Answer:
B
Step-by-step explanation:
A rectangular door for a shed has a width of 42 in and a diagonal support of 94 in. The triangle formed by the rectangle's width (first leg), rectangle's length (second leg) and rectangle's diagonal (hypotenuse) is right triangle. By the Pythagorean theorem,
Thus,
Step-by-step explanation:
A decimal is a number that represents a fractional part of a whole. For example, the decimal 0.25 represents 25/100. Numbers with decimals are not integers because an integer is defined as a whole number with no fractional part.
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.
This is the answer: X= 118
