Answer:
Step-by-step explanation:
Hey there!
No numbers go into a prime number other than one and that number. 9 and 7 go into 63, so it’s not 63. 3 and 17 go into 51, so it’s not 51. 19 and 3 go into 57, so it’s not 57. That leaves 61. Nothing goes into this other than one and 61, so the answer is 61.
I hope this helps!
y = 3(x + 4)^2 + 31
Step-by-step explanation:
We can convert the given quadratic equation into its vertex form by completing the square:
y = 3x^2 + 24x + 43
= 3(x^2 + 8x) + 43
= 3(x^2 + 8x + 4) + 31
= 3(x + 4)^2 + 31
This is the vertex form of the given quadratic equation with (-4, 31) as its vertex
Answer:
24 hours
Step-by-step explanation:
One member of the gardening club can alone plant flowers in 12 hours.
So in 1 hour he can plant 1/12 of the flowers.
Let the time required by the second member of the club to plant flowers alone be x hours.
Then in 1 hour he can plant 1/x of the flowers.
Now when the two members work together,each hour they can plant:
of the flowers.
But they can together complete the job in 8 hours. So in one hour they plant 1/8 of the flowers.
=> ![\[\frac{1}{12}+\frac{1}{x}=\frac{1}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B1%7D%7B12%7D%2B%5Cfrac%7B1%7D%7Bx%7D%3D%5Cfrac%7B1%7D%7B8%7D%5C%5D)
=> ![\[\frac{1}{x}=\frac{1}{24}\] ](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B1%7D%7Bx%7D%3D%5Cfrac%7B1%7D%7B24%7D%5C%5D%0A)
=> x=24
So the second member can plant the flowers alone in 24 hours
$48.32* (15/100)
= $7.25.
The final answer is $7.25~