Step-by-step explanation:
tan150°
= -tan30°
= -√3/3.
Remember that the vertex form of a parabola or quadratic equation is:
y=a(x-h)^2+k, where (h,k) is the "vertex" which is the maximum or minimum point of the parabola (and a is half the acceleration of the of the function, but that is maybe too much :P)
In this case we are given that the vertex is (1,1) so we have:
y=a(x-1)^2+1, and then we are told that there is a point (0,-3) so we can say:
-3=a(0-1)^2+1
-3=a+1
-4=a so our complete equation in vertex form is:
y=-4(x-1)^2+1
Now you wish to know where the x-intercepts are. x-intercepts are when the graph touches the x-axis, ie, when y=0 so
0=-4(x-1)^2+1 add 4(x-1)^2 to both sides
4(x-1)^2=1 divide both sides by 4
(x-1)^2=1/4 take the square root of both sides
x-1=±√(1/4) which is equal to
x-1=±1/2 add 1 to both sides
x=1±1/2
So x=0.5 and 1.5, thus the x-intercept points are:
(0.5, 0) and (1.5, 0) or if you like fractions:
(1/2, 0) and (3/2, 0) :P
Answer:
<u>A. Nicholas will have to pay less using plan A</u>
<u>B. He will pay US$ 4 less than plan B</u>
Step-by-step explanation:
Let's compare how much Nicholas will pay on internet service in Plan A and plan B, after using it 16 hours and 40 minutes.
Plan A
Up to 10 hours = US$ 6
Every subsequent 1/2 hour: $1
10 hours + 14 (1/2 hour)
<u>Nicholas will pay 6 + 14 * 1 = US$ 20</u>
Plan B
Up to 12 hours = US$ 4
Every subsequent 1/2 hour: $2
12 hours + 10 (1/2 hour)
<u>Nicholas will pay 4 + 2 * 10 = 24</u>
Answer : D
From the given graph , we can see that
The graph crosses the y axis at 7
So y axis is (0,7)
The graph is increasing at first and reaches (-2,8) and then start decreasing
The graph start increasing at x=-10 and goes on increasing till x= -2
then the graph start decreasing at x=-2 and goes in decreasing till x= 10
The graph crosses the y axis at (0,7), increasing from x=-10 to x=-2 and decreasing from x=-2 to x=10
Answer D is correct
Answer:
1. 10^(38)
2. total amount = 10^11 or total amount = $100000000000
Step-by-step explanation:
For every time that we multiply powers with the same base we maintain the base and sum the powers. Therefore we have:
1. (10^32)*(10^6)
10^(32 + 6)
10^(38)
2. If each of the 10^6 programmers make 10^5 then the total money they make together is the product of the number of programs with the sallary each makes. We have:
total = (10^6)*(10^5)
total = 10^(6 + 5)
total = 10^11
total = $100000000000
