Simplify each expression
1 answer:
You might be interested in
Answer:
shaded area = 113.64 cm²
Step-by-step explanation:
To find the shaded area, subtract the area of the circle from the area of the triangle.
Area of a triangle = 1/2 x base x height
⇒ area of triangle = 1/2 x 25 x 21.4 = 267.5 cm²
Area of a circle = (where r is the radius)
From inspection, we can see that the diameter of the circle = 14 cm
Therefore, as the diameter = 2r, then r = 14 ÷ 2 = 7 cm
⇒ area of circle = 3.14 x 7² = 153.86 cm²
Shaded area = area of triangle - area of circle
⇒ shaded area = 267.5 - 153.86 = 113.64 cm²
Answer:
The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.
Step-by-step explanation:
Here is the complete question
In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.
y=35x; y=-0.05(x-400)²+9,492
what does the solution of the system represent in this context?
Solution
The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .
So, 35x = -0.05(x-400)² + 9,492.
Expanding the right side, we have
35x = -0.05(x² - 800x + 160000) + 9492
35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492
35x = -0.05x² +40x - 8000 + 9492
35x = -0.05x² +40x + 1492
Collecting all the terms to the left side, we have
0.05x² - 40x - 1492 + 35x = 0
0.05x² - 5x -1492 = 0
Using the quadratic formula,
We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.
The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.
We confirm that by plugging in x = 229.83 in both equations.
y = 35x = 35(229.83) = 8044.05 ≅ 8044.1
y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1