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Nana76 [90]
3 years ago
14

Which of the following is an even function?

Mathematics
1 answer:
12345 [234]3 years ago
6 0

Answer:

  • B. g(x) = 2x² + 1

Step-by-step explanation:

<u>Even function has following property:</u>

  • g(x) = g(-x)

<u>It is easy to show this works with the second choice only. All the others don't work:</u>

  • g(x) = (x - 1)² + 1
  • g(-x) = (-x - 1)² + 1

This is not correct as x - 1 ≠ -x - 1 so as their squares, so g(x) ≠ g(-x)

The last two choices are not even similarly.

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I need help with this problem it’s due at midnight and I’m so tired of trying. Thanks it’s number 4 btw
bearhunter [10]

Answer:

Look below

Step-by-step explanation:

A.

8 + 9 + 10 = 27

9 + 10 + 11 = 30

10 + 11 + 12 = 33

B. Every answer is divisible by 3, every consecutive answer is also 3 more than the one before it.

C. Yes

19 + 20 + 21 = 60

D. No

8 is not divisible by 3. Also, the closest you can get is 6 (1 + 2 + 3) or 9 (2 + 3 + 4).

I hope this helped! If you need anything else, let me know in the comments. :)

6 0
3 years ago
A sports teacher had 1025 sweets. After distributing these equally amongst all the participants in a sports meet, he had just 1
Cerrena [4.2K]

Step-by-step explanation:

Since it remains only 1 sweet, we can subtract it from the total and get the amount of sweets distributed (=1024).

As all the sweets are distributed equally, we must divide the number of distributed sweets by all its dividers (excluding 1024 and 1, we'll see later why):

1) 512 => 2 partecipants

2) 256 => 4 partecipants

3) 128 => 8 partecipants

4) 64 => 16 partecipants

5) 32 => 32 partecipants

6) 16 => 64 partecipants

7) 8 => 128 partecipants

9) 4 => 256 partecipants

10) 2 => 512 partecipants

The number on the left represents the number of sweets given to the partecipants, and on the right we have the number of the partecipants. Note that all the numbers on the left are dividers of 1024.

Why excluding 1 and 1024? Because the problem tells us that there remains 1 sweet. If there was 1 sweet for every partecipant, the number of partecipants would be 1025, but that's not possible as there remains 1 sweet. If it was 1024, it wouldn't work as well because the sweets are 1025 and if 1 is not distributed it goes again against the problem that says all sweets are equally distributed.

5 0
3 years ago
What is the HIGHEST common factor<br> of the set of numbers (54, 72, 90}?
suter [353]

Answer:

18

Step-by-step explanation:

54/18=3

72/18=4

90/18=5

6 0
3 years ago
Read 2 more answers
A rectangular solid has width w, a length of 7 more than the width, and a height that is equivalent to 15 decreased by 3 times t
dexar [7]

Answer:

For a rectangular solid with:

width = w

length = l

height = h

The volume is equal to:

V = w*l*h

in this case we know that:

width = w.

"length of 7 more than the width"

l = w + 7.

"a height that is equivalent to 15 decreased by 3 times the width."

h = 15 - 3*w

Then the volume will be:

V = w*l*h = w*(w + 7)*(15 - 3w) = (w^2 + 7*w)*(15 - 3*w)

V =  ( -3*w^3 + 15*w^2 + 105*w - 21*w^2)

V = (-3*w^3 - 6*w^2 + 105*w)

Now, the maximum volume will be for the value of w such that:

V'(w) = 0.

and:

V''(W) < 0

Where:

dV/dw = V'(w).

dV'/dw = V''(w)

Then first we need to differentiate the equation for the volume.

V'(w) = dV/dw = ( 3*(-3*w^2) + 2*(-6*w) + 105)

V'(w) = -9*w^2 - 12*w + 105.

Then we need to find the solution for:

-9*w^2 - 12*w + 105 = 0.

We can use the Bhaskara formula, and we will get:

w = \frac{+12 +-\sqrt{(-12)^2 - 4*(-9)*105} }{2*-9}  = \frac{+12 +- 62.6}{-18}

Then the two solutions are:

w₁ = (+12 - 62.6)/(-18) = 2.81

w₂ = (+12 + 62.6)/(-18) = -15.5

But we can not have a negative width, so we can just discard the second solution.

Now let's check the second condition for the maximum, we must have:

V''(2.81) < 0.

V'' = dV'/dw = 2*(-9*w) - 12 = -18*w - 12

V''(2.81) = -18*2.81 - 12 = -62.58 < 0 .

Then the volume is maximized when w = 2.81, and the maximum volume will be:

V(2.81) =  (-3*(2.81)^3 - 6*(2.81)^2 + 105*2.81) = 180.1

 

8 0
3 years ago
Evaluate the expression. 9−32÷4
Veseljchak [2.6K]
The answer to the question is -1
3 0
3 years ago
Read 2 more answers
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