3 years ago

A line with a slope of -2 passes through the points (0,d) and (-8,9). What is the value of d?

Mathematics

1 answer:

Verizon [17]3 years ago

4 0

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have m = -2 and the points (0, d) and (-8, 9). Substitute:

$\dfrac{9-d}{-8-0}=-2\\\\\dfrac{9-d}{-8}=-2\qquad\text{multiply both sides by (-8)}\\\\9-d=16\qquad\text{subtract 9 from both sides}\\\\-d=7\qquad\text{change the signs}\\\\\boxed{d=-7}$

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$n(S\cap F \cap R)=7$

Step-by-step explanation:

The Universal Set, n(U)=2092

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Let the number who take all three subjects, $n(S\cap F \cap R)=x$

Note that in the Venn Diagram, we have subtracted $n(S\cap F \cap R)=x$ from each of the intersection of two sets.

The next step is to determine the number of students who study only each of the courses.

$n(S\:only)=1232-[103-x+x+23-x]=1106+x\\n(F\: only)=879-[103-x+x+14-x]=762+x\\n(R\:only)=114-[23-x+x+14-x]=77+x$

These values are substituted in the second Venn diagram

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2092=[1106+x]+[103-x]+x+[23-x]+[762+x]+[14-x]+[77+x]

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