-1 > -2(x-4) - 5(4x - 7)
-1 > -2x + 8 - 20x + 35
-1 > -22x + 43
-1 - 43 > - 22x
-44 > - 22x
-44/-22 < x
2 < x....or x > 2
<h3>
Answer: 48</h3>
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Explanation:
Triangle ABC is isosceles because AC = BC.
The angles opposite these congruent sides are angle ABC and angle BAC. These are the base angles.
For any isosceles triangle, the base angles are congruent.
Angle BAC = 69 degrees is given. So angle ABC = 69 as well.
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The missing angle must add to the two other angles so that all three angles in a triangle add to 180
(angle ABC) + (angle BAC) + (angle BCA) = 180
69 + 69 + (angle BCA) = 180
138 + (angle BCA) = 180
angle BCA = 180-138
angle BCA = 42
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Angle DCE is congruent to angle BCA because they are vertical angles.
Triangle DCE is a right triangle. The missing angle is 90-(angle BCA) = 90-42 = 48
angle EDC = 48 degrees
In trigonometry, the right triangle is considered a special triangle because there are derived equations solely for this type. It is really convenient when dealing right triangle problems because it is more simplified courtesy of the Pythagorean theorems. It is derived that the square of the hypotenuse (longest side of the triangle) is equal to the sum of the squares of the other two legs. In equation, that would be c² = a² + b². For this activity, all you have to do is find the sum of the squares in columns a and b. Then, see if this is equal to the square of the values in column c. Let's calculate each row:
Row 1:
3² + 4² ? 5²
25 ? 25
25 = 25
Row 2:
5² + 12² ? 13²
169 ? 169
169 = 169
Row 3:
9² + 12² ? 15²
225 ? 225
225 = 225
Therefore, all of the given values conform to a² + b² = c².
Let x = speed and y = distance
y = x * 45
y = (x - 4) * 70
45x = 70x - 280
-25x = -280
x = 11.2
Put it back into the first equation:
y = 11.2 x 45
y = 504miles
Hope this helps! Any questions let me know :)
