I’m guessing it’s 9x^2 -6x + 1 but this is basically just one. (1/3,0) use desmos if you’re curious
The answers are :
10) 25 : 24
11) 24 : 5
12) 36 : 5
13) 7 : 3
14) 15 : 1
<u>Ratio = Number of event 1 : Number of event 2</u> (in same unit, if necessary)
<u>10</u>
Girls preferring orange juice : Boys preferring orange juice
50 : 48 (Divide by 2 on both sides)
25 : 24
<u>11</u>
Boys preferring orange juice : Boys preferring grapefruit juice
48 : 10 (Divide by 2 on both sides)
24 : 5
Remember :
- <u>1 minute = 60 seconds</u>
- <u>1 week = 7 days</u>
- <u>1 hour = 60 minutes</u>
<u />
<u>12</u>
3 minutes : 25 seconds
3 × 60 : 25 (Divide by 5 on both sides)
3 × 12 : 5
36 : 5
<u>13</u>
2 weeks : 6 days
2 × 7 : 6 (Divide by 2 on both sides)
7 : 3
<u>14</u>
5 hours : 20 minutes
5 × 60 : 20 (Divide by 20 on both sides)
5 × 3 : 1
15 : 1
Answer:
A), B) and D) are true
Step-by-step explanation:
A) We can prove it as follows:

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that
. Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then
.
C) Consider
. This set is orthogonal because
, but S is not orthonormal because the norm of (0,2) is 2≠1.
D) Let A be an orthogonal matrix in
. Then the columns of A form an orthonormal set. We have that
. To see this, note than the component
of the product
is the dot product of the i-th row of
and the jth row of
. But the i-th row of
is equal to the i-th column of
. If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then
E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.
In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set
and suppose that there are coefficients a_i such that
. For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then
then
.
Answer:
17
Step-by-step explanation:
all 4 numbers added up, 68, divide by the amount of numbers, which is 4, and you get the answer