(w-2)^2 = 63
FOIL left hand side:
(w-2)^2 = w^2 - 4w + 4
So,
w^2 - 4w + 4 = 63
w^2 - 4w - 59 = 0
Then use quadratic equation to get values of w = 2 + 3*root(7) and w = 2 - 3*root(7).
±
3
√
7
A) 36 means that there are 36 students taking Italian and music AT SAME TIME
b) 59 means that there are 59 students taking only music
c) 48 means that there are 48 students taking neither Italian nor music
d) Italian OR Music = 97 + 36 +59 = 192
e) Do not take Italian: 48 + 59 = 107
This is a little long, but it gets you there.
- ΔEBH ≅ ΔEBC . . . . HA theorem
- EH ≅ EC . . . . . . . . . CPCTC
- ∠ECH ≅ ∠EHC . . . base angles of isosceles ΔEHC
- ΔAHE ~ ΔDGB ~ ΔACB . . . . AA similarity
- ∠AEH ≅ ∠ABC . . . corresponding angles of similar triangle
- ∠AEH = ∠ECH + ∠EHC = 2∠ECH . . . external angle is equal to the sum of opposite internal angles (of ΔECH)
- ΔDAC ≅ ΔDAG . . . HA theorem
- DC ≅ DG . . . . . . . . . CPCTC
- ∠DCG ≅ ∠DGC . . . base angles of isosceles ΔDGC
- ∠BDG ≅ ∠BAC . . . .corresponding angles of similar triangles
- ∠BDG = ∠DCG + ∠DGC = 2∠DCG . . . external angle is equal to the sum of opposite internal angles (of ΔDCG)
- ∠BAC + ∠ACB + ∠ABC = 180° . . . . sum of angles of a triangle
- (∠BAC)/2 + (∠ACB)/2 + (∠ABC)/2 = 90° . . . . division property of equality (divide equation of 12 by 2)
- ∠DCG + 45° + ∠ECH = 90° . . . . substitute (∠BAC)/2 = (∠BDG)/2 = ∠DCG (from 10 and 11); substitute (∠ABC)/2 = (∠AEH)/2 = ∠ECH (from 5 and 6)
- This equation represents the sum of angles at point C: ∠DCG + ∠HCG + ∠ECH = 90°, ∴ ∠HCG = 45° . . . . subtraction property of equality, transitive property of equality. (Subtract ∠DCG+∠ECH from both equations (14 and 15).)
Answer:
13
Step-by-step explanation:
Using Pythagoras Theorem:

Substitute values of a and b:


The length of the missing side is 13.
Get the distance between two acres.
2.5 - 2.4 = 0.1
Divide the diffence by 2
0.1 / 2 = 0.05 - Halfway between them.
Therefore, 0.05 must be taken from 2.5 acres. it must be added to 2.4 acres to get the exact area of the park.
2.5 - 0.05 = 2.45
2.4 + 0.04 = 2.45 acres
OR
Simply get the average of the two to get the area since it is exactly halfway between the two acres of land.
2.5 + 2.4 = 2.9 / 2 = 2.45 acres