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Serhud [2]
3 years ago
9

Find the value of k such that lim-->4 (x^2+x-k)/(x-4) exists

Mathematics
1 answer:
7nadin3 [17]3 years ago
6 0

Answer:

k=20

Step-by-step explanation:

when x approaches 4, the denominator x-4 approaches 0

if the denominator is 0, it means that this is invalid

if the function is a number over 0 when x=4, it represents a vertical asymptote, which means no limit

so the only way possible to let there be a limit is to let the function be 0/0 when we plug in x=4

so x^2 + x - k = 0 when x = 4

4^2 + 4 - k = 0 ==> 20 - k = 0 ==> k = 20

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Art [367]

Answer:

D 41/10

Step-by-step explanation:

substitute the values given into the equation. Calculate.

4 0
3 years ago
Slope-rate of change- “if there were 12,000 in the Atlantic Ocean in 1950 and there are 3,600 dolphins today, what is the yearly
jasenka [17]

\bf \begin{array}{|cc|ll} \cline{1-2} \stackrel{x}{year}&\stackrel{y}{dolphins}\\ \cline{1-2} &\\ 1950&12000\\ 2018&3600 \\&\\ \cline{1-2} \end{array}~\hspace{5em}(\stackrel{x_1}{1950}~,~\stackrel{y_1}{12000})\qquad (\stackrel{x_2}{2018}~,~\stackrel{y_2}{3600}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3600-12000}{2018-1950}\implies \cfrac{-8400}{68}~~\approx~~ \stackrel{\textit{rate of change}}{-123.53}


-8400/68 simplifies to to -2100/17,  dolphins/year, so 2100 less dolphins every 17 years.

and we can just divide those to get the decimal amount of -123.53, which means, 123.53  less dolphins every year.

of course, there's no such a thing as 0.53 of a dolphin, so, we can say "about" 123 less dolphins per year.

5 0
3 years ago
Point A, located at (-5, 0), is rotated 90°. What are the coordinates of point A?
Sveta_85 [38]

Answer:

0,-5

Step-by-step explanation:

Your answer is 0,-5

4 0
3 years ago
Read 2 more answers
PLSSS I NEED THE ANSWER
BabaBlast [244]

Answer:

1. 6.4 meters of streamers left to make pompoms

2. He will be able to make 8 pompoms

Step-by-step explanation:

1.

4 x 1.6 = 5.6 meters were used to make decorations.

Then we do 12 - 5.6 = 6.4

2.

per one pompom it takes 0.8 meters of streamers.

6.4 is the left over so we do

6.4 divided by 0.8 = 8 pompoms you can make

6 0
2 years ago
NEED THESE ANSWERS FAST
vladimir2022 [97]

Answer:

1) m=2/9; y-intercept= 17/3

2) m=7 ; y-intercept= 22

3) m= -2/11 ; y-intercept= 100/11

4) m= 13/19 ; y-intercept= -53/13

Step by Step Explanation:

Use the slope formula to find the slope m.

6 0
3 years ago
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