Radical functions are of the form f(x)=n√x.
If we want to find the inverse of a radical function, we will need to restrict the domain of the answer because the range of the original function is limited. Determine the range of the original function. Replace f(x) with y, then solve for x.
MORE: Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root. Radicand - A number or expression inside the radical symbol. Radical equation - An equation containing radical expressions with variables in the radicands.
To reverse that operation, you can find the square root of that power: In this case, the sign asks you to find which factor can be multiplied by itself twice to equal the expression inside the radical. (The expression inside the radical is also called the radicand.)
Learn more about Radical here https://brainly.com/question/13430746
#SPJ4
Nicole and Daniel are splitting a pizza. Nicole eats 1/4 of the pizza and Daniel eats 2/3 of it. How much pizza is left? Write an equation to represent this situation.
Answer:
1 - 1/4 - 2/3 = r
Step-by-step explanation:
N=1/4, D=2/3
whole pizza=1
r=remainder pizza
1 - 1/4 - 2/3 =r
(1 - 1/4 - 2/3 =r)*12 ==> multiply by 12 to get rid of denominators
12 - 12/4 - 12*2/3=12r
12-3-24/3=12r
9-8=12r
12r=1
r=1/12 of a pizza left
Answer:
1/12
Step-by-step explanation:
the common number of 3 and 4 is 12. You multiply 1/4 by three and you get 3/12, and you multiply 2/3 by 4 and you get 8/12. You add 8 and 3 and you get 11, that's the number that indicates the part of the eaten pizza. 12-11=1. 1/12 left from the pizza.
PLEASE WORK OUT THE PROBLEMS CORRECTLY. GET IT RIGHT AND GET BRAINLIEST!!!!
Answer:
Question 1 is x = 2, y = 2, z = 2
Question 2 is x = 1, y = 1, z = -3
Question 3 is x = 13, y = -10, z = -7
Question 4 is x = 5, y = -2, z = -3 (C)
Question 5 is x = 2, y = 0, z = -2
Step-by-step explanation:
I did not have time to do this...
you have c pieces of candy to share among 6 friends what epression shows the nnmber of the candies each freind will get
Answer:1
Step-by-step explanation if c is for 6 its 1 p
Answer:
C/6
Step-by-step explanation:
you have c pieces to share with 6 friends.
Find the distance between the points L(7,-1) and M(-2, 4). Answer in simplest exact
Form
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ L(\stackrel{x_1}{7}~,~\stackrel{y_1}{-1})\qquad M(\stackrel{x_2}{-2}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ LM=\sqrt{(~~-2 - 7~~)^2 + (~~4 - (-1)~~)^2} \implies LM=\sqrt{(-2 -7)^2 + (4 +1)^2} \\\\\\ LM=\sqrt{( -9 )^2 + ( 5 )^2} \implies LM=\sqrt{ 81 + 25 } \implies LM=\sqrt{ 106 }[/tex]
Write each equation in logarithmic form. 10⁻³=0.001
-3 is equation in logarithmic form.
What is the purpose of logarithm?
A logarithm is a mathematical formula that calculates how many times the base, or initial number, must be multiplied by itself to produce the target number.
A logarithm is defined simply?
The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2: log 100 = 2.10⁻³=0.001
log. 001 = -3 log 10 = -3
Learn more about logarithm
brainly.com/question/28346542
#SPJ4
Eduardo started a business selling sporting goods. He spent $7500 to obtain his merchandise, and it costs him $300 per week for general expenses. He earns $850 per week in sales. What is the minimum number of weeks it will take for Eduardo to make a profit?
Which inequality models this problem?
300w>7500+850w
850w≥7500+300w
850w<7500+300w
850w>7500+300w
The minimum number of weeks it will take for Eduardo to make a profit
850w > 7500 + 300w. Option D
This is further explained below.
What is the minimum number of weeks it will take for Eduardo to make a profit?Generally, the Total cost is mathematically given as
X= $7500+$300w
Where he is earning each week
=$850
Therefore,
He will be paid in n weeks=$850n
The information that has been presented states that the very bare minimum number of weeks that it will take for Eduardo to earn a profit is by.
Total revenue is more than total expenditures
850w > 7500 + 300w
Read more about inequality
https://brainly.com/question/20383699
#SPJ1
what is 209.3 ÷ 80 without a remainder
Answer:
2.61625
Step-by-step explanation:
209.3 divided by 80
what do i subtract with a positive number to produce a negative number?
Answer:9
Step-by-step explanation:draw a line threw the equal sign, add 36 instead of subtracting it, which then would be 9.
Answer:
down below
Step-by-step explanation:
In order for you to get a negative number, you need to put in the variables place, 9.
9 is your answer.
I dont know how to do this please help!
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
We want to find the value of 'x':
[tex]\hookrightarrow \text{ thus we must first find the value of '4x'}[/tex]
[tex]\hookrightarrow \text{EC and GH are parallel lines intersected by the same line BG}[/tex]
[tex]\hookrightarrow \text{angles formed by the parallel lines and a intersecting lines}[/tex] [tex]\hookrightarrow \text{ are equal in measure }[/tex]
[tex]\hookrightarrow \text{thus angles BEC and EGH are equal in measure}[/tex]
Angle EGH is made up of two angles, ∠EGC and ∠CGH
∠EGC is 78 degrees∠CGH = ∠FGI = 14 degrees (Vertical Angle Theorem)⇒ ∠EGH = ∠EGC + ∠CGH = 78 + 14 = 92 degrees
Since ∠BEC = ∠EGH
[tex]\hookrightarrow 4x = 92\\\hookrightarrow x = 92/4 = 23[/tex]
Answer: 23
Hope that helps!
#LearnwithBrainly
Vertical Angle Theorem: two angles that are formed by two intersecting lines and are opposite each other are equal
The value of x is 23 because Angle FGI and Angle HGC are vertically opposite angles, the answer is 23.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
It is given that:
The triangle and two parallel lines are shown in the picture.
As we know, from the definition of the vertically opposite angle, two lines intersect each other at the intersecting point.
Angle FGI = Angle HGC = 14 degrees
4x = 78 + Angle HGC
4x = 78 + 14
4x = 92
x = 92/4
x = 23
Thus, the value of x is 23 because Angle FGI and Angle HGC are vertically opposite angles, the answer is 23.
Learn more about the vertically opposite angles here:
brainly.com/question/24287162
#SPJ2
Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
5 f(x) / g(x)
The values for 5 f(x) / g(x) = (10x+25) / x²-3 x+2
What are the domain of the function f(x)=2 x+5 and g(x)=x²-3 x+2?Given;
f(x)=2 x+5 and g(x)=x²-3 x+2
5 f(x)= 5(2x+5 )
= 10x+25
5 f(x) / g(x) = (10x+25) / x²-3 x+2
To learn more about the domain, visit;
brainly.com/question/956872
#SPJ4
A Blue Line train and a Yellow Line train just left the station at the same time. Blue Line trains run every 10 minutes, and Yellow Line trains run every 12 minutes. How long will it be until a Blue Line train and a Yellow Line train are at the station at the same time?
It takes 60 minutes (1 hour) for the Blue Line train and the Yellow Line train to be at the station at the same time, using their running time LCM.
How is the meeting time determined?The time that it will take the Blue Line train and the Yellow Line train to meet again at the station is determined using the Least Common Multiple or Factor.
The LCM is the smallest positive integer that is evenly divisible by both numbers, 10 and 12.
For instance, the LCM of 10 and 12 include 60 and 120 with 60 as the least.
Data and Calculations:The time the Blue Line runs is every 10 minutes.
The time the Yellow Line runs is every 12 minutes.
The LCM of 10 and 12 is 60 because 10 and 12 can divide 60 without a remainder.
Thus, it will take 60 minutes for the two trains to meet again at the station.
Learn more about Least Common Multiple at https://brainly.com/question/16054958
#SPJ1
WHAT I SHOULD HAVE DONE
1 CUP MILK
4 SCOOPS
CHOCOLATE
WHAT I DID
1 CUP MILK
5 SCOOPS
CHOCOLATE
Answer the questions on each slide.
Use complete sentences. You do not have to show your work.
If it asks to explain, please provide an explanation.
How should I fix this to equal 1/4?
Answer:
just add more to the milk and another scoop of chocolate
Step-by-step explanation:
1.5 cups milk
6 scoops of chocolate
i need help with this
Answer:
y = 3x² + 2
Step-by-step explanation:
I'm help to number on more this, thank for subject on help for today.
WILL GIVE BRAINLIST TO BEST ANSWER
Arabella sells cars at a local dealership and gets paided by commission. she has already made $750 and will continue to earn $200 per car that's she sells. If her goal is to make $2750 by the end of the month, write + solve the equation below that models this months goal.
Answer:
$2,750 = $200x + $750
10 cars to meet the goal
Step-by-step explanation:
We will pull details we need to solve out of the question:
If her goal is to make 2,750 dollars, the money earned must equal at least $2,750.
If she's already made $750, then we can subtract that from what is needed left to make (or add it to what needs to be made).
Finally, she makes $200 per car. Let x equal the number of cars she sells.
Next, we will write an equation:
$2,750 = $200x + $750
Lastly, we will solve this equation.
$2,750 = $200x + $750
$2,000 = $200x
10 = x
She needs to sell 10 cars to meet her goal.
Read and try to solve the problem below. Look at the circumference of each of the circles below. What do you think would be the circumference of a circle with diameter 1 cm? 2 cm C = 6.28 cm 3 cm C = 9.42 cm 4 cm C = 12.56 cm 2.5 cm C = 15.70 cm
The formula for calculation of circumference of the circle = d π or 2πr where d is diameter of circle and r is the radius of circle
As given in the question the circumference of the circle whose diameter is 2 cm is 6.28cm and we come to know that value of π used here is 3.14 and not 22/7
So, the circumference of the circle whose diameter is 1cm = d π
= 1 π
= 1 3.14
= 3.14 cm
Hence the circumference of the circle whose diameter is 1cm using the value of pi as 3.14 comes out to be pi that is 3.14 cm
To know more about circumference of the circle - https://brainly.com/question/11213974
#SPJ9
What is 3/4c - 1 = 1 + 3/4c? Thanks!
Answer:
False
Step-by-step explanation:
You want to know "what is 3/4c - 1 = 1 + 3/4c?"
SolutionSubtracting the left-side expression from both sides, we get ...
(3/4c -1) -(3/4c -1) = (1 +3/4c) -(3/4c -1)
0 = 2 . . . . a False statement
__
Additional comment
Since the equation is written without parentheses, we have to assume that c is in the numerator in each expression, and that its coefficient is (3/4).
Becky created a graph to represent her distance away from home one afternoon. She left home and ran to the park, met some friends and stayed at the park, and then walked back home using the same route. Which graph could Becky have created?
A graph titled Becky's distance from home. The horizontal axis shows time (minutes) and the vertical axis shows distance (miles). Both axes are unnumbered. The line shows an increase, constant, and decrease in distance.
A graph titled Becky's distance from home. The horizontal axis shows time (minutes) and the vertical axis shows distance (miles). Both axes are unnumbered. The line shows an decrease, constant, and decrease in distance.
A graph titled Becky's distance from home. The horizontal axis shows time (minutes) and the vertical axis shows distance (miles). Both axes are unnumbered. The line shows an increase and decrease in distance.
A graph titled Becky's distance from home. The horizontal axis shows time (minutes) and the vertical axis shows distance (miles). Both axes are unnumbered. The line shows a constant, decrease, and increase in distance.
First graph is correct which satisfies the given informations.
The graph is attached below.
Given:
Becky made a graph to show how far she was from her house.
She started jogging from zero distance from the house when she left and sprinted to the park, so the second and fourth graphs are incorrect.
She then spent some time at the park with some friends before returning home on the same path. The first one is accurate since we can see that for a brief while, the graph is parallel to the time axis, but the third one demonstrates that she hasn't taken a break.
Learn more about distance here:
https://brainly.com/question/5993643
#SPJ1
The larger of two numbers is one more than four times the smaller number. If the sum of the numbers is 106, find the numbers.
a
32,56
b
32,74
c
21,85
d
52,54
Answer:
c. 21, 85
Step-by-step explanation:
Define the variables:
Let the two numbers be x and y, where x > y.
Given information:
The larger of two numbers is one more than four times the smaller number.The sum of the number is 106.Create two equations from the given information and defined variables:
[tex]\begin{cases}x = 4y + 1\\x + y = 106\end{cases}[/tex]
Substitute Equation 1 into Equation 2 and solve for y:
[tex]\implies (4y+1)+y=106[/tex]
[tex]\implies 4y+1+y=106[/tex]
[tex]\implies 5y+1=106[/tex]
[tex]\implies 5y+1-1=106-1[/tex]
[tex]\implies 5y=105[/tex]
[tex]\implies \dfrac{5y}{5}=\dfrac{105}{5}[/tex]
[tex]\implies y=21[/tex]
Substitute the found value of y into the second equation and solve for x:
[tex]\implies x+21=106[/tex]
[tex]\implies x+21-21=106-21[/tex]
[tex]\implies x=85[/tex]
Therefore, the two numbers are 21 and 85.
Learn more about systems of equations here:
https://brainly.com/question/27868564
https://brainly.com/question/28281431
(a) A booster rocket for a spacecraft has a mass ratio of about 15 , an exhaust velocity of 2.1 km /s , and a firing time of 30s . Can the spacecraft achieve a stable orbit 300km above Earth?
Using the mass ratio, the spacecraft's velocity was determined to be 7.7025 km/s.
Here, c = 2.7 km/s, t = 30s, R = 20
On substituting the values of 'R', 't', 'v', we get:
v = -0.0098 ( 30) + 2.7 ( ln (20))
=> v = - 0.294 + 2.7 (2.995)
=> v = 7.7025 km/s
What is a spacecraft?A spaceship is a machine or vehicle built to travel through space. Spacecraft are a form of artificial satellite used for a wide range of tasks, such as communications, Earth observation, meteorology, navigation, space colonization, planetary exploration, and cargo and person transfer.
Following are the main distinctions between spaceships and rockets: The spacecraft is launched into space by rockets, which then crash to Earth. Rockets are never manned, whereas spacecraft can be either manned or unmanned. Additionally, spacecraft cannot match the power of rockets.
To learn more about spacecraft from the given link:
brainly.com/question/13478702
#SPJ4
Write a radical function such that for its domain, the function is onto the set of real numbers such that y≤3
A radical function such that y≤3 is given by y=-√|x|+3 .
A radical function is defined as a function which has the independent variable within a radical sign.
A radical sign is also defined as the power of the variable to be a fraction.
We know that the n-th root of x is similar to x to the power of (1/n) .
The domain of the function is onto the set of real numbers which means that the domain contains all real numbers.
The range of the function is given as y≤3, that is the value of y can take a maximum value of 3.
Hence we can write a function where x ∈ R and y ≤ 3 .
Let us consider the function y=-√|x|+3
The above functions satisfies all the criteria for the question. It is a radical function and the maximum value can be 3 as -√|x| can have a max value of 0 for all x ∈ R .
To learn more about radical function visit:
https://brainly.com/question/11676335
#SPJ4
What is the domain of f(x) = |x+2| ?
What is the domain of f(x) = -2x²+5 ?
The range of the function f(x) = x2 is larger than or equal to zero, and its domain includes all real numbers (x can be any number).
What is domain in math?
The collection of possible inputs into a function, or the set of input values for which the function is defined, is known as the domain of the function. The set of things that the machine will accept as inputs is known as the domain in the function machine paradigm.The domain of f(x) = |x+2| -
Real numbers only
The range of the function f(x) = x2 is larger than or equal to zero, and its domain includes all real numbers (x can be any number).
The domain of f(x) = -2x²+5
All real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this instance, the phrase is defined even if there is no real number.
Learn more about domain
brainly.com/question/28135761
#SPJ9
A pair of parallel lines is cut by a transversal.
If m∠A = (5x − 4)° and m∠B = (8x − 28)°, what is the value of x?
A) 8
B) 9.4
C) 16.3
D) 36
Answer:
A
Step-by-step explanation:
∠ A and ∠ B are alternate exterior angles and are congruent , then
∠ B = ∠ A , that is
8x - 28 = 5x - 4 ( subtract 5x from both sides )
3x - 28 = - 4 ( add 28 to both sides )
3x = 24 ( divide both sides by 3 )
x = 8
Gabriel measured a house and made a scale drawing. The garage, which is 12 meters long in real life, is 4 millimeters long in the drawing. What scale did Gabriel use for the drawing?
Using proportions, it is found that the garage is 14 millimeters wide in the drawing.
What is a proportion?
A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
The rule of three is:
7 millimeters - 4 meters
x millimeters - 8 meters
Applying cross multiplication
4x = 7(8)
x = 56/4
x = 14
The garage is 14 millimeters wide in the drawing.
Learn more about proportions
brainly.com/question/2548537
#SPJ1
find many solutions to the system of inequalities:
1) Solve each inequality individually.
[tex]\dfrac{2x-3}5 - \dfrac{4x-9}6 > 1 \\\\ 6(2x-3) - 5(4x-9) > 30 \\\\ (12x-18) - (20x+45) > 30 \\\\ -8x > 3 \\\\ x < -\dfrac38[/tex]
and
[tex]5(x-1) + 7(x+2) > 3 \\\\ (5x-5) + (7x+14) > 3 \\\\ 12x > -6 \\\\ x > -\dfrac12[/tex]
Then the solution set is
[tex]-\dfrac12 < x < -\dfrac38[/tex]
since -1/2 = -4/8 is smaller than -3/8.
2)
[tex]\dfrac{x+1}2 - \dfrac{x+2}3 < \dfrac{x+12}6 \\\\ 3(x+1) - 2(x+2) < x+12 \\\\ (3x+3) - (2x+4) < x + 12 \\\\ x - 1 < x + 12 \\\\ -1 < 12[/tex]
This is true for all values of [tex]x[/tex].
For the second inequality, (I use periods in place of commas because it renders better as TeX)
[tex]0.3x - 19 \le 1.7x - 5 \\\\ -1.4x \le 14 \\\\ x \ge -10[/tex]
Taken together, the solution set is
[tex]\boxed{x\ge-10}[/tex]
3)
[tex](x-6)^2 < (x-2)^2 - 8 \\\\ x^2 - 12x + 36 < (x^2 - 4x + 4) - 8 \\\\ -8x < -40 \\\\ x > 5[/tex]
and
[tex]3(2x-1) - 8 < 34 - 3(5x-9) \\\\ (6x - 3) - 8 < 34 - (15x - 27) \\\\ 21x < 72 \\\\ x < \dfrac{72}{21} = \dfrac{24}7[/tex]
But [tex]x[/tex] cannot be both larger than 5 = 35/7 and smaller than 24/7, so there are no solutions.
4)
[tex]\dfrac{3x-2}3 - \dfrac{4x+1}4 \le 1 \\\\ 4(3x-2) - 3(4x+1) \le 12 \\\\ (12x-8) - (12x + 3) \le 12 \\\\ -11 \le 12[/tex]
This is true for all [tex]x[/tex].
[tex](x-1)(x-2) > (x+4)(x-7) \\\\ x^2 - 3x + 2 > x^2 - 3x - 28 \\\\ 2 > -28[/tex]
This is also true for all [tex]x[/tex].
Any value of [tex]x[/tex] is a solution.
combine like terms to simplify the expression. -2x^2+3y+2x^2+2+3y+2
Answer:
6y+4
Step-by-step explanation:
Let's simplify step-by-step.
−2x²+3y+2x²+2+3y+2
Combine Like Terms:
=−2x²+3y+2x²+2+3y+2
=(−2x²+2x²)+(3y+3y)+(2+2)
=6y+4
Two water tanks 50 inches tall. tank a is empty and for each minute the water increases by 3.7 inches. tank b is draining and the water decreases 1.9 inchesveach minute. how many minutes will pass so the height of the water in each tank is the same
If two water tanks are 50 inches tall and tank a is empty and for each minute the water increases by 3.7 inches and tank b is draining and the water decreases by 1.9 inches each minute, then the minutes after which the height of the water in each tank is the same is equal to 9.
The time in minutes after which the height of the water in each tank is the same can be determined by using a linear equation.
The equation for this problem can be given as,
0 + 3.7(x) = 50 - 1.9(x)
Here x is equal to minutes. To find the minutes after which the water level will be the same can be determined by calculating the value of x in this linear equation.
3.7(x) + 1.9(x) - 50 = 0
5.6(x) = 50
x = 50 / 5.6
x = 8.92 ≈ 9
Hence, the height of the water in tank a and tank b is equal after 9 minutes.
To learn more about linear equations, click here:
https://brainly.com/question/12788590
#SPJ4
What is an equation of the line that passes through the points (-5, -5) and
(5, -7)?
Answer: You can use Math apps to help you easily
Step-by-step explanation:
4. Calculate the length of each line segment.
Round answers to the nearest tenth of a
unit, when necessary.
a) AB
b) CD
c) EF
The length of AB is 4.47 units, the length of CD is 2.83 units and the length of EF is 5 units.
We are given different right angled triangles.
We need to find AB, CD and EF
We will do this by using the Pythagoras theorem.
Pythagoras theorem states that:
Hypotenuse² = Base² + Perpendicular²
For AB,
Hypotenuse = AB
Base = 2 units
Perpendicular = 4 units
So, we get that:
AB² = 2² + 4²
AB² = 4 + 16
AB² = 20
AB = √ 20
AB = 2√5 units
AB = 4.47 units.
For CD:
Hypotenuse = CD
Base = 2 units
Perpendicular = 2 units
So, we get that:
CD² = 2² + 2²
CD² = 4 + 4
CD² = 8
CD = √ 8
CD = 2√2
CD = 2.83 units
For EF:
Hypotenuse = EF
Base = 4 units
Perpendicular = 3 units
So, we get that:
EF² = 4² + 3²
EF² = 16 + 9
EF² = 25
EF = 5 units.
Therefore, we get that, the length of AB is 4.47 units, the length of CD is 2.83 units and the length of EF is 5 units.
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ9
Find the inverse of each function. Is the inverse a function?
f(x)=x⁴
The domain of f(x) to be [0,∞).
If the domain R, f(x) is not one to one, so its inverse exists not a function.
If we restrict the domain of f(x) then we can define an inverse function.
What is meant by inverse function?An inverse function, even comprehended as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function exists denoted by ' f ' or ' F '.
In order to have an inverse function, a function must be one to one.
In the case of f(x) = x⁴ we find that f(1) = f(−1) =1.
If f(x) exists not one to one on its implicit domain R.
If we restrict the domain of f(x) to [ 0, ∞) then it does contain an inverse function, then [tex]f^{-1}(y)=\sqrt[4]{y }[/tex]
Let the given function be y = f(x) = x⁴
Taking the square root of both ends, then we get
± √y = x²
Let the real values be x, then
We require the left hand side to be non-negative, so assume the non-negative square root.
Take the square root of both sides of the equation then
±[tex]\sqrt[]{\sqrt{y} }[/tex] = x
⇒ x = ± [tex]\sqrt{\sqrt{y} }[/tex] = ± [tex]\sqrt[4]{y}[/tex]
It does not give us a unique value of x in terms of y.
So the inverse function exists not defined, then x ≥ 0,
i.e., restrict the domain of f(x) to be [0,∞).
If the domain R, f(x) exists not one to one, so its inverse exists not a function.
The domain of f(x) then we can describe an inverse function.
To learn more about inverse function, refer to:
brainly.com/question/25289437
#SPJ4
Write the equation of the line that passes through (5, −2) and is perpendicular to y equals 5 thirds times x minus 3 period.
y equals negative 3 fifths times x plus 1
y equals negative 3 fifths times x plus 19 fifths
y equals 3 fifths times x minus 5
y equals 5 thirds times x minus 31 thirds
We need to use the concept of lines and slopes to solve the problem.The equation of the line that passes through (5,-2) and is perpendicular to y=[tex]\frac{5}{3} x-3[/tex] is [tex]y=\frac{-3}{5} x+\frac{19}{5}[/tex].
We will be using the concept of lines and slopes to solve the question. When two lines are parallel their slopes are equal and when two lines are perpendicular the product of their slopes equal to -1.
Here we know that the line passes through a point (5,-2) and is perpendicular to another line,we need to find out the slope of the line first.
Let slope of given line be m1 and slope of the line that we need to find out be m2.
[tex]y=\frac{5}{3} x-3[/tex]
slope is the coefficient of x, thus m1=[tex]\frac{5}{3}[/tex]
we know that m1xm2=-1
[tex]\frac{5}{3}[/tex]×m2=-1⇒m2=[tex]\frac{-3}{5}[/tex]
The formula that we need to find the equation of a line is
(y-y1)=m(x-x1)
here (x1,y1) is (5,-2) and m is m2
[tex]y-5=\frac{-3}{5} (x+2)\\y-5=-\frac{3}{5} x-\frac{6}{5} \\y=\frac{-3}{5} x+5-\frac{6}{5} \\y=\frac{-3}{5} +\frac{19}{5}[/tex]
Thus using the concept of lines and slopes we found out that the equation of line that has been asked for is [tex]y=\frac{-3}{5} x+\frac{19}{5}[/tex]
Learn more about lines and slopes here:
https://brainly.com/question/27140356
#SPJ9