Answer:
SSS is the congruence theorem that can be used to prove Δ LON is congruent to Δ LMN ⇒ 1st answer
Step-by-step explanation:
Let us revise the cases of congruence
- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ
- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ
- AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ
- HL ⇒ hypotenuse leg of the 1st right Δ ≅ hypotenuse leg of the 2nd right Δ
In triangles LON and LMN
∵ LO ≅ LM ⇒ given
∵ NO ≅ NM ⇒ given
∵ LN is a common side in the two triangles
- That means the 3 sides of Δ LON are congruent to the 3 sides
of Δ LMN
∴ Δ LON ≅ LMN ⇒ by using SSS theorem of congruence
SSS is the congruence theorem that can be used to prove Δ LON is congruent to Δ LMN
Since order does not matter, you use a combination and not a permutation, so the first one is true, which means the second one is not true.
The probability of choosing two diamonds and three hearts can be represented by (13C2 * 13C3)/52C5, which is 0.0086, not 0.089, so the third one is not true.
The probability of choosing five spades and the probability of choosing five clubs are represented by the same thing, 13C5/52C5, which is roughly 0.0005, so the fourth one is not true but the fifth one is. So the answer is the first and fifth one.
Answer:
See Annex for tree diagram and all probabilities
b) P(2y) = 0,329
Step-by-step explanation:
a) Attached
b) Probability of the second ball is yellow P(2y) is equal to the probability of the second ball is yellow given that the first one is black ( 0,204 ) plus the probability f the second ball is yellow given that the first one is yellow ( 0,125)
P(2y) = 0,204 + 0,125
P(2y) = 0,329
Answer:
p ( x ) = ( x- 6 ) ² - 256
Step-by-step explanation:
1- Add the same value to both sides
2- Add 36 to the expression
3- Add 36 to the left-hand side
4- Factor the expression
5- Move the constant to the right
6- Calculate
Answer:
318 cm.
Step-by-step explanation:
Let x represent the distance between Bill and fulcrum.
We have been given that Laura has a mass of 60 kg and is sitting 265 cm from the fulcrum of a seesaw. Bill has a mass of 50 kg.
To balance the seesaw, the product of Laura's weight and her distance from fulcrum of seesaw should be equal to the product of Bill's weight and his distance from fulcrum of seesaw as:
Therefore, Billy should be 318 cm far from the fulcrum to balance the seesaw.
