Explanation
Problem #2
We must find the solution to the following system of inequalities:
(1) We solve for y the first inequality:
Now, we multiply both sides of the inequality by (-1), this changes the signs on both sides and inverts the inequality symbol:
The solution to this inequality is the set of all the points (x, y) over the line:
This line has:
• slope m = 3/2,
,
• y-intercept b = -2.
(2) We solve for y the second inequality:
The solution to this inequality is the set of all the points (x, y) below the line:
This line has:
• slope m = -1/3,
,
• y-intercept b = 2.
(3) Plotting the lines of points (1) and (2), and painting the region:
• over the line from point (1),
,
• and below the line from point (2),
we get the following graph:
Answer
The points that satisfy both inequalities are given by the intersection of the blue and red regions:
Answer:
Isoceles Obtuse
Step-by-step explanation:
This triangle has 2 sides with the same side lengths and 2 of the same angles, so it is an isoceles triangle. Is it obtuse or actue? Well, we can see that there is an angle greater than 90 degrees, so this is an obtuse isoceles triangle.
The equation
P(t) = 1405233 * (1 - 0.011)^(t)
models the population at t years after 2010. Then, when P(t) = 1,200,000, we have
1200000 = 1405233 * (0.989)^t
(0.989)^t = 1200000/1405233
t = log(1200000/1405233)/log(0.989)
t = 14.27 years
This means 14.27 years after 2010. Therefore, the answer to this question is 2024.
For the first 6, we see that it is exactly one place behind the decimal point, therefore meaning that it is in the tenths place. The second 6 is three places behind the decimal place making it in the thousandths place. The third and final 6 is one place in front of the decimal, therefore it is in the ones place. Hope this helps!
inside angles need to equal 180
180-75-40 = 65
now the question mark and 65 need to equal 180
180-65 = 115
answer is 115
