Find the gradient of the line perpendicular to AB
Find the equation of the line perpendicular to AB and passing through point C
Answers
Answer:
a) 3
b) y=3(x-2)-2
Step-by-step explanation:
a)
Step 1: Find the gradient/slope of AB
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]=[tex]\frac{-2-2}{7-(-5)} =\frac{-4}{12} =-\frac{1}{3}[/tex]
Step 2: Find the gradient/slope of the line perpendicular to AB
The slope of the line perpendicular to AB is the reciprocal of the slope of the line AB multiplied by -1, so the slope of the line perpendicular to AB is 3.
b)
Step 1: Find the formula for the equation of a line
If you have a point and the slope, you can use the point-slope form, which is y-y1=m(x-x1).
Step 2: Plug in values to the formula
y-(-2)=3(x-2)
Step 3: Simplify
y+2=3(x-2)
y=3(x-2)-2
[tex]$a)$[/tex] The gradient of a line perpendicular to line [tex]$AB$[/tex] is [tex]$3$[/tex].
[tex]$b)$[/tex] The equation of the line perpendicular to line [tex]$AB$[/tex] and passing through point [tex]$C$[/tex] is [tex]y=-\frac{1}{3}x+\frac{13}{3}[/tex].
What is slope of perpendicular lines?
Lines that are perpendicular lines have slopes that are negative reciprocals.
It is given that the points,
[tex]$A=\left( -5,2 \right)$[/tex]
[tex]$B=\left( 7,-2 \right)$[/tex]
[tex]$C=\left( -2,5 \right)$[/tex]
[tex]$a)$[/tex] We will find the gradient of a line perpendicular to line [tex]$AB$[/tex] by using the slope formula.
So,
By the definition, the slope or gradient of a line describes its steepness, incline, or grade.
[tex]$m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$[/tex] which is equal to [tex]$\tan \left( \theta \right)$[/tex].
Where [tex]$m$[/tex] is the slope and [tex]$\theta $[/tex] is the angle of incline.
So,
Slope [tex]$\left( m \right)=\frac{-2-2}{7-\left( -5 \right)}$[/tex]
[tex]m=\frac{-1}{3}[/tex]
So, The slope of the line perpendicular to [tex]AB[/tex] is the reciprocal of the slope of the line [tex]AB[/tex] which is multiplied by [tex]-1[/tex].
so the slope of the line perpendicular to [tex]AB[/tex] is [tex]3[/tex].
[tex]b)[/tex] We will find the equation of the line perpendicular to [tex]AB[/tex] passing through the point [tex]C[/tex] that is [tex](-2,5)[/tex] by using the formula,
[tex]y=mx+b[/tex]
Here,
[tex]y=5[/tex]
[tex]x=-\frac{1}{3}[/tex]
We will find the [tex]y-[/tex] intercept of the line [tex](b)[/tex] first.
So,
[tex]$5=-\frac{1}{3}\left( -2 \right)+b$[/tex]
[tex]$5=\frac{2}{3}+b$[/tex]
Subtract [tex]\frac{2}{3}[/tex] both side.
So,
[tex]$b=\frac{13}{3}$[/tex]
So, the line perpendicular to [tex]AB[/tex] and passing throught the point [tex]C[/tex] is,
[tex]y=-\frac{1}{3}x+\frac{13}{3}[/tex].
Hence,
[tex]$a)$[/tex] The gradient of a line perpendicular to line [tex]$AB$[/tex] is [tex]$3$[/tex].
[tex]$b)$[/tex] The equation of the line perpendicular to line [tex]$AB$[/tex] and passing through point [tex]$C$[/tex] is [tex]y=-\frac{1}{3}x+\frac{13}{3}[/tex].
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Related Questions
What is the reciprocal of 3 1/8
Answers
Answer:
11
Step-by-step explanation:
because it would be the reciprical of 1/8 which is 8/1 plus 3
James's Dog, Buddy, is 2 years older than Fluffy, the neighbor's cat. Three Years ago, Buddy was three times older than fluffy. How old are the dog and cat now?
Answers
Answer: The cat is 4 years old, and the dog is 6 years old.
Step-by-step explanation:
We know that Buddy is 2 years old than Fluffy.
And 3 years ago, Buddy was 3 times older than Fluffy.
Let's define the variables:
B = age of Buddy
F = age of Fluffy.
The first statement can be written as:
B = F + 2
The second statement can be written as:
B - 3 = 3*(F - 3)
To solve this, we can replace the first equation into the second one, and solve that for F
B - 3 = 3*(F - 3)
(F + 2) - 3 = 3*F - 9
F - 1 = 3*F - 9
-1 + 9 = 3*F - F
8 = 2*F
8/2 = 4 = F
Fluffy is 4 years old, and with the first equation we can find the age of Buddy.
B = F + 2 = 4 + 2 = 6
Buddy is 6 years old
The required age of the dog buddy is 6 years old and the age of cat fluffy is 4 years old.
Given ,
James's dog buddy is 2 years older than Fluffy,
And the neighbor's cat Three Years ago, Buddy was three times older than fluffy.
Let ,
The age of buddy = B
The age of fluffy is = F
According to the question ,
Buddy, is 2 years older than Fluffy= Age of Buddy = Age of fluffy + 2 years older.
B = F +2
Again According to the question,
Three years ago age of Buddy = B - 3
Three years ago age of Fluffy = F - 3
Three years ago Buddy was three times older than fluffy = Three years ago age of Buddy = 3 × Three years ago Age of fluffy
B - 3 = 3 ( F - 3 )
Solving the equations,
B - 3 = 3 ( F - 3 )
Put the value of B from equation 1
F + 2 - 3 = 3 ( F -3 )
F - 1 = 3F - 9
F - 3F = - 9 +1
-2F = -8
2F = 8
[tex]F = \frac{8}{2}[/tex]
F = 4
The age of fluffy is 4 years old.
Then ,
The age of buddy
B = F + 2
B = 4 + 2
B = 6
The age of buddy is 6 years old.
The required age of the dog buddy is 6 years old and the age of cat fluffy is 4 years old.
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Increase £761 by 77%. Give your answer to 2 DP
Answers
Answer:
£1346.97Step-by-step explanation:
Step one
given the amount £761
we are asked to increase this amount by 77%
let us first find 77% of the amount £761
=77/100*761
=0.77*761
= £585.97
Step two:
Hence 77% of £761 is £585.97
therefore the increase will be to add the two amounts together
=£585.97+£761
=£1346.97
Pls i need help with this geometry problem. Its due today .
Answers
Answer:
63
Step-by-step explanation:
Set up the proportion
(6x+3)/17 = (8x - 1)/21 Cross Multiply
21 * (6x + 3) = 17 (8x - 1) Remove the brackets
126x + 63 = 136x - 17 Subtract 126x from both sides
63 = 136x - 126x - 17 Combine
63 = 10x - 17 Add 17 to both sides
63 + 17 = 10x Combine the left
80 = 10 x Divide by 10
80/10 = x
x = 8
Now you want 8x - 1
8*8 - 1 = 63
rewrite 4^-3 using a positive exponent an evaluate the result.
Answers
Answer: 1/4³
Step-by-step explanation:
When finding the negative exponent of a number, you turn it into a fraction, with the numerator being 1, and the denominator being the base of the exponent, and the exponent being positive.
Examples:
2^-2 = 1/2²
3^-3 = 1/3³
4^-4 = 1/4⁴
help me fast please
Answers
10y+10
COMMENT FOR A BETTER EXPLAINATION
[tex] \: \: \: \: \: \: \: \: \: \: 4y - 2(3y - 5) \\ \\ = > 4y- 6y + 10 \\ \\ = > \green{\boxed{ - 2y + 10}}[/tex]
what is the expression !! Help I’ll give brainlest
Answers
Answer:
The answer is answer choice C. A - B/2
Step-by-step explanation:
Can somebody please help me with this question!
Answers
Step-by-step explanation:
angle A = angle D
angle C common angle
angle E = 180 - 63 - 52
5x = 65
x = 13deg
Topic: congruence and similarity
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Answer:
x = 13°
Step-by-step explanation:
Because of the given congruency,
Angle A = Angle D = 63°.
Angle C = 52°
Angle B = Angle E = 5x
Now, In Triangle ABC,
Angle A + Angle B + Angle C = 180°.
63° + 5x + 52° = 180°
115° + 5x = 180
5x = 65°
x = 13°
HOPE IT HELPS!!!
cc is guaranteed the larger of $500 per week or 7% of sales. last week she 4 sold $6785. How much was her check for?
Answers
Answer:
Step-by-step explanation:
6785*7%=474.95 in commission
500 per week salary is more
Answer:
6785*7%= 474.95
Step-by-step explanation:
Hope this helps
Lemme know
Congruent polygons are _________________ polygons for which the ratio of the corresponding sides is 1:1.
Answers
9514 1404 393
Answer:
"similar"
Step-by-step explanation:
Congruent polygons will have corresponding sides in the ratio 1:1, but they must also have identical corresponding angles. The description of figures with identical corresponding angles (along with proportional sides) is that they are "similar".
Congruent polygons are similar polygons for which the ratio of the corresponding sides is 1:1.
first 1 i got the answer but i want the 2
Answers
Look
At
The
Photo
Attached
ABCD is a rectangle. Find the measure of the following angles (select an answer for each row)
Answers
Answer:
Angle 1 - 24 degrees
Angle 2 - 48 degrees
Angle 3 - 66 degrees
Angle 4 - 66 degrees
Angle 5 - 24 degrees
Angle 6 - 66 degrees
Angle 7 - 132 degrees
Step-by-step explanation:
I wanted to get this too you as fast as possible. I will add a detailed explanation in the comments.
Which statement must be true? The monthly salary of Shenika is less spread out than the monthly salary of Clarissa. The monthly salary of Kaila is less spread out than the monthly salary of Abi. The monthly salary of Abi is less spread out than the monthly salary of Shenika. The monthly salary of Clarissa is less spread out than the monthly salary of Abi.
Answers
Answer: The monthly salary of Shenika is less spread out than the monthly salary of Clarissa.
Step-by-step explanation:
Hi. Your question isn't complete but I got something close to it online.
The monthly mean salaries and standard deviations of four college students are given below. student mean standard deviation clarissa $345 12.53 abi $598 8.99 kaila $812 15.29 shenika $208 7.67 which statement must be true?
We can see that while Shenika has a mean of $208 and a standard deviation of 7.67, Clarissa has a mean of $345 and a standard deviation of 12.53. This simply means that monthly salary of Shenika is less spread out than the monthly salary of Clarissa.
Answer:
A - The monthly salary of Shenika is less spread out than the monthly salary of Clarissa.
Step-by-step explanation:
edge
Solve
493 km 43 m + 17 km 57 m
What is this answer
Answers
Answer:
510.1
Step-by-step explanation:
convert m to km by dividing by 1000 and add all of the numbers together
The senior classes at High School A and High School B planned separate trips to the water park. The senior class at High School A rented and filled 14 vans and 2 buses with 270 students. High School B rented and filled 9 vans and 9 buses with 459 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.
Answers
Answer:
x = number of students in the van = 14
y = number of students in the bus = 37
Step-by-step explanation:
Let
x = number of students in the van
y = number of students in the bus
14x + 2y = 270 (1)
9x + 9y = 459 (2)
Multiply (1) by 9 and (2) by 2
126x + 18y = 2,430 (3)
18x + 18y = 918 (4)
Subtract (4) from (3)
126x - 18x = 2,430 - 918
108x = 1,512
x = 1,512 / 108
= 14
x = 14 students in each van
Substitute x = 14 into (1)
14x + 2y = 270
14(14) + 2y = 270
196 + 2y = 270
2y = 270 - 196
2y = 74
y = 74/2
= 37
y = 37 students in each bus
x = number of students in the van = 14
y = number of students in the bus = 37
can someone help, please !!
Answers
Write a linear equation in slope intercept form of a line with a slope of 12 and y intercept of 10
Answers
Answer:
y = 12x + 10
Step-by-step explanation:
The equation of the line in slope-intercept form is y = 12x + 10.
What is a slope?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope is 12 and the y-intercept is 10, we have:
y = 12x + 10
Therefore, the equation of the line in slope-intercept form is y = 12x + 10.
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Find m∠XYZ in the figure if ∠XYZ and ∠PQR are supplementary angles.
Question 5 options:
A)
83°
B)
7°
C)
97°
D)
173°
Answers
Answer: C
Step-by-step explanation:
Supplementary angles add up to 180
x + 83 = 180
x= 97
Ms. Zerngast’s favorite candy is a snickers bar. It costs 7.80$ for 6 large snickers candy bars. She likes to buy them at our local center market. How many candy bars can Ms.Zerngast buy for $18.20
Answers
Answer:
14 bars
Step-by-step explanation:
Mark me brainliest plz
Slope is -2/3 and (-6,-5) is on the line
Explain correctly equation
Answers
Answer:
y= -2/3x - 9
Step-by-step explanation:
y-y1=m(x-x1)
y-(-5)= -2/3(x-(-6)
y+5=-2/3(x+6)
y+5= -2/3x - 4
y= -2/3x - 9
Your swim team competes in the 200-meter freestyle relay. The individual times for the four team members are 27.81, 26.89, 26.55, and 25.48 seconds. What is the total relay time for the team?
Answers
Answer:
106.73
Step-by-step explanation:
Which of the four Venn diagrams represents this?
Answers
Answer:
A i think
Step-by-step explanation:
....... X U Y
means x united y
which is both x and y
Here, Option D is the right answer in the given Venn diagram.
What is Venn diagram?
A Venn diagram is a diagram that represents the logical relation between two or more sets.
Y' represents everything except Y inside the box.
When we do X ∪ Y', it will represent the total area inside the box where only Y is not there.
Hence, Option D is right answer.
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Which diagram can be used to prove △ABC ~ △DEC using similarity transformations?
Triangle A B C is rotated about point C and then is dilated to form smaller triangle C E D.
Triangle A B C is reflected across side A C and then is dilated to form smaller triangle C E D.
Triangles A B C and C E D have different angle measures.
Right triangle A B C is shown. Line segment D E is drawn near point C to form triangle D E C.
Answers
Answer:
A
Step-by-step explanation:
I like math
Answer:
Answer is A
Step-by-step explanation:
edge2021
Line m is perpendicular to x − 2y = −1 and passes through (9, 2). What is the slope of line m?
Answers
Answer:
7
Step-by-step explanation:
What is 6-124+9?????
Answers
Answer:
the answer is -109
:)
Answer:
-109
Step-by-step explanation:
Craig has made 60% of 80 free throw attempts this season. How many free throws has he made
Answers
Answer:
Step-by-step explanation:
80*60%= 48 free throws were made
Answer: 48
Step-by-step explanation:
80x 0.01=0.8
0.8x 60=48
What’s are the answers for parts A and B
Answers
Step-by-step explanation:
hope this helps, happy learning!!!
Rahul has a farm he wishes to fence. The farm is the pentagon ABCDE, shown below. He knows that ABCD is a 140 m by 150 m rectangle, as shown below. He also knows that E is 50 m from the side AB and 30 m from the side BC. Determine the length of AE, the length of DE, and the perimeter of pentagon ABCDE
Answers
The diagram of the pentagon is missing, so i have attached it.
Answer:
|AE| = 130 m
|DE| = 150 m
Perimeter of pentagon = 720 m
Step-by-step explanation:
From the diagram, we can find AE from pythagoras theorem;
|AE| = √(|AA'|² + 50²)
Where AA' is the length from A to the perpendicular angle.
Now, AB = 150, and A'B is parallel to 30 m. Thus, A'B = 30
AA' = AB - A'B = 150 - 30
AA' = 120
Thus;
|AE| = √(120² + 50²)
|AE| = √(14400 + 2500)
|AE| = √16900
|AE| = 130
Similarly,
|DE| = √(|DD'|² + |ED'|²)
ED' = BC - 50
ED' = 140 - 50
ED' = 90
Also, DD' is parallel to AA' and is = 120
Thus;
|DE| = √(120² + 90²)
|DE| = √22500
|DE| = 150
Perimeter of pentagon = 150 + 130 + 150 + 150 + 140 = 720
plz help me due tommorow
Answers
Step-by-step explanation:
angle ABD = 180 - 116 = 64° (angles on a straight line are supplementary)
angle x = 2(64) = 128° (angle at centre = 2angle at circumference)
Topic: Circle properties
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plzz help pythagorean theorem
Answers
Answer:
very easy 65inches
Step-by-step explanation:
follow me
Explanation:
a^2+b^2=c^2
63^2+16^2=c^2
256+3969= 4225
Then you find the square root of 4225 which is 65
So you do 16+63+65