Two students start a club the first week of school. Each member invites three new members the second week of school. Each of these new members then invites three additional members the following week. If the pattern of each new member inviting three new members each week continues, how many members will be in the club after five weeks

Answers

Answer 1

Answer: I'll just make a manual computation on how 1 member recruits his members until week 5. Then multiply the sum by 2.
old new
1: 1
2: 1 x 3 = 3 ⇒ 1 3 *only new members recruit 3 more
3: 3 x 3 = 9 ⇒ 4 9
4: 9 x 3 = 27⇒ 13 27
5: 27 x 3 = 81 ⇒ 40 81

40 + 81 = 121. Total number of members under 1 founding member.

121 x 2 founding members = 242 total number of members within 5 weeks.

Answer 2

Answer:

Answer:

C. 242

Step-by-step explanation:

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Complete answer choices

Answers

Answer:

Number one is B and E

Step-by-step explanation:

And 2 is C

Based on the graph above, what is the solution to this system.

Answers

I would say infinitely many solutions because parallel lines never touch, and it isn't a case of having no slope because if it had no slope then it would be no solution. So it's D.

There is no solution because they're parallel

-1≤ 3x-10≤ 2 please help me

Answers

Answer:

3≤ x≤ 4

Step-by-step explanation:

-1≤ 3x-10≤ 2

Add 10 to each side

-1+10≤ 3x-10+10≤ 2+10

9≤ 3x≤ 12

Divide each side by 3

9/3≤ 3x/3≤ 12/3

3≤ x≤ 4

Answer:

3 ≤ x ≤ 4

Step-by-step explanation:

Step 1: Add 10 to all parts/sections.

$-1 + 10 \leq 3x - 10 + 10 \leq 2+10$
$9\leq 3x\leq 12$

Step 2: Divide all parts/sections by 3.

$(9)/(3) \leq (3x)/(3) \leq (12)/(3)$
$3 \leq x \leq 4$

Therefore, the answer is 3 ≤ x ≤ 4.

In sunlight, a vertical stick 7 ft tall casts a shadow 3 ft long. At the same time a nearby tree casts a shadow 11 ft long. How tall is the tree? Round to the nearest tenth.

Answers

Answer:

25.7 feet.

Step-by-step explanation:

Let x be the actual length of tree.

We have been given that in sunlight, a vertical stick 7 ft tall casts a shadow 3 ft long. We are asked to find the actual length of tree casting a 11 ft long shadow.

We will use proportions to solve our given problem.

$(x)/(11)=(7)/(3)$

Upon multiplying both sides of our equation by 11, we will get:

$(x)/(11)*11=(7)/(3)*11$

$x=(77)/(3)$

$x=25.6666666\approx 25.7$

Therefore, the tree is 25.7 feet tall.

$look\ at\ the\ picture\n\n\Delta ABC\sim\Delta D EF\n\n(|ED|)/(|EF|)=(|AB|)/(|BC|)\n\n(|ED|)/(11)=(7)/(3)\ \ \ \ /\cdot11\n\n|ED|=(77)/(3)\n\n|ED|\approx25.7\ (ft)\leftarrow Answer$

the ball reach after bouncing four time? how many bounces does it take for the ball to reach a height of less than one inch?

Answers

After the 'n'th bounce, the ball returns to a maximum height of

   (100) times (0.75)^n .

-- After 4 bounces, the maximum height is (100) (0.75)^4 = 31.64 inches.

-- To look for the maximum height of 1 inch,    (100) (0.75)^x = 1

Let's take the log of each side: log(100) + x log(0.75) = 0

Subtract log(100) from each side: x log(0.75) = -log(100)

Divide each side by log(0.75) :     x = -log(100) / log(0.75).

log(100) = 2 . So ... x = -2 / log(0.75) = -2 / -0.124939 = 16.00785

So the ball returns to a slim hair more than 1 inch high on the 16th bounce,
and returns to definitely less than 1 inch high on the 17th bounce.

3. Rewrite the expression as simply as you can:
3x + 11y - 2x - 4y

Answers

Answer:

x+7y

Step-by-step explanation:

First off, lets split the question into both x and y.

3x - 2x for the x

11y - 4y for the y

You can solve both of them to get x + 7y

3x - 2x = x

11y - 4y = 7y

Then, add them back up and get x + 7y

Answer:

x+7y

Step-by-step explanation:

3x + 11y -2x - 4y

(3x) + (11y) + (-2x) + (-4y)

(3x) + (-2x) = x

(11y) + (-4y) = 7y

3x + 11y -2x - 4y = x + 7y

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