Answer:
Step-by-step explanation:
Given the equation of a line expressed as y = 3x-1, we are to find y = f(x) for the following values of x in the table.
If y = 3x-1, then f(x) = 3
When x = -1
f(-1) = 3(-1)-1
f(-1) = -3-1
f(-1) = -4
<em>Hence when x = -1, f(x) = -4</em>
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When x = 0
f(0) = 3(0)-1
f(0) = 0-1
f(0) = -1
<em>Hence when x = 0, f(x) = -1</em>
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When x = 2
f(2) = 3(2)-1
f(2) = 6-1
f(2) = 5
<em>Hence when x = 2, f(x) = 5</em>
Answer:
We have the equation:
(ax^2 + 3x + 2b) - (5x^2+bx-3c)= 3x^2 - 9
First, move all to the left side.
(ax^2 + 3x + 2b) - (5x^2+bx-3c) - 3x^2 + 9 = 0
Now let's group togheter terms with the same power of x.
(a - 5 - 3)*x^2 + (3 - b)*x + (2b + 3c + 9) = 0.
This must be zero for all the values of x, then the things inside each parenthesis must be zero.
1)
a - 5 - 3 = 0
a = 3 + 5 = 8.
2)
3 - b = 0
b = 3.
3)
2b + 3c + 9 = 0
2*3 + 3c + 9 = 0
3c = -6 - 9 = -15
c = -15/3 = -5
Then we have:
a = 8, b = 3, c = -5
a + b + c = 8 + 3 - 5 = 6
Answer:
D
Step-by-step explanation:
Before the increase, the length is 6 and the width is 5, so the area is 5×6 = 30.
After the increase, the length is x+6, the width is x+5, and the area is tripled: 30×3 = 90.
Therefore:
(x+6) (x+5) = 90
Since you are dealing with hypotenuse and opposites, you need to use sine.
sin = (opposite)/(hypotenuse)
sin(60) = (opposite)/20
sin(60) * 20 = 17.3
The length of the opposite side is approximately 17.3 centimeters