Answer:
1) C. 4 - 3·i
2) D. The second graph shares the same vertex, is inverted, and opens wider than the first graph
3) C. y = (x - 2)² + 3 would shift right two units
4) B. Figure B' is congruent but not similar to figure B
5) A. m∠k' = m∠k
Step-by-step explanation:
1) Given that the real part of the complex number = 4
The imaginary of the complex number = -3
The general form of representing complex numbers is z = a + b·i, we have;
The binomial equivalent to the complex number is z = 4 - 3·i
2) The first graph equation is y = 2·x²
When x = 1, y = 2 and when x = 2, y = 8
The vertex = (h, k)
Where;
h = -b/(2.a) and b = 0, a = 2
∴ h = 0/(2 × 2) = 0
h = 0
k = f(h) = f(0) = 2 × 0² = 0
k = 0
The vertex, (h, k) = (0, 0)
The coefficient, 'a' is positive, therefore, the graph opens down
The second function, y = -(1/2)·x² also has a vertex (h, k) = (0, 0)
The coefficient, 'a' is positive, therefore, the graph opens up
When x = 1, y = -1/2 and when x = 2, y = -2
Therefore, the second function is wider
Therefore;
The second graph shares the same vertex, is inverted, and opens wider than the first graph
3) The given functions are;
First function; y = x² + 3 and second function; y = (x - 2)² + 3
First function;
When x = 1, y = x² + 3 = 1 + 3 = 4
∴ When x = 1, y = 4
Second function;
When y = 4, y = 4 = (x - 2)² + 3
√(1) = x - 2
x = 3
∴ When x = 3, y = 4
First function;
When x = 2, y = x² + 3 = 4 + 3 = 7
∴ When x = 2, y = 7
Second function;
When y = 7, y = 7 = (x - 2)² + 3
√4 = 2 = (x - 2)
x = 2 + 2 = 4
x = 4
∴ When x = 4, y = 7
Therefore, the second function, y = (x - 2)² + 3, has the x-value shifted 2 units to the right for a given value of 'y'
4) The lengths of the sides of figure B are 3 by 4, the lengths of the sides of figure B' 4.5 by 6
The ratio of the corresponding length and width of figures B and B' are;
3/4.5 = 4/6
Therefore, figure B' is similar but not congruent to figure B
5) A rotation and a reflection are rigid transformations and therefore, the dimensions and measure of the original figure and the image are the same;
∴ m∠k' = m∠k.
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