<h3>
Answer: 35</h3>
A prime number is one where the only factors are one and itself. A composite number has other factors.
You'll have to look at the list of numbers from 1 to 50
In that list, 47 is the largest prime less than 50, and 12 is the smallest composite number greater than 10.
So 47-12 = 35
It is on point (1,10). This means the snake population was at 10 after one year.
Well, notice, we can pretty much see the x-intercepts if we set f(x) = 0, clearly they're just 6 and -2,
![\bf \stackrel{f(x)}{0}=(x-6)(x+2)\implies \begin{cases} 0=x-6\implies &6=x\\ 0=x+2\implies &-2=x \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bf%28x%29%7D%7B0%7D%3D%28x-6%29%28x%2B2%29%5Cimplies%20%0A%5Cbegin%7Bcases%7D%0A0%3Dx-6%5Cimplies%20%266%3Dx%5C%5C%0A0%3Dx%2B2%5Cimplies%20%26-2%3Dx%0A%5Cend%7Bcases%7D)
now, this is a quadratic equation, since it only has 2 solutions at most, recall your fundamental theorem of algebra.
so, the vertex will be right in middle of those two x-intercepts.
what's between -2 and 6?, well is +2 or just 2, so
x = 2.
so we know the x-coordinate for the vertex is the halfway point of 2, what's the y-coordinate?
f(x) = y = (
2 - 6)(
2 + 2)
y = ( - 4)( 4 )
y = -16thus the vertex is at, well you already know.
Answer:
Question 1: 71 and 72
Question 2: Child 1: 60 lbs, Child 2: 15 lbs
Step-by-step explanation:
Question 1:
Consecutive numbers are 2 numbers right next to each other.
You know the numbers will have to be double digits number.
71 and 72 are consecutive numbers. The sum of them is 143.
71+72=143
Question 2:
For this problem, we can use system of equations to find the mass of the 2 children. Let's say x is the first child and y is the second child.
Equation 1
x+y=75
This equation comes from the combined mass of the 2 children.
Equation 2
x=4y
This equation comes from the first child being 4 times the mass of the second child.
Since we know the value of x, we can use substitution to find y.
4y+y=75
5y=75
y=15
Now that we know the second child is 15 lbs, we can plug this into any of the 2 equations to find the mass of the first child.
x=4(15)
x=60