Answer:
the solution is (-4, 2)
Step-by-step explanation:
6x + 8y = -8
x + 4y = 4
... can be solved using elimination by addition and subtraction, among other methods. Multiply the second equation by -2 to obtain
6x + 8y = -8
-2x - 8y = -8
Combining these results in
4x = -16. Thus, x = -4.
Substituting -4 for x in x + 4y = 4 results in
-4 + 4y = 4, or 4y = 8, or y = 2
Then the solution is (-4, 2)
Answer:
B) 72 cm²
Step-by-step explanation:
<u>Area of a trapezoid formula:</u>

<u>Given:</u>
a = 15
b = 9
h = 6
Work:

Answer:
126 students this year
Step-by-step explanation:
All you got to do is multiply 42 by 3
Answer:

Step-by-step explanation:
The question to be solved is the following :
Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, and that γ is unique if
. Recall that given two vectors a,b a⊥ b if and only if
where
is the dot product defined in
. Suposse that
. We want to find γ such that
. Given that the dot product can be distributed and that it is linear, the following equation is obtained

Recall that
are both real numbers, so by solving the value of γ, we get that

By construction, this γ is unique if
, since if there was a
such that
, then

Answer:
9/23
Step-by-step explanation:
Of the 23 students, 9 play both baseball and basketball. The probability of choosing one of those is 9/23.
___
Let A represent basketball, and B represent baseball. Then ...
P(A or B) = P(A) +P(B) -P(A and B)
Since 8 students play neither sport, we have ...
1 -8/23 = 11/23 +13/23 -P(A and B)
15/23 = 24/23 -P(A and B)
P(A and B) = (24 -15)/23
P(A and B) = 9/23