The number of video games in Matthew’s collection is 12
To solve the problem, we need to know what simultaneous equations are
<h3>What are simultaneous equations?</h3>
These are a pair of equations which contain two variables.
Now, let
- x = number of video games in Matthew's collection and
- y = number of video games in Anthony's collection.
Given that the number of video games in Anthony’s collection is 5 times the number in Matthew’s collection, we have that y = 5x (1)
Also, the total number of video games in both collections is 72.
So, x + y = 72 (2)
Substituting equation (1) into (2), we have
x + 5x = 72
6x = 72
x = 72/6
x = 12
So, the number of video games in Matthew’s collection is 12
Learn more about number of video games here:
brainly.com/question/12452860
5 + 10 + 12 = 27 scores are less than 3
Answer:
7.) 16.7
Step-by-step explanation:
7). First you have to find the length of the line with the triangle that is at a 90 angle with the longest side of the triangle
Using the pythagrorem theorem a² + b² = c²
4² + b² = 5²
b² = 5² - 4²
b² = 25 - 16
b² = 9
√b² =√9
b = 3
next you do the same thing to find the missing segment of the longest side
3² + b² = 13²
b² = 169 - 9
b² = 160
b = √160 or ≈ 12.7
12.7 + 4 = 16.7
so 16.7 is the length of that side
Step 1: Find the slope:

This gives you
, but we need to find b.
To find b, substitute in one (x,y) pair and it doesn't matter which one. I'll go with (4,-2):
![\begin{aligned}-2&=-\dfrac{3}{2}(4)+b\\[0.5em]-2&=-6+b\\[0.5em]4&=b\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D-2%26%3D-%5Cdfrac%7B3%7D%7B2%7D%284%29%2Bb%5C%5C%5B0.5em%5D-2%26%3D-6%2Bb%5C%5C%5B0.5em%5D4%26%3Db%5Cend%7Baligned%7D)
Now take that b-value and plug in into the slope-intercept form:

It's always a good idea to toss in the other x-value from the other point, to make sure it checks out.