The function f(x) is a parabola. We can tell it is a even degree polynomial because the axis of reflection is a vertical line (it passes through the vertex).
In this case, f(x) has a double root at (0,1), but a parabola will have up to 2 roots.
It has a positive leading (quadratic in this case) coefficient, because it is concave up.
In the case of g(x), we can tell it is an odd degree polinomial, as it has a axis of reflection that is a line with slope m=-1. It is like it is reflected two times, one on an horizontal line and then on a vertical line.
The leading coefficient is positive because g(x) tends to infinity when x increases, and the leading coefficient is the one that has more weight for large values of x, so it has to be positive to have positive values of g(x).
Then, we can go through the statements.
O f(x) is an even degree polynomial with a negative leading coefficient. FALSE (the leading coefficient is positive)
O g(x) is an even degree polynomial with a negative leading coefficient. FALSE (it is an odd degree polynomial)
O f(x) is an odd degree polynomial with a positive leading coefficient. FALSE (it is an even degree polynomial).
O g(x) is an odd degree polynomial with a positive leading coefficient. TRUE
Answer:
Here, we will use the formula from trigonometry which defines a radian
we know that an angle is a radian when the length of the radius of the circle is equal to the length of the arc formed
hence, if the radius is r and the arc is r, the angle (in radians) will be 1
if the radius is r and the arc is 2r, the angle in radians will be equal to:
length of arc / radius = 2r/r = 2 radians
I believe this will explain what is actually happening in these type of questions
So, the equation:
Θ(in radians) = s / r (where the length of arc is s and the radius is r)
π/4 = s / 12
s = 3π or 9.42 inches
Answer:
Below!
Step-by-step explanation:
Using Pythagoras theorem, I will solve all of the problems.
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<u>Question 9:</u>
- 10² = 6² + x²
- => 100 = 36 + x²
- => 100 - 36 = x²
- => 64 = x²
- => x = 8
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<u>Question 10:</u>
- 26² = 24² + x²
- => 676 = 576 + x²
- => 676 - 576 = x²
- => 100 = x²
- => x = 10
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<u>Question 11:</u>
- 15² = 12² + x²
- => 225 = 144 + x²
- => 225 - 144 = x²
- => 81 = x²
- => x = 9
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<u>Question 12:</u>
- x² = 8² + 12²
- => x² = 64 + 144
- => x² = 208
- => x = √208
- => x = 14.2 (Rounded)
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<u>Question 13:</u>
- 7² = 2² + x²
- => 49 = 4 + x²
- => 49 - 4 = x²
- => 45 = x²
- => x = √45
- => x = 6.7 (Rounded)
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<u>Question 14</u>
First, let's solve for the variable x using Pythagoras theorem.
- => 5² = 3² + x²
- => 25 = 9 + x²
- => 16 = x²
- => x = 4 units
Now, let's solve for the variable y using Pythagoras theorem.
- (3 + 6)² = 5² + y²
- => (9)² = 25 + y²
- => 81 = 25 + y²
- => y² = 56
- => y = √56
- => y = 7.5 (Rounded) units
Answers (Nearest tenth):
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<u>Question 15:</u>
First, let's find the value of the variable y using Pythagoras theorem.
- 8² = 6² + y²
- => 64 = 36 + y²
- => 28 = y²
- => y = √28
- => y = 5.3 (Rounded) units
Now, let's find the value of the variable x using multiplication.
- x = 2y
- => x = 2(5.3)
- => x = 10.6 units
Answer (Nearest tenth)
- x = 10.6 units
- y = 5.3 units
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Answer:
try (-4,6)
Step-by-step explanation:
if you use tracing paper, put a mark where the point is
put the tip of the pencil on the point which it will rotate around
spin the paper by the degrees
see where the traced point ends up
