A line that passes through th epoints (2,3) and (b,7) is parallel to the line y = -2x + 17. Find the value of b

1 answer:

4 0

Answer:

b = 0

Step-by-step explanation:

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = - 2x + 17 is in this form with slope m = - 2

• Parallel lines have equal slopes, hence

slope of line through the 2 points is - 2

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (b, 7)

m = $\frac{7-3}{b-2}$ = $\frac{4}{b-2}$ , hence

$\frac{4}{b-2}$ = - 2 ( cross- multiply )

- 2(b - 2) = 4

- 2b + 4 = 4 ( subtract 4 from both sides )

- 2b = 0 ⇒ b = 0

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stich3 [128]

Using probability concepts, it is found that P(S and D) = 0.1275.

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A probability is the number of desired outcomes divided by the number of desired outcomes.
In a standard deck, there are 52 cards.
Of those, 13 are spades, and 13 are diamond.

The probability of selecting a spade with the first card is 13/52. Then, there is a 13/51 probability of selecting a diamond with the second. The same is valid for diamond then space, which means that the probability is multiplied by 2. Thus, the desired probability is:

$P(S \cap D) = 2 \times \frac{13}{52} \times \frac{13}{51} = \frac{2\times 13 \times 13}{52 \times 51} = 0.1275$