Answer: the answer to this question is 17
Step-by-step explanation:
Answer:
The angle the wire now subtends at the center of the new circle is approximately 145.7°
Step-by-step explanation:
The radius of the arc formed by the piece of wire = 15 cm
The angle subtended at the center of the circle by the arc, θ = 68°
The radius of the circle to which the piece of wire is reshaped to = 7 cm
Let 'L' represent the length of the wire
By proportionality, we have;
L = (θ/360) × 2 × π × r
L = (68/360) × 2 × π × 15 cm = π × 17/3 = (17/3)·π cm
Similarly, when the wire is reshaped to form an arc of the circle with a radius of 7 cm, we have;
L = (θ₂/360) × 2 × π × r₂
∴ θ₂ = L × 360/(2 × π × r₂)
Where;
θ₂ = The angle the wire now subtends at the center of the new circle with radius r₂ = 7 cm
π = 22/7
Which gives;
θ₂ = (17/3 cm) × (22/7) × 360/(2 × (22/7) × 7 cm) ≈ 145.7°.
If he grew 12 flowers with 3 seed packets then there should be 4 seeds in one packet > 3 x 4 = 12
Devin needs 5 seed packets to have a total of 20 flowers in his garden
> 4 x 5 = 20
So we set up the equation:
y=4x
y is the second number in an ordered pair, x is the first.
If we plug in the values of the ordered pairs given, the only ordered pair that fits in the equation
y=4x
is
LETTER D, aka
(5,20)
Perimeter:
p = 2b + 2h = 68
b = 4h - 6 (per problem statement)
substituting for b in the perimeter equation:
p = 2(4h - 6) + 2h = 68
(2)(4h) - (2)(6) + 2h = 68
8h - 12 + 2h = 68
10h - 12 = 68
10h = 68 + 12
10h = 80
h = 80/10
h = 8
b = 4(8) - 6 = 32 - 6 = 26
p = 2(26) + 2(8)
p = 52 + 16 = 68 . . . [OK]
b = 26 cm
h = 8 cm