Answer:
y = -3/2x + 3
Step-by-step explanation:
To figure out the equation, it is very simple:
First you must find the y-int
The y-int is the point where the line touches the y-axis
The only point that touches the y-axis is (0,3)
so the y-int is 3
Next we need to find the slope, which is rise over run
we must find how far one point is from another point
so we start from the point (0,3) on the y-axis, then we go down 3 and to the right 2 and we are on the point (2,0)
so the slope is -3/2, because the line is going downwards, not upwards
now we just put the equation together, in the slope intercept form
y-int = b = 3
slope = m = -3/2
y = mx + b
y = -3/2x + 3
I think you mean "if the points <span>(2,5), (3,2) and (4,5) satisfy an unknown 3rd degree polynomial, what is the polynomial?"
Since 3 roots {2, 3, 4} are known, we might begin by assuming that this poly would have the form y = ax^3 + bx^2 + cx + d (which has three factors). Unfortunately, three roots are not enough to determine all four constants {a, b, c, d}.
So, let's assume, instead, that the poly would have the form y = ax^2 + bx + c. Three given points should make it possible to determine {a, b, c}.
(2,5): 5 = a(2)^2 + b(2) + c => 5 = 4a + 2b + c
(3,2): 2 = a(3)^2 + b(3) + c => 2 = 9a + 3b + 5 - 4a - 2b
(4,5): 5 = a(4)^2 + b(4) + c => 5 = 16a + 4b + 5 - 4a - 2b
Now we have two equations in a and b alone, which enables us to solve for a and b:
</span>2 = 9a + 3b + 5 - 4a - 2b becomes -3 = 5a + b
<span>and
</span>5 = 16a + 4b + 5 - 4a - 2b becomes 0 = 12a + 2b, or 0 = 6a + b, or 0=-6a-b
<span>
Adding this result to -3 = 5a + b, we get -3 = -a, so a =3.
Thus, since -3 = 5a + b, -3 = 5(3) + b, so b = -18
All we have to do now is to find c. Let's do this using </span>5 = 4a + 2b + c.
We know that a = 3 and b = -18, so this becomes 5 = 4(3) + 2(-18) + c.
Thus, 5 = 12 - 36 + c, or c = 29.
With a, b and c now known, we can write the poly as y = 3x^2 - 18x + 29.
Now the only thing to do remaining is to verify that each of the three given points satsifies y = 3x^2 - 18x + 29. Try this, please.
4+7 = 11
so
33 / 11 = 3
4 x 3 = 12
7 x 3 = 21
so answer
4:7 = 12:21
2(a - 3) + 2(4a - 10) =
= 2a - 6 + 8a - 20 =
= 2a + 8a - 6 - 20 = <u>1</u><u>0</u><u>a</u><u> </u><u>-</u><u> </u><u>2</u><u>6</u> ← the end
Answer:
102
Step-by-step explanation:
We have the sum for k = 1 to 4 of 3 ^ ( k-1) * ( k-1)
k =1 3 ^ (1-1) * ( 1-1) = 3^0 * 0 = 0
k =2 3 ^ (2-1) * ( 2-1) = 3^1 * 1 = 3
k =3 3 ^ (3-1) * ( 3-1) = 3^2 * 2 = 9*2 = 18
k =4 3 ^ (4-1) * ( 4-1) = 3^3 * 3 = 27 *3 = 81
Add these together
0+3+18+81 =102
