"In the xy-plane, the parabola with equation y = (x − 11) ² intersects the line with equation y = 25 at two points, A and B. What is the length of AB"

Here is my answer

Because the parabola intersects the line with equation y = 25 Substituting y = 25 in the equation of the parabola y = (x - 11)², we get

25 = (x - 11)²

<=>x - 11 = ± 5

<=> $\left \{ {{x=6} \atop {x=16}} \right.$

Thus A(16, 25) and B(6, 25) are the points of intersection of the given parabola and the given line.

So the length of AB = √[(16 - 6)² + (25 - 25)²]

= √100 = 10 units

5 0

3 years ago

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There are 36 pencils in 6 packs. Igor wants to know how many pencils are in 1 pack. Elsa wants to know how many pencils are in 3

Paraphin [41]

Answer:

18 pencils in 3 packs.

Step-by-step explanation:

Assuming that each pack will have the same amount of pencils. It is given that there are 36 pencils in all when one has 6 packs. Find the amount in each pack by dividing (total amount of pencils)/(amount of packs) = Amount of pencils per pack:

36/6 = 6

There are 6 pencils in each pack.

Now, Elsa wants to know how much pencils are in 3 packs. Multiply the amount of packs with the amount of pencils in each pack:

Total amount of pencils = amount of packs (3) x amount of pencils per pack (6)

= 3 x 6

= 18

There are 18 pencils in 3 packs.

8 0

2 years ago

The sum of a number times 6 and 21 is at least 24. what's the inequality

Alex777 [14]

Answer:

x ≥ 1/2

Step-by-step explanation:

6x + 21 ≥ 24

6x ≥ 3

x ≥ 1/2

check: (1/2 x 6) + 21 = 24

4 0

3 years ago