Find the inverse of f(x)=5x^2-3
Answers
[tex]\large\boxed{y=\pm\sqrt{\frac{x+3}{5}}}[/tex]
To find the inverse, swap the [tex]y[/tex] (or [tex]f(x)[/tex] in this case) and the [tex]x[/tex], then solve for [tex]y[/tex].
[tex]\begin{aligned}y&=5x^2-3\\x&=5y^2-3\\x+3&=5y^2-3+3\\x+3&=5y^2\\\frac{x+3}{5}&=\frac{5y^2}{5}\\\frac{x+3}{5}&=y^2\\\pm\sqrt{\frac{x+3}{5}}&=\sqrt{y^2}\\\pm\sqrt{\frac{x+3}{5}}&=y\end{aligned}[/tex]
Related Questions
Calculate the residuals for the scatter plot (image provided)
Answers
From the given graph, and using the scatter plot function of a graphing calculator, the residuals are;
-0.08693, -0.019376, -0.518, -0.183, -0.083, 0.135, 0.318, and 0.578
Which method can be used to find the residuals?From the diagram, the given points are;
(14, 4), (15, 4), (16.5, 3.5), (18, 4), (18, 3.9), (19.5, 3.85), (20, 4), (26.8, 3.8)
Utilizing a graphing calculator, using the scatter plot function we have the following predicted values;
Best fit line; y = 5.032 - 0.0676•x
Residuals = Actual - Predicted from equation
The residuals are;
y1 = 4 - 4.08693 = -0.08693
y2 = 4 - 4.019376 = -0.019376
y3 = 3.5 - 3.918 = -0.518
y4 = 4 - 3.817 = -0.183
y5 = 3.9 - 3.817 = -0.083
y6 = 3.85 - 3.715 = 0.135
y7 = 4 - 3.682 = 0.318
y8 = 3.8 - 3.222 = 0.578
The residuals are therefore;
The residuals are;
-0.08693, -0.019376, -0.518, -0.183, -0.083, 0.135, 0.318, and 0.578Learn more about finding the residuals of a scatter plot here:
https://brainly.com/question/16511034
#SPJ1
Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
Answers
Answer:
a
Step-by-step explanation:
this is the anser on e2020
73. Real-World Applications
A city's population in the year 1960 was 287,500 . In 1989 the population was 275,900 . Compute the rate of growth of the population and make a statement about the population rate of change in people per year.
Answers
Answer:
The rate of growth of the population is -400, this means the growth of the population from year 1960 to 1989 has dropped by 400 per city.
Step-by-step explanation:
It is given that in a city's population in the year 1960 was 287500 , and in the year of 1989 the population was 275900 .
It is required to compute the rate of growth of population and make a statement about the population rate of 1989 with the year 1989 and the time taken to change the population.
Step 1 of 1
It is given that in a city's population in the year 1960 was 287500 , and in the year of 1989 the population was 275900 .
To find the rate of growth of population and make a statement about the population rate of change in people per year.
Now let f(x) be the number of population and x be the year and use formula of rate of change to find the change in population,
[tex]$m=\frac{f\left(x_{2}\right)-f\left(x_{1}\right)}{x_{2}-x_{1}}$[/tex]
Now substitute, 275900 for [tex]$f\left(x_{2}\right)[/tex], 287500 for then,
[tex]$$\begin{aligned}m &=\frac{275900-287500}{1989-1960} \\&=\frac{-11600}{29} \\&=-400\end{aligned}$$[/tex]
The rate of growth of population -400, so there is a drop in the population by 400 per city.
20) Find the surface area of the solid shown. 16 dm 17 dm 30 dm
Answers
Answer:
680π dm² = 2136.28 dm²
Step-by-step explanation:
Recall:
lateral area of cone = πrs; where s = slant height = 17 dm
area of circle = πr²
lateral area of cylinder = πdh
Lateral area of cone: (3.14159)(8 dm)(17 dm) = 427.26 dm²
Area of base of cylinder: (3.14159)(8 dm)² = 201.06 dm²
Lateral area of cylinder: (3.14159)(16 dm)(30 dm) = 1507.96 dm²
Total surface area = 427.26 dm² + 201.06 dm² + 1507.96 dm²
Total surface area = 680π dm² = 2136.28 dm²
approximately how high to the nearest tenth of a metre is emma's kite above ground
Answers
16 percent of what number is 17
Answers
Work Shown:
16% of x = 17
0.16x = 17
x = 17/(0.16)
x = 106.25
he coordinate grid shows the graph of four equations: A coordinate grid is shown from negative 12 to positive 12 on the x axis and also on the y axis. Line A passes through the ordered pairs negative 3, 4 and 9, negative 2. Line B passes through the ordered pairs 2, 8 and 8, negative 8. Line C passes through the ordered pairs negative 3, negative 4 and 4, 6. Line D passes through the points 2, negative 2 and 5 and 6. Which set of equations has (5, 0) as its solution? A and B C and D B and D A and D
Answers
The set of equation that is known to have 5 and 0 as solutions is A and B.
How to solve for the system of equations.From the graph that we have here in this question, we are supposed to identify the equations that have this point.
We can do this by tracing the lines in order to locate 5 and 0 on the grid.
When we trace the bine that has 5 and 0, We would find out that it is traceable to A and B.
Read more on graphs here:
https://brainly.com/question/10465970
#SPJ1
please help me out somebody!
Answers
Answer:
Step-by-step explanation:
E
What is the solution to the system of equations?
y = 0x + 3
x = −2
O [--]
O
[22]
[2
O
[-2]
Answers
Answer:
-2
Step-by-step explanation:
The solution to the system of equations is (x, y) = (-2, 1).
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The second equation tells us that x = -2.
Substituting this value into the first equation, we get:
y = -2 + 3
Simplifying, we get:
y = 1
Therefore,
The solution to the system of equations is (x, y) = (-2, 1).
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ5
How far does judy travel in 2 3/4 hours if she travels at the rate of 5 1/2 miles per hour
Answers
Judy travel's 15.125 miles or 15[tex]\frac{1}{8}[/tex] miles in 2 3/4 hours
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time
Given:
Speed = 5 1/2 miles per hour Time = 2 3/4 hoursSubstituting it in the relationship we get,
Distance = Speed x Time
Distance = 5 1/2 miles per hour x 2 3/4 hours
Distance = [tex]\frac{11}{2} X \frac{11}{4}[/tex] miles
Distance = [tex]\frac{121}{8}[/tex] miles or 15[tex]\frac{1}{8}[/tex] miles
Thus Judy travel's 15.125 miles or 15[tex]\frac{1}{8}[/tex] miles in 2 3/4 hours
Learn more about time related questions here :
https://brainly.com/question/16403317
#SPJ4
When two variables are being examined, and one variable moves one way and the other variable moves in the opposite direction, this is called a(n):
Answers
When two variables are being examined, and one variable moves one way and the other variable moves in the opposite direction, this is called an inverse relation.
Correlation is a statistical degree (expressed as various) that describes the size and path of a courting among or extra variables. A correlation between variables, however, does now not robotically suggest that the trade in a single variable is the purpose of the alternate inside the values of the opposite variable.
A positive correlation is clear while variables move within an equal course. An inverse correlation is clear whilst variables circulate inside the opposite route.
A negative correlation is a relationship among variables that pass in contrary instructions. In other phrases, while variable A increases, variable B decreases. A poor correlation is likewise known as an inverse correlation.
Learn more about Correlation here: https://brainly.com/question/4219149
#SPJ4
When two variables are being examined, and one variable moves one way and the other variable moves in the opposite direction, this is called a(n): Inverse Relationship.
Consumption is subject to diminishing marginal utility. -A lower price increases the purchasing power of a buyer's income, enabling a buyer to purchase more of a product.
The law of supply and demand is a keystone of modern economics. According to this theory, the price of goods is inversely related to the quantity offered. This makes sense for many goods, since the more costly it becomes, fewer people will be able to afford them and demand will subsequently drop.
Learn more about Modern economics here https://brainly.com/question/639998
#SPJ4
Consider the function f(x)=1/3(6)x. What is the value of the growth factor of the function?
Answers
Answer:
F = 2
Step-by-step explanation:
Answer:6
Step-by-step explanation:i did the quiz
Solve for x
[tex]\ \textless \ br /\ \textgreater \ x = \dfrac{1}{2-\dfrac{1}{2-\dfrac{1}{2-x} } } \: \: \: , (x \neq 2)[/tex]
Help me with this!
Answers
Answer:
[tex]x= \dfrac{3-2x}{4-3x}[/tex]
Step-by-step explanation:
Given:
[tex]x=\dfrac{1}{2-\dfrac{1}{2-\dfrac{1}{2-x}}}}[/tex]
Simplify:
[tex]\begin{aligned}2-\dfrac{1}{2-x} & =\dfrac{2(2-x)-1}{2-x}\\\\ & =\dfrac{3-2x}{2-x}\end{alilgned}[/tex]
Therefore:
[tex]x=\dfrac{1}{2-\dfrac{1}{\dfrac{3-2x}{2-x}}}[/tex]
Simplify:
[tex]\begin{aligned}2-\dfrac{1}{\dfrac{3-2x}{2-x}} & =2-\dfrac{2-x}{3-2x}\\\\ & =\dfrac{2(3-2x)-(2-x)}{3-2x}\\\\ & = \dfrac{6-4x-2+x}{3-2x}\\\\ & = \dfrac{4-3x}{3-2x}\end{aligned}[/tex]
Therefore:
[tex]x & =\dfrac{1}{\dfrac{4-3x}{3-2x}}[/tex]
[tex]\textsf{Apply the fraction rule}: \quad \dfrac{1}{\frac{b}{c}}=\dfrac{c}{b}[/tex]
[tex]\implies x& = \dfrac{3-2x}{4-3x}[/tex]
pls help me in this i really need help :( :)
Answers
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
First off, let's write the line in point-slope form:
[tex]\rm \hookrightarrow (y-y_0)=m(x-x_0)[/tex]
(x₀, y₀) any random point on the line'm' is the value of the slopeLet's calculate the slope:
[tex]\rm \hookrightarrow Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]
(x₁, y₁): any random point on the line ⇒ (-2, -6)(x₂,y₂): any random point on the line that is not (x₁, y₁) ⇒ (2, -3)[tex]\rm \hookrightarrow slope = \frac{-3--6}{2--2} =\frac{3}{4}[/tex]
Now that we found the slope, let's put it into the point-slope form
⇒ we need (x₀, y₀) ⇒ let's use (2,-3)
[tex](y-(-3))=\frac{3}{4} (x-2)\\y+3=\frac{3}{4} (x-2)[/tex]
The equation, however, could also be put into 'slope-intercept form'
⇒ gotten by isolating the 'y' variable to the left
[tex]y = \frac{3}{4}x-\frac{9}{2}[/tex]
Answer:[tex]y = \frac{3}{4}x-\frac{9}{2}[/tex] or [tex]y+3=\frac{3}{4} (x-2)[/tex]
*Either equations work, put the one that you are the most familiar with
Hope that helps!
#LearnwithBrainly
NOTE: Angles not necessarily drawn to scale.
Answers
Answer:
60
Step-by-step explanation:
I'm assuming that ED is an exactly straight line, that would mean the angle is 180 degrees. So the sum of the angles in between should also equal 180. This gives you the equation
100 + 20 + x = 180
120 + x = 180
60 = x
A solid right pyramid has a square base with an edge length of s units and a height of h units.
Which expression represents the volume of the pyramid?
One-fourth s^2h units^3
One-third s^2h units^3
s^2h units^3
3^s2h units^3
Answers
The volume of the square pyramid is: B. One-third s^2h units^3.
What is the Volume of a Square Pyramid?An example of a square pyramid is given in the image attached below. It has a square base and 4 triangular faces.
A right pyramid that has a square base has a volume that can be calculated using the following volume formula, given as: 1/3(a² × h), where "a" is the length of the edge of the square base, and "h" is the height of the square pyramid.
Given the following parameters for a square pyramid:
The length of the edge of the square base (a) = s units
The height of the square pyramid = h units.
Plug in the values into 1/3(a² × h) to find the expression that represents the volume of the pyramid:
Volume of the square pyramid = 1/3(a² × h) = 1/3(s² × h)
Volume of the square pyramid = 1/3s²h units ³.
The expression that represents the volume of the square pyramid is: B. One-third s^2h units^3.
Learn more about square pyramid on:
https://brainly.com/question/3688277
#SPJ1
Copy the figure below onto a separate sheet of paper. Find the image of the figure under reflections in line m and then line t. In the box below, describe the rotation equivalent to the composition of reflections with respect to lines m and t.
Answers
The reflection of the triangle DEFG will be given in the figure.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.
Reflection does not change the size and shape of the geometry.
The image of the figure under reflections in line m and then line t.
The reflection of the triangle DEF will be given in the figure.
More about the transformation of geometry link is given below.
https://brainly.com/question/22532832
#SPJ1
A space shuttle can orbit the earth at 330 mi above sea level. The average commercial airplane can fly at 5.7 mi above sea level. What is the distance between the two aircraft?
Answers
Answer:
324.3mi
Step-by-step explanation:
Given Space Shuttle height above ground = 330mi
Airplane height above ground = 5.7mi
Difference between two aircrafts = Space Shuttle height - airplane height above ground
= 330 - 5.7
= 324.3mi
use an exponential expression to calculate the area covered by purple loosestrife seven years from now. is this a valid prediction? What does this result tell you about the constraints on the exponential model?
Answers
The area of the wetland that will be covered in purple loosestrife 7 years from now is modeled by this expression 500(1.2)^7
How to illustrate the information?The exponential expression to calculate the area covered by purple loosestrife seven years from now will be:
= 500 × 1.2^7
After evaluating the expression, the model predicts that approximately 1,792 acres of the wetland will be covered in purple loosestrife 7 years from now.
This is not a valid prediction because the total area of the wetland is only 1,240 acres. Therefore, a constraint on the model is that the value of the expression 500(1.2)^t must be less than or equal to 1,240.
Learn more about exponential on:
https://brainly.com/question/12940982
#SPJ1
37. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
37. x-intercept at (-5, 0) and y-intercept at (0, 4)
Answers
Answer:
The linear equation for the line with an x-intercept at (-5,0) and y-intercept at (0,4) is found as [tex]$y=\frac{4}{5} x+4$[/tex].
Step-by-step explanation:
A condition is given that a line has an x- intercept at (-5,0) and y- intercept at (0,4).
It is asked to find a linear equation satisfying the given condition.
To do so, first determine the slope of the line using coordinates of the given intercepts. Then write the equation in the slope-intercept form using the slope and the y- intercept.
Step 1 of 2
Determine the slope of the line.
The points of the intercepts of the line are given as (-5,0) and (0,4). Next, the formula for the slope is given as,[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute 4&0 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex]respectively, and 0&-5 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]$$\begin{aligned}m &=\frac{4-0}{0-(-5)} \\m &=\frac{4}{5}\end{aligned}$$[/tex]
Step 2 of 2
Write the equation in the slope-intercept form.
The slope-intercept form of a line is given as follows,
[tex]$$y=m x+b$$[/tex]
The coordinates at the y- intercept is (0,4). Now, as the y- coordinate is 4 , so b=4.
So, substitute 4 for b and [tex]$\frac{4}{5}$[/tex] for m in the equation y=mx+b, as follows,
[tex]$y=\frac{4}{5} x+4$$[/tex]
This is the required linear equation.
What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?
f(x)=2x²+x+4
Answers
The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (1, 7)
How to solve system of equation?The solution to the linear and quadratic equation is as follows:
For the linear, a solution is 1 and 7.
This is because when x = 1, f(x) = 7
For the quadratic equation, 1 and 7 also works.
2x² + x + 4
2(1)² + 1 + 4
2 + 1 + 4 = 7
learn more on system of equation here: https://brainly.com/question/27168614
#SPJ1
Having some trouble here
Answers
Answer:
None of them are correct i believe
Step-by-step explanation:
its sideways lol
N= ???
Please help asap
Answers
Answer:
N=[tex]\sqrt{61}[/tex]
Step-by-step explanation:
We have the first point as (2,4), and the second point as (-3,-2). This means that [tex]x_1=2, y_1=4,x_2=-3,y_2=-2.[/tex] Using the distance formula, we get [tex]\sqrt{(2-(-3))^2+(4-(-2))^2} \\\sqrt{(2+3)^2+(4+2)^2}\\\sqrt{25+36}=\sqrt{61}[/tex]
Answer:
[tex]\sqrt{61}[/tex]
Step-by-step explanation:
In a binomial experiement, what does it mean to say that each trial is independent of the other trials?.
Answers
In a binomial experiment to say that each trial is independent of the other trials means that the outcome of one trial does not affect the other trial.
An experiment with a set number of independent trials and just two results is referred to as a binomial experiment.
To say that in a binomial experiment, each trial is independent of the other trials means that the outcome of one trial does not affect the other trials.
This means that whatever we get in the first trial, does not affect the outcome of the second or any other trial.
For example, in the tossing of a coin 10 times, the outcome of the first trial doesn't affect any of the other nine trials.
Learn more about binomial experiments at
https://brainly.com/question/24756209
#SPJ4
HELPP!!!
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction
if needed.
Answers
S: sine
C: cosine
T: tangent
O:opposite
H:hypotenuse
A:adjacent
Sin A means opposite/hypotenuse
=15/17
Hope this helped :)
Answer:
15/17
Step-by-step explanation:
question on the image
Answers
Let [tex]x,y[/tex] be the legs of the triangle, with [tex]x[tex]\mathrm{area}_{\rm square} = y^2[/tex]
[tex]\mathrm{area}_{\rm triangle} = \dfrac12 xy[/tex]
The square has 3 times the area of the triangle, so
[tex]y^2 = \dfrac32 xy[/tex]
Meanwhile, in the triangle we have
[tex]\tan(\theta) = \dfrac xy[/tex]
Now,
[tex]y^2 = \dfrac32 xy \implies \dfrac23 = \dfrac xy \implies \boxed{\tan(\theta) = \dfrac23}[/tex]
When doing his homework, a student uses the addition property of equality to solve for c below. Which statement BEST applies to the sample? 6 + c = 10 6 + (–6) + c = 10 + (–6) c = 4 A. The student failed to keep both sides of the equation balanced. B. The student’s final answer does not have the variable c isolated. C. The use of the addition property of equality is sound, and the answer is correct. D. The student should have used the subtraction property of equality.
Answers
Answer:
The answer would be C
Solve the equation
(6x18) (3x + 2) = 0
Answers
Answer:
[tex] - \frac{2}{3} [/tex]
Step-by-step explanation:
Given (6x18)(3x+2) = 0
[tex]108(3x + 2) = 0 \\ 324x + 216 = 0 \\ 324x = - 216 \\ x = \frac{ - 216}{324} \\ = - \frac{2}{3} [/tex]
Solve for y
:
V=−4y+4x
Answers
[tex] - 4y = v - 4x \\ y = \frac{ - v}{4} + x[/tex]
[tex]\\ \rm\dashrightarrow V=-4y+4x[/tex]
[tex]\\ \rm\dashrightarrow -4y=V-4x[/tex]
[tex]\\ \rm\dashrightarrow y=\dfrac{V-4x}{-4}[/tex]
[tex]\\ \rm\dashrightarrow y=x-\dfrac{V}{4}[/tex]
What is the area of the sector
shown in the diagram below?
OA. 11.1 cm²
OB. 2.5 cm²
OC. 39.3 cm²
OD. 50 cm²
Answers
Answer:
OC. 39.3 cm²
Step-by-step explanation:
Area of a circle = πr² (π ≈ 3.14)
45 degrees = 1/8 of a full circle
Area of the full circle : 3.14 × 10² =
3.14 × 100 = 314 cm²
Area of the sector : 314 × 1/8 = 39.25 cm² ≈ 39.3 cm²