First, put each grade in terms of x. Most grades are compared to Sophomores, so I made that x
Freshmen = x + 10
Sophomores = x
Juniors = x + 20
Seniors = (x + 10) + 7 = x + 17
Then, the total number of students = 363, so we’ll make an equation that adds them all up in terms of x to equal 363
(x + 10) + x + (x + 20) + (x + 17) = 363
Combine like terms:
4x + 47 = 363
Subtract 47 from both sides:
4x = 316
Divide both sides by 4:
x = 79
The question was how many seniors there are. Seniors were x + 17, so 79 + 17 = 96
Step-by-step explanation:
Sum of angles in a triangle = 180°.
Question 3:
We have 90° + 61° + (14x + 1)° = 180°.
=> 14x° + 152° = 180°
=> 14x° = 28°
=> x = 2.
Question 4:
We have 70° + 55° + (4x + 3)° = 180°.
=> 4x° + 128° = 180°
=> 4x° = 52°
=> x = 13.
Ok this one is a little bit more tricky since there are more possible answers. But we can do it! So look at the y-intercept. It lands on 25. Now we do "Rise over Run". So we go up 4 and left 1. Since the line is going left, the slope is a negative. And the line is solid instead of dotted so it is , ≤. Your answer would be the first option. I hope this helps love! :)
Step-by-step explanation:
Let y1 and y2 be (e^x)/2, and (xe^x)/2 respectively.
The Wronskian of them functions be
W = (y1y2' - y1'y2)
y1 = (e^x)/2 = y1'
y2 = (xe^x)/2
y2' = (1/2)(x + 1)e^x
W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)
= (1/4)(x + 1 - x)e^(2x)
W = (1/4)e^(2x)
Since the Wronskian ≠ 0, we conclude that functions are linearly independent, and hence, form a set of fundamental solutions.
