Answer:
x=5, y=2
Step-by-step explanation:
You simply write down what you see:
3x - 4y + 4x - 5y = 17
2x - 3y + 3x - 5y = 9
Then you simplify by grouping the x and the y terms:
7x - 9y = 17
5x - 8y = 9
Now you want to get equal amounts of x or y. Let's go for x. If we multiply the top eq with 5 and the bottom one with -7, we get:
35x - 45y = 85
-35x + 56y = -63
-------------------------+ now we can add them:
11y = 22 divide by -11
y = 2
So 7x - 18 = 17, x =5
Finally, it makes sense to double check by filling in these answers in the original equations, just to see if no mistakes were made:
3*5 - 4*2 = 7
4*5 - 5*2 = 10
7+10 = 17: ok!
2*5 - 3*2 = 4
3*5 - 5*2 = 5
4+5 = 9: ok!
Answer:
x = 8 and y = 10
Step-by-step explanation:
Since the figures are congruent:
Angle PQR = EFG
6y + x = 68
Segment QR = FG
2x - 4 = 12
Solving that:
2x - 4 = 12
2x = 16
x = 8
Replacing x in 6y + x =68
6y + 8 = 68
6y = 60
y = 10
The total amount of money Kylie spent to go to talent camp is 115.
76.5 *10 =765 (Amount of money she deposited in 10 months)
30.5 *10 = 305 (Amount of money she used to pay for singing lessons in 10 months)
765 - 305 = 460 (Amount remaining after singing lessons for 10 months)
460/4 = 115 (Amount she used to go to a talent camp)
Answer:
108?
Step-by-step explanation:
Answer:
A ≈ 119.7°, b ≈ 25.7, C ≈ 24.3°
Step-by-step explanation:
A suitable app or calculator does this easily. (Since you're asking here, you're obviously not unwilling to use technology to help.)
_____
Given two sides and the included angle, the Law of Cosines can help you find the third side.
... b² = a² + c² - 2ac·cos(B)
... b² = 38² + 18² -2·38·18·cos(36°) ≈ 661.26475
... b ≈ 25.715
Then the Law of Sines can help you find the other angles. It can work well to find the smaller angle first (the one opposite the shortest side). That way, you can tell if the larger angle is obtuse or acute.
... sin(C)/c = sin(B)/b
... C = arcsin(c/b·sin(B)) ≈ 24.29515°
This angle and angle B add to less than 90°, so the remaining angle is obtuse. (∠A can also be found as 180° - ∠B - ∠C.)
... A = arcsin(a/b·sin(B)) ≈ 119.70485°
