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4 years ago

13

Simplify the following:

-16-8x%29%7D%7B-2%20-x%7D" id="TexFormula1" title="\frac{-1(-8x - 16)}{-2 -x} = \frac{-1(-16-8x)}{-2 -x}" alt="\frac{-1(-8x - 16)}{-2 -x} = \frac{-1(-16-8x)}{-2 -x}" align="absmiddle" class="latex-formula">

1 answer:

lianna [129]4 years ago

3 0

They both came out as =-8

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Please give a good explanation and show your work as well

Vadim26 [7]

Answer:

A) down

B) x intercept (5, 0)

y intercept (0, 80)

C) 144 ft

Step-by-step explanation:

y = Ax² + Bx + C

y = -16x² + 64x + 80

A)

Parabola opens down because A is negative

B)

x intercept (5, 0)

x = (-64 ±√(64² - 4(-16)(80))) / (2(-16))

x = -1 which means if the profile is continuous, the balloon launched one hour ago.

or

x = 5 which means the balloon will be on the ground in 5 hours.

(assuming level ground or no wind at all.

y intercept

y = -16(0)² + 64(0) + 80

y = 80 ft

meaning the balloon is already 80 feet above the ground when we start looking at t = 0

C)

Maximum altitude will occur when the vertical velocity is zero. Velocity is the derivative of position.

x' = -32x + 64

0 = -32x + 64

32x = 64

x = 2 hrs

y = -16(2)² + 64(2) + 80

y = 144 ft

4 0

3 years ago

What is the sum of the first 51 consecutive odd positive integers?

Angelina_Jolie [31]

We call:

$a_{n}$ as the set of <span>the first 51 consecutive odd positive integers, so:

</span> $a_{n} = \{1, 3, 5, 7, 9...\}$

Where:
$a_{1} = 1$
$a_{2} = 3$
$a_{3} = 5$
$a_{4} = 7$
$a_{5} = 9$
<span>and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

</span> $a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\}$
<span>
Then:

</span> $a_{n} = a_{1} + (n-1)d$
<span>
So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

</span> $S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k$
<span>
Therefore, we need to find:
</span> $a_{k} = a_{51}$

Given that $a_{1} = 1$ , then:

$a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1$

Thus:
$a_{k} = a_{51} = 2(51)-1 = 101$

Lastly:

$S_{51} = ( \frac{1 + 101}{2} ).51 = 2601$

4 0

3 years ago

Linear equation 5v=-6v-33

s344n2d4d5 [400]

Step 1: Add 6v to both sides.

5v+6v=−6v−33+6v

11v=−33

Step 2: Divide both sides by 11.

11v

11

=

−33

11

v=−3

answer: v=−3

6 0

3 years ago

What can be concluded about the line represented in the table? Check all that apply.

alisha [4.7K]

Answer: the second one, the third one, and the fifth

Step-by-step explanation:

I am almost certain that is correct, but don't quote me on it

6 0

3 years ago

Read 2 more answers

I need help with #3 & #4

lina2011 [118]

Step-by-step explanation:

Q3, B

Q4, I'm not too sure about this one but I think its D

5 0

3 years ago