The line whose equation is
y = (any number) - 2x
is parallel to the line y = 3 - 2x , because they have the same slope.
Answer:
11 degrees
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees.
From 180 degrees we subtract the sum of 102 degrees and 67 degrees, obtaining 11 degrees (first answer choice)
Answer:
B
Step-by-step explanation:
Remark
The easiest way to do this is to Substitute for y in the top equation.
2x + 4y = 18 Divide by 2
2x/2 + 4y/2 = 18/2
x + 2y = 9
Substitute -3x + 2 in for y in the equation above
x + 2(-3x + 2) = 9
x - 6x + 4 = 9
Combine like terms on the left
-5x + 4 = 9
Subtract 4 from both sides.
-5x + 4-4 = 9- 4
-5x = 5
Divide by -5
-5x/-5 = 5/-5
x = - 1
That makes A and C incorrect.
y = -3x + 2
y = -3(-1) + 2
y = 3 + 2
y = 5
The correct answer should be (-1,5) which is B
Answer:
Associative Property
Step-by-step explanation:Because it includes grouping of three numbers and the parentheses group around two different numbers
∫(t = 2 to 3) t^3 dt
= (1/4)t^4 {for t = 2 to 3}
= 65/4.
----
∫(t = 2 to 3) t √(t - 2) dt
= ∫(u = 0 to 1) (u + 2) √u du, letting u = t - 2
= ∫(u = 0 to 1) (u^(3/2) + 2u^(1/2)) du
= [(2/5) u^(5/2) + (4/3) u^(3/2)] {for u = 0 to 1}
= 26/15.
----
For the k-entry, use integration by parts with
u = t, dv = sin(πt) dt
du = 1 dt, v = (-1/π) cos(πt).
So, ∫(t = 2 to 3) t sin(πt) dt
= (-1/π) t cos(πt) {for t = 2 to 3} - ∫(t = 2 to 3) (-1/π) cos(πt) dt
= (-1/π) (3 * -1 - 2 * 1) + [(1/π^2) sin(πt) {for t = 2 to 3}]
= 5/π + 0
= 5/π.
Therefore,
∫(t = 2 to 3) <t^3, t√(t - 2), t sin(πt)> dt = <65/4, 26/15, 5/π>.
