Answer:
Rotate the triangle until it makes a right angle. It should be somewhere around the coordinates (2,-1)
Step-by-step explanation:
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Answer:
∫₂³ √(1 + 64y²) dy
Step-by-step explanation:
∫ₐᵇ f(y) dy is an integral with respect to y, so the limits of integration are going to be the y coordinates. a = 2 and b = 3.
Arc length ds is:
ds = √(1 + (dy/dx)²) dx
ds = √(1 + (dx/dy)²) dy
Since we want the integral to be in terms of dy, we need to use the second one.
ds = √(1 + (8y)²) dy
ds = √(1 + 64y²) dy
Therefore, the arc length is:
∫₂³ √(1 + 64y²) dy
Answer:
a). Area = 54 square units
b). Perimeter = 33.7 units
Step-by-step explanation:
Vertices of the triangle ABC are A(-4, -2), B(1, 7) and C(8, -2).
(a). Area of the triangle ABC =
(Absolute value)
By substituting the values from the given vertices,
Area = ![\frac{1}{2}[(-4)(7+2)+(1)(-2+2)+8(-2-7)]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5B%28-4%29%287%2B2%29%2B%281%29%28-2%2B2%29%2B8%28-2-7%29%5D)
= ![\frac{1}{2}[-36+0-72]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5B-36%2B0-72%5D)
= 
= (-54) unit²
Therefore, absolute value of the area = 54 square units
(b). Distance between two vertices (a, b) and (c, d)
d = 
AB = 
= 
= 10.295 units
BC = 
= 
= 11.402 units
AC = 
= 12 units
Perimeter of the triangle = AB + BC + AC = 10.295 + 11.402 + 12
= 33.697
≈ 33.7 units
Adding to the solutions and points gotten, we can further say that: Opposite angles of the parallelogram are congruent, by the theorem of Side Angle side (SAS) (i.e angle AEB = CED )
<h3>Meaning of Congruence</h3>
Congruence can be defined as a term used to depict a state of two object being equal, in harmony, and in agreement.
The congruence of a shaped is verified by some laws which they both must satisfy.
In conclusion, the triangle is congruent with the fact stated in the question and the additional fact added above.
Learn more about congruence: brainly.com/question/3168048
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Answer:
They show as intersections with the x-axis
Step-by-step explanation:
For example, the quadratic y = x² - 1 has roots x = -1 and x = 1.
They show on the graph as intersections of the parabola with the x axis at x = -1 and x = 1.