Using Pythagorean identities:
If the sum of the height and base squared is greater than the hypotenuse squared, it would be an acute triangle.
If the sum of the height and base squared is less than the hypotenuse squared, it would be an obtuse triangle.
If the sum of the height and base squared is equal to the hypotenuse squared, it would be a right triangle.
The height = 10
The base = 24
10^2 + 24^2 = 100 + 576 = 676
The hypotenuse = 27 = 27^2 = 729
Because the sum of the height and base squared (676) is smaller than the hypotenuse squared (729) the triangle is an obtuse triangle.
I would add 7 to get ...
... 2x² = 16
then divide by 2 to get
... x² = 8
Now, I would take the square root, recognizing that both positive and negative values will solve the problem.
... x = ±√8
The root can be simplified, so we have ...
... x = ±2√2
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The above method seemed the most obvious method to me. One could use the quadratic formula, but that seems to involve more operations.
... 2x² -16 = 0 . . . . subtract 9
... x = (-0 ± √(0² -4·2·(-16)))/(2·2) . . . . put the coefficients into the formula
... x = ±(√128)/4 = ±√8 = ±2√2 . . . . . simplify the result
Well, because it is two years, 50x2 is 100 so 1000+100=1100
Then, you would do .25x1000 which is 2.5. That would mean you get 2.5 dollars back every month.
Therefore, your answer is...
C. $1161.76
- x - y - z = - 8 ------- (1)
- 4x + 4y + 5z = 7 -------- (2)
2x + 2z = 4 --------- (3)
From (3): x + z = 2
x = 2 - z --------- (4)
Substitute (4) into (1),
- x - y - z = - 8
- (2-z) - y - z = - 8
- 2 + z - y - z = -8
- 2 - y = - 8
2 + y = 8
Therefore, y = 6
Substitute y = 6 and (4) into (2),
- 4x + 4y + 5z = 7
- 4(2 - z) + 4(6) + 5z = 7
- 8 + 4z + 24 + 5z = 7
9z + 16 = 7
9z = - 9
Therefore, z = - 9
Substitute z = - 9 into (4),
x = 2 - z
x = 2 - (-9)
x = 2 + 9
Therefore x = 11
Solution:
x = 11
y = 6
z = -9
