Its 75 because you at the 2 variables and then subtract them by 180 so 180-105=75
Answer:
68×32= 2176
Step-by-step explanation:
A) There are a number of ways to compute the determinant of a 3x3 matrix. Since k is on the bottom row, it is convenient to compute the cofactors of the numbers on the bottom row. Then the determinant is ...
1×(2×-1 -3×1) -k×(3×-1 -2×1) +2×(3×3 -2×2) = 5 -5k
bi) Π₁ can be written using r = (x, y, z).
Π₁ ⇒ 3x +2y +z = 4
bii) The cross product of the coefficients of λ and μ will give the normal to the plane. The dot-product of that with the constant vector will give the desired constant.
Π₂ ⇒ ((1, 0, 2)×(1, -1, -1))•(x, y, z) = ((1, 0, 2)×(1, -1, -1))•(1, 2, 3)
Π₂ ⇒ 2x +3y -z = 5
c) If the three planes form a sheath, the ranks of their coefficient matrix and that of the augmented matrix must be 2. That is, the determinant must be zero. The value of k that makes the determinant zero is found in part (a) to be -1.
A common approach to determining the rank of a matrix is to reduce it to row echelon form. Then the number of independent rows becomes obvious. (It is the number of non-zero rows.) This form for k=-1 is shown in the picture.
Answer:

Step-by-step explanation:
Subtract (6x-3y) from (9x+2y):

This can also be seen as:

Distribute the -1 to (6x-3y):

Simplify the parentheses:

Group like terms:

Combine:

This expression can't be further simplified. Therefore, 3x+5y is the answer.
:Done
Hello from MrBillDoesMath!
Answer:
x = 10
Discussion:
A plane triangle contains 180 degrees. Adding the angles in the triangle shown in #8 gives
(4x + 7) + (3x + 13) + 90 = 180
Note the "right angle" shown in the triangle has been replaced by its 90 degree equivalent in the above equation.
Combining like terms gives
( 4x + 3x) + (7 + 13) + 90 = 180
7x + 20 + 90 = 180 => (subtract 90 from each side)
7x + 20 + 90 - 90 = 180 - 90 = 90 =>
7x +20 = 90 => (subtract 20 from each side)
7x + 20 -20 = 90 -20 =>
7x = 70 =>
x 70/7 =10.
Thank you,
MrB