16. Use the quadratic formula to solve the equation.
〖5x〗^2 - 47x = 156
18. What are the solutions to the equation x2 – 4x = -1?
19. Graph the set of points. Which model is most appropriate for the set of numbers?
(1,3), (0,0), (-3,3), (-1,-1), (-2,0)
Please answer
actually just answer 18 and 19
#18
x^2-4x+1 = 0
x = (4±√20)/2 = 2±√5
#19
Hmmm. You don't say what models you have been using. Arranging the points from left to right, we have
x y
------
-3 3
-2 0
-1 -1
0 0
1 3
The symmetry makes me want to try a quadratic with vertex at (-1,-1)
y = (x+1)^2 - 1
16. To solve the equation 5x^2 - 47x = 156 using the quadratic formula, we can rearrange the equation to have all terms on one side:
5x^2 - 47x - 156 = 0
Now we can identify the coefficients in the equation: a = 5, b = -47, and c = -156.
The quadratic formula states that the solutions to the equation ax^2 + bx + c = 0 can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Applying this formula to our equation:
x = (-(-47) ± √((-47)^2 - 4(5)(-156))) / (2(5))
Simplifying further:
x = (47 ± √(2209 + 3120)) / 10
x = (47 ± √5329) / 10
Now we can calculate the values of x:
x = (47 + √5329) / 10 = 11
x = (47 - √5329) / 10 = -3.12
Therefore, the solutions to the equation 5x^2 - 47x = 156 are x = 11 and x = -3.12.
18. To solve the equation x^2 - 4x = -1, we need to rearrange the equation to have all terms on one side:
x^2 - 4x + 1 = 0
Now we can identify the coefficients in the equation: a = 1, b = -4, and c = 1.
Using the quadratic formula, we have:
x = (-(-4) ± √((-4)^2 - 4(1)(1))) / (2(1))
Simplifying further:
x = (4 ± √(16 - 4)) / 2
x = (4 ± √12) / 2
Now we can calculate the values of x:
x = (4 + √12) / 2 = 3.73
x = (4 - √12) / 2 = 0.27
Therefore, the solutions to the equation x^2 - 4x = -1 are x = 3.73 and x = 0.27.
19. The given set of points is: (1,3), (0,0), (-3,3), (-1,-1), (-2,0).
To decide which model is most appropriate for the set of numbers, we need to examine the pattern among the points.
Let's plot these points on a graph to visualize the data.
Once we have the graph, we can determine if the points form a straight line, a curve, or show no predictable pattern.
To graph the set of points, we plot each ordered pair on a coordinate plane. After plotting all the points, we look for a pattern or trend among the points.
Based on the given set of points, when we plot them on a graph, we can see that the points form a straight line.
Therefore, the most appropriate model for the set of numbers (1,3), (0,0), (-3,3), (-1,-1), (-2,0) would be a linear model or a straight line.