Answer: At least 3
Step-by-step explanation:
Lets solve this problem by the pidgeon hole principle. Suppose that Matt pulls out 2 socks, if he gets a matching pair then he is done and that's it. But now suppose that he gets one black sock and one white sock, if he then pulls out a third sock it will be either white or black, in either case he would have gotten with a 100% certainty a matching pair, since he already has a black and a white sock. So the minimum number to ensure he gets a matching pair is 3 socks.
Answer:
56 is the other number
Step-by-step explanation:
let the first number be a
the other number is 5/14 from the question
a x 5/14 = 20
5a/14 = 20
5a = 14 x 20 = 280
a = 280/5 = 56
Part A: A pair of similar triangles is triangle DEF and triangle GFD.
Part B: Traingle DEF ~ triangle GFD by the AA Similarity Theorem
Part C: By applying the Leg Rule, the length of segment ED = 4 units.
<em><u>Recall:</u></em>
- Based on the Angle-Angle Similarity Theorem (AA) two triangles that have two pairs of congruent triangles can be proven to be similar to each other.
- In a right triangle where the altitude intersects the hypotenuse, the Leg Rule applies, which is: Hypotenuse/Leg = Leg/Part
The Figure of the given triangle DEF is shown in the attachment below.
<em><u>Part A: A Pair of Similar Triangles</u></em>
A pair of similar triangles are traingle DEF and triangle GDF
<em><u>Part B: Reason for Similarity</u></em>
Triangle DEF and GDF have two pairs of congruent angles, ∠EDF ≅∠DGF and ∠EFD ≅∠GFD.
- Therefore, based on the AA Similarity Theorem, Traingle DEF ~ Triangle GDF.
<em><u>Part C: Length of Segment ED</u></em>
Given the following,
- EF = 8 (Hypotenuse)
- EG = 2 (Part)
- ED = ? (Leg)
Thus:
8/ED = ED/2 (Leg Rule)
ED² = (8)(2)
ED² = 16
- Find the square root of both sides
ED = 4
Learn more about AA Similarity Theorem on:
brainly.com/question/24147586
<u>Rectangle</u>
3 * 8 = 24
<u>Triangle</u>
4 * 3 = 12
12 / 2 = 6
Now add those two areas together, and you get 30
Answer:
z = 69°
Step-by-step explanation:
The sum of all interior angles in a quadrilateral is 360°, and a right angle is worth 90°. We're given the values of the interior angles as 90, 122, 79, and z degrees.
- We can solve this question algebraically with the equation
Step 1: Combine like terms.
Step 2: Subtract 291 from both sides.
Step 3: Check if solution is correct.
Therefore, z = 69°.
Have a lovely rest of your day/night, and good luck with your assignments! ♡