Answers
This type of function is non linear.
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output. You can tell if a relation is a function by looking at the inputs (the x-coordinates) and outputs (the y-coordinates). Keep in mind that each input has only one output in a function. A function is an equation with a single solution for y for each value of x. Each input of a particular type receives exactly one output when using a function.
Given,
f(x) = x²
This type of function is non linear.
The end behavior is:
as x ⇒ ∞ , y ⇒ ∞
x ⇒ -∞ , y ⇒ -∞
The function graphed is f(x) = (x -3)²
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Related Questions
How many soultions?x + 3 = 2x - 18A single solutionInfinite solutionsNo solution
Answers
The given equation is expressed as
x + 3 = 2x - 18
Subtracting x from both sides of the equation, it becomes
x - x + 3 = 2x - x - 18
3 = x - 18
Adding 18 to both sides of the equation, it becomes
3 + 18 = x - 18 + 18
21 = x
x = 21
Since there is only one value for x, the correct option is
a. A single solution
Fill in the gaps to factorise the expression.
2x^2+7x+3
Answers
The factorised form of the expression given in the task content is; 2x² + 7x + 3 is; (2x + 1) (x + 1).
Factorisation of quadratic expressions.It follows from the task content that the factorised form of the expression is to be determined.
On this note, the factorised form of the expression is as follows;
2x² + 6x + x + 3.
By grouping terms; we have;
(2x² + 6x) + (x + 3).
Factorise two terms each at as follows;
2x(x + 1) + 1(x+3)
(2x + 1) (x + 1)
Therefore, the factorised form of the expression; 2x² + 7x + 3 is; (2x + 1) (x + 1).
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The height of a triangle is 4x more than the base, and the area of the triangle is 6 square units. Find the length of the base. Let x =the length of the base.
Write a quadratic equation in factored form. Write entire equation
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Answer:
The length of the base is:
3 unitsThe resulting quadratic is
x² - 3= 0Step-by-step explanation:
Base = x
Height = 4x
Area, A = 1/2* base * Height
A = (1/2) * (x) * (4x)
A = 2x² (1)
But, A = 6 (2)
Since (1) = (2);
2x²= 6
x²= 3
Resulting quadratic:
x² - 3= 0
For the difference between 2 squares:
a² - b² = (a-b)(a+b)
Using that identity, we can factorize our quadratic:
(x-3)(x+3) = 0
So, we have 2 roots:
x = 3 and x = -3
Now, noting that length must take a positive value, we go for the first:
x = 3
CONCLUSION:The length of the base is:
3 unitsThe resulting quadratic is
x² - 3= 0a sociology Professor assigns letter grades on a test according to the following scheme Scores on the test are normally distributed with the meaning of 67.2 and a standard deviation of 8.5Find the minimum score required for an a grade. Round your answer to the nearest whole number if necessary
Answers
In order to have grade A, the score needs to be in the top 9%.
Since the scores are normally distributed, the top 9% scores correspond to 91% of the area under the normal curve. That means we need to find a value of z in the z-table that corresponds to the value 0.91 (that is, 91%).
Looking at the z-table, the value of z for a probability of 0.91 is z = 1.34.
Now, to find the score that this value of z represents, we can use the formula below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}\\ \\ 1.34=\frac{x-67.2}{8.5}\\ \\ x-67.2=11.39\\ \\ x=11.39+67.2\\ \\ x=78.59 \end{gathered}[/tex]Rounding to the nearest whole number, the minimum score for grade A is 79.
At the airport, the new runway will be parallel to a nearby highway. The equation that represents the highway is 6y = 8x - 11. Which equation could represent the new runway? A. 9y = 12x + 5B. 9x = 12y + 8C. 12y = -9x + 2 D. 12x = -9y + 4
Answers
At the airport, the new runway will be parallel to a nearby highway. The equation that represents the highway is 6y = 8x - 11. Which equation could represent the new runway?
A. 9y = 12x + 5
B. 9x = 12y + 8
C. 12y = -9x + 2
D. 12x = -9y + 4
______________________________________________________
Parallel equations have the same slope
6y = 8x - 11
y= 8/6 x - 11/6
y= 4/3 x-11/6
y = m x +b (m is the slope )
_____________________________________________
You need to find the other equation with the same slope
____________________________
A. 9y = 12x + 5
y = 12/ 9 x + 5/9
y = 4/3 x + 5/9
_________________________
B. 9x = 12y + 8
12 y= 9x-8
y= 9/ 12 x- 8/12
y= 3/4 x - 4/6
discarded
________________________
C. 12y = -9x + 2
y = -9/12 x + 2/12
y = -3/4 x + 1/6
discarded
_________________________
D. 12x = -9y + 4
12x -4 = -9y
y = -12/9 x +4/9
y = -4/3 x+4/9
discarded
_______________
So then, A 9y = 12x + 5 is the equation that could represent the new runway because is parallel to the highway 6y = 8x - 11.
A bank offers a CD that pays a simple interest rate of 8.0%. How much must you put in this CD now in order to have $2500 for a home-entertainment center in 3 years.
Answers
Okay, here we have this:
Considering that the formula for the simple interest rate is:
A = P (1 + rt)
In this case A is equal to $2500, P is the value we need to find, r is the interest rate (in decimal) 0.08, and t is the time, so it's 3 years, replacing we obtain:
2500=P(1+0.08*3)
Now, let's clear P:
2500=P(1+0.24)
2500=P(1.24)
2500/1.24=P
P=2016.13
Finally we obtain that the bank must put $ 2016.13 on a CD to get $ 2,500 in three years.
Find the volume of a pyramid with a square base, where the side length of the base is19.3 ft and the height of the pyramid is 16.2 ft. Round your answer to the nearesttenth of a cubic foot.
Answers
Find the volume of a pyramid with a square base, where the side length of the base is
19.3 ft and the height of the pyramid is 16.2 ft. Round your answer to the nearest
tenth of a cubic foo
Remember that
the volume of the pyramid is equal to
[tex]V=\frac{1}{3}\cdot B\cdot h[/tex]where
B is the area of the base
h is the height
step 1
Find out the area of the base
B=19.3^2
B=372.49 ft2
h=16.2 ft
substitute the given values in the formula
[tex]V=\frac{1}{3}\cdot372.49\cdot16.2[/tex]V=2,011.4 ft3if f(x)=3x-2/x+4 and g(x)=4x+2/3-x,prove that f and g are inverses of each other
Answers
9. A researcher gathered data on hours of video games played by school-aged children and young adults. She collected the following data:601241215171711409914110131015163915121698131016651717129(a) Complete the frequency distribution for the data.HoursFrequencyRelative Frequency0-23-56-89-1112-1415-17(b) Which of the following is the correct histogram for this data?246810Hours0369121518Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,10);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.2],[0,0.2]); text([0,0],"0","below");line([3,-0.2],[3,0.2]); text([3,0],"3","below");line([6,-0.2],[6,0.2]); text([6,0],"6","below");line([9,-0.2],[9,0.2]); text([9,0],"9","below");line([12,-0.2],[12,0.2]); text([12,0],"12","below");line([15,-0.2],[15,0.2]); text([15,0],"15","below");line([18,-0.2],[18,0.2]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[3,6]);rect([3,0],[6,4]);rect([6,0],[9,5]);rect([9,0],[12,7]);rect([12,0],[15,6]);rect([15,0],[18,10]);]246810121416Hours061218Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,16);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.32],[0,0.32]); text([0,0],"0","below");line([6,-0.32],[6,0.32]); text([6,0],"6","below");line([12,-0.32],[12,0.32]); text([12,0],"12","below");line([18,-0.32],[18,0.32]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[6,10]);rect([6,0],[12,12]);rect([12,0],[18,16]);]2468101214Hours061218Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,14);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.28],[0,0.28]); text([0,0],"0","below");line([6,-0.28],[6,0.28]); text([6,0],"6","below");line([12,-0.28],[12,0.28]); text([12,0],"12","below");line([18,-0.28],[18,0.28]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[6,12]);rect([6,0],[12,14]);rect([12,0],[18,12]);]2468Hours0369121518
Answers
Remember that the frequency refers to the number of times a data shows up. In this case, the frequency is the number of data that falls into each interval.la
To find the relative frequency is calculated by dividing each frequency by 38 (the total number of data).
[tex]\begin{gathered} \frac{6}{38}=0.1579 \\ \frac{4}{38}=0.1053 \\ \frac{4}{38}=0.1053 \\ \frac{8}{38}=0.2105 \\ \frac{7}{38}=0.1842 \\ \frac{9}{38}=0.2368 \end{gathered}[/tex]Let's include the relative frequencies in the table.
On the other hand, the correct histogram has to show the frequencies in the same order. The following histogram shows the correct frequency distribution.
How many area codes of the form (XYZ) are possible if the digit 'X' and 'Y' can be any number ( through 9 but they can't repeat and the digit 7 can be any number 1 through 9?
Answers
Start to see the possible options
[tex]XYZ=-\cdot-\cdot-_{}[/tex]The first digit will have 10 possible numbers to choose from 0 to 9, however in the second digit since it cannot repeat there will be only 9 possible to choose from. As for ther third number 0 is not an option meaning that there are 9 to choose as well.
[tex]\begin{gathered} XYZ=10\cdot9\cdot9 \\ XYZ=810 \end{gathered}[/tex]Represent each sum as a single rational number. -14+(-8/9) due tomorrow pls answer
Answers
the given expression is
-14 + (-8/9)
so,
[tex]\begin{gathered} =-14+\frac{-8}{9} \\ =-14-\frac{8}{9} \end{gathered}[/tex][tex]\begin{gathered} =\frac{-126-8}{9} \\ =-\frac{134}{9} \end{gathered}[/tex][tex]=-\frac{134}{9}=-14\frac{8}{9}[/tex]so the answer is -14 8/9 or -134/9
f (x) = 4x^2+2x+6find the value of the discriminate of f and how many distinct real number zeros f has.
Answers
The Solution:
Given:
Required:
To find the discriminant of f.
By formula, the discriminant (D) is:
[tex]D=b^2-4ac[/tex]Where:
[tex]\begin{gathered} a=4 \\ b=2 \\ c=6 \end{gathered}[/tex]Substitute:
[tex]\begin{gathered} D=2^2-4(4)(6)=4-96=-92 \\ No\text{ real root since D}<0 \end{gathered}[/tex]Therefore, the correct answers are:
Discriminant = -92
No distinct real root.
how do you find a point slope in geometry
Answers
see explanation below
Explanation:
To find the point slope form of an equation, we will apply the formula:
[tex]y-y_1=m(x-x_1)[/tex]Given two points, we will be able to find the slope = m
for example: (1, 2), (2, 4)
m = slope = change in y/ change in x
m = (4-2)/(2-1)
m = 2/1
m = 2
Then, we will pick any of the points and insert into the formula for the point slope.
Let's assume we are using point (1, 2) = (x1, y1)
inserting into the formula together with the slope gives:
y - 2 = 2(x - 1)
The above is a point slope for the points given.
Solve the system by graphing:2x – y= -14x - 2y = 6Solution(s):
Answers
To find the solution of the system by graphing we need to plot each line in the plane and look for the intersection.
First we need to write both equations in terms of y:
[tex]\begin{gathered} y=2x+1 \\ y=2x-3 \end{gathered}[/tex]now we need to find two points for each of this lines. To do this we give values to the variable x and find y.
For the equation 2x-y=-1, if x=0 then:
[tex]y=1[/tex]so we have the point (0,1).
If x=1, then:
[tex]y=3[/tex]so we have the point (1,3).
Now we plot this points on the plane and join them with a straight line.
Now we look for two points of the second equation.
If x=0, then:
[tex]y=-3[/tex]so we have the point (0,-3)
If x=1, then:
[tex]y=-1[/tex]so we have the point (1,-1).
We plot the points and join them wiith a line, then we have:
once we have both lines in the plane we look for the intersection. In this case we notice that the lines are parallel; this means that they wont intersect.
Therefore the system of equations has no solutions.
Yea I think and her dad is doing great so
Answers
Given the following function:
[tex]tan\text{ }\theta=\frac{10}{y}[/tex]Both θ and y are functions of the time (t)
We will find the derivatives of θ and y with respect of the time (t) as follows:
[tex]sec^2θ*\frac{dθ}{dt}=-\frac{10}{y^2}*\frac{dy}{dt}[/tex]Now, we will find dy/dt when θ = π/6 and dθ/dt = π/12
First, we need to find the value of y when θ = π/6
[tex]\begin{gathered} tan(\frac{\pi}{6})=\frac{10}{y} \\ \frac{1}{\sqrt{3}}=\frac{10}{y} \\ \\ y=10\sqrt{3} \end{gathered}[/tex]so, we will substitute the values to find dy/dt as follows:
[tex]\begin{gathered} sec^2(\frac{\pi}{6})*\frac{\pi}{12}=-\frac{10}{(10\sqrt{3})^2}*\frac{dy}{dt} \\ \\ so,\frac{dy}{dt}=-\frac{(10\sqrt{3})^2}{10}*sec^2(\frac{\pi}{6})*\frac{\pi}{12}=-10.4719755 \end{gathered}[/tex]Rounding to 2 decimal places
So, the answer will be:
[tex]\frac{dy}{dt}=-10.47\text{ feet/hour}[/tex]Which of the following is equivalent to the expression below? (2+31) + (8-21) O A. 6+1 O B. 6+5; O C. 10+57 O D. 10 + 1
Answers
Given the expression:
[tex](2+3i)+(8-2i)[/tex]Let's find the equivalent expression from the choices given.
To find the equivalent expression, let simplify.
To simplify the expression, take the following steps:
• Remove the parentheses:
[tex]2+3i+8-2i[/tex]• Combine like terms:
[tex]\begin{gathered} 2+8+3i-2i \\ \\ 10+i \end{gathered}[/tex]Therefore, the equivalent expression is:
[tex]10+i[/tex]ANSWER: D
D. 10 + i
x^2 = 16, therefore x = 4.
Is this a valid conclusion? If not, give a counterexample.
Answers
help meeeee pleaseeeee!!!
thank you
Answers
The values of the given polynomial are:-
f(0) = 12
f(2) = 28
f(-2) = 52
Given polynomial:-
[tex]f(x)=-x^3+7x^2-2x+12[/tex]
We have to find the values of f(0), f(2) and f(-2).
Putting x = 0 in f(x), we get,
[tex]f(0)=-(0)^3+7(0)^2-2(0)+12[/tex]
f(0) = 0 +0 - 0 + 12 = 12
Hence, the value of f(0) is 12.
Putting x = 2 in f(x), we get,
[tex]f(2)=-(2)^3+7(2)^2-2(2)+12[/tex]
f(2) = -8 + 28 - 4 + 12 = 28
Hence, the value of f(2) is 28.
Putting x = -2 in f(x), we get,
[tex]f(-2)=-(-2)^3+7(-2)^2-2(-2)+12[/tex]
f(-2) = 8 +28 + 4 +12 = 52
Hence, the value of f(-2) is 52.
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Consider these functions:/(=) =-{=2 + 51g(I) = =2 + 2What is the value of fg(-2))?
Answers
Answer: Provided the two functions, f(x) and g(x), we have to find the composite of these two functions at x = - 2:
[tex]\begin{gathered} f(x)=-\frac{1}{2}x^2+5x \\ \\ g(x)=x^2+2 \end{gathered}[/tex]
The composite function is as follows:
[tex]\begin{gathered} f(g(x))=-\frac{1}{2}(x^2+2)^2+5(x^2+2) \\ \\ \\ f(g(x))=-\frac{1}{2}[x^4+4x^2+4]+5x^2+10 \\ \\ \\ f(g(x))=-\frac{x^4}{2}-2x^2-2+5x^2+10 \\ \\ f(g(x))=-\frac{x^4}{2}-2x^2-2+5x^2+10 \\ \\ \\ f(g(x))=-\frac{x^4}{2}+3x^2+8 \\ \\ \\ f(g(-2))=-\frac{(-2)^4}{2}+3(-2)^2+8 \\ \\ \\ f(g(-2))=-\frac{(-2)^4}{2}+3(-2)^2+8=-8+12+8=12 \\ \\ \\ f(g(-2))=12 \end{gathered}[/tex]The answer is 12.
How do I solve and what would the answer be?
Answers
To find the inverse of a function:
[tex]f(x)=\frac{2}{x-5}[/tex]We will follow the steps below
Step 1: Replace f(x) witth y
[tex]y=\frac{2}{x-5}[/tex]Step 2: interchange x with y
[tex]x=\frac{2}{y-5}[/tex]Step 3: Make y the subject of the formula
[tex]\begin{gathered} y-5=\frac{2}{x} \\ \\ y=\frac{2}{x}+5 \end{gathered}[/tex]Thus, the inverse of the function is:
[tex]y=\frac{2}{x}+5[/tex]Referring to the figure, find the unknown measure of ABC.
Answers
According to the Inscribed Angle Theorem, the measure of an angle inscribed in a circle equals half the arc that it intercepts.
Then:
[tex]m\angle ABC=\frac{1}{2}m\overset{\frown}{AC}[/tex]Since the measure of the arc AC is equal to 84º, then:
[tex]m\angle ABC=\frac{1}{2}(84º)=42º[/tex]Therefore, the answer is:
The measure of ABC is 42º.
Point A is shown on the complex plane.What is the standard form of the complex number that point A represents?
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Hello there. To solve this question, we have to remember some properties about the representation of a complex number in the complex or Argand-Gauss plane.
Given the complex plane with the point A representing a complex number:
We have to remember that in the complex plane, a complex number z:
[tex]z=a+ib[/tex]has coordinates
[tex](a,\,b)[/tex]And it is more commonly represented by a vector starting at the origin and with the tip on this point.
In this case, we find that the coordinates of the point A are:
[tex]A=(-5,\,3)[/tex]Which means that the complex number is
[tex]-5+3i[/tex]And this is the answer contained in the last option.
Find the measure of the indicated amgle to the nearest degree.
Answers
The correct option is
C. 69 degrees
Explanation:Let the indicated angle be represented by x, then
[tex]\begin{gathered} \cos x=\frac{Adjacent}{Hypotenuse}=\frac{13}{36} \\ \\ \\ x=\cos^{-1}(\frac{13}{36})\approx69^o \end{gathered}[/tex]What is the value of x in the equation7 (4x + 1) – 32 5.7 · 13?X=
Answers
Given
[tex]\begin{gathered} 7(4x+1)-3x=5x-13 \\ 28x+7-3x=5x-13 \\ 25x-5x=-13-7 \\ 20x=-20 \\ x=-1 \end{gathered}[/tex]There's a roughly linear relationship between the number of times a species of cricketwill chirp in one minute and the temperature outside. For a certain type of cricket,this relationship can be expressed using the formula I = 0.3lc + 36, where Trepresents the temperature in degrees Fahrenheit and c represents the number oftimes the cricket chirps in one minute. What is the meaning of the I'-value whenc= 148?
Answers
The function T = T(c) tells us the temperature based on the number of times c the cricket has chirped in one minute. In other words, if we plug c = 148 in the formula we get:
[tex]\begin{gathered} T(c)=0.31c+36 \\ T(148)=0.31\times(148)+36 \\ T(148)=81.88^oF \end{gathered}[/tex]That means if the cricket chirps 148 times per minute, the temperature must be 81.88 ºF.
Answer: The expected temperature in degrees Farenheit if the cricket has chirped 148 times perminute.
Which of the following options correctly represents the complete factored form of the polynomial F(x)= x - x2 - 4x-6?
Answers
Notice that:
[tex]F(3)=3^3-3^2-4\cdot3-6=27-9-12-6=27-27=0.[/tex]Therefore 3 is a root of the given polynomial.
Now, we can use this root to factor the polynomial:
[tex]F(x)=(x-3)\frac{x^3-x^2-4x-6}{x-3}.[/tex]Using the synthetic division algorithm we get that:
[tex]\frac{x^3-x^2-4x-6}{x-3}=x^2+2x+2.[/tex]The roots of the above polynomial are:
[tex]\begin{gathered} x=-1+i, \\ x=-1-i\text{.} \end{gathered}[/tex]Therefore:
[tex]F(x)=\mleft(x-3\mright)(x+1+i)(x+1-i)\text{.}[/tex]Answer:
[tex]F(x)=(x-3)(x+1+i)(x+1-i)\text{.}[/tex]Simplify the following sum of polynomials completely ( - 12s raise to power 2 + 10s - 3) + ( 2s raise to power 2 - 12s - 2)
Answers
ANSWER
[tex]-10s^2-2s-5[/tex]EXPLANATION
Given
[tex]\mleft(-12s^2+10s-3\mright)+\mleft(2s^2-12s-2\mright)[/tex]removing the brackets, we have;
[tex]-12s^2+10s-3+2s^2-12s-2[/tex]collecting like terms, we have
[tex]\begin{gathered} -12s^2+2s^2+10s-12s-3-2 \\ \end{gathered}[/tex]adding similar terms, we have;
[tex]-10s^2-2s-5[/tex]The solution is
[tex]-10s^2-2s-5[/tex]Evaluate 7a - 5b when a = 3 and b = 4 .
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Answer A= f(x)>0 on the interval x <0 Answer B=f(x)>0 on the interval x<0 Answer C=is f(x)<0 on the interval 00 on the interval 00 on the interval 1
Answers
EXPLANATION
Given the function f(x)= -x ²+4x - 3, the statements that apply are:
A) TRUE
B) FALSE
C) TRUE
D) FALSE
E) FALSE
F) TRUE
G) TRUE
H) FALSE
need help with image
Answers
Step by step explanation:
sum of co-exterior angle is 180°
(10x-48)+(6x)=180°
4x-48=180°
4x=180-48
4x=132
x=132/4
x=33
