Because line QS is outside the circle and only touches it at point S the line is a tangent line
We need to find m and b to find in the equation of a line:
y = mx + b
↑ <span>↑
slope y-intercept
To find m, the slope, we need to find the rise over the run of the line. You pick two points and use the y values finding the difference of them and do the same for the x values and put them on the bottom. Let's use the points (0, -2) and (4, 0):
</span>↑ ↑<span>
(x₁, y₁) (x₂, y₂)
m = (y</span>₂ - y₁)/(x₂ - x₁)
m = (-2 - 0)/(0 - 4)
m = (-2)/(-4)
m = 1/2
The slope is positive since the line is going upward from left to right.
Now we need b, the y intercept, where the line intersects with the y axis, simply by looking at the graph. b is -2.
Thus, the answer is C. y = 1/2x - 2.
Answer:
25 + 10h = 50+5h
Step-by-step explanation:
Black Diamond Ski Resort
25 + 10h
Bunny Hill Ski Resort
50+5h
Set them equal to each other to find when the cost is the same
25 + 10h = 50+5h
Answer:
a = 2/27
b = 13/27
Step-by-step explanation:
The given polynomial is presented as follows;
f(x) = a·x³ + b·x² + x + 2/3
Given that x + 3 is a factor, we have;
f(-3) = 0 = a·(-3)³ + b·(-3)² - 3 +2/3 = 0
-27·a + 9·b - 3 + 2/3 = 0
-27·a + 9·b = 7/3........(1)
Also we have
(a·x³ + b·x² + x + 2/3) ÷ (x + 2) the remainder = 5
Therefore;
a·(-2)³ + b·(-2)² + (-2) + 2/3 = 5
-8·a + 4·b - 2 + 2/3 = 5
-8·a + 4·b = 2 - 2/3 = 4/3........(2)
Multiplying equation (1) by 4/9 and subtracting it from equation (2), we have;
-8·a + 4·b - 4/9×(-27·a + 9·b) = 4/3 - 4/9 × 7/3
-8·a + 12·a = 8/27
4·a = 8/27
a = 2/27 ≈ 0.0741
imputing the a value in equation (1) gives;
-27×2/27 + 9·b = 7/3
-2 + 9·b = 7/3
9·b = 7/3 + 2 = 13/3
b = 13/27 ≈ 0.481.
Answer:
18.18%
Step-by-step explanation:
Percent change formula:
(new amount - old amount)/(old amount) * 100%
new amount: 6500
old amount: 5500
percent change:
(6500 - 5500)/5500 * 100% = 18.18%
