Please answer this giving brainliest and 20 points. If you say something weird i will make sure you get banned.
1 answer:
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<h3>Given</h3>
- ΔABC
- A(-3, -1), B(0, 3), C(1, 2)
- the length of the perimeter of ΔABC to the nearest tenth
The perimeter of a triangle is the sum of the lengths of its sides. The length of each side can be found using the Pythagorean theorem. Effectively, each pair of points is treated as the end-points of the hypotenuse of a right triangle with legs parallel to the x- and y-axes. The leg lengths are the differences betweeen the x- and y- coordinates of the points.
The difference of the x-coordinates of segment AB are 0-(-3) = 3. The y-coordinate difference is 3-(-1) = 4. So, the leg lengths of the right triangle whose hypotenuse is segment AB are 3 and 4. The Pythagorean theorem tells us
... AB² = 3² +4² = 9 +16 = 25
... AB = √25 = 5
You may recognize this as the 3-4-5 triangle often introduced as one of the first ones you play with when you learn the Pythagorean theorem.
LIkewise, segment AC has coordinate differences of ...
... C - A = (1, 2) -(-3, -1) = (4, 3)
These are the same leg lengths (in the other order) as for segment AB, so its length is also 5.
Segment BC has coordinate differences ...
... C - B = (1, 2) -(0, 3) = (1, -1)
The length of the line segment is figured as the root of the sum of squares, even though one of the coordinate differences is negative. The leg lengths of the right triangle used for finding the length of BC are the absolute value of these differences, or 1 and 1. Then the length BC is
... BC = √(1² +1²) = √2 ≈ 1.4
So the perimeter of the triangle ABC is
... AB + BC + AC = 5 + 1.4 + 5 = 11.4 . . . . perimeter of ∆ABC in units
_____
Please be aware that the advice to "round each step" is <em>bad advice,</em> in general. For real-world math problems, you only round the final result. You always carry at least enough precision in the numbers to ensure that there will not be any error in the final rounding.
In this problem, the only number that is not an integer is √2, so it doesn't really matter.
Answer:
(A)
As per the given condition.
You have 2 equations for y.
i,e y =8x and y= 2x+2
then, they will intersect at some point where y is the same for both equations.
That is why in equation y=8x you exchange y with other equation you got which is y=2x+2 once you do this you will have
8x = 2x+2 and the solution of which will satisfy both equation.
(B)
8x = 2x + 2
to find the solutions take the integer values of x between -3 and 3.
x = -3 , then
8(-3) = 2(-3) +2
-24 = -6+2
-12 = -4 False.
similarly, for x = -2
8(-2) = 2(-2)+2
-16 = -2 False
x = -1
8(-1) = 2(-1)+2
-8= 0 False
x = 0
8(0) = 2(0)+2
0= 2 False
x = 1
8(1) = 2(1)+2
8= 4 False
x = 2
8(2) = 2(2)+2
16 = 6 False
x = 3
8(3) = 2(3)+2
24 = 8 False
there is no solution to 8x = 2x +2 for the integers values of x between -3 and 3.
(C)
The equations cab be solved graphically by plotting the two given functions on a coordinate plane and identifying the point of intersection of the two graphs.
The point of intersection are the values of the variables which satisfy both equations at a particular point.
you can see the graph as shown below , the point of intersection at x =0.333 and value of y = 2.667
