Answer:
A. (3,1)
B. g(x)=|x-3|+6
C. h(x)=-|x-3|-6
Step-by-step explanation:
A. To graph the absolute value function f(x) = |x - 3| + 1, first graph the parent absolute value function y=|x| and then translate it 3 units to the right and 1 unit up (see green graph in attached diagram). The vertex of the function f(x) is at point (3,1).
B. The function g(x) translates f(x) 5 units up, so its equation is
g(x)=f(x)+5
g(x)=|x-3|+1+5
g(x)=|x-3|+6
Blue graph in attached diagram.
C. The function h(x) reflects g(x) over the x-axis, so the equation of the function h(x) is
h(x)=-g(x)
h(x)=-(|x-3|+6)
h(x)=-|x-3|-6
Red graph in attached diagram.
Answer:
Even
Step-by-step explanation:
Well if you have an odd number like 3, 5, 7, 9, and etc multiplied by an even number like 2, 4, 6, 8, and etc you will always get an even number
2 x 3 = 6 which is even 3+3
5 x 4 = 20 which is even 10+10
7 x 6 = 42 which is even 21+21
Answer:
B. 97.2
Step-by-step explanation:
The sequence of positive terms is ...
54, 24, 10 2/3, 4 20/27, ...
This sequence has first term 54 and common ratio 24/54 = 4/9. The sum of the infinite series is ...
S = a1/(1 -r) = 54/(1 -4/9) = 54(9/5)
S = 97.2
The sum of the positive terms in the infinite series is 97.2.
Answer:
Step-by-step explanation:
Given AB with coordinates A(3, -3) and B(1, -1)
Perpendicular bisector passes through midpoint of the segment.
<u>Midpoint of AB has coordinates:</u>
- x = (3 + 1)/2 = 2, y = (-3 - 1)/2 = -2
<u>Slope of AB</u>
- m = (-1 + 3)/(1 - 3) = 2/-2 = -1
<u>Slope of the perpendicular line is:</u>
<u>The equation of the line in point-slope form:</u>
- y - y₁ = m(x - x₁), where m = 1, x₁ = 2, y₁ = -2
- y - (-2) = 1(x - 2) ⇒ y + 2 = x - 2
<u>Converted into slope-intercept form:</u>
A. 999 numbers under 1000, so prob of picking one is 999/6296 = 0.1587
<span>B. 6 numbers divisible by 1000, so prob 6/6296 = 0.000953 </span>
<span>C. (6296 - 6)/6296 = 1 - 0.000953 = 0.999047</span>
