In a triangle, the measure of an angle is in the same order of size as the length of the opposite side. The smallest angle is opposite the shortest side. The largest angle is opposite the longest side. The middle-sized angle is opposite the middle-sized side.
Also, in a triangle, the sum of the measures of the interior angles is 180.
We can now calculate the measures of the three angles by writing and solving an equation.
m<A + m<B + m<C = 180
9x - 7 + 7x - 9 + 28 - 2x = 180
Collect like terms on the left side.
9x + 7x - 2x - 7 - 9 + 28 = 180
14x + 12 = 180
Subtract 12 from both sides.
14x = 168
x = 12
Now that we know x, we can find the measure of each angle.
m<A = 9x - 7 = 9(12) - 7 = 108 - 7 = 101
m<B = 7x - 9 = 7(12) - 9 = 84 - 9 = 75
m<C = 28 - 2x = 28 - 2(12) = 28 - 24 = 4
(Quick check: Add the angles measures: 101 + 75 + 4 = 180. The sum is 180 as it should be.)
Now that we know the angle measures, the opposite sides are in the same order of size.
AB < AC < BC
The sides are, in increasing order of length:
AB, AC, BC
Answer:
If the lifetime of batteries in the packet is 40.83 hours or more then, it exceeds for 5% of all packages.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 15
Standard Deviation, σ = 1
Sample size = 4
Total lifetime of 4 batteries = 40 hours
We are given that the distribution of lifetime is a bell shaped distribution that is a normal distribution.
Formula:
Standard error due to sampling:
We have to find the value of x such that the probability is 0.05
P(X > x) = 0.05
Calculation the value from standard normal z table, we have,
Hence, if the lifetime of batteries in the packet is 40.83 hours or more then, it exceeds for 5% of all packages.
Remember that the standard form of a line equation is y = mx + b. Since you need a line that is parallel to y = 5x - 2, the first thing to do is use the same slope (m), which is 5 in this case.
The new line would look like this: y = 5x + b. I use "b" instead of -2, since we'll calculate a "b" for the new line by substituting the given point of (2, -1) into y = 5x + b.
-1 = 5*(2) + b
b = -11
The parallel line that goes through (2,-1) is y = 5x - 11
The new line is the blue, on the right. Note that it is parallel to the original (green) line and also intersects at (2, -1). (Each chart is is 0.5 unit).
Answer:
hehsbsbshsi
Step-by-step explanation:
ksjsnsbsbsb