Answer:
Isosceles
Step-by-step explanation:
In order to figure what type of triangle this is out, we need to start by plotting the given points. That will help us visualize the triangle better and see if our conclusions make sense. (See attached picture).
Once we got the triangle, the strategy to follow is to use the distance between two points formula to see what the measurement of each side of the triangle is. This will help us determine if 2, 3 or none of the sides of the tirangle are the same.
The distance formula is the following:
so now we can find the desired distances, let's start with the distance between P and Q:
which yields:
next, let's find the distance between P and R:
which yields:
and finally the distance between Q and R:
which yields:
As you may see from the result, only two of the three sides are the same, |PQ| and |PR|, so this will be an Isosceles triangle.
Yards= 42 2/3 yd=42 + 2/3 yd=(42*3 + 2)/3 yd=128/3 yd
Gallons=1 1/3 Gallons=1+1/3 gallons=(3*1+1)/3 gallons=4/3 gallons.
Rate=number of yards / number of gallons.
Rate=(128/3 yd) / (4/3 gallons)=32 yd/gallon.
Answer: Angela´s rate=32 yards / gallons
By Sine Rule
a/sinA = b/sinB = c/sinC
Given a = 3, b = 4, A = 76°
<span>43sin76° = 4/sinB
</span>
==> sinB = 1.195380945
<span>
But sine function is only defined in the range [-1, 1], so there's no solution.
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1) Parallel lines have equal slopes.
We need to find the slope of the given line by solving for y.
5x - 15y = 30
-15y = -5x + 30
y = (1/3)x - 2
The slope of the given line is 1/3, so the slope of the parallel line is also 1/3.
2) Line 1 has slope 2/3.
Line 2 has slope 2/3.
3) Line 1 is a vertical line through x = 2. Line 2 is a horizontal line through y = -5. The lines are perpendicular.
4) The given line can is solved for y, so we can see its slope is -5/2. The slopes of perpendicular lines are negative reciprocals. The perpendicular line has slope 2/5. We have point (5, 0) which is (x1, y1) in the slope-point formula.
y - 0 = (2/5)(x - 5)
y = 2/5 x - 2
5) The given equation has slope -3. To find the negative reciprocal, write the slope as a fraction, flip it, and change the sign.
Slope of perpendicular line is 1/3.
Since there are 100 squares and 6 aren’t colored in, the answer should be .94. It’s kind of like counting a dollar since 100 pennies = a dollar.
