Simplifying the function, it's graph is given at the end of this answer.
The function is:
\(f(x) = \frac{x^2 - 3x}{x^2 - 9}\)
The numerator can be factored as:
\(x^2 - 3x = x(x - 3)\)
Using subtraction of perfect squares, the denominator can be factored as:
\(x^2 - 9 = (x + 3)(x - 3)\)
Hence, the simplified function is:
\(f(x) = \frac{x^2 - 3x}{x^2 - 9} = \frac{x(x - 3)}{(x + 3)(x - 3)} = \frac{x}{x + 3}\)
Using a calculator, the graph is sketched at the end of this answer.
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0.05 is _____ of 0.5
Answer:
1/10 th
Step-by-step explanation:
Refer the attached photo.
Answer:
hello 10%
good luck
PLEASE JUST HELP MEE :(
angle relationships in triangles...
What is the scale factor from Figure A to Figure B? PLEASE HELP
Answer:
Its 3 bro
Step-by-step explanation:
my guy A is just B scaled 3 times, every number on B times 3 equals their counterpart in A
Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = x3 − x2 − 4x + 4
g(x) = x3 + 2x2 − 9x − 18
g(x) = x3 − 3x2 − 4x + 12
g(x) = x3 + 2x2 − 25x − 50
g(x) = 2x3 + 14x2 − 2x − 14
Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
Create a graph of the polynomial function you created in Question 4.
Part C
Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
Part D
Create an ad campaign to promote Ray and Kelsey's roller coaster. It can be a 15-second advertisement for television or radio, an interview for a magazine or news report, or a song, poem, or slideshow presentation for a company. These are just examples; you are not limited to how you prepare your advertisement, so be creative. Make sure to include a script of what each of you will say if you are preparing an interview or a report. The purpose of this ad is to get everyone excited about the roller coaster.
Answer:
Step-by-step explanation:
print of clip a sample research or article from a newspaper or internet and write your reaction on this paper
Anwser the question above
\( \large \mathfrak{Solution : }\)
let's solve :
2 [30 - (1 + 4)²]2 [30 - (5)²]2 [30 - 25]2 [5]10\( \huge \boxed{\mathfrak{Question} \downarrow}\)
2 [30 - (1 + 4)²]\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)
\( \sf2 [ 30 - ( 1 + 4 ) ^ { 2 } ]\)
Add 1 and 4 to get 5.\( \sf2\left(30-5^{2}\right) \)
Calculate 5 to the power of 2 and you'll get 25.\( \sf2\left(30-25\right) \)
Subtract 25 from 30 to get 5.\( \sf2\times 5 \)
Multiply 2 and 5 to get 10.\( \boxed{ \boxed{ \boxed{ \mathfrak{ = 10}}}}\)
angle A and angle B are supplementary angles. Find m angle A and m angle B.
m angle A=(x+11) m angle B=(x-15)
Graph the inequality
Answer:
the last option is correct
Look over the probability rules/concepts (independent event, multiplication rule, and addition rule). Make sure you understand them. What is the probability that a couple will have a girl, a boy, a girl, and a boy in this specific order
The probability of a couple having a girl, a boy, a girl, and a boy in this specific order is 1/16, or 0.0625.
This can be calculated using the multiplication rule for probabilities, which states that the probability of two independent events both occurring is the product of their individual probabilities.
The probability of each birth being a girl or a boy is 1/2, so the probability of having a girl and a boy in any order is 1/2 * 1/2 = 1/4. The probability of having a girl, a boy, a girl, and a boy in this specific order is the product of the probabilities of each event, which is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.
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What is the measure of an angle that is the complement of angle C?
Answer:
80°
Step-by-step explanation:
complimentary angles total 90°
Rational Functions
Create a Model to represent the scenario.
Shrek, Donkey, and Fiona are riding in a carriage to Far Far Away. The horses, Prescott and Thaddeus, are pulling the carriage all the way. Prescott alone could pull the carriage all the way to Far Far Away and back to The Swamp in 21 days, but together they are able to pull the carriage to Far Far Away in 9 days.
Answer:
Step-by-step explanation:
Remark
I suppose the question is what is Thaddeus' time to make the trip. This is a fairly common question but not everyone knows how to solve it.
Derivation of the Formula
Prescott + Thaddeus = 1 trip
So the logic of the equation is this.
distance = 1 trip
time = number of dates
rate = ?
rate = distance / time
To find out what the contribution of Thaddeus is set up a distance time formula.
1/21 days is the rate for Prescott
1/x days is the rate for Thaddeus
Together the rate is 1/9
Solution
1/21 + 1/x = 1/9
Subtract 1/21 from both sides
1/x = 1/9 - 1/21
It's not obvious what the LCM is.
9 = 3 * 3
21 = 3 * 7
LCM: 7 * 3 *3 = 63
1/x = 7/63 - 3/63 = 4/63
1/x = 4/63 Cross Multiply
4x = 63 Divide by 4
x = 63/4
Answer
x = 15 3/4
x = 15.75
A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the homework grade, to the nearest integer, for a student with a test grade of 50.
The linear regression equation models is y = 1.20x - 14.32
The homework grade for a student with a test grade of 50 is 54.
What is regression line?An estimate of the line that depicts the actual, but unidentified, linear relationship between the two variables is called a regression line. When the value of the explanatory variable is known, the regression line's equation is used to predict (or estimate) the value of the response variable.
As, linear regression calculator which gives the linear equation in the form :
y = bx + c
y = 1.20x - 14.32
where y = Test grade and x = homework grade
Also, Slope, b = 1.20, intercept, c = - 14.32
So, Using the model equation we have Test grade, y =
y = 1.20x - 14.32
50 = 1.20x - 14.32
50 + 14.32 = 1.20x
64.32 = 1.20x
x = (64.32 ÷ 1.20)
x = 53.6
Hence, the estimated homework grade for a test score of 50 is 54.
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The probability of getting an order from restaurant a or an order that is accurate is
The probability of getting an order from restaurant a or an order that is accurate is 1029/1125.
From the given table we can see that,
Total number of order = 332 + 271 + 245 + 149 + 32 + 51 + 31 + 14 = 1125.
Number of getting order from restaurant A = 332 + 32 = 364
Number of getting order which is accurate = 332 + 271 + 245 + 149 = 997
Number of getting order which is accurate and from restaurant A = 332.
So the probability of getting order from restaurant A = P(getting order from restaurant A) = 364/1125
Probability of getting order which is accurate = P(Accurate order) = 997/1125
Probability of getting order which is accurate and from restaurant A = P(restaurant A and accurate order) = 332/1125.
So the probability of getting an order from restaurant a or an order that is accurate is given by
= P(restaurant A or Accurate Order)
= P(restaurant A) + P(Accurate Order) - P(restaurant A and accurate order)
= 364/1125 + 997/1125 - 332/1125
= (364 + 997 - 332)/1125
= 1029/1125
Hence the probability of getting an order from restaurant a or an order that is accurate is 1029/1125.
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The given question is incomplete. The complete question will be -
Using the given table find the probability of getting an order from restaurant a or an order that is accurate?
which polynomial is prime? 3x3 3x2 – 2x – 2 3x3 – 2x2 3x – 4 4x3 2x2 6x 3 4x3 4x2 – 3x – 3
To determine which polynomial is prime, we need to check if it can be factored into simpler polynomials or if it is irreducible.
Let's analyze the given polynomials:
3x^3 + 3x^2 - 2x - 2
3x^3 - 2x^2 + 3x - 4
4x^3 + 2x^2 + 6x + 3
4x^3 + 4x^2 - 3x - 3
To determine if these polynomials are prime, we need to check if they can be factored further. If they cannot be factored into simpler polynomials, they are considered prime.
The polynomial 3x^3 + 3x^2 - 2x - 2 can be factored as (x + 1)(3x^2 - 2).
The polynomial 3x^3 - 2x^2 + 3x - 4 cannot be factored further.
The polynomial 4x^3 + 2x^2 + 6x + 3 can be factored as (2x + 1)(2x^2 + 3).
The polynomial 4x^3 + 4x^2 - 3x - 3 can be factored as (2x + 1)(2x^2 - 3).
Based on the factorizations, the only polynomial that is prime (cannot be factored further) is 3x^3 - 2x^2 + 3x - 4.
Therefore, the polynomial 3x^3 - 2x^2 + 3x - 4 is prime.
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What is the value of the expression when a = 3 and b = 5?
3a+b−4
4
7
10
34
what is the value of the x in this equation 6x = 54
Answer:
x = 9
Step-by-step explanation:
6x = 54
Simple way of solving, all you have to do is isolate the variable "x." To do that, divide the number, 6, by both sides.
6x / 6 = 54 / 6
54 / 6 = 9
Hence,
x = 9
Hope this helps :)
Answer:
x= 9
6x= 54
\( \frac{6x}{6} = \frac{54}{6} \)
x = 9
hope it's helpful ❤❤❤
THANK YOU.
On a coordinate plane, an exponential function approached y = 0 in quadrant 2 and increases into quadrant 1. It crosses the x-axis at (0, 2). What is the initial value of the exponential function shown on the graph? 0 1 2 4.
The initial value of an exponential function is the y-intercept of the function
The initial value of the exponential function is 2.
From the question, we understand that the exponential function crosses the y-axis at point (0,2)
This means that, the value of y when x = 0 is 2
In other words, the y-intercept is 2.
Hence, the initial value of the exponential function is 2.
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Answer:
the answer is C
Step-by-step explanation:
just took the test
which equation is true
The equation that must be true if A and B are independent is P(B | A) = P(B)
Independent ProbabilityTwo events A and B are regarded as independent in probability theory if the occurrence or non-occurrence of one event has no impact on the likelihood that the other event will occur.
The likelihood of both events A and B occurring simultaneously is equal to the product of their individual probabilities, according to the equation. This equation is valid for unrelated occurrences.
The assumption made by the equation that the occurrences are truly independent and that there is no correlation or interaction between them; must be understood. This equation would not apply if the events were interdependent, and other analysis or computations may be required to establish the joint probability of the events.
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Pls help I’m getting confused even though should be pretty easy.
Answer:
V = 108
Step-by-step explanation:
B = 9 x 4 = 36 Height of Triangular prism is 3 so 36 x 3 = 108
Triangle X Y Z is shown. Angle X Y Z is 75 degrees and angle Y Z X is 50 degrees. The length of X Y is 2 and the length of Y Z is x.
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
Which is the best approximation of the value of x? Use the law of sines to find the answer.
1.5 units
2.1 units
2.9 units
3.6 units
By using the sines law we conclude that the best approximation of the value of x is 2.9 units. Answer: 2.9 units.
What is sines law?
The Law of Sines is a trigonometric law that relates the sides of a triangle to the sine of its angles. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal to the same ratio for each of the other two sides and their opposite angles. In other words, it can be expressed as:
a/sin(A) = b/sin(B) = c/sin(C)
We can use the Law of Sines to find the length of YZ:
sin(75) / 2 = sin(50) / x
Multiplying both sides by x:
x * sin(75) / 2 = sin(50)
Dividing both sides by sin(75) / 2:
x = 2 * sin(50) / sin(75)
Using a calculator to evaluate sin(50) and sin(75), we get:
x ≈ 2.9 units
Therefore, the best approximation of the value of x is 2.9 units. Answer: 2.9 units.
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If m/CDE is a straight angle, DE bisects m/GDH, mZGDE = (8x-1), m/EDH = (6x +
m/CDF = 43°, find each measure.
x =
m/GDH=
mZFDH=
m/FDE =
Answer:
From the way the problem is worded:
CDE is a straight angle made up of three angles: CDF of measure 43, FDG of unknown measure and GDE of measure 8x + 1.
EDH is outside CDE and is of measure 6x + 15.
Since DE bisects GDH to form GDE and EDH, those latter two angles are equal and thus 8x + 1 = 6x + 15 and x = 7 and substituting 7 for x, both angles are equal to 57 degrees.
Since CDF is 43 and GDE is 57 and CDE is 180 in total, then FDG = 180 - 43 - 57 = 80 degrees.
I am in need of assitance, question shown in picture.
Answer:
it's going to be 7.4
Step-by-step explanation:
5 x 4 = 20
4 / 2 since you want to get radius
2 x 2 = 4 x pi for both half circles.
4 x pi = 12.5 --> 13
20 - 12.5663706 = 7.43 ---> 7.4
Evaluate.
2 to the power of 3 + 4 ⋅ 2 − 7
Answer:
9
Step-by-step explanation:
Answer: 9
Step-by-step explanation: calculator
Construct two functions, f and g where both f,g: [0,1] → R such
that f is injective and g is surjective to show that [0,1] and R
have the same cardinality.
The functions with the sets [0,1] and `R` have the same cardinality are
f(x) = tan(π(x - 1/2)) and
g(x) = (1/π) arctan(tan(π(y - 1/2))) + 1/2 = (1/π) π(y - 1/2) + 1/2
Function `f: [0,1] → R` can be defined as follows:
f(x) = `tan(π(x - 1/2))
The domain of `f` is [0,1], and the range of `f` is `R`.
The function `f` is one-to-one or injective.
To see why, assume that f(a) = f(b) for some `a` and `b` in [0,1].
Then, tan(π(a - 1/2)) = tan(π(b - 1/2))
Let `n` be any integer.
Then, π(a - 1/2) - nπ = π(b - 1/2) - nπ
Or π(a - b) = nπ
Thus, a - b = n, but this contradicts the fact that `a, b ∈ [0,1]`.
Therefore, `f` is injective.
Function g: R → [0,1] can be defined as follows:
g(x) = (1/π) arctan(x) + 1/2
The domain of `g` is `R`, and the range of `g` is [0,1].
The function `g` is onto or surjective.
To see why, let `y` be any number in [0,1].
Then, we must find some `x` in `R` such that g(x) = y.
Let x = tan(π(y - 1/2)).
Then, g(x) = (1/π) arctan(tan(π(y - 1/2))) + 1/2 = (1/π) π(y - 1/2) + 1/2
= y
Therefore, `g` is surjective.
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HELP PLEASE!! WILL CROWN BRAINLIEST.....
On October 1, Gary’s bank balance was $130. During October, he made two
withdrawals and one deposit. At the end of the month, his bank balance was
$95. List two withdrawals and one deposit that would give this final balance.
Answer: i am not sure but thanks for the points have a good day
Step-by-step explanation:
Which graph represents a linear equation?
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
What does this problem want us to find:
\(\hookrightarrow \text{which graph is a linear equation}\)
A linear equation's
\(\hookrightarrow \text{would be a straight line}\)
\(\hookrightarrow \text{ because linear lines are lines with one set slope }\)
\(\hookrightarrow \text{across the whole graph}\)
All other lines in general:
\(\hookrightarrow \text{slope's change as you move along their graph}\)
Thus Top-right graph is a linear equation graph
Answer: Top-Right Graph
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For each positive integer n, the nth term of the sequence S is 1 + (-1)n
Quantity A: The sum of the first 39 terms of S
Quantity B: 39
A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Quantity A and Quantity B are equal, so the answer is C.
The sequence S is an alternating sequence that starts with 2 and alternates between 0 and 2 at each subsequent term. The sum of the first n terms of this sequence is given by:
S_n = (n/2) * (2 + (-1)^n)
So, the sum of the first 39 terms is:
S_39 = (39/2) * (2 + (-1)^39) ≈ 19.5 * 2 ≈ 39
what is sequence?
In mathematics, a sequence is a list of numbers arranged in a specific order. Each number in the sequence is called a term, and the position of a term in the sequence is called its index or subscript.
Sequences can be defined either explicitly, by giving a formula or rule for the nth term, or recursively, by giving a formula or rule for each term in terms of one or more of the preceding terms.
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Slope = 2; y-intercept = -1
Answer: y=2x-1
Step-by-step explanation:
In slope intercept form y=Mx+b
Mx=slope and b=intercept
Y=2x-1
The equation of line with slope m = 2 and y-intercept is -1 is given by
y = 2x - 1
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the slope of the line m = 2
Let the y intercept of the line b = -1
Now , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
y = 2x - 1 be equation (1)
Therefore , the value of A is y = 2x - 1
Hence , the equation of line is y = 2x - 1
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If the area of the rug in this den 48 square feet and the width of the carpet is 6’, what is the perimeter of the rug?
A. 112’
B. 28’
C. 8’
D. 108’
Answer:
B
Step-by-step explanation:
The perimeter of rug is 28 feet's.
We have a rug.
We have to determine its perimeter.
What is the Perimeter of a Rectangle ?The perimeter of rectangle will be -
P = 2(L + B)
According to the question -
Area = 48 square feet
Width = 6 feet
Then -
L x 6 = 48
L = 8 feet
Therefore, the perimeter will be -
2(L + B) = 2 x 14 = 28 feet's.
Hence, the perimeter of rug is 28 feet's.
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Alex records the running time—the number of minutes a movie lasts from start to finish—of 50 popular movies. The distribution of times, in minutes, is displayed in the histogram below.
Answer:
You forgot to attach the question and the histogram.
Is your question “the interval containing the most movies” ? If yes, then the answer is :
Interval 90-100 minutes
Step-by-step explanation:
A histogram is a chart that is used to represent data in form of bars.
Like every other chart, it consists of both the x and y axis. The y axis contains the frequency or percentage of occurrences while the x axis contains the range or intervals.
To determine the interval with the most occurrences, that is the interval containing most movies, we look for the bar with the most height. The bar that is tallest amongst others has the most movies in its running time.
From the attached histogram, the interval containing the most movies is the 90- 100 minutes interval.
This simply means that from Alex’s record, out of the 50 popular movies, more movies run with the 90-100 minutes interval.
PS: view the attached histogram
Answer:
There are two problems like this, one involving median and the shape.
Here are your answers for both.
Shape is skewed right, this is because it decreases towards the right, like a hill. (C)
Extra info/this part isnt right: It would be skewed left but it isn't because it is not decreasing towards the left like a hill.
The median is between the interval 90-100, because it looks to be the typical number. (A)
The temperature at Jade's cabin was negative 13 ° Celsius when he got up in the morning. It dropped 2 ° Celsius by 10 a.m. and then rose 8 ° Celsius by lunchtime.
What was the temperature at lunchtime?
Answer:
19 ° Celsius
Step-by-step explanation:
13 -2 = 11 +8 = 19