In order to rationalize the denominator of each expression, we need to multiply the expression by the same radical in the denominator, this way we can remove the radical from the denominator.
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1. Answer: Vertical shift up 3 units and vertical stretch by factor of 2
<u>Step-by-step explanation:</u>
f(x) = √x
g(x) = 2√x + 3
- adding 3 is a vertical shift up 3 units
- multiplying by 2 is a vertical stretch by factor of 2
2. Answer: Domain: [0, ∞)
Range: [3, ∞)
<u>Step-by-step explanation:</u>
g(x) = 2√x + 3
Domain: The restriction on "x" is that the radical must be greater than or equal to 0. So, x ≥ 0 Interval Notation: [0, ∞)
Range: Since the radical must be greater than or equal to 0, then 2√x is also greater than or equal to 0. Add 3 to that and y ≥ 3. Interval Notation: [3, ∞)
-3w-5(4x-4w)-4x
multiply the bracket by -5
(-5)(4x)=-20x
(-5)(-4w)=20w
-3w-20x+20w-4x
-3w+20w-20x-4x ( combine like terms)
answer:
17w-24x or -24x+17w
V = (4/3)π.R³
Diameter - 24 units so Radius = 24/2 = 12 Inits
V= (4π/3).12³ =(4π/3). 1728
V=1728 x 4/3 x π = 2,304.π units³
Answer:
90 mm^2
Step-by-step explanation:
split into two rectangles.
First rectangle: 5 x 6 = 30 mm^2
Second rectangle: 10 x 6 = 60 mm^2
30 + 60 = 90 mm^2
