The rational function is (x + 2)/(x - 3)(x + 2) which has a vertical asymptote at X = 3, and a removable discontinuity at x = -2.
Function
The function is referred as a mathematical expression that defines a relationship between one variable and another variable.
Given,
Here we need to construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2.
Through the given question, we have been given that the rational function that has a vertical asymptote at x = 3, and a removable discontinuity at x = -2.
Here the x = 3 is a vertical asymptote.
So the one factor in the denominator is (x - 3),
And the discontinuity at x = - 2 can be removed, so the another common factor in the numerator and denominator is x+2.
Therefore, the rational function would be :
f(x) = (x + 2)/(x - 3)(x + 2)
So, the rational function would be (x + 2)/(x - 3)(x + 2).
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for questions 4-6: The table below shows
e average price of a gallon of gasoline.
Year
2000
2004
2010
2012
2015
Price
2.02
2.32
3.02
3.64
2.45
4. Find the rate of change from 2004 to 2010.
5. Find the rate of change from 2000 to 2012.
6. Find the rate of change from 2012 to 2015
Answer:6/13/3
Step-by-step explanation:look at how the year’s difference are
Quandale Jiga has $2.5 the sussy battle pass cost $0.75 how many battle passes can he buy?
What set of line segments could create a right triangle:
15, 30, 35 - 15, 36, 39 - 15, 20, 29 or 5, 15, 30
Answer:
(b) 15, 36, 39
Step-by-step explanation:
You want to know which sets of segment lengths could form a right triangle.
Right triangleFor segments to form a right triangle, the lengths must satisfy the triangle inequality and the Pythagorean theorem. The latter condition can often be determined by looking at the reduced ratios of the lengths, and comparing to known Pythagorean triples.
15, 30, 35The ratio of lengths is 3:6:7. There are no integer side lengths that will form a right triangle when one of them is double another. Not a right triangle.
15, 36, 39The ratio lengths is 5:12:13. These numbers are a common Pythagorean triple, so will form a right triangle.
15, 20, 29The ratio of the smaller two numbers is 3:4. In order for these to form a right triangle, they must be part of a triangle with ratios 3:4:5. That would be 15, 20, 25. The side length 29 is too long for a right triangle. Not a right triangle.
5, 15, 30The two short sides are too short to reach the ends of the long side. These lengths will not form a triangle.
__
Additional comment
The table in the attachment computes a²+b²-c². When that value is 0, the Pythagorean theorem is satisfied, and the triangle is a right triangle. Positive numbers indicate an acute triangle; negative numbers indicate an obtuse triangle.
The Pythagorean triples that came into play in this answer are {3, 4, 5} and {5, 12, 13}. Other triples commonly seen are {7, 24, 25} and {8, 15, 17}.
PLS HELP QUICK!! IL MARK YOU BRAINLIEST
A cooler is filled with containers of yogurt. Some of the containers have low-fat yogurt and some have non-fat yogurt. There are three flavors for each type of yogurt, as shown in the table. Sophie chooses a container at random. What is the probability that she chooses low-fat yogurt?
Answer:
Step-by-step explanation 2/3 is the answer :
The required probability, that she chooses low-fat yogurt is 2/3.
Given that, a cooler is filled with containers of yogurt. Some of the containers have low-fat yogurt and some have non-fat yogurt. There are three flavors for each type of yogurt, as shown in the table.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
From the given,
Sample space = 24
Low Fat =16
Non-fat = 8
The probability that she chooses low-fat yogurt
= 16/24
= 2/3
Thus, the required probability, that she chooses low-fat yogurt is 2/3.
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What will be the rule for a negative fraction?
Maybe like -m/n instead of just m/n?
The generalized rule of the indices to be negative fraction can be written as [tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex].
What is the law of indices?Index (indices) in Maths is the power or exponent which is raised to a number or a variable.
An algebraic expression is a quantity made up of symbols and processes + - / and multiplication Expressions utilizing indices are made simpler using the laws of indices.
Let's consider a negative fraction exponent as, [tex]a^{-m/n}[/tex]
[tex]a^{-m/n}=1/a^{m/n}[/tex]
Since,[tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex]
Therefore, the above expression converts as,
[tex]a^{-m/n} =1/(\sqrt[n]{a})^{-m}[/tex]
[tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex]
Hence "The generalized rule of the indices to be negative fraction can be written as [tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex].".
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PLEASE HELP
19- 4x + x² can be written in the form
(x + a)² + b, where a and b are numbers.
Work out the values of a and b.
Step-by-step explanation:
so, let's do the multiplications and squaring. and then compare the result with the target.
(x + a)² + b = x² + 2ax + a² + b
and the original expression is
x² - 4x + 19
x² = x² done
2ax = -4x
2a = -4
a = -2
a² + b = 19
(-2)² + b = 19
4 + b = 19
b = 15
so, the result is
(x - 2)² + 15
Answer: (x-2)^2+15
Step-by-step explanation:
Given x^2-4x+19
=here b=-4 and c=19
B=b/2=-4/2=-2
C=c-B^2=19-(-2)^2=19-4-15
so
(x-B)^2+C
(x-2)^2+15
A road is 8/9 of a mile long. A crew needs to repave 2/5 of the road. How long is the section that needs to be repaved?
Can someone help me out with this math problem and weather it converges or diverges?
The given infinite series is divergent.
Given,
[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\frac{3n^2+n+1}{2n^2-1}}[/tex]
it is in the form,
[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\ a_n[/tex]
If the series is convergent then it satisfies,
i)[tex]b_{n+1}\ \leq\ b_n\ for\ all\ n[/tex]
ii)[tex]\lim_{n \to \infty} a_n =0[/tex]
if any of the above condition dissatisfies then the series is divergent
First check the 2nd condition,
[tex]\lim_{n \to \infty}\frac{3n^2+n+1}{2n^2-1}}\\\\= \lim_{n \to \infty}\frac{n^2(3+\frac{1}{n}+\frac{1}{n^2})}{n^2(2-\frac{1}{n^2})}}\\\\=\frac{3+0+0}{2-0}\\\\=\frac{3}{2}[/tex]
Here, [tex]\lim_{n \to \infty} a_n \neq 0[/tex]
Thus, the given series is divergent.
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The graph shows a proportional relationship between the variables y and x.
Answer:
the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, is equal to k, where k is the unit rate.
The midpoint of AB is M (5, 1). If the coordinates of A are (3,6), what are
the coordinates of B?
Two consecutive odd integers have a sum of 40. Find the integers
Answer:
19 and 21|
Step-by-step explanation:
a + (a+2) = 40
2a + 2 = 40
2a = 40 - 2
2a = 38
a = 38/2
a = 19
a+2 = 21
Check:
19 + 21 = 40
A telephone exchange operator assumes that 8% of the phone calls are wrong numbers.
If the operator is correct, what is the probability that the proportion of wrong numbers in a sample of 494 phone calls would differ from the population proportion by more than 3%? Round your answer to four decimal places.
The probability that the phone calls would differ from the population proportion by more than 3% is 0
How to determine the probability value?From the question, the given parameters about the distribution are
Proportion, p = 8%Sample size, n = 494The actual proportion, x = greater than 3%The mean is calculated as
Mean = np
So, we have
Mean = 8% * 494 = 39.52
The standard deviation is calculated as
Standard deviation = √np(1 - p)
So, we have
Standard deviation = √494 * 8% (1 - 8%) = 0.77
The z-score is calculated using the following formula
[tex]z = \frac{\bar p - p}{\sqrt{p(1 - p)}/n}[/tex]
Substitute the given parameters in the above equation
[tex]z = \frac{8\% - 3\%}{\sqrt{8\% * (1 - 8\%)}/494}[/tex]
Evaluate
z = 90.9
The probability is then calculated as:
P(x > 3%) = P(z > 90.9)
From the z table of probabilities, we have;
P(x > 3%) = 0
Hence, the probability is 0
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Which linear function is graphed on the grid?
90
80
70
60
8
50
30
20
10
-9-8-7-6-5- -3 -2 -1
-10
20
у
-30
-40
-50
-60
-70
-80
88
-90
1234
56789
X
The linear function that is graphed on the grid is g(x) = (15/2)x + 45 , the correct option is (d) .
In the question ,
a linear function graph is shown ,
we have to find that linear function .
So , From the given graph we can see that
the graph passes from the points (2 , 60) and (6 , 90)
in order to find the equation , we first need to find the slope .
slope = (90 - 60)/(6 - 2)
= 30/4
= 15/2
So , the equation of the line passing through the points (2 , 60) and slope 15/2 is
(y - 60) = 15/2(x - 2)
y - 60 = (15/2)x - 15
Adding 60 to both the sides ,
we get
y - 60 + 60 = (15/2)x - 15 + 60
y = (15/2)x - 15 + 60
y = (15/2)x + 45
function is (15/2)x + 45
Therefore , The linear function that is graphed on the grid is g(x) = (15/2)x + 45 .
The given question is incomplete , the complete question is
Which linear function is graphed on the grid shown below ?
(a) g(x) = (2/15)x - 6
(b) g(x) = (2/15)x + 45
(c) g(x) = (15/2)x - 6
(d) g(x) = (15/2)x + 45
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PLEASE HELP AND FAST
Answer:
d [tex]\frac{-4}{3}[/tex]
Step-by-step explanation:
change in y over the change in x
[tex]\frac{-2-2}{1- -2}[/tex] = [tex]\frac{-4}{3}[/tex]
Ms. Jones washed
2
7
of her laundry. Her son washed
1
3
of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
Let ()=94+2+2. Compute (5)() .
Based on the given equation and the given value of (), the value of 5() from the equation is 490
How to solve equation?If
() = 94 + 2 + 2
The equation can be solved by substituting the value of () into 5()
Substituting is the method of inserting the known value of a variable into an equation to solve for the value of the equation.
Then,
Substitute the value of () into (5)()(5)()
= 5(94 + 2 + 2)
= 5(98)
= 490
So therefore, the value of 5() is given by 490.
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find the amount on $ 6,250 at 8%p.a compounded annually for 2 years. also, find the compounded intrest
The Compound Interest is $7,290.00.
What is Compound Interest?In order to calculate compound interest, multiply the principal of the original loan by the annual interest rate multiplied by the number of compound periods minus one.
Given:
P= 6250
T= 2 years
r = R/100
r = 8/100
r = 0.08 rate per year,
Then solve the equation for A
A = P[tex](1 + r/n)^{nt[/tex]
A = 6,250.00[tex](1 + 0.08/1)^{(1)(2)[/tex]
A = 6,250.00(1 + 0.08)²
A = $7,290.00
Hence, The Compound Interest is $7,290.00.
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evaluate the expression
SIN² 225° - COS² 270° + TAN ² 60°
[tex] = ( \sin(180 + 45) )^{2} - ( \cos(180 + 90) )^{2} + ( \frac{ \sqrt{3} }{1} )^{2} \\ = ( - \sin(45) )^{2} - ( - \cos(90) )^{2} + 3 \\ = ( - \frac{1}{ \sqrt{2} } ) ^{2} - ( \frac{0}{1})^{2} + 3 \\ = \frac{1}{2} - 0 + 3 \\ = \frac{1}{2} + 3 \\ = \frac{7}{2} [/tex]
ATTACHED IS THE SOLUTION
In TY’s math class, 20% of students earned an A on a test. If there were 30 students in the class, how many got the A
Answer:
Step-by-step explanation
Answer:
6 students
Step-by-step explanation:
[tex]\frac{1}{5} = \frac{x}{30}[/tex]
[tex]30 = 5x[/tex]
[tex]6=x[/tex]
A researcher collected sample data for 12 middle-aged women. The sample had a mean serum cholesterol level (measured in milligrams per one hundred
milliliters) of 189.6, with a standard deviation of 10. Assuming that serum cholesterol levels for middle-aged women are normally distributed, find a 95%
confidence interval for the mean serum cholesterol level of all women in this age group. Give the lower limit and upper limit of the 95% confidence interval.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
Lower limit:
Upper limit:
X
5
The lower and upper limit of the 95% confidence interval is 183.2 and 196.0 unit.
What is a confidence interval ?
When you run your experiment again or resample the population in the same way, you can expect your estimate to fall within a certain range of values a certain percentage of the time. This is known as the confidence interval.
Main Body:
Given in question :
x- bar = 189.6
standard deviation = 10
C.I. = 95% =0.95
N=12
so, degree of freedom (D.F) = N-1 = 11
confidence level (α) = (1- C.I.)/2
= 0.025
according to t- distribution table for d.f = 11 and α= 0.025 , my result is 2.201
Now dividing standard deviation by square root of samples, we get
= 10/√12= 2.887
Lower limit = Mean - 2.201*2.887
= 189.6- 6.354
= 183.246
Upper limit = Mean + 2.201*2.887
= 189.6 + 6.354
= 195.954
Hence the result is 183.2 and 196.
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What is the solution to the system graphed below? PLS ANSWER ASAP
The system of equations has its solutions to be (0, 3)
How to determine the solution to the system of equations?From the question, the system of equations is represented on the graph
On the graph, we have the following representations
Two lines of different colorsBoth lines intersect at a pointSay the functions are f(x) and g(x)
To determine the solution to the system of equations, we set both equations equal
i.e. f(x) = g(x)
This in other words mean that we determine the coordinates of the points where the graphs intersect
In this case, they intersect at point (0, 3)
This represents the solution
Hence, the solution to the system of equations is (0, 3)
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what does d = math help please..................
The value of d in the expression, 4d/5+3 = -2-d/5, is -5.
According to the question,
We have the following expression:
4d/5+3 = -2-d/5
Now, moving the terms with the same variables on the left hand side will result in the change of the sign from minus to plus:
4d/5+d/5 -3 = -2
5d/5+3 = -2
d+3 = -2
Now, moving 3 from the left hand side to the right hand side will result in the change of the sign from plus to minus:
d = -2-3
We know that two negative integers are added but the sign before the result remains negative.
d = -5
Hence, the value of d is -5.
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Let f(x)=x/x+1 and g(x)=√x-1
Find the following
i. f(a − 1) + g(a + 1)
ii. f(a² + 1)g(a² + 1)
Answer:
Step-by-step explanation: a square x b square
Examine the worked examples. Then, answer the questions.
Alessa's car uses 2 gallons of gas to drive 45 miles. How many miles can
Alessa's car drive using 15 gallons of gas?
Let m represent the number of miles and g represent the gallons of gas.
m=
11 L
m=
m=
Write an equation in the form y = kx for the number of
miles in terms of the gallons of gas.
(15) Substitute the value for the given quantity.
Evaluate the right hand side of the equation.
Alessa's car can drive
miles using 15 gallons of gas.
Answer: if you multiply you will end up with 675
Step-by-step explanation:
Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the wire they need. Andy needs 24 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?
Step-by-step explanation:
Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the wire they need. Andy needs 24 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?
Looking at your chart:
cost/length in inches
6/100 = $0.06 per inch
8.1/135 = $0.06 per inch
9.6/160 = $0.06 per inch
10.8/180 = $0.06 per inch
So the rate stays at a constant rate of $0.06 per inch.
Andy needs 24 feet or 288 inches at a constant rate of $0.06 per inch.
= 288 * $0.06
= $17.28
________________________________
Emily needs 15 yards or 540 inches at a constant rate of $0.06 per inch.
= 540 * $0.06
= $32.40
A child welfare officer asserts that the mean sleep of young babies is 14 hours a day. A random
sample of 64 babies shows that the mean sleep was only 13 hours 30 minutes with standard
deviation of 3 hours. At 5% level of significance, test the assertion that the mean sleep of babies is
less than 14 hours a day
There is not enough evidence to conclude that the mean is less than 14 hours, as the p-value of the test is greater than 0.05, using the t-distribution.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is not less than 14 hours, hence:
[tex]H_0: \mu \geq 14[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the mean is less than 14 hours, hence:
[tex]H_1: \mu < 14[/tex]
What is the test statistic?The test statistic is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which the parameters are defined as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In the context of this problem, the values of these parameters are:
[tex]\overline{x} = 13.5, \mu = 14, s = 3, n = 64[/tex]
Hence the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{13.5 - 14}{\frac{3}{\sqrt{64}}}[/tex]
t = -1.33.
P-value and conclusionUsing a z-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with t = -1.33 and 64 - 1 = 63 df, the p-value of the test is of 0.094.
Since the p-value of the test is greater than the significance level of 0.05, there is not enough evidence to conclude that the mean is less than 14 hours.
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Select all of the following that are ordered pairs of the given function.
h(x) = 3x²
(1, 3)
(-1, -3)
(-1,3)
(1, -3)
The ordered pairs of the function, h(x) = 3x², are (1,3) and (-1,3).
According to the question,
We have the following information:
h(x) = 3x²
Now, we will look at the options to know the correct option of ordered pairs.
Now, in the options, there are only two values of x (1 and -1). So, we will solve the given function using these two values and we will find the value of h(x).
h(x) = 3x²
h(1) = 3*1*1
h(1) = 3
So, the first ordered pair is (1,3).
When x = -1:
h(x) = 3x²
h(-1) = 3*-1*-1
h(-1) = 3
Now, the second ordered pair of the function is (-1,3).
Hence, the correct options are A and C.
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rewrite 11/12 in two different ways
Jotes
Check
A dime is 1.35 x 10-3 meter thick. What would be the height, in
meters, of a stack of 1 million dimes?
A1.35 x 10^2meters
B 1.35 x 10^3meters
1.35 x 10^4 meters
1.35 x 10^9meters
Go Online You can complete an Extra Example online.
Show
your work
here
Answer:
Step-by-step explanation:
Which triangle congruence postulate would be used to prove the following triangles congruent?
1. SSS
2. HL
3. AAS
4. SAS
According to the SSS Postulate, two triangles are congruent if three of one triangle's sides are congruent with three of another triangle's sides.
Explain about the Congruence postulate?
A postulate is an assertion that is not backed by any evidence. Axiom is another name for a postulate. For instance, you would believe Pam if she said that all of her siblings were at least five feet one tall since you are aware of her height and that of all of her siblings, who are all taller than her.
When two figures or objects in geometry have the same shapes, sizes, or are mirror images of one another, they are said to be congruent.
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.
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