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Andreas93 [3]
3 years ago
8

What are the vertex, axis of symmetry, maximum or minimum value, and range of y = 3x2 + 6x − 1?

Mathematics
1 answer:
Basile [38]3 years ago
6 0

Answer: 29

Step-by-step explanation: You have 3+2 that = 5 then you get that 5 and x that by 6 that = 30 then you - 30 from 1 then you have 29

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Jane sells hatch for sale she marked down 20% of her original price is 59.95 for half what is her sale price?
Illusion [34]
I believe the answer would be 11.99, because 20% times 59.95 is 11.99
4 0
3 years ago
Consider the following function.
Kryger [21]

Answer:

See below

Step-by-step explanation:

I assume the function is f(x)=1+\frac{5}{x}-\frac{4}{x^2}

A) The vertical asymptotes are located where the denominator is equal to 0. Therefore, x=0 is the only vertical asymptote.

B) Set the first derivative equal to 0 and solve:

f(x)=1+\frac{5}{x}-\frac{4}{x^2}

f'(x)=-\frac{5}{x^2}+\frac{8}{x^3}

0=-\frac{5}{x^2}+\frac{8}{x^3}

0=-5x+8

5x=8

x=\frac{8}{5}

Now we test where the function is increasing and decreasing on each side. I will use 2 and 1 to test this:

f'(2)=-\frac{5}{2^2}+\frac{8}{2^3}=-\frac{5}{4}+\frac{8}{8}=-\frac{5}{4}+1=-\frac{1}{4}

f'(1)=-\frac{5}{1^2}+\frac{8}{1^3}=-\frac{5}{1}+\frac{8}{1}=-5+8=3

Therefore, the function increases on the interval (0,\frac{8}{5}) and decreases on the interval (-\infty,0),(\frac{8}{5},\infty).

C) Since we determined that the slope is 0 when x=\frac{8}{5} from the first derivative, plugging it into the original function tells us where the extrema are. Therefore, f(\frac{8}{5})=1+\frac{5}{\frac{8}{5}}-\frac{4}{\frac{8}{5}^2 }=\frac{41}{16}, meaning there's an extreme at the point (\frac{8}{5},\frac{41}{16}), but is it a maximum or minimum? To answer that, we will plug in x=\frac{8}{5} into the second derivative which is f''(x)=\frac{10}{x^3}-\frac{24}{x^4}. If f''(x)>0, then it's a minimum. If f''(x), then it's a maximum. If f''(x)=0, the test fails. So, f''(\frac{8}{5})=\frac{10}{\frac{8}{5}^3}-\frac{24}{\frac{8}{5}^4}=-\frac{625}{512}, which means (\frac{8}{5},\frac{41}{16}) is a local maximum.

D) Now set the second derivative equal to 0 and solve:

f''(x)=\frac{10}{x^3}-\frac{24}{x^4}

0=\frac{10}{x^3}-\frac{24}{x^4}

0=10x-24

-10x=-24

x=\frac{24}{10}

x=\frac{12}{5}

We then test where f''(x) is negative or positive by plugging in test values. I will use -1 and 3 to test this:

f''(-1)=\frac{10}{(-1)^3}-\frac{24}{(-1)^4}=-34, so the function is concave down on the interval (-\infty,0)\cup(0,\frac{12}{5})

f''(3)=\frac{10}{3^3}-\frac{24}{3^4}=\frac{2}{27}>0, so the function is concave up on the interval (\frac{12}{5},\infty)

The inflection point is where concavity changes, which can be determined by plugging in x=\frac{12}{5} into the original function, which would be f(\frac{12}{5})=1+\frac{5}{\frac{12}{5}}+\frac{4}{\frac{12}{5}^2 }=\frac{43}{18}, or (\frac{12}{5},\frac{43}{18}).

E) See attached graph

5 0
3 years ago
I need to know this help
antoniya [11.8K]

Answer:

The slope is 2/3 and the y intercept is 5/9

Step-by-step explanation:

This is written in the form

y= mx+b where m is the slope and b is the y intercept

y = 2/3x +5/9

m = 2/3 and b=5/9

The slope is 2/3 and the y intercept is 5/9

4 0
3 years ago
What is the lowest fraction of 14.7cm and 26.3dm?
Blababa [14]
14.7 cm = 14 7/10


26.3dm = 26 3/10
3 0
3 years ago
Which one is the best prediction! Please and no link answer :(
MariettaO [177]

Answer:

Prediction = 35

Step-by-step explanation:

Given

The attached table

Required

Expected number of Daffodil when N = 150

First, we calculate the probability of having a Daffodil.

Pr = \frac{Daffodil}{Total}

This gives:

Pr = \frac{14}{14+10+24+12}

Pr = \frac{14}{60}

Simplify

Pr = \frac{7}{30}

When there are 150 flowers, the prediction of Daffodils is:

Prediction = Pr * N

Prediction = \frac{7}{30} * 150

Prediction = 7*5

Prediction = 35

8 0
3 years ago
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