Find the distance from point A(-1/4,5) to the line -x+2y=14. Round your answer to the nearest tenth.
Answers
Answer:
The distance from A(-1/4, 5) to the line -x + 2·y = 14 is approximately 1.7 units
Step-by-step explanation:
The shortest distance from a point to a line is the perpendicular from the line to the point
The equation of the given line is -x + 2·y = 14, which can be written in slope and intercept form as follows;
-x + 2·y = 14
2·y = 14 + x
y = 14/2 + x/2 = x/2 + 7
y = x/2 + 7
The slope, m₁ = 1/2 and the y-intercept = 7
Therefore, the slope, m₂, of the perpendicular line to the line -x + 2·y = 14 which was rewritten as y = x/2 + 7 is m₂ = -1/m₁ = -1/(1/2) = -2
Therefore, we have that the slope of the line from A(-1/4, 5) to the line -x + 2·y = 14, is -2
The equation of the line is therefore;
y - 5 = -2(x - (-1/4))
y - 5 = -2·x - 1/2
y = -2·x - 1/2 + 5 = -2·x + 9/2
y = -2·x + 9/2
The coordinates of the point on the line -x + 2·y = 14 (y = x/2 + 7) that coincides with the perpendicular from the point A(-1/4, 5) is therefore given as follows;
-2·x + 9/2 = x/2 + 7
9/2 - 7= x/2 + 2·x
-2.5 = 2.5·x
x = -2.5/2.5 = -1
x = -1
y = x/2 + 7 = -1/2 + 7 = 6.5
y = 6.5
The coordinates of the point on the line -x + 2·y = 14 (y = x/2 + 7) that coincides with the perpendicular from the point A(-1/4, 5) is (-1, 6.5)
The distance from A(-1/4, 5) to B(-1, 6.5), is given as follows;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Where;
(x₁, y₁) = (-1/4, 5), and (x₂, y₂) = B(-1, 6.5)
Plugging in the values, we have;
[tex]l_{AB} = \sqrt{\left (6.5-5 \right )^{2}+\left ((-1)-(-1/4) \right )^{2}} = \sqrt{\left (-0.75 \right )^{2}+\left (1.5 \right )^{2}} = \sqrt{\dfrac{45}{16} } = \dfrac{3}{4} \cdot \sqrt{5}[/tex]
[tex]l_{AB} = \dfrac{3}{4} \cdot \sqrt{5} \approx 1.677[/tex]
Therefore, the distance from A(-1/4, 5) to the line -x + 2·y = 14 ≈ 1.7 units, rounding to the nearest tenth.
Answer:
Step-by-step explanation: no work shown?
Related Questions
3. Corbett’s sold 3 more footballs than basketballs on Saturday. In total, they sold 27 balls. How many of each kind were sold?
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5. Carmen’s golf score was 6 strokes less than Lisa’s. Their two scores totalled 168. What was each girl’s score?
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Answers
Answer:
3.
let basketballs be x
and footballs will be 3 + x
3 + x + x = 27
2x = 27 - 3
2x = 24
x = 12
basketballs were 12 and footballs 15
4.bowl of soup x
hamburger 2x
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x = 246
bowl of soup 246 calories
hamburger 492 calories
5. lisa x
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lisa 87 strokes and carmen 81 strokes
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x = 95
first number is 95 and second number is 96
Help me out please an thank you
Answers
So answer B would be correct
They are vertical angles to those expressions are equivalent
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y-intercept =
Answers
Answer:
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Step-by-step explanation:
The slope will always be the point by the x and the y-intercept is where the line crosses the y axis.
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Answers
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Answers
Answer:
3
Step-by-step explanation:
INTERQUARTILE RANGE (IQR) = Q3 - Q1
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Q3 = 0.75(10 + 1) th term
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Answers
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
3x+4y-3xy+5x+3y-2xy-2x+y-3xy+10x-9y-8xy
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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What value of x satisfies the system of equations below?
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A.
4
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Answers
Answer:
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Step-by-step explanation:
Answer:
b
Step-by-step explanation:
What is Y?
8.4=y-4.6
Answers
Answer:
13
Step-by-step explanation:
8.4 = 13-4.6
8.4 = 8.4
Answer: y=13
Step-by-step explanation:
-
Michael uses lemonade concentrate and water to make lemonade for the family. The ratio of cups of lemonade
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Answers
Answer:
8 cupsStep-by-step explanation:
Given that the ratio is 1:3
concentrate =1
water=3
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What is |2(-7.5)| ?
Answers
Answer:
15
Step-by-step explanation:
sorry if this is wrong :)
The meaning of this annotation: "| |" is Absolute value.
It is important to note that the absolute value of a negative number = a positive number.Solving for : |2(-7.5)|
Step 1: Expand the bracket|2(-7.5)| = |2 x (-7.5)|
= |-15|
Step 2: The absolute value of |-15| is :|-15| = 15
Therefore, |2(-7.5)| = 15
To learn more, visit the link below:
brainly.com/question/17291634
Jenny wants to buy a new dress for her first school dance she barrows $25.63 from her sister to help pay for the dress then Jenny earns $16.33 helping her dad organize his home office if she gives all the earnings to her sister Jenny will still owe her sister $
Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
Step-by-step explanation:
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Answers
Answer:
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Answers
Answer:
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Answer:
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Step-by-step explanation:
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Answers
Answers:
x = 16
MB = 31
==================================================
Work Shown:
M is the midpoint of AB
This means AM is half as long as AB and AM = MB
Put another way, AB is twice as long as AM
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Answers
Answer:
y=-6x+36
Step-by-step explanation:
у + 6x — 36 = 0
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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-by-step explanation:
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Answers
Answer:
9) five hundred and forty three thousand, six hundred and ninety-eight
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what's 4 divided by 142.09 in long division
Answers
Answer: 35.522
Step-by-step explanation:
Answer:
35.5225
Step-by-step explanation:
4/142.09
look at each place starting in the hundredth place
how many times does 4 go into 14, 3 times
subtract the 12 from th 14 and you get a remainder of 2
drag the 2 down and you get 22
4 goes into 22 5 times
22-20=2
so on and so on
4/142.09
14-12=22 (3 times)
22-20=2 (5 times)
20-20=0 (5 times)
09-8=1 (2 times)
10-8=2 (2 times)
20-20=0 (5 times)
Thats as best as I can explain it, sorry if its confusing
Jimmy practices hitting baseballs every day. His first time at bat, the baseball goes 10 feet. For every day he
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Answers
Answer:
I think it is 10 + (6x)
Step-by-step explanation:
because he starts at ten and every day it adds 6 and x represents the number of days