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Lunna [17]
2 years ago
14

The square of number is 12 more than the number.Find the number.

SAT
2 answers:
lidiya [134]2 years ago
7 0

Answer: Translate the problem into an equation, and solve to find that the number is 4.

Explanation: Translate the problem into an equation: x2=x+12.

ICE Princess25 [194]2 years ago
4 0
Explanation:
Translate the problem into an equation:
x
2
=
x
+
12
Solve the quadratic equation:
x
2
−
x
−
12
=
0
Try factoring. If this does not work, we can use the quadratic formula:
(
x
+
3
)
(
x
−
4
)
=
0
x
=
−
3
or
x
=
4
Throw out the negative result:
x
=
4
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Lydia graphed δlmn at the coordinates l (0, 0), m (2, 2), and n (2, −1). She thinks δlmn is a right triangle. Is lydia's asserti
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No product results in -1, hence δlmn is NOT a right triangle showing that  lydia's assertion is incorrect

<h3>Perpendicular lines</h3>

In order to determine whether triangle lmn  is right-angled, we need to determine the slope of lm, ln, and mn first as shown:

For the slope of lm:

m_{lm} = \frac{2-0}{2-0}\\ m_{lm} =2/2\\m_{lm} =1

For the slope of ln:

m_{ln} = \frac{-1-0}{2-0}\\m_{ln} =-1/2\\

For the slope of mn:

m_{mn} = \frac{-1-2}{2-2}\\m_{ln} =-3/0 = \infty\\

  • If any of the two lines is perpendicular, hence the triangle lmn is right-angled.

  • To check, we will take the product of the slopes and see if it is equivalent to -1.

Product of slope lm and ln

m_{lm}\times m_{ln} = 1 \times -1/2\\m_{lm}\times m_{ln} = -1/2

Since no product results in -1, hence δlmn is NOT a right triangle showing that  Lydia's assertion is incorrect

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