Given : A = 24 sq feet
A = 0.5 base x height
base = x , height = x+2
A = 0.5 x(x+2) = 24 sq feet
1) 0.5 x(x+2) = 24 (A)
2) x^2 + 2x - 48 = 0 (D)
To check the rest un-wrap the bracket:
x^2 + (x+2)^2 = 24
x^2 + x^2 + 4 + 4x = 24
2x^2 + 4x - 20 = 0
x^2 + 2x - 10= 0 (NO)
Likewise:
x^2 + (x+2)^2 = 100
x^2 + x^2 +4 + 4x = 100
2x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
3) x^2 + 2x - 48 = 0 (F)
To sum up: that's what apply:
1) 0.5 x(x+2) = 24 (A)
2) x^2 + 2x - 48 = 0 (D)
3) x^2 + 2x - 48 = 0 (F)
It would be option D because a dilation means an increase in size, where as a translation, rotation, and reflection are all movements that does not increase it size, so it will remain congruent
When two triangles are similar, they're sides are in proportion.
In order to find the unknown side, we first have to find the ratio of the larger triangle to the smaller triangle.
We can use the sides TV and LN to make the proportion.
= ![\frac{21}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B21%7D%7B6%7D)
The ratio between the two triangles is 21:6
Now we can solve for the unknown side.
= ![\frac{LM}{8}](https://tex.z-dn.net/?f=%5Cfrac%7BLM%7D%7B8%7D)
Cross multiply:
8 * 21 = 6 * LM
168 = 6LM
Divide both sides by 6:
LM = 28
The unknown side's length is 28 centimeters
Good luck!
Answer:
The expected value of this game is -$0.26.
Step-by-step explanation:
Expected value:
Each possible earning/loss multiplied by it's probability.
Probability:
Number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the numbers are chosen is not important. So we use the combinations formula to solve.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
Probability of winning:
Desired outcomes:
The 6 correct numbers, so ![D = 6](https://tex.z-dn.net/?f=D%20%3D%206)
Total outcomes:
6 numbers from a set of 21. So
![T = C_{21,6} = \frac{21!}{6!15!} = 54264](https://tex.z-dn.net/?f=T%20%3D%20C_%7B21%2C6%7D%20%3D%20%5Cfrac%7B21%21%7D%7B6%2115%21%7D%20%3D%2054264)
Probability:
![p = \frac{1}{54265}](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B1%7D%7B54265%7D)
Expected value
probability of earning 40,000.
probability of losing 1. So
![E = \frac{40,000}{54265} - \frac{54264}{54265} = -0.26](https://tex.z-dn.net/?f=E%20%3D%20%5Cfrac%7B40%2C000%7D%7B54265%7D%20-%20%5Cfrac%7B54264%7D%7B54265%7D%20%3D%20-0.26)
The expected value of this game is -$0.26.