a square is split into four triangles, and then three of the four triangles are shaded as shown. If the areas of the shaded triangles are 3,4, and 6, as shown, what is the area of the unshaded triangle?

11

Step-by-step explanation

We first let the side of the square be defined as x.

Therefore, we have ax/2 = 4, and bx/2= 3. Where a and b are the legs of the triangles with areas 4 and 3 respectively.

For the Triangle with area 6, we then have ((x-a)(x-b))/2 = 6. Expanding gives us x^2-bx-ax+ab=12. Using the equation above and plugging in values where bx = 6, ax=8, a = 8/x, and b = 6/x. We get

x^2-6-8+48/x^2 = 12.

Simplified gives us,

x^4-26x^2+48.

Factored gives us,

((x^2-2)(x^2-24).

Since the area cannot be any negative values and bigger than 6 (since there is already a triangle with area 6), we then have x^2 = 24.

Therefore a of unshaded region = 24-6-4-3= 11

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

45

step-by-step explanation: