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oksian1 [2.3K]
3 years ago
11

Determine whether each of the following functions is even, odd, or neither even nor odd.

Mathematics
1 answer:
Illusion [34]3 years ago
5 0

Answer:

A.) Even.

Step-by-step explanation:

If a function is an even function, then

F(-x) = f(x)

Also, if a function is an odd function, then, f(-x) = -f(x)

You are given the below function

f(x) = 1 + 3x^2 − x^4

Let x = 2

Substitute 2 for x in the function

F(x) = 1 + 3(2)^2 - (2)^4

F(x) = 1 + 3(4) - 16

F(x) = 1 + 12 - 16

F(x) = -3

Also, Substitute -2 for x in the function

F(x) = 1 + 3(-2)^2 - (-2)^4

F(x) = 1 + 3(4) - 16

F(x) = 1 + 12 - 16

F(x) = -3

Since f(-x) = f(x), we can conclude that

F(x) = 1 + 3x^2 - x^4 is even

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Determine the domain of the function. <br> f(x) = 13/3-x
Sedbober [7]
Hi..... the domain(D) will be:

\mathtt {f(x)=\dfrac{13}{3-x}\rightarrow \boxed{D=\{x\in R\,|\,x\neq 3\}}}

Thanks... :)
6 0
3 years ago
Ginger buys lunch at school every day. She always gets
shepuryov [24]

Answer:

The estimated probability that Ginger will eat a a pizza everyday of the week is;

D. 8/10 = 80%

Step-by-step explanation:

The given parameters are;

The frequency with which Ginger buys launch = Everyday

The percentage of the time the cafeteria has pizza out = 80%

The outcome of 0 and 1 = No pizza available

The outcome of 2, 3, 4, 5, 6, 7, 8, and 9 = Pizza available

Therefore, we have the;

Group number  {}                          Percentage of time pizza available

1                     {}                          80%

2                     {}                          80%

3                     {}                          80%

4                     {}                          80%

5                     {}                          40%

6                     {}                          100%

7                     {}                          80%

8                     {}                          100%

9                     {}                          80%

10                     {}                          80%

Therefore, the sum of the percentages outcome the days Ginger eats pizza = 0.8 + 0.8 + 0.8 + 0.8 + 0.4 + 1 + 0.8 + 1 + 0.8 + 0.8 = 8

The number of runs of simulation = 10 runs

The estimated probability that Ginger will eat a a pizza everyday of the week = (The sum of the percentages outcome the days Ginger eats pizza)/(The number of runs of simulation)

∴ The estimated probability that Ginger will eat a a pizza everyday of the week = 8/10

6 0
3 years ago
Read 2 more answers
write an equation of the line that's passes through the point (1,6) and is parallel to the line whose equation is y= 3x - 5
Alex Ar [27]
Parallel lines have the same slope.
so to find any line, you need a set of points, and a slope.
we already have the slope, being 3.
so, use the equation
y- (y-point)/ x-(x-point)=slope.
y-6. 3
---- = ---- (make it a fraction by puttingitover 1)
x-1. 1
cross multiply.
1(y-6)=3 (x-1)
y-6=3x-3
add 6 to both sides
Final answer: Y=3x+3
7 0
3 years ago
For a club gathering you were having, you bought a total of 50 burgers, and spent $90. You paid $2 per turkey burger, and $1.50
Sedaia [141]

Answer:

<u></u>

  • <u>No. You would have to cut the number of veggie burgers in more than half.</u>

Explanation:

<u>1. Model the situation with a system of equations</u>

<u />

<u>a) Name the variables:</u>

  • number of turkey burgers: t
  • number of veggie burgers: v

<u />

<u>b) Number of burgers:</u>

  • 50 = t + v

<u />

<u>c) Cost of the 50 burgers:</u>

  • $90 = 2t + 1.50v

<u>2. Solve that system of equations:</u>

<u />

<u>a) System</u>

  • 50 = t + v
  • 90 = 2t + 1.50v

<u>b) Mutliply the first equation by 2 and subtract the second equation</u>

  • 100 = 2t + 2v
  •  90 = 2t + 1.50v

  • 10 = 0.5v
  • v = 20 ⇒ t = 50 - 20 = 30

<u />

<u>c) How much would you spend if the next year you buy the double of 20 turkey burgers (40) and the half of 30 veggie burgers (15)</u>

  • $2(40) + $1.50(15) = $80 + $22.50 = $102.50

Then, you if you double the number of turkey burgers, and cut the number burgers in half, you would spend more than $90 ($102.50).

6 0
3 years ago
The initial cost of an office fax machine is $100. After 1 year, its value becomes $80. Which is the correct linear depreciation
Elis [28]

Answer:

y=100-20x

Step-by-step explanation:

Let the x-axis be the time (in years) and the y-axis the value of the fax machine (in dollars).

We know that the initial value of the fax machine is $100; in other words, when the time is zero years, the value is $100, or as an ordered pair (0, 100). We also know that after 1 year the value decreases to $80, so (1, 80).

Now we can find the slope of the line passing through those two points using the slope formula

m=\frac{y_2-y_1}{x_2-x_1}

where

m is the slope

(x_1,y_1) are the coordinates of the first point

(x_2,y_2) are the coordinates of the second point

Replacing values:

m=\frac{80-100}{1-0}

m=-20

Now, to complete our model we are using the point slope formula

y-y_1=m(x-x_1)

where

m is the slope

(x_1,y_1) are the coordinates of the first point

Replacing values:

y-100=-20(x-0)

y-100=-20x

y=-20x+100

y=100-20x

We can conclude that the correct linear depreciation model is y=100-20x

7 0
3 years ago
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