By the Pythagorean Theorem, the length of x is
a^2 + b^2 = c^2 Pythagorean Theorem
6^2 + b^2 = 10^2 Substitute known variables
6^2 + b^2 - 10^2 = 0 Subtract 10^2 from each side
6^2 - 10^2 = b^2 Subtract b^2 from each side
√6^2-10^2 = √b^2 Take square root of each side
8 = b Simplify
So, the length of x is 8. I hope this helps!
Answer:

Step-by-step explanation:
From the diagram you can see that
- 17 people watch only basketball;
- 7 people watch both basketball and soccer;
- 12 people watch only soccer;
- in total, 17+7+12=36 people watch some sports;
- so, 49-36=13 people do not watch sports.
So, you can fill the table in following way

Answer:
5y+3x=4
Step-by-step explanation:
The standard form for the equation of a line is Ax+By=C In this case with the equation 5y-4=-3x B=5 and A=-3 and C=-4 in order to get Ax and By on the same side we can add both -4 and -3x to both sides to get this in the correct form and we get 5y+3x=4
I hope this helps and please don't hesitate to ask if there is anything still unclear!
Answer:
54. slope: -1/5 y-intercept: -6
55. slope: -3x y-intercept: 12
Step-by-step explanation:
Answer:
3, 8 and 24.
Step-by-step explanation:
Let's write some equations that satisfy this problem (x = smallest, y = middle, z = largest):
z = 3y
x + y + z = 35
x = y - 5
We can use substitution to solve this problem! I will take x + y + z = 35, replace x with y - 5 (since we know x = y - 5) and replace z with 3y (since we know z = 3y).
This leaves us with:
(y - 5) + y + (3y) = 35
y - 5 + y + 3y = 35
5y - 5 = 35
5y = 40
y = 8
Since we know y (the middle number) is 8, we can now find the other numbers:
Largest is 3 times the middle, so 8 * 3 = 24.
Smallest is 5 less than the middle, so 8 - 5 = 3.
The 3 numbers are therefore 3, 8 and 24.