Answer:
................
Step-by-step explanation:
Answer:
Angle 3 is 113°
Step-by-step explanation:
Angles 2 & 3 is supplementary, so it equals 180°. Subtract 67 from 180 and you get 113. DUH.
Good Luck!!
(a) y >_ 13
(b) x > 17.5
Explanations:
(a)
24.2 - y <_ 11.2
- y <_ 11.2 - 24.2
-y <_ -13
y >_ 13
(b)
- 12.5 + x > 5
x > 5 + 12.5
x > 17.5
(<_ means “less than or equal to” and >_ means “greater than or equal to”)
Answer:
x-intercept: (6,0)
y-intercept: (0,4)
Step-by-step explanation:
The x-intercepts lay on the x-axis and therefore their y-coordinate is 0.
To find the x-intercept, you set y to 0 and solve for x.
2x+3y=12
Set y=0.
2x+3(0)=12
2x+0 =12
2x =12
Divide both sides by 2:
x =12/2
x =6
The x-intercept is (x,y)=(6,0).
The y-intercepts lay on the y-axis and therefore their x-coordinate is 0.
To find the y-intercept, you set x to 0 solve for y.
2x+3y=12
2(0)+3y=12
0+3y =12
3y =12
Divide both sides by 3:
y =12/3
y =4
The y-intercept is (0,4).
Check the discriminant (always a good idea).
b^2 - 4ac
b = -19
c = -15
a = 10
(-19)^2 - 4(10)(-15)
361 + 600
961
Yes it can be factored, but if you like, you could use the quadratic formula.
x = [- (-19) +/- sqrt(961)]/(2 * 10)
x = [19 +/- 31 ] / 20
x = (19 + 31/20
x = (50)/20
x = 5/2
x = [19 - 31] / 20
x = [- 12]/20
x = -3/5
Getting the factors is a little tricky.
(x - 5/2)(x + 3/5) = 0
The first factor is found by putting
x - 5/2 in that form and multiplying through by 2
1/2 (2x - 5) The 1/2 comes from multiplying by 2.
The second factor is
1/5 (5x + 3)
So the equation will look like
1/2(2x - 5)1/5(5x + 3) = 0 If you multiply by 2 you get
(2x - 5)1/5(5x + 3) = 0 and now multiply by 5 you get
(2x - 5) (5x + 3)
Check
2x*5x - 25x + 6x - 15
10x^2 - 19x - 15 = 0
So everything works out.
