Find the values of x and y.
1 answer:
Look at the picture.
We have the equation (1) 12x + 4y = 40.
We know, the sum of the acute angles in a right triangle is 90°.
Therefore we have the equation (2) (12x + 4y) + (17x - y) = 90
Substitute (1) to (2):
40 + 17x - y = 90 <em>subtract 40 from both sides</em>
17x - y = 50 (3)
We have the system of equations:
Substitute the value of x to (3)
Answer: x = 3 and y = 1.
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Answer:
The area of the shaded figure is:
- <u>20 units^2</u>
Step-by-step explanation:
To obtain the area of the shaded figure, first, you must calculate this as a rectangle, with the measurements: wide (4 units), and long (6 units):
- Area of a rectangle = long * wide
- Area of a rectangle = 6 * 4
- Area of a rectangle = 24 units^2
How the figure isn't a rectangle, you must subtract the triangle on the top, so, now we calculate the area of that triangle with measurements: wide (4 units), and height (2 units):
- Area of a triangle =
- Area of a triangle =
- Area of a triangle =
- Area of a triangle = 4 units^2
In the end, you subtract the area of the triangle to the area of the rectangle, to obtain the area of the shaded figure:
- Area of the shaded figure = Area of the rectangle - Area of the triangle
- Area of the shaded figure = 24 units^2 - 4 units^2
- <u>Area of the shaded figure = 20 units^2</u>
I use the name "units" because the exercise doesn't say if they are feet, inches, or another, but you can replace this in case you need it.