If by "long leg lengths" you mean the hypotenuse then the area is 116 sq. units. If you mean the bases of the triangles then the area is 170 sq. units.
If the length of 12 is the hypotenuse, we first must find the base of the triangles using the Pythagorean theorem:
10² + b² = 12²
100 + b² = 144
b² = 44
b = √44 = 6.6
This means we have two triangles and a rectangle. The area of the rectangle is 5(10) = 50 sq. units. The area of each triangle is 1/2(6.6)(10) = 33. Adding all 3 together we have:
50+33+33 = 116 sq. units.
If the 12 is the base, then we have the rectangle with the area of 5(10) = 50 and two triangles each with an area of 1/2(12)(10) = 60:
50+60+60 = 170 sq. units.
Answer:
Step-by-step explanation:
Since we are given a right triangle, we can use right trigonometric ratios.
<em>x</em> is the opposite side to our angle. 10 is the adjacent side to it. Thus, we can use the tangent ratio:
Substitute:
Solve for <em>x:</em>
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Use a calculator:
Answer: Part A:
A linear graph is one with a line that has the same slope all the way through. In this case, you can tell the line doesn't have the same slope the whole way through because at one part it flattens and also decreases.
Part B:
Increasing would mean the slope of the line is positive, or it appears to be going upwards. Constant would be the slope is 0, and it's just a horizontal line. Decreasing would be the slope of the line is negative, and it appears to be going downwards. In this case, this would mean that the segment K is increasing, because it appears to be going upwards, L would be constant, because it is a horizontal line, and M would be decreasing, because it's going downwards.
Part C:
I would say the ant started moving away from the hole for 2 seconds, and then stopped for 3 seconds, and then started moving again back to the hole for another 3 seconds.
-4x > 500
Divide -4 on both sides.
(Now this is very important, whenever you divide OR multiply an equality by a NEGATIVE number the sign will ALWAYS flip.)
x < -125
~
To find the percent, we first find the decimal.
To do that we divide 5 / 6, which gives us approximately 0.83333, now we multiply it by 100 since percentages are parts of 100.
0.83333 * 100 = 83.33%
