9514 1404 393
Answer:
- see below for a sketch
- 12 km
Step-by-step explanation:
The distance can be calculated using the Law of Cosines. The angle internal to the triangle at Q is (180°-(146° -65°)) = 99°. Then the distance PR can be found from ...
PR² = PQ² +QR² -2·PQ·QR·cos(∠PQR)
PR² = 6² +10² -2·6·10·cos(99°) ≈ 154.77
PR ≈ √154.77 ≈ 12.44 . . . . km
The distance PR is about 12 km.
The simplified expression of
is ![x^2+xy+y^2](https://tex.z-dn.net/?f=x%5E2%2Bxy%2By%5E2)
<h3>Complete question</h3>
Simplify the expression: (x³ + (-y)³) / (x - y)
Do not include parentheses in your answer.
<h3>How to simplify the expression?</h3>
The expression is given as:
![\frac{x^3 + (-y)^3}{(x - y}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E3%20%2B%20%28-y%29%5E3%7D%7B%28x%20-%20y%7D)
Open the inner bracket
![\frac{x^3 -y^3}{(x - y}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E3%20-y%5E3%7D%7B%28x%20-%20y%7D)
Apply the difference of two cubes to the numerator
![\frac{(x-y)(x^2+xy+y^2)}{(x - y}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-y%29%28x%5E2%2Bxy%2By%5E2%29%7D%7B%28x%20-%20y%7D)
Cancel out the common factors
![x^2+xy+y^2](https://tex.z-dn.net/?f=x%5E2%2Bxy%2By%5E2)
Hence, the simplified expression of
is ![x^2+xy+y^2](https://tex.z-dn.net/?f=x%5E2%2Bxy%2By%5E2)
Read more about expressions at:
brainly.com/question/723406
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Answer:
Step-by-step explanation:
External angle equals to the sum of opposite internal angles
z - 41° + z - 20° = z + 40°
2z - 61° = z + 40°
2z - z - 61° = 40°
z - 61° = 40
z = 40° + 61°
z = 101°
Answer:
a rational number
Step-by-step explanation:
a rational number + a rational number will always be a rational number.
7x - y= -5. Standard form is when it is written with x and y on the same side, but x is not negative or a fraction. To find the slope and y intercept, you must change the first two equations to slope intercept. You get y=7x-5 for the first one and y=11/3x+5 for the seccond equation. Take the 5 as your y intercept and the 7 as your slope and you get y=7x+5. Now you need to change it into standard form. When all is said and done, your final answer should be 7x - y = -5.