Answer:
c.
Step-by-step explanation:
Negative numbers are always less than positive numbers. 3/10 is less that 1/4:
Making the answer c.
Answer:
It is not a right triangles because 15^2 + 13^2 is NOT EQUAL to 19^2
let x, y, and z be the angles inside the triangle.
Law of cosines says:
19^2 = 13^2 + 15^2 - 2(13)(15)cos x
361 = 169 + 225 - 390 cos x
-33 = -390 cos x
-33/-390 = cos x
11/130 = cos x
x = inverse cosine (11/130)
= 85.14609471338569.....
Per law of sines:
sin x/19 = sin y / 13
(13/19)sinx = sin y
inverse_sine ( (13/19) sin x) = y
y = 42.9810733896016548....
Per law of sines
sin x/19 = sin z / 15
z = inverse_sine( (15/19) sin x)
= 51.8728352950227805....
So it is an acute triangle and yes, these angles add up to 180
Answer:
About 95 miles
Step-by-step explanation:
Let's set up a proportion using the following set up:
miles / gallons = miles / gallons
We know the car can travel 38 miles on 2.4 gallons of gas.
38 miles / 2.4 gallons = miles/ gallons
We don't know how far the car can travel on 6 gallons. Therefore, we can say the car travels x miles on 6 gallons of gas.
38 miles / 2.4 gallons = x miles /6 gallons
38/2.4=x/6
We want to find x (miles for 6 gallons). Therefore, we must isolate x.
x is being divided by 6. The inverse of division is multiplication. Multiply both sides by 6.
6*(38/2.4)=(x/6)*6
6*(38/2.4)=x
6*15.8333333=x
94.9999998=x
Let's round to the nearest whole number. The 9 in the tenth place tells us to round up.
95 ≈x
x ≈95 miles
The car can travel about 95 miles on 6 gallons of gas.
This is a fairly tedious problem. The only way to solve that I see is to simply list out all the possible cases and go through each one by one. You'll use the triangle inequality theorem to see if the triangles can be formed. The theorem says that a+b > c must be true for all sets of pairs. In other words, take any two sides and add them up. The sum must be greater than the third side.
Going through all the combos possible (that I could find), this is what I got
Blue9,Green7,Orange4
Blue9,Green7,Purple12
Blue9,Green7,Red3
Blue9,Green7,Yellow5
Blue9,Orange4,Purple12
Blue9,Purple12,Yellow5
Green7,Orange4,Yellow5
Green7,Red3,Yellow5
Orange4,Red3,Yellow5
In all, I count 9 cases. So the answer to problem 1 is 9.
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For problem 2, the best way may be to pick two segments at a time instead of one. However, I have a feeling that will take just as long as the first method. I haven't tried it out. Even though going through the rods one at a time takes a while, it's probably the best option so you don't overlook any cases.
