!!!!!!Please help ASAP!!!!!
AB and BC form a right angle at their point of intersection, B. If the coordinates of A and Bare (14, -1) and (2, 1), respectively, the y-intercept of AB is 4/3 and the equation of BC is y= 6 X + If the y-coordinate of point Cis 13, its x-coordinate is
Answers
Answer:
Step-by-step explanation:
Segments AB and BC intersect each other at 90° at B.
Let the equation of the segment AB → y = mx + b
Here, m = Slope of the line
b = y-intercept
Slope of the line AB passing through A(14, -1) and B(2, 1)
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{1+1}{2-14}[/tex]
= [tex]-\frac{2}{12}[/tex]
= [tex]-\frac{1}{6}[/tex]
Equation of the line will be,
[tex]y=-\frac{1}{6}(x)+b[/tex]
Since, AB passes through (2, 1)
[tex]1=-\frac{1}{6}(2)+b[/tex]
[tex]b=1+\frac{1}{3}[/tex]
[tex]b=\frac{4}{3}[/tex]
Therefore, y-intercept of AB = [tex]\frac{4}{3}[/tex]
Equation of AB → [tex]y=-\frac{1}{6}(x)+\frac{4}{3}[/tex]
Since, line BC is perpendicular to AB,
By the property of perpendicular lines,
[tex]m_1\times m_2=-1[/tex]
Here, [tex]m_1[/tex] and [tex]m_2[/tex] are the slopes of line AB and BC respectively.
By this property,
[tex]-\frac{1}{6}\times m_2=-1[/tex]
[tex]m_2=6[/tex]
Equation of a line passing through a point (h, k) and slope 'm' is,
(y - k) = m(x - h)
Therefore, equation of line BC passing through B(2, 1) and slope = 6,
y - 1 = 6(x - 2)
y = 6x - 11
Since, line BC passes through C(x, 13),
13 = 6x - 11
6x = 24
x = 4
Therefore, x-coordinate of point C will be, x = 4
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Answer:
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Answer:
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Answer:
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Answer:
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Step-by-step explanation:
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Answer:
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Answers
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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corresponding angle because 1 is correspondence to 45 degree
Hannah and Corrine are playing a game by rolling two cubes, each numbered 1 through 6. If the sum of the numbers on the cubes is 7, Hannah wins. If the sum is not 7, Corrine wins. Corrine says Hannah can win only if the following occurs:
1 on the first cube, 6 on the second cube
2 on the first cube, 5 on the second cube
3 on the first cube, 4 on the second cube
Which best explains if Corrine is correct?
Corrine is correct because there are only three ways to have a sum of 7 when the cubes are rolled.
Corrine is correct because there are no 7s on the cubes, so Hannah must roll a greater number on the second cube.
Corrine is not correct because Hannah can also roll doubles on the cubes, such as 3 on the first cube and 3 on the second cube or 4 on the first cube and 4 on the second cube.
Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.
Answers
D. Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.
Step-by-step explanation:
To get a sum of 7 by rolling two cubes, we need to get one of the combinations from the list below:
1 on the first cube, 6 on the second cube
or
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2 on the first cube, 5 on the second cube
or
5 on the first cube, 2 on the second cube
3 on the first cube, 4 on the second cube
or
4 on the first cube, 3 on the second cube
Therefore, the correct answer option is D. Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.