Answer:
A
Step-by-step explanation:
Noting that i² = - 1
Given
(7 - 3i)(8 + 4i) ← expand factors using FOIL
= 56 + 28i - 24i - 12i²
= 56 + 4i - 12(- 1)
= 56 + 4i + 12
= 68 + 4i → A
This question is difficult to give a definite answer to because it's an approximation, but I estimate the solutions to be around x = 2.6 and x = -2.6.
When they ask for solutions of the graphed function they are asking for an approximation of where the graph intercepts the x-axis, and we can see it kind of intercepts in the middle of 2 and 3, except slightly closer to 3, which is why I estimated 2.6.
The graph also appears to be symmetrical, which means the solutions will be the same except one would be negative and one would be positive, which means the second solution would be -2.6.
I hope this helps! Let me know if you have any questions :)
Answer:
10 boys, 15 girls
Step-by-step explanation:
Original ratio: 2 boys/3 girls
let x be the scale factor of the ratio
2x plus 5 boys over 3x girls = 1 (because the # of boys/girls are the same)-------> 2x+5/3x = 1
Simplify: 2x+5=3x
Simplify: 5=x
plug x back into the original ratio: 10/15
Check: 10/15 = 2/3
10 boys + 5 boys = 15, 15/15 = 1
Choice C for problem 6 is correct. The two angles (65 and 25) add to 90 degrees, proving they are complementary angles.
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The answer to problem 7 is also choice C and here's why
To find the midpoint, we add up the x coordinates and divide by 2. The two points A(-5,3) and B(3,3) have x coordinates of -5 and 3 respectively. They add to -5+3 = -2 which cuts in half to get -1. This means C has to be the answer as it's the only choice with x = -1 as an x coordinate.
Let's keep going to find the y coordinate of the midpoint. The points A(-5,3) and B(3,3) have y coordinates of y = 3 and y = 3, they add to 3+3 = 6 which cuts in half to get 3. The midpoint has the same y coordinate as the other two points
So that is why the midpoint is (-1,3)
<span>6y-5=-3(2y+1)
6y - 5 = -6y - 3
12y = -3 + 5
12y = 2
y = 2/12
y = 1/6</span>