Answer: 4 / 5
Explanation:
1) For a right triangle, the ratio sine is defined as:
sin(x) = opposite-leg / hypotenuse
2) x is the angle. In this case: A
3) As per the figure, the opposite leg to tha angle A measures 28
4) As per the figure, the hypotenuse measures 35
5) Calculations:
sin(A) = 28 / 35
Simplify dividing both numerator and denominator by 7 => 28/35 = 4/5
Answer:
972 x^16 y^24
Step-by-step explanation:
Simplify the following:
(-2 x^3 y^7)^2 (3 x^2 y^2)^5
Multiply each exponent in -2 x^3 y^7 by 2:
(-2)^2 x^(2×3) y^(2×7) (3 x^2 y^2)^5
2×7 = 14:
(-2)^2 x^(2×3) y^14 (3 x^2 y^2)^5
2×3 = 6:
(-2)^2 x^6 y^14 (3 x^2 y^2)^5
(-2)^2 = 4:
4 x^6 y^14 (3 x^2 y^2)^5
Multiply each exponent in 3 x^2 y^2 by 5:
4 x^6 y^14×3^5 x^(5×2) y^(5×2)
5×2 = 10:
4×3^5 x^6 y^14 x^(5×2) y^10
5×2 = 10:
4×3^5 x^6 y^14 x^10 y^10
3^5 = 3×3^4 = 3 (3^2)^2:
4×3 (3^2)^2 x^6 y^14 x^10 y^10
3^2 = 9:
4×3×9^2 x^6 y^14 x^10 y^10
9^2 = 81:
4×3×81 x^6 y^14 x^10 y^10
3×81 = 243:
4×243 x^6 y^14 x^10 y^10
4 x^6 y^14×243 x^10 y^10 = 4 x^(6 + 10) y^(14 + 10)×243:
4×243 x^(6 + 10) y^(14 + 10)
14 + 10 = 24:
4×243 x^(6 + 10) y^24
6 + 10 = 16:
4×243 x^16 y^24
4×243 = 972:
Answer: 972 x^16 y^24
The angles must add to 180 degrees.
Since the angles are in the ratio 7:9:4, their measures are not 7, 9, and 4 since 7, 9, and 4 do not add to 180. If you multiply 7, 9, and 4 by the same number, the new numbers will be in the same ratio. Since we do not know what that number is, we can use x for it.
Multiply 7, 9, and 4 by x to get
7x, 9x, and 4x.
Now add them and set equal to 180.
Then solve for x.
7x + 9x + 4x = 180
20x = 180
x = 9
Now that we know x equals 9, substitute x with 9 and evaluate 7x, 9x, and 4x to find the actual angle measures.
7x = 7 * 9 = 63
9x = 9 * 9 = 81
4x = 4 * 9 = 36
The angles measure 63, 81, and 36 degrees.
Answer:
-32
Step-by-step explanation:
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