Answer:
6 units
Step-by-step explanation:
I will just assume that you made a typo when typing the question when saying AB is 6√3. Here is the solution if AB = 6√2.
Since it is given that ABC is a right triangle and x labels each of the legs, the triangle is a right isoceles triangle.
Now we can use the right isoceles triangle theorem to solve the problem. This theorem states that if a leg is "x" in a right isoceles triangle, then the hypotenuse is equal to x√2.
Here, the hypotenuse is equal to 6√2. To figure out the legs, you need to solve the equation 6√2 = x√2. It is solved here:
6√2 = x√2 (Divide by √2)
x = 6
The length of the legs are 6 units.
Answers:
- x = 4
- AB = 36
- BC = 36
- AC = 36
All three sides are 36 units long.
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Explanation:
Triangle ABC is equilateral, so all three sides are the same length.
Pick any two of those sides, set them equal to each other, and solve for x
AB = BC
8x+4 = 11x-8
8x-11x = -8-4
-3x = -12
x = -12/(-3)
x = 4
Use this x value to find each side. We should get the same value (if not, then an error occurred in solving for x).
- AB = 8x+4 = 8*4+4 = 32+4 = 36
- BC = 11x-8 = 11*4-8 = 44-8 = 36
- AC = 9x = 9*4 = 36
We get the same value for the three side lengths, so this confirms we have the correct x value.
1, 3, 5, 7. 1 and 3 they are vertical meaning they are congruent. 3 and 5 are alternate interior angles meaning they are congruent. 7 and 5 are vertical so they are congruent.
Answer:
18.7
Step-by-step explanation:
The Law of Cosines is 
, where c is the unknown side length of a triangle, a and b are the remaining two side lengths, and C is the angle opposite to side c. To answer this question just plug in the known values:
Simplify:
m≈18.665...
When rounded to the nearest tenth, m=18.7
Answer: 2nd diagram, explanation below
Step-by-step explanation:
Since it is 8 magnet students for 3 magic students, the second diagram is correct.
The second part, you would need to set up a system of equations:
Let m = magnet students and t = magic students
t + 25 = m
(8/3)t = m. Since m = m, substitute: t + 25 = (8/3)(t). Now solve for t: t = 8t/3 - 25,
t = (8t - 75)/3, in this step I turned 25 into 75/3 and place it with 8t so it doesn't change the value of the equation.
3t = 8t - 75, in this step I multiplied every term by 3 to eliminate the demoninator. Now I solve the final steps:
-5t = -75, 5t = 75
t = 15
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