Properties:
1) a+ b = b+a Commutative
2) (a + b) + c = a + (b+c) Associative
3) a(b+c) = ab + ac Distributive
Here we are given
11 + (19 + 6) = (11 +___) + 6
The number 19 is missing on the right.
So we have
11 + (19 + 6) = (11 +19) + 6
This looks like Property 2 above.
Hence it is associative property.
Answer:
she can make 50 different selections!
Step-by-step explanation:
To find the different selections that can be made, we use the formula:
nCr = n! / r! * (n - r)!. Where 'n' represents the number of items available and 'r' represents the nuber of items being chosen
In this case:
'n' equals 10 and 'r' equals 2. Therefore:
![10C_{2} = \frac{10!}{2!(10-2)!} = \frac{10!}{2!8!} = \frac{90}{2} =50](https://tex.z-dn.net/?f=10C_%7B2%7D%20%3D%20%5Cfrac%7B10%21%7D%7B2%21%2810-2%29%21%7D%20%3D%20%5Cfrac%7B10%21%7D%7B2%218%21%7D%20%3D%20%5Cfrac%7B90%7D%7B2%7D%20%3D50)
So she can make 50 different selections!
Answer:
1) ![x=15, y=41](https://tex.z-dn.net/?f=x%3D15%2C%20y%3D41)
2) ![x=6, y=24](https://tex.z-dn.net/?f=x%3D6%2C%20y%3D24)
Step-by-step explanation:
1)
The two triangles are similar by AA similarity.
That means
.
We can add
to both sides to get
.
We can then subtract
from both sides to get
.
We know that the
because they both lie on a straight line.
We can plug in for
to get
.
We can divide both sides of the equation by
to get
.
We then add
to both sides to get
.
So,
and we're done!
2)
Because the two bases of a trapezoid are parallel, meaning adjacent top and bottom angles sum to
, we have that
.
We can subtract a
and an
from both sides to get
.
We then divide both sides of the equation by
to get
.
We do the same thing for
. On the other side of the trapezoid, we have that
.
We combine like terms on the left side to get
.
We subtract a
from both sides to get
.
We divide both sides of the equation to get
.
So,
and we're done!
11.75 / 0.89 = 13.2022472
she can buy 13 bananas