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8090 [49]
3 years ago
11

Explain how you could find the shortest distance from A(6, 5) to the line y = 5x – 10. (Use a diagram, be specific, and list all

your steps.
Mathematics
1 answer:
HACTEHA [7]3 years ago
3 0

Step-by-step explanation:

I cannot draw a diagram here.

but I can explain what to do in general.

the shortest distance from a point to a line is always via a connecting line that is perpendicular to the given line and his through the given point.

and then the distance from the given point to the intersection point is calculated.

every line is defined in the form like

y = ax + b

where a is the slope of the line, and b is the intersection point on the y-axis (the offset from point 0).

the slope of a line is the ratio y/x defining how many units y changes when x changes a certain amount of units.

in our example,

y = 5x - 10

5 (or rather 5/1) is the slope of the line.

it means that y grows by 5 units every time x grows by 1 unit.

a perpendicular line (cuts the original line with a 90 degree angle) has a related slope : it reverts x and y and flips the sign :

5/1 turns into -1/5

that means at the perpendicular line whenever x grows by 5 units, y goes down by 1 unit.

so, the first approach for the perpendicular line is

y = -1/5 x + b

to get b we use the given point (6, 5) that has to be in the perpendicular line.

5 = -1/5 × 6 + b

25/5 = -6/5 + b

31/5 = b

=> y = -1/5 x + 31/5

the intersecting point is now where both lines are equal

5x - 10 = -1/5 x + 31/5

25x - 50 = -x + 31

26x = 81

x = 81/26

y = 5×(81/26) - 10 = 405/26 - 260/26 = 145/26

the distance of the given point (6, 5) to the line intersection point (81/26, 145/26) is the calculated as

distance² = (6 - 81/26)² + (5 - 145/26)²

distance = sqrt((6-81/26)² + (5-145/26)²)

since the result was not requested here, I save us the calculation.

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In the following image, AB is parallel to DC, and BC is a transversal intersecting both parallel lines. The measure of angle ABC
AlexFokin [52]

Answer:

n° = 62°

p° = 62°

q° = 118°

v° = 84°

w° = 138°

Step-by-step explanation:

angle ABC is 118°

so

m° + 118° = 180

m° = 180° - 118°

m° = 62°

n° = m° = 62° (corresponding angles are equal since AB is parallel to DC, and BC)

p° = n° = 62° (vertical angles are equal)

q° + n° = 180° (linear pair angles)

q° + 62° = 180°

q° = 180° - 62°

q° = 118°

v° + 96° = 180° (linear pair angles)

v°  = 180° - 96°

v° = 84°

w° + 42° = 180 (linear pair angles)

w° = 180° - 42°

w° = 138°

8 0
3 years ago
In the spinner below, what is true about the probability of landing on 3 and the probability of landing on 4?
Karo-lina-s [1.5K]

Answer:

C.The probabilities are equal.  

The above statement is the only TRUE statement.

Step-by-step explanation:

Here, the given number of total possibilities are { 0,1,2,3,4,5,6,7,8,9}

So, number of total outcomes = 10

Let E : Event of spinner landing on 3

and E' : Even of spinner landing on 4

{Probability of Event E}  =  \frac{\textrm{Total number of favorable outcomes}}{\textrm{Toatl outcomes}}

\implies P(E) = \frac{1}{10}

⇒ P( landing on 3 ) = 1/10

and  P(E') = \frac{1}{10}

P( landing on 4 ) = 1/10

Now, the given statements are

A.The probability of landing on 3 is less than  probability of landing on 4.

FALSE, as both the probabilities are equal to 1/10.

B.The probability of landing on 3 is greater than probability of landing on 4.

FALSE, as both have same probabilities.

C.The probabilities are equal.

TRUE, both have same probability = 1/10

D.The probabilities cannot be predicted

FALSE, the probability are predictable.

3 0
3 years ago
Read 2 more answers
the peak of Mt. johnson is 19,360 feet above sea level. The top of Mt. Harrison is 23,350 feet above sea level. round each heigh
Murrr4er [49]
19,360 would round to 19,000 and 23,350 would round to 23,000.
4 0
3 years ago
Write an equation in standard form for each line.
LenaWriter [7]

The standard form: Ax + By = C.

The point-slope form:

y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}


7. We have the points (4, -7) and (2, -3). Substitute:

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8. We have the points (1, 5) and (-10, -6). Substitute:

m=\dfrac{-6-5}{-10-1}=\dfrac{-11}{-11}=1\\\\y-5=1(x-1)\\\\y-5=x-1\qquad|+5\\\\y=x+4\qquad|-x\\\\-x+y=4\qquad|\text{change the signs}\\\\\boxed{x-y=-4}


7 0
3 years ago
What is this expression in simplrest form 24v/3v
olasank [31]
If you would like to know what is the following expression in the simplest form, you can calculate it like this:

If you 24v / 3v divide by v, you will get 24 / 3. Now, if you divide 24 by 3, you will get 8.

The simplest form of 24v / 3v would be 8.
8 0
3 years ago
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