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3 years ago

Simplify (7x+42)/(x^2+13x+42)

2 answers:

Colt1911 [192]3 years ago

7 0

$\frac{7x+42}{x^2+13x+42}= \frac{7(x+6)}{x^2+7x+6x+42}= \frac{7(x+6)}{x(x+7)+6(x+7)}= \frac{7(x+6)}{(x+6)(x+7)}= \frac{7}{x+7}$

grandymaker [24]3 years ago

4 0

<h2>Answer:</h2>

The simplified expression is given by:

$\dfrac{7}{x+7}$

<h2>Step-by-step explanation:</h2>

We are asked to simplify the expression which is given in terms of variable x as:

$=\dfrac{7x+42}{x^2+13x+42}$

The given expression is a rational expression as it is a polynomial expression in the denominator as well as in the numerator.

Now we know that:

$7x+42=7(x+6)$

and

$x^2+13x+42=x^2+7x+6x+42\\\\\\i.e.\\\\\\x^2+13x+42=x(x+7)+6(x+7)\\\\\\i.e.\\\\\\x^2+13x+42=(x+7)(x+6)$

Hence, we get:

$\dfrac{7x+42}{x^2+13x+42}=\dfrac{7(x+6)}{(x+6)(x+7)}\\\\\\i.e.\\\\\\\dfrac{7x+42}{x^2+13x+42}=\dfrac{7}{x+7}$

Hence, the simplified expression is:

$\dfrac{7}{x+7}$

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2 years ago

A doctor is measuring the mean systolic blood pressure of female students at a large college. Systolic blood pressure is known t

Nana76 [90]

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The correct option is (b).

Step-by-step explanation:

The (1 - α)% confidence interval for population mean (μ) is:

$CI=\bar x\pm z_{\alpha/2}\times\frac{SD}{\sqrt{n}}$

The confidence interval for population mean can be computed using either the z-interval or t-interval.

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Also it is provided that the systolic blood pressure is known to have a skewed distribution.

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3 years ago

PLEASE NEEED HEELPP

krok68 [10]

There are many systems of equation that will satisfy the requirement for Part A.
an example is y≤(1/4)x-3 and y≥(-1/2)x-6
y≥(-1/2)x-6 goes through the point (0,-6) and (-2, -5), the shaded area is above the line. all the points fall in the shaded area, but
y≤(1/4)x-3 goes through the points (0,-3) and (4,-2), the shaded area is below the line, only A and E are in the shaded area.
only A and E satisfy both inequality, in the overlapping shaded area.

Part B. to verify, put the coordinates of A (-3,-4) and E(5,-4) in both inequalities to see if they will make the inequalities true.
for y≤(1/4)x-3: -4≤(1/4)(-3)-3
-4≤-3&3/4 This is valid.
For y≥(-1/2)x-6: -4≥(-1/2)(-3)-6
-4≥-4&1/3 this is valid as well. So Yes, A satisfies both inequalities.
Do the same for point E (5,-4)

Part C: the line y<-2x+4 is a dotted line going through (0,4) and (-2,0)
the shaded area is below the line
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