Which shows two expressions that are equivalent to (-8)(-12)(2)?
2 answers:
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Answer:
- as written, c ≈ 0.000979 or c = 4
- alternate interpretation: c = 0
Step-by-step explanation:
<em>As written</em>, you have an equation that cannot be solved algebraically.
(32^2)c = 8^c
1024c = 8^c
1024c -8^c = 0 . . . . . . rewrite as an expression compared to zero
A graphical solution shows two values for c: {0.000978551672551, 4}. We presume you're interested in c = 4.
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If you mean ...
32^(2c) = 8^c
(2^5)^(2c) = (2^3)^c . . . . rewriting as powers of 2
2^(10c) = 2^(3c) . . . . . . . simplify
10c = 3c . . . . . . . . . . . . . .log base 2
7c = 0 . . . . . . . . . . . . . . . subtract 3c
c = 0 . . . . . . . . . . . . . . . . divide by 7
Answer:
QUESTION 2:
The area of the polygon is 21.5 units²
QUESTION 3:
The area of the combined figure is 12 + 18.25·π units²
QUESTION 4:
The area of the figure is 40 units²
QUESTION 5
The area of the compost shape is 40 in.²
Step-by-step explanation:
QUESTION 2.
The area of the polygon is given as follows;
The area of two triangles + The area of trapezoid
1/2×6×3 + 1/2×3×4 + 1/2×(6 + 7) = 21.5 units²
QUESTION 3
The diameter of the semicircle, 'd', is given as follows;
d = √(8² + 3²) = √73
The area of the semicircle = π·d²/4 = π·73/4 = 18.25·π unit²
The area of the right triangle beside the semicircle is given as follows;
1/2 × 8 × 3 = 12 unit²
The area of the combined figure = The area of the semicircle + The area of the right triangle
∴ The area of the combined figure = 12 + 18.25·π units²
QUESTION 4:
The dimensions of the parallelogram are;
Width, W = √(4² + 1²) = √(17)
Length, L = √(8² + 2²) = √(68)
The area of the parallelogram, = W × L = √(17) × √(68) = √(17 × 68) = 34
The area of the parallelogram, = 34 units²
The length of a parallel side, 'A', of the parallelogram is A = 6
The height of the parallelogram, is h = 1
The area of the parallelogram is A = B·h = 6 × 1 = 6 units²
The area of the figure is the sum of the area of the rectangle and the area of the parallelogram
Therefore, we have;
The area of the figure = 34 units² + 6 units² = 40 units²
QUESTION 5
The composite shape consists of a triangle and a rectangle
Therefore, we have;
The area of the rectangle = 5 in. × 7 in. = 35 in.²
The area of the triangle = 1/2 × 2 in. × 5 in. = 5 in.²
The area of the compost shape = The area of the rectangle + The area of the triangle
∴ The area of the compost shape = 35 in.² + 5 in.² = 40 in.²
The area of the compost shape = 40 in.².