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8090 [49]
3 years ago
8

AB and BC form a right angle at point B. If A = (-3,-1) and B = (4,4), what is the equation of BC

Mathematics
1 answer:
m_a_m_a [10]3 years ago
7 0

Answer:

y=-1.4x+9.6

Step-by-step explanation:

If A = (-3,-1) and B = (4,4),  the slope of AB is

\text{Slope}_{AB}=\dfrac{-1-4}{-3-4}=\dfrac{-5}{-7}=\dfrac{5}{7}

Two perpendicular lines have slopes that have product of -1:

\text{Slopee}_{AB}\cdot \text{Slope}_{BC}=-1\\ \\\dfrac{5}{7}\cdot \text{Slope}_{BC}=-1\\ \\\text{Slope}_{BC}=-\dfrac{7}{5}=-1.4

The equation of the line BC with slope -1.4 and passing through the point B(4,4) is

y-4=-1.4(x-4)\\ \\y-4=-1.4x+5.6\\ \\y=-1.4x+9.6

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3 years ago
Solve the triangle. A = 54°, b = 11, c = 8
Delicious77 [7]
In this problem, you apply principles in trigonometry. Since it is not mentioned, you will not assume that the triangle is a special triangle such as the right triangle. Hence, you cannot use Pythagorean formulas. The only equations you can use is the Law of Sines and Law of Cosines.

For finding side a, you can answer this easily by the Law of Cosines. The equation is

a2=b2 +c2 -2bccosA
a2 = 11^2 + 8^2 -2(11)(8)(cos54)
a2 = 81.55
a = √81.55
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Then, we use the Law of Sines to find angles B and C. The formula would be

a/sinA = b/sinB = c/sinC
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B = 80.4°

9/sin54° = 8/sinC
C = 45.6°

The answer would be: a ≈ 9, C ≈ 45.6, B ≈ 80.4
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3 years ago
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3 years ago
Which values of m and b will create a system of equations with no solution? choose 1 options.
hichkok12 [17]

Answer:

The graph of a linear equation is a straight line.  The "solution" to a system of two linear equations is the point where the two lines cross.  If the two lines are parallel, they never cross; hence parallel lines have no solution.  Two lines are parallel if they have the same slope (the m value in y = mx+b).  One of your equations is y = -2x + (you left the y-intercept out).  The slope is -2.  So any line with a slope of m = -2 will be parallel to this line and will not cross it.  The second line also needs a different value of b, the y-intercept.  Otherwise it is the same line and every point is a solution.  So if your equation is:

 

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Then any equation of the form y = -2x + b, b≠1 will create a system with no solution.  Hence the values of m and b are m = -2, b ≠ 1.

5 0
2 years ago
Someone please help me
Ratling [72]

Answer:

1 mi/1.61 km

Step-by-step explanation:

we know that

1 mile= 1.61  kilometers

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use proportion

so

1/1.61 mi/km=x/1 mi/km

x=1 mi/1.61 km

5 0
3 years ago
Read 2 more answers
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