Assuming that the ratios stay the same, the answer is going to be 6 because the total number of nuts drawn originally was 48, and 9 were cashews. To maintain this ratio when 32 nuts were drawn, the number of cashews will be 6.
First let's get rid of the parenthesis:
12 - 4x + 3x = 4 + 10 + 2x
Now group the x's on the left and the numbers on the right
-4x + 3x - 2x = 4 + 10 - 12
...and simplify
-3x = 2
divide by -3 to isolate x
x = -2/3
9 2/3 total ounces is a total split up among 6 fruits.
So we need to divide 9 2/3 among the 6 fruits.
= 9 2/3 divide 6
= change 9 2 / 3 in improper fraction
= 9*3 + 2/3
= 29/3 divided by 6/1
= 29/3 x 1/6
= 29/18, change that to mixed fractions.
The answer is 1 11/18 ounces of each fruit.
Answer: A three-sided polygon is a triangle.
There are several different types of triangle (see diagram), including: Equilateral – all the sides are equal lengths, and all the internal angles are 60°. Isosceles – has two equal sides, with the third one a different length.
Step-by-step explanation:
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
.