Derek is 7 years older than Vivian. In 6 years the sum of their ages will be 75. How old is Derek now?

If K is the midpoint of JL, JK = 8x+11 and KL = 14x-1, find JL.

gladu [14]

Step-by-step explanation:

Since, K is the midpoint of JL.

$\therefore \: JK = KL \\ 8x + 11 = 14x - 1 \\ 11 + 1 = 14x - 8x \\ 12 = 6x \\ \frac{12}{6} = x \\ 2 = x \\ \\ \because \: JL = JK + KL \\ \therefore \: JL = 8x + 11 + 14x - 1 \\ \therefore \: JL = 8x + 14x + 11 - 1 \\ \therefore \: JL = 22x + 10\\ \therefore \: JL = 22 \times 2 + 10..(plug \: x = 2) \\ \therefore \:JL = 44 + 10 \\ \huge \red{ \boxed{\therefore \:JL = 54}}$

7 0

3 years ago

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A bowl contains 4 tangerines and 5 clementines. John randomly selects one piece of fruit, and then Pam randomly selects one of t

andre [41]

Answer:

5/18

Step-by-step explanation:

There are 9 pieces of fruit in the bowl, tangerines and 5 clementines.

Assuming that they do not put the fruit back

P (tangerine) = number of tangerines/ total = 4/9

Then John keeps his and there are 8 pieces of fruit in the bowl,

3 tangerines and 5 clementines.

P (Clementine) = number of clementines/ total = 5/8

P (tangerine, no replacement, Clementine) = P (tangerine) * P (Clementine)

= 4/9 * 5/8 =5/18

6 0

3 years ago

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Limit of x^2-81/x+9 As x goes toward -9

Semmy [17]

Hello,

Use the factoration

a^2 - b^2 = (a - b)(a + b)

Then,

x^2 - 81 = x^2 - 9^2

x^2 - 9^2 = ( x - 9).(x + 9)

Then,

Lim (x^2- 81) /(x+9)

= Lim (x -9)(x+9)/(x+9)

Simplity x + 9

Lim (x -9)

Now replace x = -9

Lim ( -9 -9)

Lim -18 = -18
_______________

The second method without using factorization would be to calculate the limit by the hospital rule.

Lim f(x)/g(x) = lim f(x)'/g(x)'

Where,

f(x)' and g(x)' are the derivates.

Let f(x) = x^2 -81

f(x)' = 2x + 0
f(x)' = 2x

Let g(x) = x +9

g(x)' = 1 + 0
g(x)' = 1

Then the Lim stay:

Lim (x^2 -81)/(x+9) = Lim 2x /1

Now replace x = -9

Lim 2×-9 = Lim -18

= -18

7 0

3 years ago

Write the equation of the line passing through the points (-4,-1) and (2,8)

klio [65]

<h3>Explanation:</h3>