The distance between (-5 , -8) and (-1 , -16) is 8.9 units ⇒ 1st answer
Step-by-step explanation:
The distance between points and
is
To find the distance between two points
- Chose one of the two point to be
- Use the other point to be
- Substitute them in the rule of the distance
∵ The first point is (-5 , -8)
∵ the second point is (-1 , -16)
∴ = -5 and = -1
∴ = -8 and = -16
- Substitute these values in the rule of the distance
∵
∴
∴
∴
∴
∴ d = 8.9 units
The distance between (-5 , -8) and (-1 , -16) is 8.9 units
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Answer:
9·x² - 36·x = 4·y² + 24·y + 36 in standard form is;
(x - 2)²/2² - (y + 3)²/3² = 1
Step-by-step explanation:
The standard form of a hyperbola is given as follows;
(x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1
The given equation is presented as follows;
9·x² - 36·x = 4·y² + 24·y + 36
By completing the square, we get;
(3·x - 6)·(3·x - 6) - 36 = (2·y + 6)·(2·y + 6)
(3·x - 6)² - 36 = (2·y + 6)²
(3·x - 6)² - (2·y + 6)² = 36
(3·x - 6)²/36 - (2·y + 6)²/36 = 36/36 = 1
(3·x - 6)²/6² - (2·y + 6)²/6² = 1
3²·(x - 2)²/6² - 2²·(y + 3)²/6² = 1
(x - 2)²/2² - (y + 3)²/3² = 1
The equation of the hyperbola is (x - 2)²/2² - (y + 3)²/3² = 1.
This construction shows the creation of tangents to the circle with a point outside the circle.
The next step would be the connect the point p with the two intersection points of the arcs on the circle.
Hope this helps :)
Answer:
Step-by-step explanation:
21-15=6
15 is given
6 is the difference
21-15=6
<span>0.0087, or 0.87%
In order to solve this problem, you first need to determine how many standard deviations from the norm you are. You do this by subtracting the mean from the number you have and then divide the result by the standard deviation.
127 - 100 = 27
27 / 11.35 = 2.378854626
So you're about 2.379 standard deviations above the mean. Using a standard normal table (usually good to 2 decimal digits), or you can use an online calculator or the equivalent.
Looking up 2.38 in a standard normal table, I get a value of 0.9913 which is the probability of getting a value LESS than the standard deviation I looked up. Since we're looking for the probability of getting a LARGER value, subtract the lookup value from 1, giving:
1 - 0.9913 = 0.0087 = 0.87%
Using an online calculator for the standard deviation of 2.378854626, I get the return value of 0.9913167383 which is basically the same result as using a normal table except for a few extra decimal places.
In any case, the probability of a randomly selected monthly cell phone bill being more than $127 is 0.0087, or 0.87%</span>