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 +
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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
Does anyone know how to do multiple in fractions like for a example 1/12•1/3? Please explain step by step
Answers
[tex] \frac{1}{12} \times \frac{1}{3} \\ = \frac{1 \times 1}{12 \times 3} \\ = \frac{1}{36} [/tex]
When you want to multiply 2 fractions, merge the fractions together & then multiply the numerator first & then the denominator. After that, simplify to the lowest form if possible.Ibrahim spends 1/3 of his earnings on food and 1/4 on clothes. He then saves the rest.what fraction does he (a) spend altogether (b)save 1 What fraction does he (a) spend altogether (b) Save?
Answers
Saving = 12/12 - 7/12 = 5/12
A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
The formula for adding two fractions:
= a/b + c/d
= (ad + bc) / cd
The fraction spent altogether on food and clothes is 7/12.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Fraction of earnings spend on food:
= 1/3
Fraction of earnings spend on clothes:
= 1/4
Fraction of total spending on food and clothes.
= 1/3 + 1/4
= (4 + 3) / 12
= 7/12
The formula for adding two fractions:
= a/b + c/d
= (ad + bc) / cd
Fraction of earnings saved after spending on food and clothes.
= 1 - 7/12
= (12 - 7) / 12
= 5/12
Thus,
The fraction spent altogether on food and clothes is 7/12.
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Write an equation for the line that passes through the given point and is parallel/perpendicular to the graph of the given point.
Parallel: Y=3x-2; (3,2)
Perpendicular: Y= -2x-1; (2,-1)
Also I will mark brainly to who explain what they did step by step
Answers
Answer:
Parallel: The slope is the same as in the previous equation. So, y=3x+b. To find the value of b, you plug in the given point, 2=3(3)+b, b=-7. So the equation is y=3x-7.
Perpendicular: The slope is the negative reciprocal when an equation is perpendicular. The negative reciprocal of -2 is 1/2. So, y=1/2x+b. To find the value of b, you plug in the given point, -1=1/2(2)+b, -1=1+b, b=-2. So the equation is y=1/2x-2.
:)
9514 1404 393
Answer:
parallel: y = 3x -7perpendicular: y = 1/2x -2Step-by-step explanation:
The given line equations are written in "slope-intercept" form.
y = mx + b . . . . . . . . . m is the slope; b is the y-intercept
If we solve this equation for b, we find ...
b = y - mx
This is useful for completing the equation of the line through a given point when the slope is known.
ParallelA parallel line will have the same slope as the given line. The given line has a slope (x-coefficient) of 3. We can find the "b" of the line through the desired point as ...
b = y -3x
b = 2 -(3)(3) = -7
The equation of the parallel line is ...
y = 3x -7
__
PerpendicularA perpendicular line will have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to. Here, the given line has a slope of -2, so the perpendicular line will have a slope of ...
-1/(-2) = 1/2
Then the y-intercept is ...
b = y -(1/2)x
b = -1 -(1/2)(2) = -2
And the equation of the perpendicular line is ...
y = 1/2x -2
__
The attached graph shows the original lines as dashed lines, and the corresponding desired lines as solid lines in the same color.
A man finished 2/3 of a project in 4hours. Working at the same rate, how long will it take him to finish 5/6 of the same project?
Answers
It will take 6 hours to finish the same project.
How to find the time taking to finish the project?From the given information, we get
[tex](\frac{5}{6} * \frac{2}{3} ) * 4[/tex] = 6
The answer is 6 hours.
What is problem-solving?Problem-solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution.
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Naomi is still not sure how many boxes of each type of candy to order. Her dad explains that he needs to do a little more mathematics before she can determine the best candy order. He creates a table to help her determine the solution.
He asks her to calculate how much money the band would make if she ordered 500 boxes of
each type of candy. He also asks her to calculate the profit on an order of 300 boxes of milk
chocolate and 500 boxes of dark chocolate. Determine both answers and show your work.
Answers
Answer:
how much does each box cost?
Step-by-step explanation:
0.35 x 9 = 3.15
Is this an overstatement understatement
Answers
[tex]over \: \: statement \: \\ \\ 0.35 \times 9 = 3.15 \\ \\ multiply \: 0.35 \times 9 \\ 3.15 = 3.15 \\ \\ so \: the \: answer \: is \: \: overstatemnt \\ \\ hope \: \: it \: \: helps[/tex]
y < -2x + 1
x + 2y > -4
Answers
Answer:
99
Step-by-step explanation:
Find the domain and range for the function shown in the
graph given below.
Answers
Answer:
d{0 less than or equal to x less than or equal to 20, xer}
r{0 less than or equal to y less than or equal to -6,yer}
Step-by-step explanation:
The Domain and Range of the graph given is -
Domain ↔ [1, -6]
Range ↔ [- 21, 20]
We have a graph as shown in the figure.
We have to determine its domain and range.
What do you mean by domain and range of a function?For any function y = f(x), Domain is the set of all possible values of y that exists for different values of x. Range is the set of all values of x for which y exists.
According to question, we have -
From the graph it is clear that -
The values of y belong to the set - [1, -6]
and
The values of x belong to the set - [- 21, 20]
Therefore, according to the definition of domain and range -
Domain ↔ [1, -6]
Range ↔ [- 21, 20]
Hence, the Domain and Range of the graph given is -
Domain ↔ [1, -6]
Range ↔ [- 21, 20]
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solve the following inequality for n -5n+6≥-7(5n-6)-6n
Answers
Answer: The inequality is: n ≥ 36/37
Step-by-step explanation:
Let's solve your inequality step-by-step.
n − 5n + 6 ≥ −7(5n−6)−6
----------------------------------------------------------------------------------------------------------------
Step 1: Simplify both sides of the inequality.
−4n + 6 ≥ −41n + 42
----------------------------------------------------------------------------------------------------------------
Step 2: Add 41n to both sides.
−4n + 6 + 41n ≥ − 41n+ 42 + 41n
37n + 6 ≥ 42
----------------------------------------------------------------------------------------------------------------
Step 3: Subtract 6 from both sides.
37n + 6 − 6 ≥ 42 − 6
37n ≥ 36
----------------------------------------------------------------------------------------------------------------
Step 4: Divide both sides by 37.
37n/37 ≥ 36/37
n ≥ 36/37
----------------------------------------------------------------------------------------------------------------
Answer:
n ≥ 36/37
Source: https://www.mathpapa.com/calc.html?q=x+y%3D7%2C%20x+2y%3D11
, Hope this helps :)
Have a great day!!
inver laplace
[tex] {l}^{ - 1} ( \frac{s}{( {s}^{2} + 16)^{2} } ) [/tex]
Answers
Answer:
s
_______________
ls^4 + 32ls^2 + 256l
Step-by-step explanation:
I used an algebra calculator called MathPapa to solve your equation.
Also, welcome to brainly!
In the equation 4x² - 16x + 12 = 0, the solution is?
Answers
Hope this helps<3
Answer:
x = 3 or x = 1Step-by-step explanation:
[tex] {4x}^{2} - 16x + 12 = 0 \\ {4x}^{2} - 4x - 12x + 12 = 0 \\ 4x(x - 1) - 12(x - 1) = 0 \\ (4x - 12)(x - 1) = 0 \\ [/tex]
(4x - 12) = 0 or (x - 1) = 0
[tex](4x - 12) = 0 \\ 4x - 12 = 0 \\ 4x = 0 + 12 \\ 4x = 12 \\x = \frac{12}{4} \\ x = 3 \\ [/tex]
[tex](x - 1) = 0 \\ x - 1 = 0 \\ x = 0 + 1 \\ x = 1[/tex]
x = 3 or x = 1 should be.
HELLO I NEED A MATH EXPERT RIGHT NOW TO HELP ME WITH SOME MATH STUFF
IF YOUR NOT A MATH EXPERT THEN DONT ANSWER
Answers
Answer:
what's your question
Step-by-step explanation:
what's your question
ANSWER
7y-20=3y+12
= 7y-20+20= 3y + 12 + 20
= 7y = 3y + 32
= 7y -3y = 3y + 32 - 3y
= 4y = 3y + 32 -3y
= 4y =32
= y = 32/4
= y = 8
Thank you :).....
An aquarium has 5 gallons of water in it and is being filled up at a rate of g gallons every m minute. The amount of water w in the tank can be represented by the equation
w = 5 + g - m. Write an equation that can be used to find the number of minutes m the tank has been filled if we know w and g.
Write an equation that can be used to find the number of minutes g the tank has been filled if we know w and a.
Answers
Answer:
m=5+g-w
Step-by-step explanation:
This should be the answer based on the equation given.
Answer:
See belowStep-by-step explanation:
The equation for the amount of water is:
w = 5 + gmSolve for m:
gm = w - 5m = (w - 5)/gNow solve for g:
gm = w - 5g = (w - 5)/mWhich equation represents the line that passes through C(2,4) and is perpendicular to the graph of y=1/3x-1?
Answers
Answer:
Step-by-step explanation:
y=-3x + b the slope is the negative inverse of 1/3
4=3(2) + b
b =-2
the equation is
y=-3x - 2
slope is the negative inverse. You find the y intercept, b, by plugging in the point (2,4) to get 4=3(2)+b
Members of a softball team raised $1319.25 to go to a tournament. They rented a bus
for $776.50 and budgeted $41.75 per player for meals. Write and solve an equation
which can be used to determine p, the number of players the team can bring to the
tournament. Giving 100 points please help
Answers
Answer:
13 players
Step-by-step explanation:
Money Raised=RentedBus+Meals
1319.25=776.50+41.75p (p is for the number of players)(Now we solve for x)
Subtract 776.50 from both sides: 542.75=41.75x
Divide both sides by 41.75: 13=x
Remember that x is for the number of players so there'll be 13 players going to the tournament.
Answer:
1319.25=776.50+41.75p
13 players
Step-by-step explanation:
PLEASE HELP :(
Which order do these go in?
Will mark BRAINLEST
Answers
Answer:
1 - 5
2 - 3
3 - 8
4 - 1
5 - 2
6 - 7
7 - 4
8 - 6
Step-by-step explanation:
Help very urgent, . . .
Answers
Answer: 3.1
Step-by-step explanation:
The answer is 3.1 hope this helps
Giving brainliest for number 31
Answers
Answer:
b, d, c
Step-by-step explanation:
Answer:
C.
Step-by-step explanation:
f(x)=x²-x
#CarryOnLearning
hopeithelps,,thanks
Does the point (–3, 4) satisfy the equation y = –2x + 5? Yes Or No
Answers
Answer:
No
Step-by-step explanation:
y = -2x + 5
4 = -2(-3) + 5 - Substitute both x and y
4 = 6 + 5 - Simplify
4 ≠ 11
Hence, no, (-3, 4) doesn't statify the equation y = -2x + 5
If 3x + 2y= 14 and 5x + 3y = 12, then find the value of 5x- y.
a. 100
b. 124
c. -100
d. -124
Answers
Scientists often write very large or very small numbers using exponents. How might a scientist write the number shown using exponents?
make it look like a seventh grader wrote it please
Answers
What is the value of x in the proportion below? -
2/3 over 5 = x over 15
•2
•3
•10
•75
Answers
Answer:
2/3 over 15 is 10
so 10/5=2
2 is the answer
Step-by-step explanation:
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of $950. What was the rate charged per hour by each mechanic if the sum of the two rates was $125 per hour?
Answers
Answer:
First mechanic: $65.
Second mechanic: $60.
Step-by-step explanation:
Let the rates be x for the first mechanic and y for the second.
x + y = 125
10x + 5y = 950
Multiply first equation by - 5
-5x - 5y = -625
Adding the last 2 equations:
5x = 325
x = 65
y = 125-65 = 60 .
What is the length of the red line segment on the number line?
A. 2
B. 2 1/2
C. 1
D. 1 1/2
Answers
Step-by-step explanation:
I think it's D 1 1/2......
x = - 23
y = - 5
z = - 10
[tex](x-12)/ (y+z)\\[/tex]
Answers
i had to do the answer as a pic cuz my iPad is gonna die.
sorry <:)
Answer:
7/3Step-by-step explanation:
x = - 23
y = - 5
z = - 10
(x - 12)/(y+z)=
(-23 - 12)/(-5-10)=
45/15=
7/3
six cocker spaniels have a total weight of 192 pounds. Five golden retreivers have a average weight of 71 pounds. what is the average weight of all 11 dogs.
Answers
Answer:
23.9lbs or 24lbs
Step-by-step explanation:
This may not be correct so don't bet your first born on it
What phrase in the problem indicates that estimated product is being asked for?
Pa HELP POOOOOOOO
Answers
Answer:
571 x 32 = 18,272
Step-by-step explanation:
Okay, multiplication was always a favorite.
Think of this, 571 thirty-two times.
I need help to find the side
Answers
Answer:
x = 10.55cm
Step-by-step explanation:
Sin 29 degrees = 7cm/x
X = 7cm / sin 29
= 10.55 cm
Answer:
x =14.4cm
Step-by-step explanation:
Sin x = opp/hyp
This is because we are given angle look into the triangle and see opp given =7 and need hypotenuse
Sin x = 7 / sin (29) = 14.4386574 cm = 14.4cm
This is because the opp is the 7 measure.
x = 14.4cm
We can prove the base is less through Pythagoras theorem
simply as c^2-b^2 = a^2
14.4386.....^2 -7^2 = c^2
sqrt 208.47 - sqrt 49 =c^2
c^2 = sqrt 159 = 7.43849023
therefore base = 7.44
To check angle 29 degrees for 3rd proof
cos (29) x 7/x= (x)
= 203 / x
check 203/29 = 7
Given a=7 and ∠α=29°,
b = 12.62833
c = 14.43866 proof
∠β = 61°
h = 6.12234
area = 44.19917
perimeter = 34.06699
inradius = 2.59484
circumradius = 7.2193
fill in the table using the function rule. Y=2x-1
Answers
Answer:
what table?
Step-by-step explanation:
BRAINLIEST PLEASE !!!!!!!!!!!!!!!!!!
The hypotenuse of a right triangle is 7 feet long. One leg is 4 feet longer than the other. Find the lengths of the legs, Round to the nearest tenth of a foot
The length of the shorter leg is ft, and the length of the longer leg is ft.
(Do not round until the final answer. Then round to the nearest tenth as needed)
Help Me Solve This
View any
Answers
Answer:
Shorter leg = 2.5 ft.
Longer leg = 6.5 ft.
Step-by-step explanation:
a^2 + b^2 = c^2
Because the hypotenuse = 7 ft, a^2 + b^2 = 49
To represent the two legs, we can use x and x+4.
x^2 + (x+4)^2 = 49
Simplifying this equation using FOIL gives us 2x^2 + 8x - 33 = 0.
Then, using the quadratic formula, we find that x = 2.5.
Thus, the shorter leg is 2.5 ft. and, when 4 is added, the longer leg is 6.5 ft.