Answer:
X=5.7
Step-by-step explanation:
5x-3-2x/7=24
We simplify the equation to the form, which is simple to understand
5x-3-2x/7=24
Simplifying:
5x-3-0.285714285714x=24
We move all terms containing x to the left and all other terms to the right.
+5x-0.285714285714x=+24+3
We simplify left and right side of the equation.
+4.71428571429x=+27
We divide both sides of the equation by 4.71428571429 to get x.
x=5.72727272727
The second choice is correct, but I believe that either its +1/3 ( in the question) or -3y as that will give you the answer of: y=1/3x+6
Answer:
do you have an image for that?
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.