Answer:
AB ≈ 15.7 cm, BC ≈ 18.7 cm
Step-by-step explanation:
(1)
Using the Cosine rule in Δ ABD
AB² = 12.4² + 16.5² - (2 × 12.4 × 16.5 × cos64° )
= 153.76 + 272.25 - (409.2 cos64° )
= 426.01 - 179.38
= 246.63 ( take the square root of both sides )
AB = 
≈ 15.7 cm ( to 1 dec. place )
(2)
Calculate ∠ BCD in Δ BCD
∠ BCD = 180° - (53 + 95)° ← angle sum in triangle
∠ BCD = 180° - 148° = 32°
Using the Sine rule in Δ BCD
= 
= 
( cross- multiply )
BC × sin32° = 12.4 × sin53° ( divide both sides by sin32° )
BC = 
≈ 18.7 cm ( to 1 dec. place )
Answer: then q→r
Explanation:
If p → q
and q →r , then you can use the law of transitivity to conclude
q→r.
That is a basic law of sillogisms.
An example will help you to understand the transivity law:
Make p, stand for 3 > 3/4, q stand for 3/4 > 15 / 20, the you can conclude that 3 > 15 / 20.
3 > 3/4
3 /4 > 15 / 20
Then, 3 > 15 /20.
This is, from the fact that you know that 3 is gretar than 3/4 and that 3/4 is greater than 15/20, you can conclude that 3 > 15 / 20. That is transitivity and is a law of logic, which you can use to get conclusions.
Answer:
B. 10
C. All real numbers.
Step-by-step explanation:
6 (2x-4) = 8(x + 2)
Distribute the numbers outside of the factors:
12x - 24 = 8x + 16
Subtract both sides by '8x'
12x - 8x - 24 = 8x - 8x + 16
4x - 24 = 16
Add '24' to both sides:
4x = 40
Divide both sides by 4:
x = 10. Therefore, <u>B. 10</u> is the correct answer.
3(4p - 2) = -6(1 - 2p)
Distribute the numbers similarly to the example before:
12p - 6 = -6 + 12p
Subtract '12p' from both sides:
12p - 12p -6 = -6 + 12p - 12p
0 -6 = -6
Add '6' to both sides:
0 - 6 + 6 = -6 + 6
0 = 0
Therefore, the solution consists of <u>all real numbers.</u>
Answer:
V = 64 r^(9) * s^(6)
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length
V = ( 4r^3s^2) ^3
We know that ( ab) ^c = a^c * b^c
V = 4^3 * r^3^3 * s^2^3
V = 64 * r^3^3 * s^2^3
We know that a^b^c = a^(b*c)
V = 64 r^(3*3) * s^(2*3)
V = 64 r^(9) * s^(6)
