Line l contains points (11,-1) and (-3,-11). Point P has coordinates (-1,1). Find the distance from P to l

Answers

Answer 1

For the line l:
y - y1 = [( y2 - y1 ) / ( x 2 - x 1 )] * ( x - x 1 )
y + 1 = ( -11 + 1 ) / ( - 3 - 11 ) * ( x - 11 )
y + 1 = 5/7 x - 55/7
y = 5/7 x - 55/7 - 7/7
Finally:
y = 5/7 x - 62/7
So the line that passes through P and which is perpendicular to line l has
m = - 7/5
1 = -1 * ( -7/5 ) + b
1 = 7/5 + b
b = - 2/5
Line p:
y = - 7/5 x - 2/5
Then we will find the point of intersection of lines p and l:
- 7/5 x - 2/5 = 5/7 x - 62/7 / * 35
- 49 x - 14 = 25 x - 310
x = 4
y = 5/7 * 4 - 62/7 = 6
Finally:
d = sqrt( ( 4 - (-1 ))² + ( - 6 - 1 )² ) = sqrt ( 25 + 49 ) = √ 74
Answer:
d = √ 74 ≈ 8.6

Answer 2

Distance from point (-1,1) to line l: [tex]$ \frac{60}{\sqrt{74}} $[/tex] units.

To find the distance from point P to line l, we can use the formula for the distance between a point and a line in the coordinate plane.

The formula to find the distance from a point (x1, y1) to a line Ax + By + C = 0 is given by:

[tex]\[ \text{Distance} = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}} \][/tex]

Where A, B, and C are the coefficients of the equation of the line, and (x1, y1) are the coordinates of the point.

First, let's find the equation of the line passing through the points (11, -1) and (-3, -11).

The slope of the line, m, can be calculated using the formula:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

[tex]\[ m = \frac{-11 - (-1)}{-3 - 11} = \frac{-11 + 1}{-3 - 11} = \frac{-10}{-14} = \frac{5}{7} \][/tex]

Now, we have the slope of the line. We can use the point-slope form of the equation of a line:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

Using one of the given points, let's say (11, -1):

[tex]\[ y - (-1) = \frac{5}{7}(x - 11) \][/tex]

[tex]\[ y + 1 = \frac{5}{7}(x - 11) \][/tex]

Now, let's convert this equation into the standard form Ax + By + C = 0:

[tex]\[ \frac{5}{7}x - y - \frac{5}{7} \cdot 11 + 1 = 0 \][/tex]

[tex]\[ \frac{5}{7}x - y - \frac{55}{7} + 1 = 0 \][/tex]

[tex]\[ \frac{5}{7}x - y - \frac{55}{7} + \frac{7}{7} = 0 \][/tex]

[tex]\[ \frac{5}{7}x - y - \frac{48}{7} = 0 \][/tex]

Now, we have the equation of line l:[tex]$\frac{5}{7}x - y - \frac{48}{7} = 0$[/tex]

Now, we can plug in the coordinates of point P (-1, 1) into the formula for the distance:

[tex]\[ \text{Distance} = \frac{| \frac{5}{7}(-1) - 1 - \frac{48}{7} |}{\sqrt{(\frac{5}{7})^2 + (-1)^2}} \][/tex]

[tex]\[ = \frac{| -\frac{5}{7} - 1 - \frac{48}{7} |}{\sqrt{\frac{25}{49} + 1}} \][/tex]

[tex]\[ = \frac{| -\frac{5}{7} - \frac{7}{7} - \frac{48}{7} |}{\sqrt{\frac{25 + 49}{49}}} \][/tex]

[tex]\[ = \frac{| -\frac{60}{7} |}{\sqrt{\frac{74}{49}}} \][/tex]

[tex]\[ = \frac{\frac{60}{7}}{\frac{\sqrt{74}}{7}} \][/tex]

[tex]\[ = \frac{60}{\sqrt{74}} \][/tex]

So, the distance from point P to line l is [tex]$\frac{60}{\sqrt{74}}$[/tex] units.

Related Questions

Describe the translation from AB TO AB

Answers

→A = (-5,1)

A' = (4,3)

so x moved from -5 to 4 which is an increase of 9

so x+9

y moved from 1 to 3 which is an increase of 2

so y+2

so answer should be:

(x,y) → (x+9,y+2)

BRAINLIETS ND POINTSTO ANSWER THAT SHOWS ALL WORK YOU MIGHT NEED TO WORK OUT ON PAPER!!!
you are given the following equation:
+6=4/5(+3)

3a. Identify the slope of the equation.

3b. Identify the point used in the equation.

3c. Graph the equation.

Answers

the slope is 4/5
the points used were (-3,-6) and (2,-2)

Factor 64-x^15 in mathhhhgg

Answers

Answer:

Factor of [tex]64-x^{15}[/tex] is [tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]

Step-by-step explanation:

We need to factor the expression [tex]64-x^{15}[/tex]

Re-write the given expression [tex]64-x^{15}[/tex] as;

[tex]4^{3}-(x^{5})^{3}[/tex]

Since, [tex]a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})[/tex]

so, here [tex]a = 4[/tex] and [tex]b = x^{5}[/tex]

[tex](4-x^{5})(4^{2}+4x^{5}+(x^{5})^{2})[/tex]

[tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]

Hence, factor of [tex]64-x^{15}[/tex] is

[tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]

The value of factor of expression 64 - x¹⁵ is,

⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)

We have to given that;

To factor the expression,

⇒ 64 - x¹⁵

Now, We can simplify as;

⇒ 64 - x¹⁵

⇒ 4³ - (x⁵)³

⇒ (4 - x⁵) (4² + 4x⁵ + (x⁵)²)

⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)

Therefore, The value of factor of expression 64 - x¹⁵ is,

⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)

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A television network counted 1,771,548 viewers watching the golf tournament on its channel.There where 5,861,014 viewers watching a football game on another channel. Round eack number to the nearest thousand about how many viewers were watching the two events on telveision? A. 7,500,000 B. 7,600,000 C.7,700,000 D. 8,000,000

Answers

First, we add the amount of viewers together. {1,771,548 + 5,861,014 = 7,632,562} Rounded to the nearest thousand, {7,632,562} is B. 7,600,000. Remember, when rounding, 5-9 you go up a number, but any number 1-4 is rounded to 0.

Hope I helped! ☺♥

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A simple index of three stocks opens the day with these values: The index rises 3.4% over the course of the day. What is the value of the index at the end of the day? Round your answer to the nearest hundred.

Answers

If I am doing the math correctly, the value of the index at the end of the day would be 4. I found this answer by multiplying 3 by 0.34 which equaled 1.02, and when rounded to the nearest hundred, is 1.

Answer:

The value of the index at the end of the day is $45392.6.

Step-by-step explanation:

Given : A simple index of three stocks opens the day with these values:

[name] [number of shares] [price per share]

stock x 5000 shares $4.10

stock Y 2000 shares $4.50

stock z 4000 shares $3.60

The index rises 3.4% over the course of the day.

To find : What is the value of the index at the end of the day? Round your answer to the nearest hundred ?

Solution :

Stock values of x,y and z is given by,

Stock x,

[tex]5000\times 4.10=\$20500[/tex]

Stock y,

[tex]2000\times 4.50=\$9000[/tex]

Stock z,

[tex]4000\times 3.60=\$14400[/tex]

The total amount will be

[tex]A=20500+9000+14400[/tex]

[tex]A=\$43900[/tex]

The index rises 3.4% over the course of the day.

The value of the index at the end of the day is

[tex]V=43900 \times (1+3.4\%)\\V=43900 \times (1+0.034)\\V=43900 \times 1.034\\V= 45392.6[/tex]

Therefore, the value of the index at the end of the day is $45392.6.

Find the ratio of 1 feet. 4 inches. to 1 yard

Answers

1 foot 4 inches = 1 foot * (12 inches)/(1 foot) + 4 inches = 16 inches
1 yard = (1 yard) * [(3 feet)/(1 yard)] * [(12 inches)/(1 foot)] = 36 inches

The ratio is: (16 inches)/(36 inches) = 16/36 = 4/9
(Note: the ratio has no units; it is expressed here as a fraction)

The ratio of 1 foot 4 inches to 1 yard is 16:36 or 4:9.

To find the ratio of 1 foot 4 inches to 1 yard, we first need to convert both measurements to the same unit. Since there are 3 feet in a yard and 12 inches in a foot, we can express both measurements in inches.

1 foot is equivalent to 12 inches.

Therefore, 1 foot 4 inches is:

1 [tex]\times[/tex] 12 + 4 = 12 + 4 = 16 inches

Now, since there are 3 feet in a yard, and each foot has 12 inches, 1 yard is equivalent to:

3 [tex]\times[/tex] 12 = 36 inches

Now we have both measurements in inches, and we can set up the ratio:

16 inches: 36 inches

Therefore, the simplified ratio is:

16:36.

We can further simplify this ratio by dividing both numbers by 4:

(16/4):(36/4) = 4:9.

True or false in a two column proof the right column states your reasons

Answers

In two column proof the right column states your reasons is true statement.

In a two-column proof, the right column typically contains the statements of reasons or justifications for each step taken in the left column.

The left column contains a sequence of statements that represent the logical progression of the proof, while the right column provides the reasoning or logical basis for each step to show that it follows from the previous statements.

This format is commonly used in geometry to provide a clear and organized presentation of the proof's logical structure.

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A fish tank at an aquarium has a volume of 1,568 cubic feet and a depth of 8 feet. If the base of the tank is square, what is the length of each side of the tank?

Answers

volume = l x w x h

1568 /8 = 196

sqrt(196) = 14

each side is 14 feet

Answer with Step-by-step explanation:

A fish tank is in the shape of cuboid.

It's height is 8 feet

and volume=1568 cubic feet

we know that volume of cuboid=lbh

where l is the length, b is the width and h is the height

The base of the tank is square

i.e. l=b

Volume=l²h

⇒ 1568=l²×8

⇒ l²=196

⇒ l=14

Hence, The length of base of tank=14 feet

width of tank=14 feet

and height=8 feet

x = {(2, 4), (3, 4), (4, 4), (5, 4)} Is x a function and why?

Answers

f(x). "f(x) = ... " is the classic way of writing a function. And there are other ways, as you will see! .... Example: {(2, 4), (2,5), (7,3)} is not a function because {2,4} and {2,5} means that 2 could be related to .

This is a function because no x-values repeat. If you were to graph all these numbers and then do the vertical line test it would pass because none of the x-values repeat.

What is 0.182 rounded to the 2 decimal point?

(2dp)

Answers

0.182 rounded to the 2 decimal point = 0.18

hope it helps

Which set of ordered pairs could be generated by an exponential function?

Answers

I would say C because when looking at the y-values, 1/2 x 2 = 1, 1 x 2 = 2, and 1 x 2 = 4. I hope this helps a bit!!

ANSWER

The correct answer is option C.

EXPLANATION

In order to determine which ordered pairs are generated by an exponential function, we examine the y-coordinates to see which one has a constant ratio.

As for the first ordered pairs,

[tex] \frac{0}{ \frac{1}{2} } \ne \frac{ \frac{1}{2} }{0} [/tex]
These ordered pairs cannot be generated by an exponential function.

For the second option also,
[tex] \frac{0}{ - 1} \ne \frac{ 1}{0} [/tex]

These ordered pairs too cannot be generated by an exponential function.

For the the third option,

[tex] \frac{1}{ \frac{1}{2} } = \frac{2}{1} = \frac{4}{2} = 2[/tex]

Therefore these ordered pairs were generated by an exponential function.

The fourth option too,

[tex] \frac{0}{1} \ne \: \frac{1}{0} [/tex]

The ordered pairs could not be generated by an exponential function.

A pizza is cut into eight slices the slices are all the same size Carolina ate 2 slices what fraction of the pizza did Carolina eat

Answers

if there is a total of 8 slices, and Carolina ate 2 of them, then she ate 2/8 which reduces to 1/4 of the pizza

At a canning company the daily production cost, y, is given by the quadratic equation y = 650 – 15x + 0.45x2, where x is the number of canned items. What is the MINIMUM daily production cost?
A) $1,025.00 B) $1,186.25 C) $525.00 D) $536.25

Answers

The equation is a parabola so the minimum point is the vertex.

(-b/2a, y)

x = 15/0.9 = 16.67 canned itemz
y = 524.95 $

So it's C.

Answer:

Option C) is correct

Step-by-step explanation:

Given : y is the daily production cost at a canning company such that [tex]y=650-15x+0.45x^2[/tex] wherex is the number of canned items .

To find : Minimum daily production cost

Solution :

[tex]y=650-15x+0.45x^2[/tex]

On differentiating both sides with respect to x, we get

[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=-15+0.9x[/tex]

On putting [tex]\frac{\mathrm{d} y}{\mathrm{d} x}=0[/tex] , we get [tex]-15+0.9x=0\Rightarrow 15=0.9x\Rightarrow x=\frac{15}{0.9}=\frac{150}{9}=\frac{50}{3}[/tex]

We get intervals as \left ( -\infty , \frac{50}{3}\right )\,,\,\left ( \frac{50}{3},\infty \right )[tex]\left ( -\infty , \frac{50}{3}\right )\,,\,\left ( \frac{50}{3},\infty \right )[/tex]

For [tex]x=0\epsilon \left ( -\infty ,\frac{50}{3} \right )[/tex] , [tex]f'(0)=-15< 0[/tex]

For [tex]x=16\epsilon \left ( \frac{50}{3},\infty \right )[/tex] , [tex]f'(18)=-15+0.9(18)=-15+16.2=1.2> 0[/tex]

Therefore, [tex]y=\frac{50}{3}[/tex] is a point of minima.

So, minimum cost is equal to [tex]y\left ( \frac{50}{3} \right )[/tex]

[tex]y\left ( \frac{50}{3} \right )=650-15\left ( \frac{50}{3} \right )+0.45\left ( \frac{50}{3} \right )^2=650-250+125=\$ 525[/tex]

So, option C) is correct .

A personal trainer makes $25,000 per year and has just begun contributing 6% of his salary to his 401k plan if his employer matches 9% of his contributions how much will have been contributed to the 401k plan after 4 years

Answers

(25,000 x .06) x 1.09 x 4 = answer.

Hank draws a line with a zero slope through the points (–2, 4) and (3, b). Which value of b could represent Hank’s second point? –3 –1 4 9

Answers

4
(-2,4)(3,4)

4-4. / 3- -2=. 0/5=0

So the answer is 4

Hope this helped

As per the slope of a line, the value of 'b' is 4.

What is the slope of a line passing through two points?

The slope of a line(m) passing through two points (x₁, y₁) and (x₂, y₂)can be represented as:

m = (y₂ - y₁)/(x₂ - x₁)

Given, the slope of the line is (m) = 0.

Here the given points are (–2, 4) and (3, b).

Therefore, substituting the values, we get:

0 = (b - 4)/[(3 - (- 2)]

⇒ (b - 4)/5 = 0

⇒ b - 4 = 0

⇒ b = 4

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Jane has $1000 that she would like to put in a savings account. The table below shows the balance over time in her account at a local bank.

Based on this model, how much would Jane have in her account after 12 years? Round to the nearest dollar if necessary.

time (years) balance in account
0 1000
1 1080
2 1166.40
3 1259.71
4 1360.49

answers
A.2518
B.2520
C.3000
D.2500

Answers

The answer is C. 3000

b is the answer to your question

Which of the following is the range thanks

Answers

c. Its just the right hand column.:)

Which ordered pairs are solutions to the inequality 2x+y>−4?
Select each correct answer.

(5, −12)

(−3, 0)

(−1, −1)

(0, 1)

(4, −12)

Answers

we will proceed to resolve each case to determine the solution

we have

[tex]2x+y>-4[/tex]

[tex]y>-2x-4[/tex]

we know that

If an ordered pair is the solution of the inequality, then it must satisfy the inequality.

case a) [tex](5,-12)[/tex]