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3 years ago

Determine whether the polynomial is a difference of squares and if it is, factor it.

1 answer:

8 0

Remember these three formulas (really, learn these by heart):

${(a + b)}^{2} = a^{2} + 2ab + b^{2}$

${(a - b)}^{2} = a^{2} - 2ab + b^{2}$

$(a + b)(a - b) = a^{2} - b^{2}$

The stated formula is a manifestation of the last of these three. So indeed,

$(y + 15)(y - 15) = y^{2} - 225$

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What is 2 hours and 20 minutes as a fraction

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3 years ago

Dr. Yancy conducted a correlation study in which she found that the more time children in her study read at home the better they

anzhelika [568]

Answer:

A. Positive

Step-by-step explanation:

They ask us about the relationship between reading and grades.

First you have to go to the first part of the statement that says:

"Dr. Yancy conducted a correlation study in which she found that the more time children in her study read at home the better they performed in school"

In this case they tell us that there is a positive correlation, that the more you read the better your performance in school is.

Performance is your grades, and home study can be reading, so the score is positive in the second half, too.

3 0

2 years ago

The sum of the reciprocals of two consecutive even integers is 7/24. Write an equation that can be used to find the two integers

sergejj [24]

Assume the first even integer is x.
The next even integer will be 2 digits after this digit. So the next even integer will be x+2.

The reciprocals of these two even integers can be written as $\frac{1}{x}$ and $\frac{1}{x+2}$ respectively.

The sum of their reciprocals is 7/24. So we can set up the equation as:

$\frac{1}{x}+ \frac{1}{x+2}= \frac{7}{24}$

Taking LCM on left hand side:

$\frac{x+2+x}{x(x+2)}= \frac{7}{24} \\ \\ 
 \frac{2x+2}{ x^{2} +2x}= \frac{7}{24}$

Cross Multiplying the denominators:

$24(2x+2)=7({ x^{2} +2x}) \\ \\ 
48x+48=7 x^{2} +14x \\ \\ 
7 x^{2} +14x-48x-48=0 \\ \\ 
7 x^{2} -34x-48=0 \\ \\ 

$

Using the quadratic formula to solve the above equation:
$7 x^{2} -34x-48=0 \\ \\ 
x= \frac{34+- \sqrt{1156+1344} }{14} \\ \\ 
x= \frac{34+- \sqrt{2500} }{14} \\ \\ 
x=\frac{34+-50 }{14} \\ \\ 
x=6 \\ x=- \frac{8}{7} 
$

Since, the value of x can only be an integer, we discard the fractional value and keep x=6

So the first even integer is 6 and the next even integer is 8. The sum of reciprocals of 6 and 8 is 7/24

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3 years ago