4.000 plus 200 plus 90 plus 3
Answer:
27 =x
Step-by-step explanation:
We can use the triangle angle bisector theorem
x+8 2x-5
-------- = ----------
10 14
Using cross products
14 (x+8) = 10 (2x-5)
Distribute
14x+112 = 20x -50
Subtract 14x from each side
14x-14x+112 = 20x-14x -50
112 = 6x - 50
Add 50 to each side
112+50 = 6x+50
162 = 6x
Divide by 6
162/6 = 6x/6
27 =x
The two-column proves that ΔMNP ≅ ΔNPQ by the ASA Congruence Theorem is shown in the image attached below (see attachment).
<h3>What is the ASA Congruence Theorem?</h3>
The ASA congruence theorem states that two triangles that have two pairs of congruent angles and a pair of included congruent sides are considered congruent triangles.
We are given that both triangles have two pairs of congruent angles, by the reflexive property, we can state that QP ≅ QP in each triangle.
By this, it means both triangles have two pairs of congruent angles and a pair of congruent included sides. Therefore, ΔMNP ≅ ΔNPQ by the ASA Congruence Theorem.
Thus, the two-column proves that ΔMNP ≅ ΔNPQ by the ASA Congruence Theorem is shown in the image attached below (see attachment).
Learn more about ASA congruence theorem on:
brainly.com/question/2102943
The correct answer is: Option (D) x = 72°
Explanation:
When two lines are crossed by another line, the angles in matching corners are called <em>corresponding angles</em>. When the two lines are <em>parallel</em>, the corresponding angles are <em>equal</em>.
Here in this case, the two lines are "AB" and "CD", and both are parallel and are crossed by the line; therefore, <em>the corresponding angles will be the same</em>.
Since the first corresponding angle is 72°, the second angle <em>x </em>will be 72° as well. The correct answer is: x = 72° Option (D).
The markup is $38.80.
What I did:
markup rate=40%
40%=0.4
0.4*97=38.80.