Answer:
See graph
Step-by-step explanation:
These inequalities are fully simplified, so all we have to do here is graph them.
To graph x > 1, first draw the line x = 1. Since the sign of the inequality is ">", the line will be dashed, and the shading will be done above it. (This is the blue area on the graph.)
Similarly, to graph y > 1, draw y = 1. Then, because the sign of the inequality is ">", make the line dashed and shade above it. (This is the red area on the graph.)
The solution set to the system of inequalities will be the region where the two shaded areas overlap, which is the purple area on the graph below. Hope this helps!
Answer:
x = 12.6 pennies
Step-by-step explanation:
total number of coins = 1 + 2+ 4 + 3 = 10 coins
P(penny) =
P(nickels) =
P(dimes) =
P(quarters) =
hence average value of the coin
x = Penny x P(Penny) + nickel x P(nickel) + dimes x P(dimes) + quarters x P(quarters)
nickels = 5 pennies dimes = 10 ; and quarters = 25 pennies
x = 0.1 + 1 + 4 + 7.5
x = 12.6 pennies
hence, the average pennies for the first draw is equal to x = 12.6 pennies
For this case we must follow the steps below:
step 1:
We place each of the given points on a coordinate axis
Step 2:
We join the AC points (represented by the orange line)
We join the BD points (represented by the blue line)
It is observed that the resulting figure after placing the 4 points on a coordinate axis, turns out to be a rhombus.
In addition, the blue and orange lines turn out to be perpendicular, that is, they have an angle of 90 degrees between them. This can be verified by finding the slopes of each of the two straight lines (blue and orange), which must be opposite reciprocal, that is, they comply:
In this case, the slope of the orange line is and that of the blue line is
Then , it is verified that they are perpendicular.
Thus, the conclusion is that ABCD is a rhombus and AC is perpendicular to BD.
Answer:
See attached image
Option D
