The horizontal yellow are is : 2(x+3) = 2x + 6
The vertical yellow are is : x(x+2+x) = x(2x+2) = 2x² + 2x
Total area = 2x + 6 + 2x² + 2x = 2x² +4x + 6 (answer B)
Answer: I’m pretty sure it’s 11/264 days
Step-by-step explanation:
Answer:
![K \approx 51.2^\circ](https://tex.z-dn.net/?f=K%20%5Capprox%2051.2%5E%5Ccirc)
![K \approx 128.8^\circ](https://tex.z-dn.net/?f=K%20%5Capprox%20128.8%5E%5Ccirc)
Step-by-step explanation:
Given
![k = 480](https://tex.z-dn.net/?f=k%20%3D%20480)
![j = 420](https://tex.z-dn.net/?f=j%20%3D%20420)
![\angle J = 43^\circ](https://tex.z-dn.net/?f=%5Cangle%20J%20%3D%2043%5E%5Ccirc)
Required
Find the measure of K
The value of K ranges from: ![0^\circ \le K \le 180^\circ](https://tex.z-dn.net/?f=0%5E%5Ccirc%20%5Cle%20K%20%5Cle%20180%5E%5Ccirc)
To do this, we apply sine rule;
![\frac{j}{\sin J} = \frac{k}{\sin K}](https://tex.z-dn.net/?f=%5Cfrac%7Bj%7D%7B%5Csin%20J%7D%20%3D%20%5Cfrac%7Bk%7D%7B%5Csin%20K%7D)
So, we have:
![\frac{420}{\sin 43} = \frac{480}{\sin K}](https://tex.z-dn.net/?f=%5Cfrac%7B420%7D%7B%5Csin%2043%7D%20%3D%20%5Cfrac%7B480%7D%7B%5Csin%20K%7D)
Cross multiply
![\sin K * 420 = \sin 43 * 480](https://tex.z-dn.net/?f=%5Csin%20K%20%2A%20420%20%3D%20%5Csin%2043%20%2A%20480)
Make sin K the subject
![\sin K= \frac{\sin 43 * 480}{420}](https://tex.z-dn.net/?f=%5Csin%20K%3D%20%5Cfrac%7B%5Csin%2043%20%2A%20480%7D%7B420%7D)
![\sin K= \frac{0.6820 * 480}{420}](https://tex.z-dn.net/?f=%5Csin%20K%3D%20%5Cfrac%7B0.6820%20%2A%20480%7D%7B420%7D)
![\sin K= 0.7794](https://tex.z-dn.net/?f=%5Csin%20K%3D%200.7794)
Take arc sin of both sides
![K = sin^{-1}(0.7794)](https://tex.z-dn.net/?f=K%20%3D%20sin%5E%7B-1%7D%280.7794%29)
![K \approx 51.2^\circ](https://tex.z-dn.net/?f=K%20%5Capprox%2051.2%5E%5Ccirc)
Recall that: ![0^\circ \le K \le 180^\circ](https://tex.z-dn.net/?f=0%5E%5Ccirc%20%5Cle%20K%20%5Cle%20180%5E%5Ccirc)
The other possible value of K is:
![K \approx 180 - 51.2](https://tex.z-dn.net/?f=K%20%5Capprox%20180%20-%2051.2)
![K \approx 128.8^\circ](https://tex.z-dn.net/?f=K%20%5Capprox%20128.8%5E%5Ccirc)
Answer:
b
Step-by-step explanation:
So with this type of question, you are expected to solve the systems of equations simultaneously
Let 4x + 4y = -12 ..... (1)
3x - 4y = -23 ..... (2)
By summing (2) and (1)
⇒ 4x + 3x + 4y + (-4y) = -12 + (-23)
7x = -35
⇒ 7x ÷ 7 = -35 ÷ 7
⇒ x = - 5
By substituting x into (1)
If 4x + 4y = -12 ..... (1)
then 4 (-5) + 4y = -12
⇒ 4y = -12 + 20
⇒ y = 8 ÷ 4
⇒ y = 2
∴ the solution for the system of equation are x = - 5 ; y = 2