)(4x+3)}$

Find LCD , and make the denominators same by multiplying first expression by (2x+5) both in numerator and denominator

= $\frac{3(2x+5)}{(4x+3)(2x+5)} +\frac{21}{(2x+5)(4x+3)}$

Simplify

= $\frac{3(2x+5) +21}{(4x+3)(2x+5)}$

= $\frac{6x+15 +21}{(4x+3)(2x+5)}$

= $\frac{6x+36}{(4x+3)(2x+5)}$

Factor the numerator

= $\frac{6(x+6)}{(4x+3)(2x+5)}$

Option D

nekit [7.7K]3 years ago

4 0

Answer:

-4x + 14

Step-by-step explanation:

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Answer:

a) Decrease

b) New mean = 78.43

c) Decrease

Step-by-step explanation:

We are given the following in the question:

Total number of students in class = 28

Average of 27 students = 79

Standard Deviation of 27 students = 6.5

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a) The new student's score will decrease the average.

b) New mean

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean = \dfrac{\displaystyle\sum x_i}{27} = 79\\\\\sum x_i = 27\times 79 = 2133$

New mean =

$\text{ New mean} =\dfrac{ \displaystyle\sum x_i +63}{28}\\\\ =\dfrac{2133+63}{28}= \dfrac{2196}{28} = 78.43$

Thus, the new mean is 78.43

c) Since the new mean decreases, standard deviation for new scores will decrease.

This is because the new value is within the usual values i.e. within two standard deviations of the mean. So, this wont cause a lot of variation as this value will be closer to already available data values. Also number of observations (n) in the denominator is increasing. Based on both these points we can conclude that standard deviation will decrease

Formula for Standard Deviation:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

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