For number 4, we'll need a few facts to answer our question:
- Two supplementary angles add up to 180°, forming a straight angle (the angle formed by a straight line)
- The interior angles of a triangle add up to 180°
Given those, we notice that the one unlabeled angle in the figure shares a line with 156°. In fact, this angle is <em>supplementary</em> to 156°, which means that the two add up to 180°. To find the measure of this mystery angle, we can subtract 156 from 180 to obtain 180 - 156 = 24°.
Now, let's look at the triangle. We already know the measure of one of the angles is 24°, and the other two are x°. What else do we know about the angles of a triangle? From the two facts listed at the beginning, we know their interior angles add up to 180°, so let's use that fact to solve for x.
We have:

, or

Solving for x:

So, x = 78°.
For question 5, the <em>definition</em> of a pair of parallel lines is a pair of lines which <em>never intersect</em>, so "always" would be the appropriate answer.
The given diagram is a scatter plot in which temperature is plotted against number of visitors.
As the number of visitors is rising with the rise in temperature, its a positive correlation.
As joining the dots is going to give a web of line segments, it is not going to be helpful to understand the trends.
The best way to understand the trends is to make the line of best Fit in such a way that the number of dots on either side are approximately the same.
I have attached the figure for your reference of the line of best fit.
Answer:
Step-by-step explanation:
x= money earned per hour working as a cashier.
y=money earned per hour working delivering newspapers.
We propose the following system of equations:
5x + 4y =77
6x + 3y=78
We solve the system by reduction method:
-6*(5x+4y=77) ⇒ -30x-24y=-462
5*(6x+3y=78)⇒ 30x+15y=390
---------------------------
-9y=-72 ⇒ y=-72 /-9=8
Now, we get the value of "x" replacing the value of "y" by "8" in any part of the equation above.
5x + 4(8)=77
5x+32=77
5x=77-32
5x=45
x=45/5=9
therefore;
money earned per hour working as a cashier= $9/ hour
money earned per hour working delivering newspapers=$8/hour
Answer: (11x-30)
Step-by-step explanation:
(4x+3)+(7x-33)=(11x-30)