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
The first day of Sam's vacation was a Monday.
What was the day of the week on Sam's 36
day of vacation?
Answers
Answer:
I think it was monday also
Answer:
The day of the week on Sam's 36th
day of vacation would be Tuesday.
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:
ΔLMN is isosceles with angle L being 35°.
Angle measure of M and N is same:
m∠M = m∠N = 1/2(180 - 35) = 72.5Arc measure is twice the intercepting angle, since the angle is not central:
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Answers
Answer: 171 attendees
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.
A unit price is the price in dollars per thing.
In this case, the price in dollars for the whole group is $132 for many things, 66 attendees.
Because 66 attendees costs $132, to find out how much money a single attendee costs, simply divide $132 by 66 to get 2$ for 1 attendee.
With this information, it is very straightforward to determine the number of attendees for $342. Simply divide $342 by $2 to get 171 attendees.
I really hope it helps :) and please, let me know if you want me to explain in more depth, the unit you are currently in is a fundamental part of early math, and it is important you understand it.
Solve: x^3+3x^2+4x=0
Answers
Answer:
x^3 + 3x^2 + 4x = 0
0^3 + 3(0)^2 + 4(0) = 0
Step-by-step explanation:
x = 0
please help with finding the midpoint
Answers
Answer: (-4, -6)
Step-by-step explanation:
Find the middle so find the averages of the x points and the y points
average of -6 and 2 is -4
average of -8 and -4 is -6
the point is (-4, -6)
Angle ABC measures 35 and angel BAC meausures 115
Answers
Answer:
a. 115 degrees
b. 35 degrees
c. 30 degrees
Step-by-step explanation:
For this function: f(x)=I-3x-1I
find each of the following:
a. f(-1)
b. f(0)
c. f(3)
Answers
Step-by-step explanation:
a. f(-1)=(3-1)
=2
b.f(0)=(0-1)
=-1
c.f(3)=(-9-1)
=-10
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Write 0.34 as a fraction using the steps below.
Answers
Answer:
31/90
Step-by-step explanation:
3.1 x 10 = 31 which is the numerator
9x10 = 90 which would be the denominator
Answer:
It would be 17/50 hope that helps
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).
The cost of making a cake is $9. The Baker wants to make a profit of $ 9 per cake and the cake is to be cut into 36 pieces, what is the selling price of each piece?
Answers
36/18= 0.5
Each piece= $0.50
Answer:
$0.50Step-by-step explanation:
Given
Cost price = $9Selling price of the cake is:
$9 + $9 = $18Selling price of each piece:
$18/36 = $0.50HELPPP!!! WILL MARK BRAINLIEST!!! 10 PTS
Find an equation for the graph sketched below:
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Answer:
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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Answers
Answer:
6.3
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]
d≈6.3
Answer:
6.3
Step-by-step explanation:
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Which equation does not belong? Explain your reasoning 2x + y = 4 y = -2x + 4 f(x) = -2x + 4 2x + 2y = 4
Answers
Answer:
2x + 2y = 4 does not belong
Step-by-step explanation:
2x + y = 4 → y = -2x + 4
y = -2x + 4 → y = -2x + 4
f(x) = -2x + 4 → y = -2x + 4
2x + 2y = 4 → y = -x + 2
[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.
Sam is playing a board game. He must roll dice to determine if he gets an extra turn. The probability of getting an extra turn is 6/17. Find the odds in favor of getting an extra turn.
Answers
Answer:
6 to 11
Step-by-step explanation:
By definition,
the odds in favor of getting an extra turn =
(# of chances to get an extra turn in 17 attempts) / (# of chances to not get an extra turn in 17 attempts) =
6 to (17 - 6) =
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
14 * 9(-9) - 8 = 1142 9 - 45(-3) + 7 = 151
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Answer:
Step-by-step explanation:
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Step-by-step explanation:
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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
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Answers
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Also if I can I give brainiest answer to first person
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$15 per month to manage the account. Write an equation to represent the
number of months, n, an account has been open if the total cost is $360.
Answers
Answer:
the answer is 22
the equation is 30 + 15n
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:
$15 per month is being charged
The flat fee is $30
The Total cost is 360
15n+30=360
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Tammy uses 6 inches of wire to make a necklace and 3 inches of wire to make a
bracelet. How many necklace and bracelet sets can she make if she uses 28 inches of
wire in all?
Answers
Answer:
3 sets
Step-by-step explanation:
6+3 = 9 inches of wire
28/9 = 3 1/9
so 9 can go into 28 three times
so tammy can make three sets of neclaces and bracelets
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