9514 1404 393
Answer:
∠BDC = 46°
Step-by-step explanation:
Angle BDC intercepts arc BC, identified as having a measure of 92°. The angle's vertex, point D, is on the circle, so the angle is called an "inscribed angle." The measure of an inscribed angle is half the measure of the arc it intercepts.
∠BDC = (1/2)arc BC = 1/2(92°)
∠BDC = 46°
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.
Answer:
The image shows the graph for given function.
Step-by-step explanation:
We are given the following information in the question:
It is clear function is an exponential function and have shape similar to exponential function.
An exponential function is of the form:
,
where b is a parameter of the function and read as b raised to the power x.
The exponential function enjoys the following properties:
- If 0 < b < 1, then the graph decreases as we move from left to right.
- If b > 1, then the graph will increase as we move from left to right.
Answer:
63 i think if its not correct then delete the answer i gave u. hope it helped :)
Step-by-step explanation:
Step 1
Multiplication property of equality
Multiplying the first equation by 5 and the second equation by 7
Step 2
Addition property of equality
Adding the two equations you get 31a =217
step 3
Division property of equality
Dividing both sides of the above equation by 31 to get the value of a
step 4
Substitution property of equality
Substituting a with 7 in the first equation
step 5
Simplify
simplifying the equation got above
step 6
Using associative property of addition by taking 14 to the other side of the equation.
step 7
Division property of equality
Dividing both side of the equation by 7 to get the value of b
