Answer:
Interior: 135 degrees
Exterior: 45 degrees
Step-by-step explanation:
The interior angle of a regular octagon is exactly 135 degrees, which can be found using the (n – 2)180 formula. The exterior is simply 180 - the interior, which is 45. :)
Answer:
y=-3x-2
Step-by-step explanation:
Equation of a line is y=mx+b, where m is the slope given, -3.
Y=-3x+b
To find b, sub in the points (-3,7) for x and y in the equation
7=-3(-3)+b
7=9+b
-2=b
Answer:
OD. (-1,11), (0,7), (1,3), (2,-1)
Slope:
4
y-intercept:
(0,7)
Step-by-step explanation:
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values. Graph the line using the slope and the y-intercept, or the points.
Answer:
3
Step-by-step explanation:
9/3=3
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.