A summer camp has 32 campers. A total of 22 of them swim, 20 play softball, and 5 do not swim or play softball. Which values com
plete the table?
a = 15, b = 10, c = 7, d = 5, e = 12
a = 15, b = 7, c = 5, d = 10, e = 12
a = 14, b = 7, c = 5, d = 12, e = 10
a = 14, b = 12, c = 7, d = 5, e = 10
a = 15, b = 10, c = 7, d = 5, e = 12
a = 15, b = 7, c = 5, d = 10, e = 12
a = 14, b = 7, c = 5, d = 12, e = 10
a = 14, b = 12, c = 7, d = 5, e = 10
2 answers:
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Answer: see below
<u>Step-by-step explanation:</u>
1) 10, 2, 1.2, 1.12, 1.112, 1.1112
t₁ = 10
t₂ = 10/10 + 1 = 2
t₃ = 2/10 + 1 = 1.2
t₄ = 1.2/10 + 1 = 1.12
t₅ = 1.12/10 + 1 = 1.112
t₆ = 1.112/10 + 1 = 1.1112
2) 10, 2, -2, -4, -5, -5.5, ...
t₁ = 10
t₂ = 10/2 - 3 = 2
t₃ = 2/2 - 3 = -2
t₄ = -2/2 - 3 = -4
t₅ = -4/2 - 3 = -5
t₆ = -5/2 - 3 = -5.5
Answer:
The option is C i.e 115°, 65°. proof is given below.
Step-by-step explanation:
Given:
ABCD is a quadrilateral.
m∠ A = 100 + 5x
m∠ B = 77 - 4y
m∠ C = 106 + 3x
m∠ D = 47 + 6y
To Prove:
ABCD is a parallelogram if opposing angles are congruent by finding the measures of angles.
m∠ A = m∠ C and
m∠ B = m∠ D
Proof:
ABCD is a quadrilateral and is a parallelogram if opposing angles are congruent.
∴ m∠ A = m∠ C
On substituting the given values we get
∴ 100 + 5x = 106 +3x
∴
m∠ A = 100 + 5x = 100 + 5 × 3 =100 + 15 = 115°
m∠ C = 106 + 3x = 106 + 3 ×3 =106 + 9 = 115°
∴ m∠ A = m∠ C = 115°
Similarly,
∴ m∠ B = m∠ D
77 - 4y = 47 + 6y
10y = 77 - 47
10y =30
∴
m∠ B = 77 - 4y =77 - 4 × 3 = 77 - 12 = 65°
m∠ D = 47 + 6y = 47 + 6 × 3 = 47 + 18 = 65°
∴ m∠ B = m∠ D = 65°
Therefore the option is C i.e 115°, 65°
