Mathematics, 14.10.2020 14:01 5001Je

Given B(17,5), C(11, -3), D-1, 2), and
E(x, -6), find the value of x so that BC || DE.

Answers: 2

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Answer from: jordystafford8186

x=-7

Step-by-step explanation:

Remember that:

Two lines are parallel if their slopes are the same.Two lines are perpendicular if their slopes are negative reciprocals.And two lines are neither (a.k.a intersecting) if they are neither parallel nor perpendicular.

We want to find the value of x such that $\overline{BC}\parallel\overline{DE}$ .

Therefore, the slopes of BC and DE must be equivalent.

So, let's find the slope of BC first.

BC)

We can use the slope formula:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Let B(17, 5) be (x₁, y₁) and let C(11, -3) be (x₂, y₂). Substitute:

$\displaystyle m=\frac{-3-5}{11-17}$

Subtract:

m=-8/-6=4/3

So, the slope of BC is 4/3.

DE)

Let D(-1, 2) be (x₁, y₁) and let E(x, -6) be (x, y₂). Substitute:

$\displaystyle m=\frac{-6-2}{x-(-1)}$

We know that the two slopes must be equal. So, the slope of DE must also be 4/3. Substitute 4/3 for m:

$\displaystyle \frac{4}{3}=\frac{-6-2}{x-(-1)}$

Solve for x. Simplify the right:

$\displaystyle \frac{4}{3}=\frac{-8}{x+1}$

Cross multiply:

4(x+1)=-8(3)

Multiply on the right:

4(x+1)=-24

Divide both sides by 4:

x+1=-6

Subtract 1 from both sides:

x=-7

So, the value of x is -7.

And we're done!

Answer from: Quest

just needed some points but try socratic

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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Given B(17,5), C(11, -3), D-1, 2), and
E(x, -6), find the value of x so that BC || DE.
...