Show Work: <span>Calculate 9 x 8, which is 72. Since 72 is two-digit, we carry the first digit 7 to the next column. </span> 3 <span>Calculate 8 x 8, which is 64. Now add the carry digit of 7, which is 71. Since 71 is two-digit, we carry the first digit 7 to the next column. </span> 4 <span>Calculate 7 x 8, which is 56. Now add the carry digit of 7, which is 63. Since 63 is two-digit, we carry the first digit 6 to the next column. </span>
5 <span>Calculate 2 x 8, which is 16. Now add the carry digit of 6, which is 22. Since 22 is two-digit, we carry the first digit 2 to the next column. </span> 6 <span>Calculate 4 x 8, which is 32. Now add the carry digit of 2, which is 34. Since 34 is two-digit, we carry the first digit 3 to the next column. </span> 7 <span>Bring down the carry digit of 3. </span> 8 <span>Calculate 9 x 7, which is 63. Since 63 is two-digit, we carry the first digit 6 to the next column. </span> 9 <span>Calculate 8 x 7, which is 56. Now add the carry digit of 6, which is 62. Since 62 is two-digit, we carry the first digit 6 to the next column. </span> 10 <span>Calculate 7 x 7, which is 49. Now add the carry digit of 6, which is 55. Since 55 is two-digit, we carry the first digit 5 to the next column. </span> 11 <span>Calculate 2 x 7, which is 14. Now add the carry digit of 5, which is 19. Since 19 is two-digit, we carry the first digit 1 to the next column. </span> 12 <span>Calculate 4 x 7, which is 28. Now add the carry digit of 1, which is 29. Since 29 is two-digit, we carry the first digit 2 to the next column. </span>
13 <span>Bring down the carry digit of 2. </span> 14 <span>Calculate 9 x 6, which is 54. Since 54 is two-digit, we carry the first digit 5 to the next column. </span> 15 <span>Calculate 8 x 6, which is 48. Now add the carry digit of 5, which is 53. Since 53 is two-digit, we carry the first digit 5 to the next column. </span>
16 <span>Calculate 7 x 6, which is 42. Now add the carry digit of 5, which is 47. Since 47 is two-digit, we carry the first digit 4 to the next column. </span>
17 <span>Calculate 2 x 6, which is 12. Now add the carry digit of 4, which is 16. Since 16 is two-digit, we carry the first digit 1 to the next column. </span>
18 <span>Calculate 4 x 6, which is 24. Now add the carry digit of 1, which is 25. Since 25 is two-digit, we carry the first digit 2 to the next column. </span>
19 <span>Bring down the carry digit of 2. </span>
20 <span>Calculate 9 x 4, which is 36. Since 36 is two-digit, we carry the first digit 3 to the next column. </span> 21 <span>Calculate 8 x 4, which is 32. Now add the carry digit of 3, which is 35. Since 35 is two-digit, we carry the first digit 3 to the next column. </span> 22 <span>Calculate 7 x 4, which is 28. Now add the carry digit of 3, which is 31. Since 31 is two-digit, we carry the first digit 3 to the next column. </span> 23 <span>Calculate 2 x 4, which is 8. Now add the carry digit of 3, which is 11. Since 11 is two-digit, we carry the first digit 1 to the next column. </span> 24 <span>Calculate 4 x 4, which is 16. Now add the carry digit of 1, which is 17. Since 17 is two-digit, we carry the first digit 1 to the next column. </span> 25 <span>Bring down the carry digit of 1. </span> 26 <span>Calculate 9 x 5, which is 45. Since 45 is two-digit, we carry the first digit 4 to the next column. </span> 27 <span>Calculate 8 x 5, which is 40. Now add the carry digit of 4, which is 44. Since 44 is two-digit, we carry the first digit 4 to the next column. </span> 28 <span>Calculate 7 x 5, which is 35. Now add the carry digit of 4, which is 39. Since 39 is two-digit, we carry the first digit 3 to the next column. </span> 29 <span>Calculate 2 x 5, which is 10. Now add the carry digit of 3, which is 13. Since 13 is two-digit, we carry the first digit 1 to the next column. </span> 30 <span>Calculate 4 x 5, which is 20. Now add the carry digit of 1, which is 21. Since 21 is two-digit, we carry the first digit 2 to the next column. </span> 31 <span>Bring down the carry digit of 2. </span> 32 <span>Calculate 342312 + 2995230 + 25673400 + 171156000 + 2139450000, which is 2339616942</span> <span> </span>
4) Reflected, narrower by a factor of 2/5, slides right 4 units and slides up 6 (units)
Step-by-step explanation:
1) The graph does not intercept the x-axis, therefore, there are no real solutions at the point y = 0
We get;
y = a·x² + b·x + c
At y = 6, x = -2
Therefore;
6 = a·(-2)² - 2·b + c = 4·a - 2·b + c
6 = 4·a - 2·b + c...(1)
At y = 8, x = 0
8 = a·(0)² + b·0 + c
∴ c = 8...(2)
Similarly, we have;
At y = 8, x = -4
8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8
16·a - 4·b = 0
∴ b = 16·a/4 = 4·a
b = 4·a...(3)
From equation (1), (2) and (3), we have;
6 = 4·a - 2·b + c
∴ 6 = b - 2·b + 8 = -b + 8
6 - 8 = -b
∴ -b = -2
b = 2
b = 4·a
∴ a = b/4 = 2/4 = 1/2
The equation is therefor;
y = (1/2)·x² + 2·x + 8
Solving we get;
x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))
x =( -2 ± √(-12))/1 = -2 ± √(-12)
Therefore, we have;
2 nonreal complex roots
2) Give that the graph of the function touches the x-axis once, we have;
1 Real Solution
3) The given function is f(x) = 2·x² + 8·x + 6
The general form of the quadratic function is f(x) = a·x² + b·x + c
Comparing, we have;
a = 2, b = 8, c = 6
The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;
D = 8² - 4 × 2 × 6 = 16
The discriminant of the function, D = 16
4.) The given function is g(x) = (-2/5)·(x - 4)² + 6
The parent function of a quadratic equation is y = x²
A vertical translation is given by the following equation;
y = f(x) + b
A horizontal to the right by 'a' translation is given by an equation of the form; y = f(x - a)
A vertical reflection is given by an equation of the form; y = -f(x) = -x²
A narrowing is given by an equation of the form; y = b·f(x), where b < 1
Therefore, the transformations of g(x) from the parent function are;
g(x) is a reflection of the parent function, with the graph of g(x) being narrower by 2/5 than the graph of the parent function. The graph of g(x) is shifted right by 4 units and is then slides up by 6 units.
The profit maximization will be when the sum of the products will be greater. The maximum profit will be when x is 300 and y is 400. If we put in the equation :
