Answer:
B) 5 (x minus 3)
C) 4 x + 3 y minus 15 minus 3 y + x
E) Negative 20 minus 3 x + 5 + 8 x
tep-by-step explanation:
5x minus 15
5x - 15
5(x - 3)
4 x + 3 y minus 15 minus 3 y + x
4x + 3y - 15 - 3y + x
5x - 15
Negative 20 minus 3 x + 5 + 8 x
-20 - 3x + 5 + 8x
5x - 15
Let
x--------> the amount in dollars that Luis make last week
we know that
------> equation that represent the situation
solve for x
Divide by 
both sides
therefore
<u>the answer is</u>
Answer:
The intervals in which the population is less than 20,000 include
(0 ≤ t < 0.74) and (11.26 < t ≤ 12)
Step-by-step explanation:
P(t) = 82.5 - 67.5 cos [(π/6)t]
where
P = population in thousands.
t = time in months.
During a year, in what intervals is the population less than 20,000?
That is, during (0 ≤ t ≤ 12), when is (P < 20)
82.5 - 67.5 cos [(π/6)t] < 20
- 67.5 cos [(π/6)t] < 20 - 82.5
-67.5 cos [(π/6)t] < -62.5
Dividing both sides by (-67.5) changes the inequality sign
cos [(π/6)t] > (62.5/67.5)
Cos [(π/6)t] > 0.9259
Note: cos 22.2° = 0.9259 = cos (0.1233π) or cos 337.8° = cos (1.8767π) = 0.9259
If cos (0.1233π) = 0.9259
Cos [(π/6)t] > cos (0.1233π)
Since (cos θ) is a decreasing function, as θ increases in the first quadrant
(π/6)t < 0.1233π
(t/6) < 0.1233
t < 6×0.1233
t < 0.74 months
If cos (1.8767π) = 0.9259
Cos [(π/6)t] > cos (1.8767π)
cos θ is an increasing function, as θ increases in the 4th quadrant,
[(π/6)t] > 1.8767π (as long as (π/6)t < 2π, that is t ≤ 12)
(t/6) > 1.8767
t > 6 × 1.8767
t > 11.26
Second interval is 11.26 < t ≤ 12.
Hope this Helps!!!
Answer:
- <u>He should graph the functions f(x) = 4x and g(x) = 26 in the same coordinate plane. The x-coordinate of the intersection point of the two graphs is the solution of the equation.</u>
Explanation:
<em>To solve the equation 4x = 26</em> using graphs, he should graph two functions in the same coordinate plane. The intersection of the two graphs is the solution of the equation.
The functions to graph are f(x) = 4x, and g(x) = 26.
The graph of f(x) = 4x is a line that goes through the origin (0,0) and has slope 4.
Some of the points to graph that line are:
<u>x f(x) = 4x </u>
0 4(0) = 0 → (0,0)
2 4(2) = 8 → (2,8)
4 4(4) = 16 → (4,16)
6 4(6) = 24 → (4, 24)
With those points you can do an excellent graph of f(x) = 4x
The graph of g(x) = 26 is horizontal line (parallel to the y-axis) that passes through the point (0, 26), which is the y -intercept.
You have to extend both graphs until they intersect each other. The x-coordinate of the intersection point is the solution of the function.
A = {1, 2, 5, 6, 8}
{1} U {2, 5, 6, 8}
{2} U {1, 5, 6, 8}
{5} U {1, 2, 6, 8}
{6} U {1, 2, 5, 8}
{8} U {1, 2, 5, 6}
{1, 2} U {5, 6, 8}
{1, 5} U {2, 6, 8}
{1, 6} U {2, 5, 8}
{1, 8} U {2, 5, 6}
{1, 2, 5} U {6, 8}
{1, 2, 6} U {5, 8}
{1, 2, 8} U {5, 6}
{1, 5, 6} U {2, 8}
{1, 5, 8} U {2, 6}
{1, 6, 8} U {2, 5}
The answer is 15 distinct pairs of disjoint non-empty subsets.
