While the question gives us the coordinates for 4 points, we only need 2. You can choose any pair of points and the process I will demonstrate will still be applicable and you will get the same results. I will just pick the first two points.
Points: (4,-4) and (8,-1)
As you may already have known, the first number in the parentheses is the x value and the second number is the y value. In order to solve for the slope of the line created by the two points, we must find the difference between the y values of the two points and divide by the difference between the x values of the two points. This can more commonly be called delta y over delta x.
(y of point 1 - y of point 2)/(x of point 1 - x of point 2)
= (-4 + 1)/(4 - 8)
= (-3)/(-4)
=3/4
Slope = 3/4
Answer:
The 3 cyclists will meet at the starting point again after 150 minutes.
Step-by-step explanation:
Since they start at the same point but then take different times to each route, then to find the first time they will each meet at the starting point, we have to find the lowest common multiple (LCM).
Let's use prime factorization to get it.
Prime factorization of 10 = 2 × 5
Prime factorization of 15 = 3 × 5
Prime factorization of 25 = 5 × 5
Thus,super set = 2, 3, 5, 5
Thus,LCM = 2 × 3 × 5 × 5 = 150
Thus,the 3 cyclists will meet at the starting point again after 150 minutes.
Answer: 
Step-by-step explanation:
<u>Given equation</u>
<u>Subtract 9 on both sides</u>
<u>Conclusion</u>
Hope this helps!! :)
Please let me know if you have any questions
Answer:
- 12x +15y = 4140; x + y = 300
- x = 120; y = 180
Step-by-step explanation:
The first equation is for receipts. Each x ticket generated $12 in receipts, so the first term needs to be 12x. Each y ticket generated $15 in receipts, so the second term needs to be 15y. U in this set of equations is the total number of tickets, said to be 300.
The equations are ...
12x +15y = 4140; x +y = 300
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Using the second equation to write an expression for x, we have ...
x = 300 -y
Substituting this into the first equation gives ...
12(300 -y) +15y = 4140
3600 +3y = 4140
y = (4140 -3600)/3 = 180
x = 300 -180 = 120
The number of tickets sold is ...
$12 tickets -- 120
$15 tickets -- 180
_____
You might want to notice that the equation we ended up with:
4140 -12(300) = 3y
is equivalent to this "word solution." This can be done in your head; no equations required.
If all the tickets sold were $12 tickets, the revenue would be $3600. The revenue is $540 more than that. Each $15 ticket generates $3 more revenue than a $12 ticket, so to have $540 more revenue, we must have 540/3 = 180 $15 tickets.
Answer:
x = 24°
Step-by-step explanation:
What do the sum of all angles in a triangle add up to?
- The sum of all angles in a triangle add up to 180°.
First, let's find the missing angle of the big triangle (the angle next to 111°).
- 94 + 41 = 135
- 180 - 135 = 45°
Now, we can find the value of x given the smaller triangle's angle.
- x + 111 + 45 = 180
- x + 156 = 180
- x = 24
Therefore, x = 24°.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
