Answer:
(5,2,2)
Step-by-step explanation:
-3x+4y+2z = -3
2x-4y-z=0
y = 3x-13
Multiply the second equation by 2
2*(2x-4y-z)=0*2
4x -8y -2z =0
Add this to the first equation to eliminate z
-3x+4y+2z = -3
4x -8y -2z =0
-------------------------
x -4y = -3
Take the third equation and substitute it in for y
x - 4(3x-13) = -3
Distribute the 4
x - 12x +52 = -3
Combine like terms
-11x +52 = -3
Subtract 52 from each side
-11x +52-52 = -3-52
-11x = -55
Divide by -11
-11x/-11 = -55/-11
x=5
Now we can solve for y
y =3x-13
y =3*5 -13
y = 15-13
y=2
Now we need to find z
2x-4y-z=0
2(5) -4(2) -z=0
10-8 -z=0
2-z=0
Add z to each side
2-z+z= 0+z
2=z
x=5, y=2, z=2
(5,2,2)
What i think the answer is 6.66 because u multiply 1/3 by 20
Answers:
x = 24
y = 8√3
Explanation:
1) Since, the given triangle is a right triangle, and you have both an angle and the hypotenuse length, you can use some trigonometric ratios to find the variables.
2) The variables given represent:
x: adjacent-leg to angle 30°
y: opposite length to angle 30°
3) sine ratio:
sin 30° = opposite-leg / hypotenuse = y / (16√3)
⇒ y = 16√3 sin 30° = 16√3 × (1/2) = 8√3
4) cosine ratio
cos 30° = adjacent-leg / hypotenuse = x / (16√3)
⇒ x = 16√3 cos 30° = 16√3 (√3 / 2) = 16 × 3 / 2 = 24
The distances between the given pairs of points are:
- (-8, -2) and (6, -1); d = 14.04
- (-4, 5) and (4,0); d = 9.85
<h3>
How to find the distance between two points?</h3>
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √( (x₁ - x₂)^2 - (y₁ - y₂)^2)
1) The first pair of points is (-8, -2) and (6, -1), using the above formula we can see that the distance is:
d = √( (-8 - 6)^2 - (-2 +1)^2) = 14.04
2) The second pair is (-4, 5) and (4,0), and using the distance formula, we get:
d = √( (-4 - 5)^2 - (4 - 0)^2) = 9.85
If you want to learn more about the distance between points:
brainly.com/question/7243416
#SPJ1
The histogram for the data is given at the end of this answer.
<h3>What is an histogram?</h3>
An histogram is a graph that shows the number of times each element of x was observed.
In this problem:
- The elements of x are given by the time in hours.
- The histogram shows the number of runners that finished the race in x hours.
Hence, the graph given at the end of this answer is the histogram.
You can learn more about histogram at brainly.com/question/2962546
