Answer:
Step-by-step explanation:
a. Yes, the following statement is true. The police officer is gathering data by writing down all the speeding tickets and seperating them into two categories, red and non-red cars. He can later analyze this data and compare them to determine whether or not his hypothesis is true.
b. The color of the car is the only variable that would not be a confounding variable in this scenario. This would instead be the independent variable and does not in any way affect the dependent variable which would be the number of speeding tickets received.
Perpendicular lines have slopes that are the negative reciprocals of each others slopes. this means that you can:
1. write the slope as a fraction (if not already one),
2. flip the fraction over
3. multiply the fraction by - 1
4. And you have perpendicular lines slope.
so the slope of this line is - 1 so:
1. - 1 = - 1/1 convert to fraction
2. - 1/1 = - 1/1 flip but this case stays same
3. - 1/1 * - 1 = 1 multiply by - 1
4. slope is 1
we have slope and point so we can plug into equation:
y = mx + b
with m as slope and b is y intercept.
plug values:
4 = 1 * (- 2) + b
6 = b
so y intercept would be (0,6)
Answer:
<u>The solution for this system is x = 1/2 and y = 9/2</u>
Step-by-step explanation:
1. We have this system of equations:
x - 3y = -13 and 5x + 7y = 34
2. Let's try to find out the value of x on the first equation:
x - 3y = - 13
x = 3y - 13
3. Now, let's replace x on the second equation for finding y:
5x + 7y = 34
5 (3y - 13) + 7y = 34
15y - 65 + 7y = 34
22y = 34 +65
22y = 99
2y = 9 (Dividing by 11 at both sides)
<u>y = 9/2</u> (Diving by 2 at both sides)
4. Now, let's find out the value of x on the first equation, using the value of y:
x - 3y = - 13
x - 3 (9/2) = - 13
x - 27/2 = -13
x = -13 + 27/2
x = (-26 + 27)/2 (Adding - 13 and 27/2)
<u>x = 1/2</u>
5. Finally, let's prove the values of x and y are correct on the second equation of the system:
5x + 7y = 34
5 (1/2) + 7 (9/2) = 34
5/2 + 63/2 = 34
(5 + 63)/2 = 34
68/2 = 34
<u>34 = 34</u>
<u>It has been proved that x = 1/2 and y = 9/2 are correct</u>
if Olivia has x songs, then Ryan has 4x-1.
So, x+(4x-1)=469
Solving for x, you get 94, so Olivia has 94 songs.
27/8 or 3 3/8 is your answer :)