Last year 40 people adopted a manatee through Fias Foundation. This year 30%more people adopted a manetee.How many more people a
1 answer:
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Answer:
m=7
Remainder =4
If q=1 then r=3 or r=-1.
If q=2 then r=3.
They are probably looking for q=1 and r=3 because the other combinations were used earlier in the problem.
Step-by-step explanation:
Let's assume the remainders left when doing P divided by (x-1) and P divided by (2x+3) is R.
By remainder theorem we have that:
P(1)=R
P(-3/2)=R
Both of these are equal to R.
I'm going to substitute second R which is (9m-47)/4 in place of first R.
Multiply both sides by 4:
Distribute:
Subtract 4m on both sides:
Add 47 on both sides:
Simplify left hand side:
Divide both sides by 5:
So the value for m is 7.
What is the remainder when dividing P by (x-1) or (2x+3)?
Well recall that we said m-3=R which means r=m-3=7-3=4.
So the remainder is 4 when dividing P by (x-1) or (2x+3).
Now P divided by (qx+r) will also give the same remainder R=4.
So by remainder theorem we have that P(-r/q)=4.
Let's plug this in:
Let x=-r/q
This is equal to 4 so we have this equation:
Subtract 4 on both sides:
I see one obvious solution of 1.
I seen this because I see 2+7-9 is 0.
u=1 would do that.
Let's see if we can find any other real solutions.
Dividing:
1 | 2 7 0 -9
| 2 9 9
-----------------------
2 9 9 0
This gives us the quadratic equation to solve:
Compare this to
Since the coefficient of is not 1, we have to find two numbers that multiply to be
and add up to be
.
Those numbers are 6 and 3 because while
.
So we are going to replace or
with
then factor by grouping:
This means x+3=0 or 2x+3=0.
We need to solve both of these:
x+3=0
Subtract 3 on both sides:
x=-3
----
2x+3=0
Subtract 3 on both sides:
2x=-3
Divide both sides by 2:
x=-3/2
So the solutions to P(x)=4:
If x=-3 is a solution then (x+3) is a factor that you can divide P by to get remainder 4.
If x=-3/2 is a solution then (2x+3) is a factor that you can divide P by to get remainder 4.
If x=1 is a solution then (x-1) is a factor that you can divide P by to get remainder 4.
Compare (qx+r) to (x+3); we see one possibility for (q,r)=(1,3).
Compare (qx+r) to (2x+3); we see another possibility is (q,r)=(2,3).
Compare (qx+r) to (x-1); we see another possibility is (q,r)=(1,-1).
Answer:
8
Step-by-step explanation:
Create an expression to model the situation. One can do this by simply rewriting the written expression in terms of numbers and variables. Use the variable (x) to represent the unknown value.
Simplify this expression,
Use inverse operations to solve for (x),