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IgorLugansk [536]
3 years ago
9

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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Answer:

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

Step-by-step explanation:

The Universal Set, n(U)=2092

n(S)=1232\\n(F)=879\\n(R)=114

n(S\cap R)=23\\n(S\cap F)=103\\n(F\cap R)=14

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

Adding up all the values

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

2092=2085+x

x=2092-2085

x=7

The number of students who have taken courses in all three subjects, n(S\cap F \cap R)=7

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