Answer:
x² – x – 12 = (x – 4)(x + 3)
Step-by-step explanation:
Identify two numbers that add to -1 and multiply to -12, let's call them p and q.
So ax² + bx + c = (x + p)(x + q)
pq = c
p + q = b.
It is easier to find these numbers by finding factors of -12.
This can be done by splitting the number up until all the numbers are prime.
-12 → 6 × -2 or -6 × 2 → -(3 × 2 × 2)
There can only be two numbers so the only options we have are 6 and -2, -6 and 2, 3, and -4, or -3 and 4.
We can eliminate them by adding them up.
6 + -2 = 4 ≠ -1 so that can't be it.
-6 + 2 = -4 ≠ -1 so that can't be it either.
-3 + 4 = 1 ≠ -1
therefore p and q are 3 and -4 because 3 + -4 = -1.
so x² – x – 12 = (x – 4)(x + 3)
p = -4, and q = 3.
(x – 4)(x + 3) = x(x + 3) – 4(x + 3) = x² + 3x – 4x + 12 = x² – x – 12
For the given graph , slope of the line is equal to ( 1 / 2 ).
As given in the question,
Form the given graph,
Scale is given by,
On x-axis each unit of the graph represent 1 unit.
On y- axis each unit of the graph represent 1 unit.
Consider two coordinates from the line of the graph,
( x₁ , y₁ ) = ( 1, 2 )
( x₂ , y₂ ) = ( 3, 3 )
Slope of the line = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substitute the value in the formula of the slope we get,
Slope of the line = ( 3 - 2 ) / ( 3 - 1 )
⇒ Slope of the line = 1 / 2
Therefore, for the given graph , slope of the line is equal to ( 1 / 2 ).
Learn more about slope here
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Answer:
A = 8, C = 2 => T = 33
A=100, C = 2 => T = 401
A = any, C = 2 => T = 4A + 1
A = 8, C = 4 => T = 37
As long as the boat can carry one adult or one or two children, the following equation should solve the problem.
T = 4A + 2(C-2) + 1
Step-by-step explanation:
To transfer one adult, 4 one-way trips need to be made as follows:
1. Two children cross the river
2. One of them takes the boat back to the other side
3. One adult crosses the river
4. The other child takes the boat back
These four steps are repeated until all adults are crossed. At this point no children has crossed yet.
Then for every 2 children except the last 2, 2 one-way trips need to be made if the number of children is greater than 2:
1. Two children cross
2. One takes the boat back
For the last 2,only one trip needs to be made.
A = number of adults
C = number of children >= 2
T = total trips
T = 4A + 2(C-2) + 1
Answer:
Step-by-step explanation:
Answer-116
