<u>AREA OF THE TRIANGLE
AREA OF THE ARC</u>
<u>
</u>
<u>A</u><u>R</u><u>E</u><u>A</u><u> </u><u>OF</u><u> </u><u>THE</u><u> </u><u>FIGURE</u>
96+100.53=<u>196.53</u><u>c</u><u>m</u><u>^</u><u>2</u>
The value of x equals 24
<h2>
Explanation:</h2>
In order to find the solution to this problem, we know that ∠ABC and ∠DBE are vertical angles because they share the same vertex. Eureka! Vertical angles are always congruent meaning they measure the same value. So, it is true that:
![(3x-14)^{\circ}=(2x+10^{\circ}) \\ \\ 3x-14=2x+10 \\ \\ Solving \ for \ x: \\ \\ 3x-2x=14+10 \\ \\ \boxed{x=24}](https://tex.z-dn.net/?f=%283x-14%29%5E%7B%5Ccirc%7D%3D%282x%2B10%5E%7B%5Ccirc%7D%29%20%5C%5C%20%5C%5C%203x-14%3D2x%2B10%20%5C%5C%20%5C%5C%20Solving%20%5C%20for%20%5C%20x%3A%20%5C%5C%20%5C%5C%203x-2x%3D14%2B10%20%5C%5C%20%5C%5C%20%5Cboxed%7Bx%3D24%7D)
<h2>Learn more:</h2>
Characteristics of vertical angles: brainly.com/question/13410134
#LearnWithBrainly
I wish I could post a link to Wkipedia because I found a good explanation of corresponding angles.
7 and 3 are corresponding angles.
Hello there! The answer would be B) translation and dilation.
When shapes are congruent, they are the same shape and size. To be changed where the shapes are no longer congruent , the size or shape has to change. In the options you've provided, B would be the correct option since it is the only one that includes changing size, when mentioning dilation (or making something bigger, hence changing it's size). In the other options, which include reflection and translations and rotations, they just change the placement of the shape, but other than that the shape is the same as the others.
I hope this helps, have a great day!
Answer:
![x=7,\\y=4\sqrt{2}](https://tex.z-dn.net/?f=x%3D7%2C%5C%5Cy%3D4%5Csqrt%7B2%7D)
Step-by-step explanation:
Draw an auxiliary line in the trapezoid forming a triangle and a rectangle. The dimensions of the rectangle are 3 x 4, so the length of the auxiliary line must be 4.
The auxiliary line also creates a 45-45-90 triangle. The auxiliary line itself makes up one leg of the triangle, and since we know it is 4, we can use the Pythagorean Theorem to find y:
![4^2+4^2=y^2,\\y^2=32,\\y=\sqrt{32}=\boxed{4\sqrt{2}}](https://tex.z-dn.net/?f=4%5E2%2B4%5E2%3Dy%5E2%2C%5C%5Cy%5E2%3D32%2C%5C%5Cy%3D%5Csqrt%7B32%7D%3D%5Cboxed%7B4%5Csqrt%7B2%7D%7D)
The length of x can be found by adding the bottom leg of the 45-45-90 triangle and the bottom dimension of the rectangle:
![x=4+3=\boxed{7}](https://tex.z-dn.net/?f=x%3D4%2B3%3D%5Cboxed%7B7%7D)