The expression (-1)^n means the number -1 multiplies itself n times.
So for example if n = 2, we have that:
[tex](-1)^2=(-1)\cdot(-1)=1[/tex]For n = 3, we have:
[tex](-1)^3=(-1)\cdot(-1)\cdot(-1)=1\cdot(-1)=-1[/tex]For n = 4:
[tex](-1)^4=(-1)^2\cdot(-1)^2=1\cdot1=1[/tex]We can see that the result alternates from -1 and 1, and when n is odd, the result is -1, and when n is even, the result is 1.
So for any even number n, the result will be 1.
create an original function that has at least one asymptote and possibly a removable discontinuity list these features of your function: asymptote(s) (vertical horizontal slant) removable discontinuity(ies) x intercept(s) y intercept and end behavior provide any other details that would enable another student to graph and determine the equation for your function do not state your function
We have to create a function that has at least one asymptote and one removable discontinuity (a "hole").
We then have to list the type of feature.
We can start with a function like y = 1/x. This function will have a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.
We can translate it one unit up and one unit to the right and write the equation as:
[tex]y=\frac{1}{x-1}+1=\frac{1}{x-1}+\frac{x-1}{x-1}=\frac{x}{x-1}[/tex]Then, the asymptotes will be x = 1 and y = 1. We have at least one asymptote for this function.
We can now add a removable discontinuity. This type of discontinuity is one that is present in the original equation but, when factorizing numerator and denominator, it can be cancelled. This happens when both the numerator and denominator have a common root: the rational function can be simplified, but the root is still present in the original expression.
We than can add a removable discontinuity to the expression by multiplying both the numerator and denominator by a common factor, like (x-2). This will add a removable discontinuity at x = 2.
We can do it as:
[tex]y=\frac{x(x-2)}{(x-1)(x-2)}=\frac{x^2-2x}{x^2-3x+2}[/tex]This will have the same shape as y =x/(x-1) but with a hole at x = 2, as the function can not take a value that makes the denominator become 0, so it is not defined for x = 2.
Finally, we can find the x and y intercepts.
The y-intercepts happens when x = 0, so we can calculate it as:
[tex]\begin{gathered} f(x)=\frac{x^2-2x}{x^2-3x+2} \\ f(0)=\frac{0^2-2\cdot0}{0^2-3\cdot0+2}=\frac{0}{2}=0 \end{gathered}[/tex]The y-intercept is y = 0, with the function passing through the point (0,0).
As the x-intercept is the value of x when y = 0, we already know that the x-intercept is x = 0, as the function pass through (0,0).
Then, we can list the features as:
Asymptotes: Vertical asymptote at x = 1 and horizontal asymptote at y = 1.
Removable discontinuity: x = 2.
y-intercept: y = 0.
End behaviour: the function tends to y = 1 when x approaches infinity or minus infinity.
With that information, the function can be graphed.
Let f(x)=3x-2. What is f^-1 (x) ?
Given the function:
f(x) = 3x - 2
Let's find the inverse of the function f⁻¹(x).
To find the inverse of the function, apply the following steps:
• Step 1.
Rewrite y for f(x)
[tex]y=3x-2[/tex]• Step 2.
Interchange the x and y variables:
[tex]x=3y-2[/tex]• Step 3.
Solve for y.
Add 2 to both sides:
[tex]\begin{gathered} x+2=3y-2+2 \\ \\ x+2=3y \end{gathered}[/tex]• Step 4.
Divide all terms by 3:
[tex]undefined[/tex]
Which of the following statements are true regarding functions? Check all that apply. A. The horizontal line test may be used to determine whether a function is one-to-one. B. The vertical line test may be used to determine whether a relatio is a function. C. A sequence is a function whose domain is the set of rational numbers. PREVIOUS
Statement A is true.
In the next example, we can see a function that is not one-to-one with the help of the horizontal line test:
Statement B is true.
In the next example, we can see a relationship that is not a function because it doesn't pass the vertical line test
Statement C is false.
A sequence is a function whose domain is the set of natural numbers
Given a function described by the table below, what is y when x is 5?XY264859612
Given a function described by the table
We will find the value of (y) when x = 5
As shown in the table
When x = 5, y = 9
so, the answer will be y = 9
A box has 14 candies in it: 3 are taffy, 7 are butterscotch, and 4 are caramel. Juan wants to select two candies to eat for dessert. The first candy will be selectedat random, and then the second candy will be selected at random from the remaining candies. What is the probability that the two candies selected are taffy?Do not round your intermediate computations. Round your final answer to three decimal places.
Okay, here we have this:
Considering the provided information we are going to calculate what is the probability that the two candies selected are taffy. So, for this, first we are going to calculate the probability that the first is taffy, and then the probability that the second is taffy. Finally we will multiply these two probabilities to find the total probability.
Remember that the simple probability of an event is equal to favorable events, over possible events.
First is taffy:
At the beginning there are 14 sweets, and 3 are taffy, so there are 3 favorable events and 14 possible, then:
First is taffy=3/14
Second is taffy:
Now, in the bag there are 13 sweets left, and of those 2 are taffy, so now there are 2 favorable events out of 13 possible:
Second is taffy=2/13
The first and second are taffy:
First is taffy*Second is taffy=3/14*2/13
First is taffy*Second is taffy=3/91
First is taffy*Second is taffy=0.033
First is taffy*Second is taffy=3.3%
Finally we obtain that the probability that the two candies selected are taffy is aproximately 0.033 or 3.3%.
The slope of the line containing the points (-2, 3) and (-3, 1) is
Hey :)
[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
Apply the little slope equation. By doing that successfully, we should get our correct slope.
[tex]\large\boldsymbol{\frac{y2-y1}{x2-x1}}[/tex]
[tex]\large\boldsymbol{\frac{1-3}{-3-(-2)}}[/tex]
[tex]\large\boldsymbol{\frac{-2}{-3+2}}[/tex]
[tex]\large\boldsymbol{\frac{-2}{-1}}[/tex]
[tex]\large\boldsymbol{-2}}[/tex]
So, the calculations showed that the slope is -2. I hope i could provide a good explanation and a correct answer to you. Thank you for taking the time to read my answer.
here for further service,
silennia[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
May I please get help with this I have tried multiple times to get the correct answer but still could not get them right. I am confused on how I should draw the dilation as I have tried many times as well.
After performing dilation centered at the origin we get
(a) shortest side of original figure=2 units
shortest side of the final figure=6units
(b) shortest side of the final figure=3×shortest side of the original figure
(c) True
(d) False
What is the dilation of the figure centered at origin?A transformation called a dilatation alters a figure's size without altering its shape. A figure might become larger or smaller due to dilation. For instance.
The image is smaller than the preimage when the scaling factor is between 0 and 1. Reductions are referred to as dilations with scale factors between 0 and 1.
The image is larger than the preimage if the scaling factor is greater than 1. Enlargements are defined as a dilation with a scale factor greater than 1.
To get the size of the edge we multiply the size of original lenght by scale factor.
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The given point (-3,-4) is on the terminal side of an angle in standard position. How do you determine the exact value of the six trig functions of the angle?
In this problem -3 will be the adyacent side, -4 will be the opposite side and wwe can calculate the hypotenuse so:
[tex]\begin{gathered} h^{}=\sqrt[]{(-3)^2+(-4)^2} \\ h=\sqrt[]{9+16} \\ h=\sqrt[]{25} \\ h=5 \end{gathered}[/tex]So the trigonometric function will be:
[tex]\begin{gathered} \sin (\theta)=-\frac{4}{5} \\ \cos (\theta)=-\frac{3}{5} \\ \tan (\theta)=\frac{4}{3} \\ \csc (\theta)=-\frac{5}{4} \\ \sec (\theta)=-\frac{5}{3} \\ \cot (\theta)=\frac{3}{4} \end{gathered}[/tex]When we use function notation, f(x)=# is asking you to find the input when the output is the given number. We can also consider that an ordered pair can be written as (x,#). With this is mind, explain why f(x)=0 is special.
Notice that f(x)=0 is special because is the intercept of the graph with the x-axis and if f(x) corresponds to a function, the x-intercepts are the roots of the function.
The ordered pair can be written as (x,0), where x is such that f(x)=0.
I need to find the radius and the diameter but I don't understand.
ANSWER
Radius = 3 yd
Diameter = 6 yd
EXPLANATION
We are given the circle in the figure.
The radius of a circle is defined as the distance between the centre of a circle and its circumference.
Therefore, from the circle given, the radius is 3 yards
The diameter of a circle is defined as the total distance (through the centre) from one end of a circle to another.
It is twice the radius. Therefore, the diameter of the given circle is:
D = 3 * 2
D = 6 yards
The diameter is 6 yards.
A cashier has 24 bills, all of which are $10 or $20 bills. The total value of the money is $410. How many of each type of bill does the cashier have?
The cashier has 7 bills of $10 and 17 bills of $20 (found using linear equation).
According to the question,
We have the following information:
A cashier has 24 bills, all of which are $10 or $20 bills. The total value of the money is $410.
Now, let's take the number of $10 bills to be x and the number of $20 bills to be y.
So, we have the following expression:
x+y = 24
x = 24-y .... (1)
10x+20y = 410
Taking 10 as a common factor from the terms on the left hand side:
10(x+2y) = 410
x+2y = 410/10
x+2y = 41
Now, putting the value of x from equation 1:
24-y+2y = 41
24+y = 41
y = 41-24
y = 17
Now, putting this value of y in equation 1:
x = 24-y
x = 24-17
x = 7
Hence, the cashier has 7 bills of $10 and 17 bills of $20 when the total value of the money is $410.
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A ball is thrown from an initial height of 4 feet with an initial upward velocity of 23 ft/s. The ball's height h (in feet) after 1 seconds is given by the following.h=4+231-167Find all values of 1 for which the ball's height is 12 feet.Round your answer(s) to the nearest hundredth.(If there is more than one answer, use the "or" button.)Please just provide the answer my last tutor lost connection abruptly.
Answer
t = 0.59 seconds or t = 0.85 seconds
Step-by-step explanation:
[tex]\begin{gathered} Given\text{ the following equation} \\ h=4+23t-16t^2\text{ } \\ h\text{ = 12 f}eet \\ 12=4+23t-16t^2 \\ \text{Collect the like terms} \\ 12-4=23t-16t^2 \\ 8=23t-16t^2 \\ 23t-16t^2\text{ = 8} \\ -16t^2\text{ + 23t - 8 = 0} \\ \text{ Using the general formula} \\ t\text{ }=\text{ }\frac{-b\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ \text{let a = -16, b = 23, c = -8} \\ t\text{ = }\frac{-23\pm\sqrt[]{(23)^2\text{ - 4}\cdot\text{ }}(-16)\text{ x (-8)}}{2(-16)} \\ t\text{ = }\frac{-23\pm\sqrt[]{529\text{ - 512}}}{-32} \\ t\text{ = }\frac{-23\pm\sqrt[]{17}}{-32} \\ \text{t = -23+}\frac{\sqrt[]{17}}{-32}\text{ or -23-}\frac{\sqrt[]{17}}{-32} \\ t\text{ = -23 }+\text{ 4.12/-32 or t = }\frac{-23\text{ - 4.12}}{-32} \\ t\text{ = }0.59\text{ seconds or t =0.85 seconds} \end{gathered}[/tex]Therefore, t = 0.59 seconds or t = 0.85 seconds
Determine the frequency of each class and the table shown
Given:
The dataset and table with class.
Required:
Determine the frequency of each class.
Explanation:
Answer:
Answered the question.
im taking geometry A and i have a hard time with the keeping the properties straight in mathematical reasoning. the question im struggling with at the moment is in the picture here:thank you for your time
The given proposition is
[tex]m\angle UJN=m\angle EJN\rightarrow m\angle UJN+m\angle YJN=m\angle EJN+m\angle YJN[/tex]As you can observe, it was added angle YJN to the equation on both sides. The property that allows us to do that it's call addition property of equalities.
Therefore, the right answer is "addition property".Evaluate the expression when a=3 and b=6. b2-4a
b² - 4a
evaluated when a = 3 and b = 6 is:
6² - 4(3) =
= 36 - 12=
= 24
Drag the correct algebraic representation of the reflection to the white box
Question 1
When any point (x,y) is reflected over the x-axis, the reflection coordinate is (x,-y).
So, the x coordinate remains the same, and the y coordinate goes negative.
A = ( -6, 6 ) → A' = (-6,-6 )
B = (-2,6 ) → B' = (-2,-6)
C= (-6,1 ) → C' = (-6,- 1)
Algebraic representation: ( x, -y )
I will provide another picture with the questions to this problemBefore beginning: please note that this is lengthy, pre calculus practice problem
A. Marvin worked 4 hours a day plus an additional 5-hour day for a total of 29 hours.B. Marvin worked 9 hours a day for a total of 29 hoursC. Marvin worked 4 hours one day plus an additional 5 hours for a total of 29 hours.D. Marvin worked 4 days plus 5 hours for a total of 29 hours.
According to the Florida Agency for Workforce, the monthly average number of unemployment claims in a certain county is given by () = 22.16^2 − 238.5 + 2005, where t is the number of years after 1990. a) During what years did the number of claims decrease? b) Find the relative extrema and interpret it.
SOLUTION
(a) Now from the question, we want to find during what years the number of claims decrease. Let us make the graph of the function to help us answer this
[tex]N(t)=22.16^2-238.5t+2005[/tex]We have
From the graph above, we can see that the function decreased at between x = 0 to x = 5.381
Hence the number of claims decreased between 1990 to 1995, that is 1990, 1991, 1992, 1993, 1994 and 1995
Note that 1990 was taken as zero
(b) The relative extrema from the graph is at 5.381, which represents 1995.
Hence the interpretation is that it is at 1995 that the minimum number of claims is approximately 1363.
Note that 1363 is approximately the y-value 1363.278
•is this function linear? •what’s the pattern in the table•what would be a equation that represents the function
Given data:
The given table.
The given function can be express as,
[tex]\begin{gathered} y-0=\frac{2-0}{1-0}(x-0) \\ y=2x \end{gathered}[/tex]As the equation of the above function is in the form of y=2x, it is linear function because for single value of x we got single value of y.
Thus, the function can be express as y=2x form which is linear function.
help ! it may or may not have multiple answers
From the given problem, there are 3 computer labs and each lab has "s" computer stations.
So the total number of computers is :
[tex]3\times s=3s[/tex]Mr. Baxter is ordering a new keyboard and a mouse for each computer, since the cost of a keyboard is $13.50 and the cost of a mouse is $6.50.
Each computer has 1 keyboard and 1 mouse, so the total cost needed for 1 computer is :
[tex]\$13.50+\$6.50[/tex]Since you now have the cost for 1 computer, multiply this to the total number of computers which is 3s to get the total cost needed by Mr. Brax :
[tex]3s\times(13.50+6.50)[/tex]Using distributive property :
[tex]a(b+c)=(ab+ac)[/tex]Distribute s inside the parenthesis :
[tex]3(13.50s+6.50s)[/tex]One answer is 1st Option 3(13.50s + 6.50s)
Simplifying the expression further :
[tex]\begin{gathered} 3(13.50s+6.50s) \\ =3(20.00s) \end{gathered}[/tex]Another answer is 4th Option 3(20.00s)
A rectangular field of corn is averaging 125 bu/acre. The field measures 1080 yd by 924 yd. How many bushels of corn will there be?
Based on the dimensions of the rectangular field, and the corn per acre, the number of bushels of corn can be found to be 25,772 bushels
How to find the number of bushels of corn?First, find the area of the rectangular field:
= 1,080 x 924
= 997,920 yard²
Then convert this to acres with a single acre being 4,840 yards²:
= 997,920 / 4,840 square yards per acre
= 206.18 acres
The number of bushels of corn that can be grown is:
= 206.18 x 125 bushel per acre
= 25,772 bushels
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Not sure on how to do this. Would really like some help.
Given:
[tex]\cos60^{\circ}[/tex]To find:
The value
Explanation:
We know that,
[tex]\cos\theta=\sin(90-\theta)[/tex]So, we write,
[tex]\begin{gathered} \cos60^{\circ}=\sin(90-60) \\ =\sin30^{\circ} \\ =\frac{1}{2} \end{gathered}[/tex]Final answer:
[tex]\cos60^{\circ}=\frac{1}{2}[/tex]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.
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 ft32.) On the first night of a concert, Fish Ticket Outlet collected $67,200 on the sale of 1600 lawn
seats and 2400 reserved seats. On the second night, the outlet collected $73,200 by selling
2000 lawn seats and 2400 reserved seats. Solve the system of equations to determine the cost
of each type of seat.
Answer:
L=$15
R=$18
Step-by-step explanation:
i cant really explain the work
Identify the constant of variation. 8y-7x=0
A direct variation between two variables "x" and "y" is given by the following formula:
y = kx
We can rewrite the given expression 8y-7x=0 to get an equation of the form y = kx like this:
8y - 7x = 0
8y - 7x + 7x = 0 + 7x
8y = 7x
8y/8 = 7x/8
y = 7/8x
The number that is being multiplied by x should be the constant of variation k, then in this case, the constant of variation equals 7/8
Factor the following expression using the GCF.5dr - 40rr(5 dr - 40)5 r( d - 8)r(5 d - 40)5( dr - 8 r)
The greatest common factor (GCF) is: 5r
You multiply 5r by d to get the first term and multiply 5r by -8 to get the second term, then the factors are:
[tex]5r(d-8)[/tex]Answer: 5r(d-8)What type of number is - Choose all answers that apply:AWhole numberBIntegerRationalDIrratio
It is whole, integer, rational
Professor Ahmad Shaoki please help me! The length of each side of a square is extended 5 in. The area of the resulting square is 64 in,2 Find the length of a side of the
original square. Help me! From: Jessie
The length of the original square must be equal to 3 inches.
Length of the Original SquareTo find the length of the original square, we have to first assume the unknown length is equal x and then use formula of area of a square to determine it's length.
Since the new length is stretched by 5in, the new length would be.
[tex]l = (x + 5)in[/tex]
The area of a square is given as
[tex]A = l^2[/tex]
But the area is equal 64 squared inches; let's use substitute the value of l into the equation above.
[tex]A = l^2\\l = x + 5\\A = 64\\64 = (x+5)^2\\64 = x^2 + 10x + 25\\x^2 + 10x - 39 = 0\\[/tex]
Solving the quadratic equation above;
[tex]x^2 + 10x - 39 = 0\\x = 3 or x = -13[/tex]
Taking the positive root only, x = 3.
The side length of the original square is equal to 3 inches.
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Lisa's rectangular living room is 15 feet wide. If the length is 7 feet less than twice the width, what is the area of her living room?
345ft²
1) Since we have the following data then we can write it down:
width: 15 ft
length: 2w-7
2) And we can write out the following equation regarding that the area of a rectangle is given by:
[tex]S=l\cdot w[/tex]We can plug into that the given data:
[tex]\begin{gathered} S=15(2(15)-7)) \\ S=15(30-7) \\ S=15\cdot23 \\ S=345 \end{gathered}[/tex]Notice we have used the FOIL acronym. And the PEMDAS order of operations prioritizing the inner parentheses.
3) So we can state that the area of her living room is 345ft²