Call the length
and the width
We are told:
1. "<span>The length of a rectangle is 3 times its width." i.e.:
2. "</span><span>The rectangle’s width is 4 m." i.e.:
So, by substitution we have:
Then we can use our area formula:
</span>
Answer:
114°
Step-by-step explanation:
mesure of 6 is equal to that of 8,both inclined at same angle
Answer:
Step-by-step explanation:
Perpendicular bisector of the chord connecting the the points (-1,2) and (2,3) is also passing through the center of the circle.
We'll find the equation of the line and solve the system to find the center.
<u>Midpoint of the chord:</u>
- ((-1 + 2)/2, (2 + 3)/2) = (0.5, 2.5)
<u>Equation of the line through chord (-1,2) and (2,3):</u>
- m = (3 - 2)/(2 + 1) = 1/3
- y - 2 = 1/3(x + 1)
- y = 1/3x + 7/3
<u>Perpendicular bisector is:</u>
- y - 2.5 = -3(x - 0.5)
- y = -3x + 4 >> (1)
<u>And the given line is:</u>
- 2x - 3y + 1 = 0
- y = 2/3x + 1/3 >> (2)
<u>Solve the system:</u>
- -3x + 4 = 2/3x + 1/3
- -9x + 12 = 2x + 1
- 11x = -11
- x = -1
<u>Find y:</u>
- y = -3(-1) + 4 = 3 + 4 = 7
The center is (-1, 7)
<u>Find the radius, the distance from center to one of points on circle </u>
- (-1, 7) and (-1, 2)
- 7 - 2 = 5
<u>The equation of circle is:</u>
- (x + 1)² + (y - 7)² = 5²
- (x + 1)² + (y - 7)² = 25
Since she wrote the numbers 1-100, we know that the probability for one number is 1/100.
If she selects a number without looking, it's a 1/100 chance she'll pull out one specific number.
However, here we need to find the probability of a number below 5. There are four numbers below 5 from the range to 1-100 and they are 1, 2, 3, and 4.
Therefore, since there are 4 numbers below 5, we have a 4/100 chance of Jane pulling out a number below 5.
In simplified terms it would be
In decimal form, it would be 0.04