Answer:
Step-by-step explanation:
In Δ AFB,
∠AFB + ∠ABF + ∠A = 180 {Angle sum property of triangle}
90 + 48 + ∠1 = 180
138 + ∠1 = 180
∠1 = 180 - 138
∠1 = 42°
FC // ED and FD is transversal
So, ∠CFD ≅∠EDF {Alternate interior angles are congruent}
∠2 = 39°
In ΔFCD,
∠2 + ∠3 + ∠FCD = 180
39 + ∠3 + 90 = 180
129 +∠3 = 180
∠3 = 180- 129
∠3 = 51°
Answer:
14x - 8 = 22 + 20x
x = -5
Step-by-step explanation:
Let "the number" be represented by x
Take each part of the statement and translate into algebraic form
"14 times a number" 14x
"decreased By eight" -8
"is" =
"22 Increased by" 22 +
"20 times The same number" 20x
Put the equation together. Solve for x by isolating.
(
14x - 8 = 22 + 20x
14x - 8 - 20x = 22 + 20x - 20x Subtract 20x from both sides
-6x - 8 = 22
-6x - 8 + 8 = 22 + 8 Add 8 to both sides
-6x = 30
-6x ÷ -6 = 30 ÷ -6 Divide both sides by -6
x = -5
<u>Answer</u>
4m
<u>Explanation</u>
Δqrp is a right triangle.
If ps = 6m then, qp = 3m. So we can find line pr using pythagoras theorem.
rp = √(5²-3²) = √16 = 4m
The Δqrp≡Δqtp.
Filipe can choose his favorite from 4 bands, so he has 4 ways to determine the favorite.
Then only 3 bands left and he can choose his second favorite in 3 ways. After selecting second favorite, only 2 bands left and there are 2 ways to select the third favorite.
Use the product rule to count all possible votes:
4·3·2=24 ways.
Answer: 24.
