Answer:
y = |x-3| -1
Step-by-step explanation:
The parent function has been shifted right 3 units and down 1 unit. That is f(x)=|x| has been moved to ...
y = f(x -3) -1
y = |x -3| -1 . . . . matches the last choice
Answer:
The answer to your question is below
Step-by-step explanation:
csc α - cot α = 
Work with the left part
Simplify
Multiply by the reciprocal
Simplify
Remember that
sin²α = 1 -cos²α
Substitute the previous equation
Simplify
The identity i proved.
Answer:
2a) -2
b) 8
Step-by-step explanation:
<u>Equation of a parabola in vertex form</u>
f(x) = a(x - h)² + k
where (h, k) is the vertex and the axis of symmetry is x = h
2 a)
Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):
f(x) = a(x - 2)² - 6
If one of the x-axis intercepts is 6, then
f(6) = 0
⇒ a(6 - 2)² - 6 = 0
⇒ 16a - 6 = 0
⇒ 16a = 6
⇒ a = 6/16 = 3/8
So f(x) = 3/8(x - 2)² - 6
To find the other intercept, set f(x) = 0 and solve for x:
f(x) = 0
⇒ 3/8(x - 2)² - 6 = 0
⇒ 3/8(x - 2)² = 6
⇒ (x - 2)² = 16
⇒ x - 2 = ±4
⇒ x = 6, -2
Therefore, the other x-axis intercept is -2
b)
Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):
f(x) = a(x - 2)² - 6
If one of the x-axis intercepts is -4, then
f(-4) = 0
⇒ a(-4 - 2)² - 6 = 0
⇒ 36a - 6 = 0
⇒ 36a = 6
⇒ a = 6/36 = 1/6
So f(x) = 1/6(x - 2)² - 6
To find the other intercept, set f(x) = 0 and solve for x:
f(x) = 0
⇒ 1/6(x - 2)² - 6 = 0
⇒ 1/6(x - 2)² = 6
⇒ (x - 2)² = 36
⇒ x - 2 = ±6
⇒ x = 8, -4
Therefore, the other x-axis intercept is 8
Answer:
$51.1
Step-by-step explanation:
If Joe spent 15/22 of his pocket money in a story book which costs $75, he had $51.1 at first.
15/22 of 75 = 51.1363636364 or 51.1
Answer:
2,3,4,5,6,7,8,9,10,...29
Step-by-step explanation:
