Answer:
Solving for variable x
Move all terms containing x to the left, all other terms to the right
<u>Add -2x to each side of the equation</u>
<u></u><u></u>
<u></u>
<u>Combine like terms: 3x + -2x = 1x
</u>
<u></u><u></u>
<u></u>
<u>Combine like terms: 2x + -2x = 0
</u>
<u></u><u></u>
<u></u>
<u>Add 61 to each side of the equation.
</u>
<u></u><u></u>
<u></u>
<u>Combine like terms: -61 + 61 = 0
</u>
<u></u><u></u>
<u></u>
<u>Combine like terms: -50 + 61 = 11
</u>
<u></u><u></u>
<u></u>
<u>Divide each side by 1
</u>
<u></u><u></u>
Rectangles are recognized to have the same qualities as parallelograms. The alternative with the additional information would demonstrate that LMNP is a rectangle is LP ⊥ PN.
<h3>
What are rectangles?</h3>
- A rectangle is a quadrilateral with four right angles in Euclidean plane geometry.
- It can also be classified as an equiangular quadrilateral because all of its angles are equal, or a parallelogram with a right angle.
- A square is a rectangle with four equal-length sides.
What to know about parallelogram and rectangle:
- They both have two sorts of parallel sides as well as two pairs of opposite sides that are said to be congruent. All of the properties of a parallelogram are said to be shared by a rectangle.
- This results in a rectangle and, invariably, a parallelogram.
- However, a parallelogram is not generally referred to as a rectangle.
- Option d, LP ⊥ PN as the supplementary information, would demonstrate that LMNP is a rectangle.
Therefore, rectangles are recognized to have the same qualities as parallelograms. The alternative with the additional information would demonstrate that LMNP is a rectangle is LP ⊥ PN.
Know more about rectangles here:
brainly.com/question/1549055
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The correct question is given below:
LMNP is a parallelogram.
What additional information would prove that LMNP is a rectangle?
A. The length of LM is √45 and the length of MN is √5.
B. The slope of LP and MN is –2.
C. LM ∥ PN
D. LP ⊥ PN
Answer:
These have no solution:
- 2x < x+1 and x+1 > 3
- 3x -5 > 1 and x < 2
Step-by-step explanation:
1. 2x < x+1
x < 1 . . . . . subtract x
__
x + 1 > 3
x > 2 . . . . subtract x
No solution: x cannot be both > 2 and < 1.
_____
2. 3(x +2) > x
3x + 6 > x . . . . eliminate parentheses
2x + 6 > 0 . . . subtract x
x + 3 > 0 . . . . . divide by 2
x > 0
Solution: 0 < x < 2
_____
3. 5x ≥ 10
x ≥ 2 . . . . . divide by 5
__
2x ≤ 4
x ≤ 2 . . . . . divide by 2
Solution: 2 ≤ x ≤ 2 . . . . x = 2
_____
4. 3x -5 > 1
3x > 6 . . . . . . . add 5
x > 2 . . . . . . . . divide by 3
No solution: x cannot be both < 2 and > 2.
<u>Your question:</u> The amount of water leaking from a water tank can be modeled with the function f(x) = −x3 − 10x2 − x + 120, where x measures the number of minutes since the leak began and f(x) measures the volume of the tank. During what time period is there water in the tank? (0, 3) (0, 3]
(0, 3) is the best answer