Answer:
y-intercept: (0, 5)
Step-by-step explanation:
This parabola has an equation of -x² + 4x + 5.
It's y-intercept is (0, 5).
It's x-intercepts or roots are (-1, 0) and (5, 0).
It's vertex is (2, 9).
___________________________________
Keep in mind that the y-intercept is when x = 0.
Answer:
32901 gallons
Step-by-step explanation:
First, we find the volume of the cylindrical water tank when it is full.
The volume of a cylinder is given as:
V = 
where r = radius and h = height of the cylinder
The diameter of the tank is 20 feet, hence, its radius is 10 feet.
Volume, V, is therefore:
V = 
This is the volume of the tank, when it is full.
When it is 70% full, the volume will be:

1 cubic foot (
) is 7.48 gallons.
Therefore, the volume of the 70% full tank in gallons will be:
4398.23 * 7.48 = 32901.05 gallons ≅ 32901 gallons
The tank contains 32901 gallons of water.
Answer:
Domain {x : x > 1}
Range {y : y ∈ R}
Vertical asymptote x = 0
x-intercept (1, 0)
End behavior consistent
Graph attached down
Step-by-step explanation:
Let us study the equation:
∵ y = log(x)
→ It is a logarithmic function, so no negative values for x
∴ Its domain is {x : x > 1}
∴ Its range is {y : y ∈ R}, where R is the set of the real numbers
→ An asymptote is a line that a curve approaches, but never touches
∵ x can not be zero
∴ It has a vertical asymptote whose equation is x = 0
→ x-intercept means values of x at y = 0, y-intercept means
values of y at x = 0
∵ x can not be zero
∴ There is no y-intercept
∵ y can be zero
∴ The x-intercept is (1, 0)
→ The end behavior of the parent function is consistent.
As x approaches infinity, the y-values slowly get larger,
approaching infinity
∵ y = log(x) is a parent function
∴ The end behavior is consistent
→ The graph is attached down
10 red marbles
Multiply the # of blue marbles by 2 (since there was TWICE as many red marbles), and you have your answer (above)
Answer:
Step-by-step explanation:
Givens
The triangle is equilateral. Given
<K = < M = 60 Property of an equilateral triangle.
IE = IE Reflexive property
Proof
- <IEK = <IEM = 90 Property of perpendicular
- <EIK = 180 - 60 - 90 All triangles have 180 degrees
- <EIK = 30 Subtraction
- <MIK = 180 - 60 - 90 All triangles have 180 degrees
- <MIK = 30 Subtraction
- <MIE = <KIE Both = 30 degrees
- IE = IE Reflexive property
- <IEK = <MEI Both are right angles.
- ΔMIK ≡ΔKIE ASA