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3 years ago

Graph the function g(x) =x^2+4x+1

Mathematics

1 answer:

gladu [14]3 years ago

6 0

Answer:

Step-by-step explanation:

Let's "complete the square," which will give us the vertex of this vertical, opens-up parabola:

g(x) =x^2+4x+1 can be rewritten as g(x) =x^2+4x + 4 - 4 +1, where that +4 comes from squaring half of the coefficient of x.

Then we have g(x) =x^2+4x + 4 - 4 + 1 => g(x) = (x + 2)^2 - 3.

Comparing this to y = (x - h)^2 + k,

we see that the vertex, (h, k), is located at (-2, -3).

Plot this vertex. Also, plot the y-intercept (0, g(0) ), which is (0, 1).

This information is enough to permit graphing the function roughly.

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You roll a pair of honest dice. If you roll a total of 7, you win $18; if you roll a total of 11, you win $54; if you roll any o

amm1812

Answer: -1
The negative value indicates a loss

============================================================

Explanation:

Define the three events
A = rolling a 7
B = rolling an 11
C = roll any other total (don't roll 7, don't roll 11)

There are 6 ways to roll a 7. They are
1+6 = 7
2+5 = 7
3+4 = 7
4+3 = 7
5+2 = 7
6+1 = 7
Use this to compute the probability of rolling a 7
P(A) = (number of ways to roll 7)/(number total rolls) = 6/36 = 1/6
Note: the 36 comes from 6*6 = 36 since there are 6 sides per die

There are only 2 ways to roll an 11. Those 2 ways are:
5+6 = 11
6+5 = 11
The probability for event B is P(B) = 2/36 = 1/18

Since there are 6 ways to roll a "7" and 2 ways to roll "11", there are 6+2 = 8 ways to roll either event.
This leaves 36-8 = 28 ways to roll anything else
P(C) = 28/36 = 7/9

-----------------------------

In summary so far,
P(A) = 1/6
P(B) = 1/18
P(C) = 7/9

The winnings for each event, let's call it W(X), represents the prize amounts.
Any losses are negative values
W(A) = amount of winnings if event A happens
W(B) = amount of winnings if event B happens
W(C) = amount of winnings if event C happens
W(A) = 18
W(B) = 54
W(C) = -9

Multiply the probability P(X) values with the corresponding W(X) values
P(A)*W(A) = (1/6)*(18) = 3
P(B)*W(B) = (1/18)*(54) = 3
P(C)*W(C) = (7/9)*(-9) = -7

Add up those results
3+3+(-7) = -1

The expected value for this game is -1.
The player is expected to lose on average 1 dollar per game played.

Note: because the expected value is not 0, this is not a fair game.

7 0

3 years ago

Read 2 more answers

Is this a negative, positive, or zero slope?

sveticcg [70]

Answer:

i think 0 slop. wait for the other person to answers this, to be sure of the answer

Step-by-step explanation:

5 0

2 years ago

What value of p makes the equation true?<br> -3p+1/8=-1/4<br> P= ____

Dmitriy789 [7]

Answer:

1/8

Step-by-step explanation:

-3p+1/8=-1/4

subtract 1/8

-3p=-3/8

divide by -3

p=1/8

8 0

3 years ago

Plz help ill give u brainlist

Basile [38]

2x + 40
Divide both sides by 2
You get x + 20

7 0

3 years ago

Can you give me the answer please

uranmaximum [27]

[Chorus]

I might just K.O., the Perc' up in my Faygo

Run up on me wrong, turn his head into a bagel

On the opposition block, just like a Lego

I'm big homie, b, so you know that I got say-so

4 0

3 years ago