Answer:
There are 5 whole numbers.
Step-by-step explanation:
3,4,5,6,7
Answer:
jdjjdjeo
Step-by-step explanation:
I LOVE TURTLES
-4, -9/4, 1/2, square root of 5 (which is 2.23), 3.7
Answer:
f(x) = -2x +7
Step-by-step explanation:
The 2-point form of the equation for a line is suitable for this. For points (x1, y1) and (x2, y2), the equation is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
For the given points (0, 7) and (3, 1), the equation is ...
y = (1 -7)/(3 -0)(x -0) +7
y = -6/3x +7 . . . . . . . . simplify.
We can use f(x) for y to get ...
f(x) = -2x +7
Part I - First synthetic division
You need to use synthetic division to come up with an expression for a and b:
(x + 2) is a factor, and the remainder is 7, so we can draw a synthetic division table...
coefficients = 1 for X^3; A for X^2; B for X^1; and 3
-2 | 1 A B 3
-2 -2(A-2) 4(A-2)-2B
1 (A-2) -2(A-2)+B 4(A-2)-2B + 3
Remainder = 7
<u>So...</u>
4(A-2)-2B + 3 = 7
4 * (A - 2) - 2B + 3 = 7
4A - 8 - 2B = 4
4A - 2B = 12
2A - B = 6
Proved
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Part II - Second Synthetic Division
We draw another synthetic division table, this time with (x - 1), so the number on the left hand side will be +1
1 | 1 A B 3
1 (A+1) A+B+1
1 (A+1) A+B+1 A+B+4
Remainder = 4
<u>So...</u>
A + B + 4 = 4
A + B = 0
<u>A = -B
</u>
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Part III - Solving for A and B with our two simultaneous equations
We know that<u> </u><u>A = -B</u><u /> and we also know that 2A - B = 6
Since we know that A is equal to -B We can substitute in A for -B, to get:
2A - B = 6
Therefore...
2A + A = 6
3A = 6
<u>A = 2</u>
Again, as we know that A = -B, and as we have found that A = 2, we can see:
A = -B
Therefore...
2 = -B
<u>B = -2
</u>
So our final answer is <u>A = 2, B = -2</u><u />
Hopefully this answer is more useful than the last one, and isn't so confusing!
