Answer:
Equivalent systems of equations review
Step-by-step explanation:
We're given two systems of equations and asked if they're equivalent.
x + 4y = 8 (1)
4x + y = 2 (2)
Interestingly, if we sum the equations in System A, we get:
Replacing the first equation in System A with this new equation, we get a system that's equivalent to System A:
This is System B, which means that System A is equivalent to System B.
The answer is 43 because it is half of 86 which is the radius
Answer:
(i) (f - g)(x) = x² + 2·x + 1
(ii) (f + g)(x) = x² + 4·x + 3
(iii) (f·g)(x) = x³ + 4·x² + 5·x + 2
Step-by-step explanation:
The given functions are;
f(x) = x² + 3·x + 2
g(x) = x + 1
(i) (f - g)(x) = f(x) - g(x)
∴ (f - g)(x) = x² + 3·x + 2 - (x + 1) = x² + 3·x + 2 - x - 1 = x² + 2·x + 1
(f - g)(x) = x² + 2·x + 1
(ii) (f + g)(x) = f(x) + g(x)
∴ (f + g)(x) = x² + 3·x + 2 + (x + 1) = x² + 3·x + 2 + x + 1 = x² + 4·x + 3
(f + g)(x) = x² + 4·x + 3
(iii) (f·g)(x) = f(x) × g(x)
∴ (f·g)(x) = (x² + 3·x + 2) × (x + 1) = x³ + 3·x² + 2·x + x² + 3·x + 2 = x³ + 4·x² + 5·x + 2
(f·g)(x) = x³ + 4·x² + 5·x + 2
Recall that 2sin(x) cos(x) is actually equal to sin(2x).
We can prove this by expanding sin(2x) to sin(x + x).
sin(x + x) = sin(x) cos(x) + cos(x) sin(x) = 2sinxcosx
Thus, 2sin(x/2)cos(x/2) can be rewritten in the form:
sin(2x/2), and this simplifies down to sinx.
We know that the slope formula is m = (y1 - y2)/(x1 - x2)
Your points are: (3, 7) and (4, -8)
In this case,
x1 = 3
x2 = 4
y1 = 7
y2 = -8
Now, just plug in the numbers:
m = (7 - -8)/(3-4)
m = 15/-1
m = -15
Your slope is -15.
