y = x³ + 3x² - x - 3
0 = x³ + 3x² - x - 3
0 = x²(x) + x²(3) - 1(x) - 1(3)
0 = x²(x + 3) - 1(x + 3)
0 = (x² - 1)(x + 3)
0 = (x² + x - x - 1)(x + 3)
0 = (x(x) + x(1) - 1(x) - 1(1))(x + 3)
0 = (x(x + 1) - 1(x + 1))(x + 3)
0 = (x - 1)(x + 1)(x + 3)
0 = x - 1 or 0 = x + 1 or 0 = x + 3
+ 1 + 1 - 1 - 1 - 3 - 3
1 = x or -1 = x or -3 = x
Solution Set: {-3, -1, 1}
Okay, so I'm almost positive the slope is m=1/1. I know this because the line rises one and runs one.
Answer:
Step-by-step explanation:
As the two figure are the image and pre-image of a dilation.
Considering the left sided triangle is original and right sided triangle ( smaller one) is the image.
As one of the sides of the left triangle (original figure) is 4 in. And the corresponding length of the side on the right triangle (image of the figure) is 2 in.
It means the image of the side (2 in) is obtained when the side (4 in) of the original object is dilated by a scale factor of 1/2. In other words, the side of the image (2 in) is obtained multiplying the side (4 in) of original figure by 1/2. i.e. 4/2 = 2 in
Lets determine the missing side of the right side triangle by the same rule.
As the original object has one of the sides is 5 in and the corresponding side of the image has x in. As the original figure is dilated by a scale factor of 1/2. so the missing side of x will be: x = 5/2 = 2.5
So, the value of x will be 2.5
Similarly, the original object has one of the sides with length (y + 1 in). As the As the original figure is dilated by a scale factor of 1/2. As the corresponding length of the side of the image triangle is 3 in.
so
y + 1 = 2(3) ∵ 3 in (image side) is multiplied by 2
y + 1 = 6
y = 6 - 1
y = 5
So, the value of y = 5
Therefore,
Answer: The amount of Karen's bill = $ 60
Step-by-step explanation:
Given : The expression 10+0.25m can be used to determine the amount o, where <em>m =</em> The number of minutes she talks.
If she talks for 200 minutes in one month, then put m= 200 in the above expression we will get the amount of Karen's bill = 10+0.25(200)
= 10+ 50
= 60
Hence, the amount of Karen's bill = $ 60
