Please help me with full calculation
1 answer:
9514 1404 393
Answer:
a. 12
b. 15
c. (2, -2.5)
Step-by-step explanation:
a. The points lie on a horizontal line, so the distance between them is the difference of their x-coordinates: 4 -(-8) = 12 units.
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b. The length BD is the diagonal of the rectangle. Its length is given by the distance formula as ...
d = √((x2 -x1)^2 +(y2 -y1)^2)
d = √((-8 -4)^2 +(-7 -2)^2) = √((-12)^2 +(-9)^2) = √(144 +81) = √225
d = 15
The distance between B and D is 15 units.
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c. The midpoints of AC and BD are the same:
(A +C)/2 = ((-8, 2) +(4, -7))/2 = (4, -5)/2 = (2, -2.5)
(B +D)/2 = ((4, 2) +(-8, -7))/2 = (4, -5)/2 = (2, -2.5)
Point (2, -2.5) can be used to locate the lake.
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Answer:
Option (1)
Step-by-step explanation:
The given triangle JKL is an equilateral triangle.
Therefore, all three sides of this triangle will be equal in measure.
Side JK = JL = KL = 48 units
Perpendicular LM drawn to the base JK bisects the base in two equal parts JM and MK.
By applying tangent rule in ΔJML,
tan(∠KJL) =
=
=
Since, Sin(K) =
Sin(60)° =
LM = 24√3
Now, tan(∠KJL) =
=
Therefore, Option (1) will be the answer.
Option C and Option D
3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4 has infinite number of solutions
4(x + 2) + x + 1 = 2x - 3 + 3(x + 4) has infinite number of solutions
<h3><u>Solution:</u></h3>Given that we have to find the equations that has infinite number of solutions
If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions.
If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.
<h3><u>Option A</u></h3>-2(x - 2) + 3x = x - 4
Multiply the terms inside the bracket
-2x + 4 + 3x = x - 4
x + 4 = x - 4
Thus this equation does not have infinite number of solutions
<h3><u>Option B</u></h3>2x + 4(x - 1) = 3(2x + 1) - 2(x - 1)
2x + 4x - 4 = 6x + 3 - 2x + 2
6x - 4 = 4x + 5
6x - 4x = 5 + 4
2x = 9
Thus this equation has only one solution.
Thus this equation does not have infinite number of solutions
<h3><u>Option C</u></h3>3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4
3x + 2x - 4 + 6 = 4x + 6 + x - 4
5x + 2 = 5x + 2
Thus this equation has infinite number of solutions
<h3><u>Option D</u></h3>4(x + 2) + x + 1 = 2x - 3 + 3(x + 4)
4x + 8 + x + 1 = 2x - 3 + 3x + 12
5x + 9 = 5x + 9
Thus this equation has infinite number of solutions