For a better understanding of the solution given here please find the attached file which has the relevant diagram.
To answer this question we will have to make use of <u>the Isosceles Triangle Theorem</u> which states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. Thus, as a corollary we know that is EF is the angle bisector of the vertex angle ∠E, then, EF is the perpendicular bisector of the of the base DK.
Please follow the diagram of a complete understanding of the logic and the solution.
As EF is the angle bisector as given in the question, thus we will have:
.
Also, from the Theorem we know that KF will be half of DK and thus, KF will be:
centimeters.
Likewise, from the same theorem we have: 
Answer: the awnser is b 22.2.
Step-by-step explanation: have a nice day
The number of ways of picking up a red cube out of 12 cubes are 5/12. Number of ways of picking up a second red cube is 4/11.
<span>Thus probability of picking up 2 red cubes = 5/12 * 4/11 = 20/121.
20 / 121 = .165 or .17
So the probability of Celinda getting two red cubes is .17.</span>
Answer:
2) d. 60°
3) a. AB
Step-by-step explanation:
<u>Question 2</u>
ΔABC and ΔCDA are <u>congruent</u> because:
- they are both <u>right triangles</u>
- they <u>share one side</u> (AC)
- their hypotenuse are <u>parallel</u> (marked by the arrows)
This means the corresponding side lengths and angles are equal.
Therefore,
∠CDA = ∠ABC
⇒ x = 60°
<u>Question 3</u>
The <u>hypotenuse</u> is the <u>longest side</u> of a <u>right triangle</u> - the side opposite the right angle (the right angle is shown as a small square).
Therefore, the hypotenuse of ΔABC is the line AB.
I hope this is correct
Simplifying (2x + -1)(x + -3) = 18 Reorder the terms: (-1 + 2x)(x + -3) = 18 Reorder the terms: (-1 + 2x)(-3 + x) = 18 Multiply (-1 + 2x) * (-3 + x) (-1(-3 + x) + 2x * (-3 + x)) = 18 ((-3 * -1 + x * -1) + 2x * (-3 + x)) = 18 ((3 + -1x) + 2x * (-3 + x)) = 18 (3 + -1x + (-3 * 2x + x * 2x)) = 18 (3 + -1x + (-6x + 2x2)) = 18 Combine like terms: -1x + -6x = -7x (3 + -7x + 2x2) = 18 Solving 3 + -7x + 2x2 = 18 Solving for variable 'x'. Reorder the terms: 3 + -18 + -7x + 2x2 = 18 + -18 Combine like terms: 3 + -18 = -15 -15 + -7x + 2x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -15 + -7x + 2x2 = 0 Factor a trinomial. (-3 + -2x)(5 + -1x) = 0