Answer:
m∠ABC = m∠BED; Corresponding Angles Theorem
Step-by-step explanation:
<u>Given:</u> line BC is parallel to line ED m∠ABC = 70° m∠CED = 30°
<u>Prove:</u> m∠BEC = 40°
Statement Justification
1. line BC is parallel to line ED - Given
2. m∠ABC = 70° - Given
3. m∠CED = 30° - Given
4. m∠BEC + m∠CED = m∠BED - Angle Addition Postulate
5. m∠ABC = m∠BED - Corresponding Angles Theorem
6. m∠BEC + 30° = 70° - Substitution Property of Equality
7. m∠BEC = 40° Subtraction Property of Equality
Sin2x = 2sinxcosx;
cos2x = (cosx)^2 - (sinx)^2;
tan2x = (sin2x)/(cos2x);
cosx = 5/13 from formula (sinx)^2 + (cosx)^2 = 1;
=> sin2x = 120/169;
.................................
Answer and Step-by-step explanation:
First, we need to find out the circumference of the circle.
We know that the circle has a radius of 1, and that we are finding the circumference. We'll use the circumference equation of a circle.
2
r
<u>Plug in 1 for r.</u>
= 
= circumference of circle
<u>Now, multiply the answer (the circumference) by 4 to get the perimeter of the square.</u>
<u /> x 4 = 
= perimeter of square
<u>Now, divide the perimeter by 4 to get what the side of the square is.</u>
<u /> ÷ 4 =
<u>Now, multiply </u><u> by </u><u> (side times side) to get the area.</u>
x = 
The answer is A.
<em><u>#teamtrees #PAW (Plant And Water)</u></em>
<em><u>I hope this helps!</u></em>
<em><u>Brainliest is appreciated,</u></em>
V(p) = x-n, where V(p) is the volume after the boxes have been together, x is the volume of the larger box, and n is the volume of the smaller box.
x = 15 cm x 25 cm x 20 cm = 7500 cubic centimeters (cm^3)
n = 10 cm x 10 cm x 10 cm = 1000 cm^3
V(p) = 7500 - 1000 = 6500 cm^3
So your answer is 6500 cubic centimeters.
Answer:
AC ≅ AE
Step-by-step explanation:
According to the SAS Congruence Theorem, for two triangles to be considered equal or congruent, they both must have 2 corresponding sides that are of equal length, and 1 included corresponding angle that is of the same measure in both triangles.
Given that in ∆ABC and ∆ADE, AB ≅ AD, and <BAC ≅ DAE, <em>the additional information we need to prove that ∆ABC ≅ ADE is AC ≅ AE. </em>This will satisfy the SAS Congruence Theorem. As there would be 2 corresponding sides that are congruent, and 1 corresponding angle in both triangles that are congruent to each other.
