I think it is 32 don’t count me on it but not for sure
Answer:
![\cos(A + B) = \frac{23}{265}](https://tex.z-dn.net/?f=%5Ccos%28A%20%2B%20B%29%20%3D%20%5Cfrac%7B23%7D%7B265%7D)
Step-by-step explanation:
Given
![\tan A=\frac{28}{45}](https://tex.z-dn.net/?f=%5Ctan%20A%3D%5Cfrac%7B28%7D%7B45%7D)
![\cos B=\frac{3}{5}](https://tex.z-dn.net/?f=%5Ccos%20B%3D%5Cfrac%7B3%7D%7B5%7D)
Required
![\cos(A+B)](https://tex.z-dn.net/?f=%5Ccos%28A%2BB%29)
In trigonometry:
![\cos(A+B) = \cos\ A\ cosB - sinA\ sinB](https://tex.z-dn.net/?f=%5Ccos%28A%2BB%29%20%3D%20%5Ccos%5C%20A%5C%20cosB%20-%20sinA%5C%20sinB)
We need to solve for cosA, sinA and sinB
Given that:
and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),
So, we have:
and ![y = 45](https://tex.z-dn.net/?f=y%20%3D%2045)
For this angle A, we need t calculate its hypotenuse (z).
Using Pythagoras,
![z^2 = x^2 + y^2](https://tex.z-dn.net/?f=z%5E2%20%3D%20x%5E2%20%2B%20y%5E2)
![z = \sqrt{x^2 + y^2](https://tex.z-dn.net/?f=z%20%3D%20%5Csqrt%7Bx%5E2%20%2B%20y%5E2)
![z = \sqrt{28^2 + 45^2](https://tex.z-dn.net/?f=z%20%3D%20%5Csqrt%7B28%5E2%20%2B%2045%5E2)
![z = \sqrt{2809](https://tex.z-dn.net/?f=z%20%3D%20%5Csqrt%7B2809)
![z = 53](https://tex.z-dn.net/?f=z%20%3D%2053)
From here, we can calculate sin and cos A
and ![\cos A= \frac{adjacent}{hypotenuse}](https://tex.z-dn.net/?f=%5Ccos%20A%3D%20%5Cfrac%7Badjacent%7D%7Bhypotenuse%7D)
![\sin A= \frac{x}{z}](https://tex.z-dn.net/?f=%5Csin%20A%3D%20%5Cfrac%7Bx%7D%7Bz%7D)
![\sin A= \frac{28}{53}](https://tex.z-dn.net/?f=%5Csin%20A%3D%20%5Cfrac%7B28%7D%7B53%7D)
![\cos A= \frac{y}{z}](https://tex.z-dn.net/?f=%5Ccos%20A%3D%20%5Cfrac%7By%7D%7Bz%7D)
![\cos A= \frac{45}{53}](https://tex.z-dn.net/?f=%5Ccos%20A%3D%20%5Cfrac%7B45%7D%7B53%7D)
To angle B.
Give that
and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),
So, we have:
and ![b = 5](https://tex.z-dn.net/?f=b%20%3D%205)
For this angle B, we need to calculate its opposite (b).
Using Pythagoras,
![c^2 = a^2 + b^2](https://tex.z-dn.net/?f=c%5E2%20%3D%20a%5E2%20%2B%20b%5E2)
![5^2 = 3^2 + b^2](https://tex.z-dn.net/?f=5%5E2%20%3D%203%5E2%20%2B%20b%5E2)
![25 = 9 + b^2](https://tex.z-dn.net/?f=25%20%3D%209%20%2B%20b%5E2)
Collect like terms
![b^2 = 25 - 9](https://tex.z-dn.net/?f=b%5E2%20%3D%2025%20-%209)
![b^2 = 16](https://tex.z-dn.net/?f=b%5E2%20%3D%2016)
![b = \sqrt{16](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%7B16)
![b = 4](https://tex.z-dn.net/?f=b%20%3D%204)
From here, we can calculate sin B
![\sin B= \frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=%5Csin%20B%3D%20%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D)
![\sin B = \frac{b}{c}](https://tex.z-dn.net/?f=%5Csin%20B%20%3D%20%5Cfrac%7Bb%7D%7Bc%7D)
![\sin B = \frac{4}{5}](https://tex.z-dn.net/?f=%5Csin%20B%20%3D%20%5Cfrac%7B4%7D%7B5%7D)
Recall that:
and
![\cos A= \frac{45}{53}](https://tex.z-dn.net/?f=%5Ccos%20A%3D%20%5Cfrac%7B45%7D%7B53%7D)
![\cos(A + B) = \frac{45}{53} * \frac{3}{5} - \frac{28}{53} * \frac{4}{5}](https://tex.z-dn.net/?f=%5Ccos%28A%20%2B%20B%29%20%3D%20%5Cfrac%7B45%7D%7B53%7D%20%2A%20%5Cfrac%7B3%7D%7B5%7D%20-%20%5Cfrac%7B28%7D%7B53%7D%20%2A%20%5Cfrac%7B4%7D%7B5%7D)
![\cos(A + B) = \frac{135}{265} - \frac{112}{265}](https://tex.z-dn.net/?f=%5Ccos%28A%20%2B%20B%29%20%3D%20%5Cfrac%7B135%7D%7B265%7D%20-%20%5Cfrac%7B112%7D%7B265%7D)
![\cos(A + B) = \frac{135-112}{265}](https://tex.z-dn.net/?f=%5Ccos%28A%20%2B%20B%29%20%3D%20%5Cfrac%7B135-112%7D%7B265%7D)
![\cos(A + B) = \frac{23}{265}](https://tex.z-dn.net/?f=%5Ccos%28A%20%2B%20B%29%20%3D%20%5Cfrac%7B23%7D%7B265%7D)
The missing step in solving the inequality is x > -9
<h3>Solving inequalities </h3>
From the question, we are to determine the missing step in solving the given inequality
1. The distributive property: 4x – 12 + 4 < 10 + 6x
2. Combine like terms: 4x – 8 < 10 + 6x
3. The addition property of inequality: 4x < 18 + 6x
4. The subtraction property of inequality: –2x < 18
5. The division property of inequality: ________
Applying the division property of inequality
-2x/-2 < 18/-2
x > -9
Hence, the missing step in solving the inequality is x > -9
Learn more on Solving inequalities here: brainly.com/question/246993
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The answer is 117.5 because to find the interquartile range first u need to find the median. Then you fave to find the lower quartile which is 125 and thenearest u need to find the upper quartile which is 242.5. Finally u subtract 242.5 by 125 to get 117.5.
Hope it helped
Answer:
Soleil and Malvin would have $ 5,000 all together after 13 days.
Step-by-step explanation:
Since Soleil and Malvin each work a job, and Soleil starts with $ 700 and makes $ 100 per day while Malvin starts out with $ 200 and makes $ 120 per day, to determine after how many days will they have at least $ 5000 all together it must be done the following calculation:
5,000 - 700 - 200 = 4,100
200X + 120X = 4,100
320X = 4,100
X = 4,100 / 320
X = 12.8
So Soleil and Malvin would have $ 5,000 all together after 13 days.