Answer:
Step-by-step explanation:
1. Replace F(x) with y.
2. Interchange x and y in y = 2x + 1: x = 2y + 1
3. Solve this result for y: 2y = x - 1, or y = (x - 1)/2
4. Replace y with:
-1
F (x):
-1 x - 1
F (x) = -----------
2
Answer:
The two angles are 69° and 21°.
Step-by-step explanation:
Write out the expression:
let x and y be two angles that are complementary and the sum of their measures is 90°
-> x° + y° = 90°
if one angle is 6º more than three times the other angle:
-> x° = 6° +3y°
Plug x = 6+3y into x° + y° = 90°
6° + 3y° + y° = 90°
Solve for y
4y° = 84°
y° = 21°
Plug y into x° + y° = 90°
x° + 21° = 90°
Solve for x°
x° = 90° - 21° = 69°
Answer:
a) look at the figure
b) i) x = 2.5 , y = 3
ii) x-intercept is 2.333
iii) y-intercept is 2.8
Step-by-step explanation:
a) The points of the graph f(x) = 3+1/2x - 5 are:
f(-5) = 2.9333
f(-4) = 2.923
f(-3) = 2.909
f(-2) = 2.888
f(-1) = 2.857
f(0) = 2.8
f(1) = 2.666
f(2) = 2
f(3) = 4
f(4) = 3.333
f(5) = 3.2
b)
i) to find the vertical asymptotic put the denominator = 0
2x - 5 = 0 ⇒ 2x = 5 ⇒ x = 5 ÷ 2 = 2.5
∴ The equation of the vertical asymptotic is x = 2.5
To find the horizontal asymptotic look at the degree of the numerator and denominator
∵ they are equal f(x) = (6x -14)/(2x - 5) ⇒ 6x ÷ 2x = 3
∴ The equation of the horizontal asymptotic is y = 3
ii) the value of x-intercept means put f(x) = 0
∴3 + 1/2x - 5 = 0 ⇒ 1/2x - 5 = -3 ⇒ -6x + 15 = 1 ⇒ 6x = 14
x = 14/6 = 2.333
iii) The value of y-intercept means x = 0
∴ f(x) = 3 + 1/0 - 5 = 3 + (-0.2) = 2.8