Triangle ABC is an isosceles triangle.
Solution:
Given data:
∠ABC = 70° and ∠ACD = 55°
<em>If two parallel lines are cut by a transversal, then alternate interior angles are congruent.</em>
m∠BAC = m∠ACD
m∠BAC = 55°
<em>Sum of the angles in a straight line add up to 180°.</em>
m∠ACD + m∠ACB + m∠ABC = 180°
55° + m∠ACB + 70° = 180°
m∠ACB + 125° = 180°
Subtract 125° from both sides, we get
m∠ACB = 55°
In triangle ABC,
∠BAC = 55° and ∠ACB = 55°
∠BAC = ∠ACB
Two angles in the triangle are equal.
Therefor triangle ABC is an isosceles triangle.
Answer:
300 percent change
Step-by-step explanation:
300 is 400 percent of 75.(75x4 is 300.) Therefore, the percent change is
400 - 100 = 300.
Answer:
D is false
Step-by-step explanation:
Answer:
![p=10\sqrt[3]{54}x^2](https://tex.z-dn.net/?f=p%3D10%5Csqrt%5B3%5D%7B54%7Dx%5E2)
Step-by-step explanation:
We are given parallelogram
Since, two opposite sides of any parallelogram are always equal
Let's assume first side =a
second side =b
so, we get
![a=2\sqrt[3]{54}x^2](https://tex.z-dn.net/?f=a%3D2%5Csqrt%5B3%5D%7B54%7Dx%5E2)
![b=3\sqrt[3]{54}x^2](https://tex.z-dn.net/?f=b%3D3%5Csqrt%5B3%5D%7B54%7Dx%5E2)
now, we can find perimeter
perimeter=2a+2b
so, we get
![p=2(2\sqrt[3]{54}x^2)+2(3\sqrt[3]{54}x^2)](https://tex.z-dn.net/?f=p%3D2%282%5Csqrt%5B3%5D%7B54%7Dx%5E2%29%2B2%283%5Csqrt%5B3%5D%7B54%7Dx%5E2%29)
we can simplify it
![p=4\sqrt[3]{54}x^2+6\sqrt[3]{54}x^2](https://tex.z-dn.net/?f=p%3D4%5Csqrt%5B3%5D%7B54%7Dx%5E2%2B6%5Csqrt%5B3%5D%7B54%7Dx%5E2)
................Answer
<span>let 2x be the length of rectangw where x is value of x of point on parabola width is represented as y is the length.
Area = 2x*y = 2x (5-x^2) = 10x -2x^3
maximize Area by finding x value where derivative is zero
dA/dx = 10 -6x^2 = 0
--> x = sqrt(5/3)
optimal dimensions: length = 2sqrt(5/3) width = 10/3</span>