Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Triangle ABC is defined by the points A(3,8), B(7,5), and C(2,3).
Create an equation for a line passing through point A and perpendicular to BC.
y=
X +
Reset
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Answers
Answer:
y = - [tex]\frac{5}{2}[/tex] x + [tex]\frac{31}{2}[/tex]
Step-by-step explanation:
Calculate the slope m of BC using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = B (7, 5 ) and (x₂, y₂ ) = C (2, 3 )
[tex]m_{BC}[/tex] = [tex]\frac{3-5}{2-7}[/tex] = [tex]\frac{-2}{-5}[/tex] = [tex]\frac{2}{5}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{5} }[/tex] = - [tex]\frac{5}{2}[/tex] , then
y = - [tex]\frac{5}{2}[/tex] x + c ← is the partial equation
To find c substitute A (3, 8 ) into the partial equation
8 = - [tex]\frac{15}{2}[/tex] + c ⇒ c = 8 + [tex]\frac{15}{2}[/tex] = [tex]\frac{16}{2}[/tex] +[tex]\frac{15}{2}[/tex] = [tex]\frac{31}{2}[/tex]
y = - [tex]\frac{5}{2}[/tex] x + [tex]\frac{31}{2}[/tex] ← equation of perpendicular line
The equation for a line passing through point A and perpendicular to BC is 2y = -5x +31 or y = -2.5x +15.5.
What is the equation of a Straight Line ?The equation of the straight line is represented by
y = mx+c
where m is the slope , and c is the intercept on y axis.
The equation of the line BC for points B(7,5), and C(2,3) is
y- y' = m(x-x')
m = 2/5
and c =
y-5 = (2/5)x - (14/5)
y = (2/5)x+(11/5)
The slope of the line perpendicular rot this line is given by
as the product of two perpendicular lines should be -1
m = -5/2
y = (-5/2)x +c
8 = (-15/2) + c
8 +(15/2) = 0
31/2 = c
Therefore the equation for a line passing through point A and perpendicular to BC is
2y = -5x +31
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Related Questions
If 400 kids went to the amusement park and only 120 came back how many got lost?
Answers
Answer:
280
Step-by-step explanation:
400 - 120=280
280= number of children lost
11. Find the slope of a line which passes through the points (3,4) and (8,-1).
a. -1
b. 1
c. ⅗
d. 5/3
Answers
Answer:
A
Step-by-step explanation:
Slope = (change in y)/ (change in x)
= (-1 - 4)/ (8 - 3)
= -5/5
= -1
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Answer:
x^3 + 3x^2 + 4x = 0
0^3 + 3(0)^2 + 4(0) = 0
Step-by-step explanation:
x = 0
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HELPPP!!! WILL MARK BRAINLIEST!!! 10 PTS
Find an equation for the graph sketched below:
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Plot the coordinate points and connect them with a smooth curve.
Hope This Help you po..
pa brainlest?
The equation for the graph is y = [tex]2(3)^{x} -5[/tex] .
What are Exponential Equations?An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.
Standard exponential equation :
y = [tex]a(b)^{x} + k[/tex]
where a is the initial value
b represents the base of the exponential function
x will represent the input of the function
y = k is the single horizontal asymptote
k is constant
According to the question
The figure in the graph is an exponential graph .
To derive the equation
we will use Standard exponential equation :
y = [tex]a(b)^{x} + k[/tex]
Now,
There are two points in graph
(0.-3) and (1,1)
k = - 5 ( distance from 0)
now ,
Substituting the values
y = [tex]a(b)^{x} + k[/tex]
y = [tex]a(b)^{x} -5[/tex]
for point (0.-3)
-3 = [tex]a(b)^{0} -5[/tex]
-3 = [tex]a -5[/tex]
a = 2
for point (1,1)
1 = [tex]2(b)^{1} -5[/tex]
1 = 2b - 5
b = 3
Therefore , equation of exponential graph is
y = [tex]2(3)^{x} -5[/tex]
Hence ,The equation for the graph is y = [tex]2(3)^{x} -5[/tex] .
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weak spots on a human body
Answers
Answer:
eyes
Step-by-step explanation:
Answer:
the heart the brain the eyes
Step-by-step explanation:
[tex]-3\log_{3}\left(x-2\right)=-25[/tex]
Thanks!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!...........
Answers
[tex] - 3 log_{3}(x - 2) = - 25 \\ = > log_{3}(x - 2) = \frac{ - 25}{ - 3} \\ = > log_{3}(x - 2) = \frac{25}{3} \\ = > (x - 2) = ( \frac{25}{3} ) ^{3} \\ = > x - 2 = \frac{15625}{27} \\ = > x = \frac{15625}{27} + 2 \\ = > x = \frac{15625 + 54}{27} \\ = > x = \frac{15679}{27} \\ = > x = 5226.33[/tex]
Answer:
5226.33 (approximate value)
Hope you could get an idea from here.
Doubt clarification - use comment section.
Also if I can I give brainiest answer to first person
10. A stockbroker charges his customers $30 to open an account and
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Answers
Answer:
the answer is 22
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Step-by-step explanation:
15n as it increases each month and 30 as it never changes and will always be a value of 30
Answer:
15n+30=360
Step-by-step explanation:
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15n+30=360
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when we went shopping I had $15 i lent $5 and spen $8 then borrow $12 from down at the end did I have money in my purse or did I owe money how much
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Step-by-step explanation:
The first day of Sam's vacation was a Monday.
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Answer:
I think it was monday also
Answer:
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Angle ABC measures 35 and angel BAC meausures 115
Answers
Answer:
a. 115 degrees
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c. 30 degrees
Step-by-step explanation:
In a circle L, M, N are the points on the circle forming a triangle with LM = LN and mZMLN is 35' then what is m(arc LN)?
Answers
Answer:
145°Step-by-step explanation:
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Answer:
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Step-by-step explanation:
By definition,
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Step-by-step explanation:
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b. f(0)
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Answers
Step-by-step explanation:
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b.f(0)=(0-1)
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Answers
Answer:
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Step-by-step explanation:
2x + y = 4 → y = -2x + 4
y = -2x + 4 → y = -2x + 4
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2x + 2y = 4 → y = -x + 2
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Answers
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Answer:
$0.50Step-by-step explanation:
Given
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Answer:
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6+3 = 9 inches of wire
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Answers
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Step-by-step explanation:
I answered another similar question by you earlier, so I really hope you read through this explanation, as I will go far in depth. It's important you learn to do this so as not to simply skate through homework, then struggle with assessment.
For this problem, you have to find something called a unit price.
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9514 1404 393
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Step-by-step explanation:
Figure B appears to be a reflection of Figure A across the origin. Such a reflection can be described by any of ...
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Step-by-step explanation:
1) rule:
[tex]d=\sqrt{(X_A-X_B)^2+(Y_A-Y_B)^2)}[/tex]
2) according to the rule above:
[tex]d=\sqrt{36+4}=2\sqrt{10};[/tex]
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6.3
Step-by-step explanation:
help please
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Answers
Answer:
57+20= 90 (false)
40+39= 79 (true)
Answer:
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Step-by-step explanation:
14 * 9(-9) - 8 = 1142 9 - 45(-3) + 7 = 151
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Answer:
B= 40 degress
Step-by-step explanation:
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Answer:
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You have at most $20 to spend at an arcade. Arcade games cost $0.75 each, and snacks cost $2.25 each. Write an inequality that represents the numbers of games (x )you can play and snacks( y) you can buy.
The inequality is ??
Answers
Answer:
y ≤ -1/3x+80/9
Step-by-step explanation:
(1). 0.75(x)+2.25(y) ≤ 20
0.75 - Number of arcade games (X).
2.25 - Number of snacks (Y).
20 - The total.
(2). 0.75x+2.25y≤20
(After multiplying the x's and y's together, with the numbers).
(3). 0.75x (-0.75x) + 2.25y ≤ 20 (-0.75x)
(Subtract -0.75x to each side, which allows the equation to get closer to the answer).
(4). 2.25y -0.75x + 20
———— = ————
2.25 2.25
(Divide by 2.25 to each side).
(5). y ≤ -1/3x + 80/9
(The result and the inequality).