Given that the triangles are similar.
When triangles are similar, all three pairs of corresponding sides are in the same ratio.
Similarly in the given triangles, the ratio of the corresponding sides are equal.
![\frac{8}{2x-2}= \frac{8+6}{3x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7B2x-2%7D%3D%20%5Cfrac%7B8%2B6%7D%7B3x%7D%20)
![\frac{8}{2x-2}= \frac{14}{3x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7B2x-2%7D%3D%20%5Cfrac%7B14%7D%7B3x%7D%20)
Cross multiplying, we get
![8 \times 3x = 14 \times (2x-2)](https://tex.z-dn.net/?f=%208%20%5Ctimes%203x%20%3D%2014%20%5Ctimes%20%282x-2%29%20)
![24x = 28x-28](https://tex.z-dn.net/?f=%2024x%20%3D%2028x-28%20)
![-4x = -28](https://tex.z-dn.net/?f=%20-4x%20%3D%20-28%20)
Dividing both sides of the equation by -4.
So, we get
x = 7.
Original Income = 15,000
New income = 20,000
The percentage Increase in the income can be calculated as:
![\frac{Change}{Original} * 100](https://tex.z-dn.net/?f=%20%5Cfrac%7BChange%7D%7BOriginal%7D%20%2A%20100)
%
The change in income = 20000 - 15000 = 5000
Using the values, we get:
![\frac{5000}{15000}*100](https://tex.z-dn.net/?f=%20%5Cfrac%7B5000%7D%7B15000%7D%2A100%20)
%
=
![33.33](https://tex.z-dn.net/?f=33.33)
%
This means, Pats income increased by 33.33% in a period of ten years
m∠R = 27.03°
Solution:
Given In ΔQRP, p = 28 km, q = 17 km, r = 15 km
To find the measure of angle R:
Law of cosine formula for ΔQRP:
![r^{2}=p^{2}+q^{2}-2 pq \cos R](https://tex.z-dn.net/?f=r%5E%7B2%7D%3Dp%5E%7B2%7D%2Bq%5E%7B2%7D-2%20pq%20%5Ccos%20R)
Substitute the given values in the above formula.
![(15)^{2}=(28)^{2}+(17)^{2}-2 (28)(17) \cos R](https://tex.z-dn.net/?f=%2815%29%5E%7B2%7D%3D%2828%29%5E%7B2%7D%2B%2817%29%5E%7B2%7D-2%20%2828%29%2817%29%20%5Ccos%20R)
![225=784+289-952 \cos R](https://tex.z-dn.net/?f=225%3D784%2B289-952%20%5Ccos%20R)
![225=1073-952 \cos R](https://tex.z-dn.net/?f=225%3D1073-952%20%5Ccos%20R)
Switch the given equation.
![1073-952 \cos R=225](https://tex.z-dn.net/?f=1073-952%20%5Ccos%20R%3D225)
Subtract 1073 from both side of the equation.
![-952 \cos R=-848](https://tex.z-dn.net/?f=-952%20%5Ccos%20R%3D-848)
Divide by –952 on both sides.
![$ \cos R=\frac{106}{119}](https://tex.z-dn.net/?f=%24%20%5Ccos%20R%3D%5Cfrac%7B106%7D%7B119%7D)
![$ R=\cos^{-1} \left(\frac{106}{119}\right)](https://tex.z-dn.net/?f=%24%20%20R%3D%5Ccos%5E%7B-1%7D%20%5Cleft%28%5Cfrac%7B106%7D%7B119%7D%5Cright%29)
![R=27.03^\circ](https://tex.z-dn.net/?f=R%3D27.03%5E%5Ccirc)
Hence m∠R = 27.03°.
Answer:
5X + 8Y >= 300; intersection at (-20, 50)
Step-by-step explanation:
let t = work hours
0 < t < 30
X = time lawn mowing
Y = time babysitting.
X + Y < 30
5X + 8Y >= 300
We could solve...
X < 30 - Y
5(30 - Y) + 8Y >=300
150 - 5Y + 8Y >= 300
3Y >=150
Y >=50
then X < -20
intersection at (-20, 50)
Step-by-step explanation:
204+272/14=34 years old