Answer:
a = 5
b = 12
c = 13
Step-by-step explanation:
a^2+b^2=c^2
b-a=7(b=a+7)
c=a+8
Then, substitute
a^2+((a+7)*(a+7))=c^2
a^2+a^2+7a+7a+49=c^2
2a^2+14a+49=c^2
Because c = a+8
2a^2+14a+49=(a+8)(a+8)
2a^2+14a+49=a^2+16a+64
a^2-2a=15
a^2-2a-15=0
(a-5)(a+3)=0
a = 5,-3
a = 5(a side cannot be negative)
Plug in a=5 to the other equations to get
a = 5, b = 12, c = 13
Hope it helps <3
Answer:
6.125 minutes per song
Step-by-step explanation:
Unit rates are based on a single unit of something. Like price per 1 gallon of gas; price for 1 pound of bananas; miles driven per 1 gallon of gas, etc. What we are looking for in minutes per song.
Use a proportion to solve this with minutes on top and number of songs on the bottom. We know that 49 minutes = 8 songs, and we want to know how many minutes (x) per 1 song:
Cross multiply to get
8x = 49 so
x = 6.125 minutes per song
Answer:
A. y = x^2 -6x + 13
Step-by-step explanation:
The parabola that opens up and has line of symmetry x=3 and a minimum at x=3 is
The reason is that, we can write this function in the vertex form to get;
Hence the line of symmetry is x=3 and the vertex is (3,4)
Answer:
122
Step-by-step explanation:
An arithmetic sequence means a number is added each term. There is a term for where a number is multiplied as well. But in this case the first number is -103, the second number is -94 and the third number is -85. Can you tell what number is added each time?
The number is 9. -103+9=-94 and -94+9=-85 and so on. Now we want a way to find the term way further down the line.
Think of it doing it all at once. -103+9+9 gets us the third term right? so that's 2*9. -103+3*9 would get us the fourth. Hopefully that makes sense, but let me know if it doesn't. But for a few more examples, if we want the fifth term we would do -103+4*9 and getting the tenth would need -103+9*9. So basically we take the number term we want (in this case we want the 26th) and then take -103+ n*9, where n is the term we want minus 1, or in this case 25. so that's -103+25*9
Let me know if you need more of an explanation.
