Answer:
Try entering 2x+3=15 @ x=6 into the text box. After you enter the expression, Algebra Calculator will plug x=6 in for the equation 2x+3=15: 2(6)+3 = 15. The calculator prints "True" to let you know that the answer is right. More Examples Here are more examples of how to check your answers with Algebra Calculator. Feel free to try them now.
Step-by-step explanation:
<h2>
AREA</h2>
The formula for finding area of a square is:
In a square, all the sides are the same. Each side is 6 meters long. Plug in 6 to the formula.
Multiply:
The area of the square is 36 m²
<h2>PERIMETER</h2>
Perimeter is the distance around a shape. To find perimeter, you have to add all all the side lengths. The formula for finding perimeter is:
Remember that squares have 4 sides, and all length(s) and width(s) measure the same. The length and width measure the same. Plug in the numbers into the formula:
Simplify:
Add:
The perimeter of the square is 24 m
Answer: -1
The negative value indicates a loss
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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
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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.
A repeating decimal can be written like this
Answer: Choice A
Proof:
Replace x with 1 and y with 2. This is because (x,y) = (1,2) so x = 1 and y = 2.
Doing both replacements and simplifying leads to...
2*x - y = 0
2*1 - 2 = 0
2 - 2 = 0
0 = 0
That confirms (x,y) = (1,2) is a point on the line.
It confirms (1,2) is a solution to the equation.
