3 tens
7 ones
This is the same as 30+7 which is 37
Answer:
cos(a + b) = ![\frac{1}{12}(1-2\sqrt{30})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B12%7D%281-2%5Csqrt%7B30%7D%29)
Step-by-step explanation:
cos(a + b) = cos(a).cos(b) - sin(a).sin(b) [Identity]
cos(a) = ![-\frac{1}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B3%7D)
cos(b) = ![-\frac{1}{4}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B4%7D)
Since, terminal side of angle 'a' lies in quadrant 3, sine of angle 'a' will be negative.
sin(a) =
[Since, sin(a) =
]
= ![-\sqrt{\frac{8}{9}}](https://tex.z-dn.net/?f=-%5Csqrt%7B%5Cfrac%7B8%7D%7B9%7D%7D)
= ![-\frac{2\sqrt{2}}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B2%5Csqrt%7B2%7D%7D%7B3%7D)
Similarly, terminal side of angle 'b' lies in quadrant 2, sine of angle 'b' will be negative.
sin(b) =
= ![-\sqrt{\frac{15}{16}}](https://tex.z-dn.net/?f=-%5Csqrt%7B%5Cfrac%7B15%7D%7B16%7D%7D)
= ![-\frac{\sqrt{15}}{4}](https://tex.z-dn.net/?f=-%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B4%7D)
By substituting these values in the identity,
cos(a + b) = ![(-\frac{1}{3})(-\frac{1}{4})-(-\frac{2\sqrt{2}}{3})(-\frac{\sqrt{15}}{4})](https://tex.z-dn.net/?f=%28-%5Cfrac%7B1%7D%7B3%7D%29%28-%5Cfrac%7B1%7D%7B4%7D%29-%28-%5Cfrac%7B2%5Csqrt%7B2%7D%7D%7B3%7D%29%28-%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B4%7D%29)
= ![\frac{1}{12}-\frac{\sqrt{120}}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B12%7D-%5Cfrac%7B%5Csqrt%7B120%7D%7D%7B12%7D)
= ![\frac{1}{12}(1-\sqrt{120})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B12%7D%281-%5Csqrt%7B120%7D%29)
= ![\frac{1}{12}(1-2\sqrt{30})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B12%7D%281-2%5Csqrt%7B30%7D%29)
Therefore, cos(a + b) = ![\frac{1}{12}(1-2\sqrt{30})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B12%7D%281-2%5Csqrt%7B30%7D%29)
<span>Area of the upper rectangle = x(16 - 6) = 10x </span>yd²<span>
Area of the bottom rectangle = 6(x + 6) = 6x + 36 </span>yd²<span>
Total area = 10x + 6x + 36 = 16x + 36 yd</span>²
Answer:
10 points
Step-by-step explanation:
Points scored in each of the first 3 quarter = x
Total points scored in the first 3 quarter = x + x + x
= 3x
Points scored in the fourth quarter = 14
Total points scored = 44 point
Total points scored = Total points scored in the first 3 quarter + Points scored in the fourth quarter
44 = 3x + 14
Subtract 14 from both sides
44 = 3x + 14
44 - 14 = 3x + 14 - 14
30 = 3x
Divide both sides by 3
x = 30/3
= 10
x = 10 points
Points scored in each of the first 3 quarter = x = 10 points
The school football team scored 10 points points in the first quarter
Answer:
the kit can produce 99*89*105*74 = 68,461,470 faces
Step-by-step explanation:
Hope this helps : )