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Iteru [2.4K]
3 years ago
14

Solve by completing the square? Could you please work it out step-by-step?

Mathematics
1 answer:
DaniilM [7]3 years ago
4 0
16 n^2 -10n + 129 = 8n^2 -8

We collect the terms:
8n^2 -10n + 137 = 0

The steps for completing the square:

1) Move the "non X" (or "non N") term to the right:

8n^2 -10n  = -137

<span>2)<span> Divide the equation by the coefficient of N² which in this case is 8
n^2 -1.2n = </span></span><span><span>-17.125 </span>

3) Take the coefficient of "N"; divide it by 2; square it; add it to both sides of the equation.
-1.2 / 2 = -.6
-.6^2 = .36

</span>
n^2 -1.2n +.36 = <span>-17.125 +.36

Take the square root of both sides:</span>
(n-.6)*(n-.6) = sq root( <span> <span> <span> -16.765 </span> </span> </span> )
That's about as far as I can go.

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What is the exponential function that best models the number of gnats the scientists have gathered after the number of hours lis
Serjik [45]

Answer:

Option A

f(x) = 12.5(1.6)^x

Step-by-step explanation:

The number of gnats the scientists have gathered

At 0 hours, they gathered 12 gnats.

Checking all the options, applying x = 0 makes the index part become 1 (Anything raised to the power zero is 1).

So, we have the following functions

f(x) = 12.5

f(x) = 12.6

f(x) = 6.2

f(x) = 1.6

This has reduced our work, as we can screen out options C and D, they are too far from 12. This leaves us with option A and B.

At 1 hour, they gathered 20 gnats.

Checking options A and B

A. f(x) = 12.5(1.6)

= 20

B. f(x) = 12.6(6.2)

By inspection, 12 × 6 is already 72,

12.6 × 6.2 will be more.

By these, we can conclude that f(x) = 12.5(1.6)^x has the best models the number of gnats the scientists have gathered after the number of hours listed in the given table.

5 0
3 years ago
For the graph, what is a reasonable constraint so that the function is at least 600?
Harman [31]

Answer:

I remember taking this too. So, the correct answer is A! I SWEAR ITS RIGHT!

Step-by-step explanation:

7 0
3 years ago
250 kids go to the local pool on a hot summers day. Each kid dives off the diving board 9 times. How many dives are there altoge
Paraphin [41]
<h3>Answer: </h3>

2250 dives

<h3>Explanation</h3>

If each kid dives off the diving board 9 times, for 250 kids, you need to resolve a simple operation:

9 \times 250 = 2250

4 0
3 years ago
Read 2 more answers
Graph the solution of y – 2 &gt; 1 on a number line.
Hunter-Best [27]
<span> y-2 > 1
 y-2+2 > 1+2
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5 0
3 years ago
Suppose that your net income for the month is $1,500 and that your total expenses are $2,500
Aleks [24]

Answer:

You will need to double your net income in order to make a profit.

Step-by-step explanation:

1500 x 2 = 3000 - 2500 = 500 which is 500 dollars profit

6 0
3 years ago
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