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f(x)= (x^2 + x - 12)/(x^2 + 6x + 9)
Discuss the behavior of f near any excluded x-values/
a. f(x) --> -∞ as x --> 3^+ and as x--> 4^-, f(x) --> ∞ as x --> 4^+ and as x --> 3^-
b. f(x) --> ∞ as x --> 4^+ and as x --> 4^-
c. f(x) --> -∞ as 4^+ and as x --> 4^-, f(x) --> ∞ as 3^+ and as x --> 3^-
d. f(x) --> -∞ as x --> 3^+ and as x --> 3^-, f(x) --> ∞ as x --> -4^+ and as x --> -4^-
e. f(x) --> -∞ as x --> -3^+ and as x --> -3^-
Answers
Answer:
e. f(x) --> -∞ as x --> -3^+ and as x --> -3^-
Step-by-step explanation:
You want to know the behavior of f(x)= (x^2 + x - 12)/(x^2 + 6x + 9) near any excluded x-values.
DomainThe function can be factored as ...
[tex]f(x)=\dfrac{x^2+x-12}{x^2+6x+9}=\dfrac{(x+4)(x-3)}{(x+3)^2}[/tex]
The excluded values are values of x where the denominator is zero. The only excluded value is x = -3. (eliminates all answer choices except E)
Asymptotic behaviorAt either side of x = -3, the sign of the numerator is negative and the sign of the denominator is positive. That makes f(3-) < 0 and f(3+) < 0.
f(x) will never approach +∞, but f(x) approaches -∞ as x nears -3 from either direction.
Answer:
[tex]\textsf{e)} \quad f(x) \rightarrow -\infty\;\;\textsf{as}\;\; x \rightarrow -3^+ \;\;\textsf{and as}\;\;x \rightarrow -3^-[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=\dfrac{x^2+x-12}{x^2+6x+9}[/tex]
Factor the numerator:
[tex]\implies x^2+x-12[/tex]
[tex]\implies x^2+4x-3x-12[/tex]
[tex]\implies x(x+4)-3(x+4)[/tex]
[tex]\implies (x-3)(x+4)[/tex]
Factor the denominator:
[tex]\implies x^2+6x+9[/tex]
[tex]\implies x^2+3x+3x+9[/tex]
[tex]\implies x(x+3)+3(x+3)[/tex]
[tex]\implies (x+3)(x+3)[/tex]
[tex]\implies (x+3)^2[/tex]
Therefore, the rational function is:
[tex]f(x)=\dfrac{(x-3)(x+4)}{(x+3)^2}[/tex]
As the degree of the numerator is equal to the degree of the denominator, there is a horizontal asymptote at y = 1.
A vertical asymptote occurs at the x-value(s) that make the denominator of a rational function zero.
[tex]\implies (x+3)^2=0[/tex]
[tex]\implies x+3=0[/tex]
[tex]\implies x=-3[/tex]
Therefore, there is a vertical asymptote at x = -3.
As there is a vertical asymptote at x = -3, the excluded x-value is x = -3.
As x approaches x = -3 from both sides, the numerator of the rational function approaches -6 and the denominator approaches a very small positive number. Therefore, the function approaches a very large negative number.
Therefore, the end behaviour of the function as it approaches the excluded value is:
[tex]f(x) \rightarrow -\infty\;\;\textsf{as}\;\; x \rightarrow -3^+ \;\;\textsf{and as}\;\;x \rightarrow -3^-[/tex]Related Questions
Multiply (2+3i)(13 – 6i) .
Answers
Answer:
44+27i
Step-by-step explanation:
Multiply using the FOIL method, then combine the real and imaginary parts of the expression.
for each of the three plots, identify the strength of the relationship (e.g. weak, moderate, or strong) in the data and whether fitting a linear model would be reasonable.
Answers
These following answers are correct
We are given residual plots
In given(a) plot there is weak relationship between scatter points
we see curved relationship in this residual plot therefore model is unreasonable .
Note - This model is reasonable when this plot should look approximately normal and scatterplot of residuals should show random
scatter. In these plots we see weak relationship and line as model is unreasonable
2)We are given residual plot.
Given 2nd (c) plot there is strong relationship between scatter points we see positive straigh line relationship in this plot therefore model is resonable.
Also these model look approximately normal land scatterplot of residuals show random scatter.
In these plot we see strong relationship and linear model is reasonable
Therefore, these statements are correct.
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PLEASE HELP! I'LL MARK YOU AS THE BRAINIEST AND I'LL GIVE YOU A LOT OF POINTS!
Answers
Answer:
B) -2x+y=8
Step-by-step explanation:
First I looked at the graph and found the y-intercept and slope.
Y-intercept = 8
I found that because the point was the on the y-axis line like (0,8)
To find the slope I identified the next point. From the Y-intercept (0,8), you have to go down 8 units. Then I saw the point go left 4 units which makes it negative.
Slope = -8/4, which is also -2
Slope Intercept Equation (y=mx+b) would be: y=-2x+8
Then I compared it to the options and that's what I got.
In a simple random sample of 144 households in a city in Kentucky, the average number of children in these households was 1.12 children. The standard deviation from this sample was
2.40 children. A 90 percent confidence interval for the mean number of children in all
households in this city is:
Select one:
O a. 1.12 ± 0.2.
O b. 2.40 ± 0.2.
c. It is impossible to tell without a census.
O d. 1.12 ± 2.40.
O e. 1.12 ± 0.328.
Answers
A 90% confidence interval for the mean number of children in all household in this city is 1.12 ± 0.328, using formula for confidence interval.
What are mean and standard deviation ?
The standard deviation is a summary measure of the differences of each observation from the mean.
Formula to calculate confidence interval using mean and deviation:
mean ± Z*(std deviation/√n)
where n = sample size,
Given that :
mean = 1.12
deviation = 2.40
n = 144
We know Z is fixed for 90% confidence i.e. 1.64
So, the confidence interval = 1.12 ± 1.64*(2.4/√144)
= 1.12 ± 1.64 * .2
= 1.12 ± .328
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hese are curves obtained by the intersection of right circular cone and a plane.
a. Parabola
b. Ellipse
c. Hyperbola
d. Conic sections
Answers
Answer: conic sections
Step-by-step explanation: the other options are a part of conic sections that are named depending on the angle of the plane relative to the cone, and the intersection.
What is ? x 5 = 9 for 5th grade
Answers
Answer:
The answer is 1.8
Step-by-step explanation:
Let the number be y
So,
y × 5 = 9
5y = 9
Divide both side by 5
5y/5 = 9/5
y = 9/5 = 1.8
Thus, The value of y is 1.8
Can someone help me with this, please?
Answers
π√π÷√π is an irrational number. So option (a) is required answer.
What is irrational number?A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number 2. Any irrational number, such as p/q, where p and q are integers, q, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.
Examples of irrational number: √3, ∛2, π
π is an irrational because it is neither ending nor recurrent.
Solving each part of options, we get
π√π÷√π = π
√25 = 5
√π÷π = 1
2√2 ÷ √2 = 2
As most of the option give rational number only one option gives irrational number which is π
We get π from option (a)
So, option (a) is correct option.
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the area of a rectangle is square feet. determine the length and width if the length is times the width.
Answers
According to the given area of rectangle, the length and width of the rectangle is 7 and 21 respectively.
Area of rectangle
The standard form of calculating the area of the rectangle is written as,
A = l x w
where l refers the length and w refers the width of the rectangle.
Given,
Here we have given that the area of a rectangle is 147 square feet. And we need to determine the length and width if the length is three times the width.
Let us consider length of rectangle is n,
Then the width of rectangle is 3n.
Here we have to remember that the area of a rectangle is
=> A = n x 3n = 3n²
Here we are told that the area,
=> 3n²=147
Then the value of n² = 49
Therefore, the length is 7 and the width is 21.
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What are rational numbers but not natural numbers?; Which set of numbers are rational numbers but not integers whole numbers or natural numbers?; Does the set of rational numbers contain the set of natural numbers?; What is a rational number that is not a real number?
Answers
The distinction between them is that an integer is a negative number without a decimal point.
What is integers?All whole numbers and negative numbers are considered integers. This means if we include negative numbers together with whole numbers, we form a set of integers.
Positive, negative, and zero are all examples of integers.
The Latin word "integer" signifies "whole" or "intact."
As a result, fractions and decimals are not included in integers. In this article, let's learn more about integers, their definition, and their characteristics.
According to our question-
The group of integers that are neither whole nor a natural number are:
As previously noted, the third set of integers lacks a decimal point;
However, the difference between them is that; a negative number without a decimal point is referred to as an integer
From the provided set: only fit into the description of an integer, because
It does not have a decimal point
And that is unfavorable.
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Each person in a random sample of adults was asked how many DVD, he or she wwned. Summary Statistics are given below Variable DVDs N 117 Mean 129.4 Median 50.0 TIMean 76.5 SE Mean StDev 3236 Variable DVDs Minimum 00 Maximum 3000.0 Q1 30.0 03 950 Which of the following statements is true? (A) Seventy-five percent of the adults in the sample own more than 95 DVDs. (B) Fifty percent of the adults in the sample own between 0 and 129.4 DVDs (C) The distribution of the number of DVDs owned appears to be approximately symmetric (D) The interquartile range of the number of DVDs owned is 65. (E) The distribution of the number of DVDs owned contains outliers on both the low side and the high side.
Answers
Hence, the option D "The interquartile range of the number of DVDs owned is 65" is correct.
In the given question, we have to in each person in a random sample of adults was asked how many DVD, he or she owned.
Summary Statistics are given below
Variable N Mean Median TiMean St Dev St Mean
DVDs 117 129.4 50.0 76.5 3236 29.2
Variable Minimum Maximum Q1 Q3
DVDs 00 3000 30.0 95.0
We have to which of the following statements is true?
(A) Seventy-five percent of the adults in the sample own more than 95 DVDs.
(B) Fifty percent of the adults in the sample own between 0 and 129.4 DVDs
(C) The distribution of the number of DVDs owned appears to be approximately symmetric
(D) The interquartile range of the number of DVDs owned is 65.
(E) The distribution of the number of DVDs owned contains outliers on both the low side and the high side.
Option (A) is incorrect because 95 is third quartile value and there is only 25% values above third quartile. So, statement is incorrect.
Option (B) is incorrect because 0 is minimum value and 129.4 is mean value. Percent between mean and minimum is not always fixed, so we cannot say that 50% of values are between 0 and 129.4. So, statement is incorrect.
Option (C) is incorrect because median and mean must be equal for symmetric curve, but these are not equal. So, it is not a symmetric curve.
Option (D) is correct because
IQR (Interquartile range)
IQR = Q3 - Q1
IQR = 95 - 30
IQR = 65.
So, option D is correct answer.
Option (E) is incorrect because
lower outlier limit = Q1-1.5*IQR
lower outlier limit = 30 - 1.5*65
lower outlier limit = -67.5
upper outlier limit = Q3 + 1.5*IQR
upper outlier limit = 95 + 1.5*65
upper outlier limit = 192.5
So, there is outliers only on upper side because maximum is 3000>192.5, but there is not value below 0.
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A car that travels 20 miles in 1/2 hour at constant speed is traveling at the same speed as a car that travels 30 miles. In how many hours (at a constant speed)
Answers
The required time to travel 30 miles is given as 45 minutes and 3/4 hours.
Given that,
A car that travels 20 miles in 1/2 hour at constant speed is traveling at the same speed as a car that travels 30 miles.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Speed = Distance/time
Speed = 20 / [1/2]
Speed = 40 miles per hour,
Time = Distance / Speed
Time = 30 / 40
Time = 3 / 4 hour
Thus, the required time to travel 30 miles is given as 45 minutes and 3/4 hours.
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$6,000 for six years at 8½% compounded daily will grow to:
Multiple Choice
$9,060.00
$9,788.81
$9,991.15
Answers
It will grow to $9991.15
Question 1 of 10
If two triangles are congruent, which of the following statements must be
true? Check all that apply.
A. The corresponding sides of the triangles are congruent.
B. The triangles have the same shape.
C. The corresponding angles of the triangles are congruent.
D. The triangles have the same size.
Answers
Answer:
b c and d
Step-by-step explanation:
5-55.
Additional Challenge: At the beginning of 1990, oil prices were $20 a barrel. Some oil investors predicted that the price
of oil would increase by $2.25 a barrel per year.
In the beginning of 2005, the price of oil was $30 a barrel. With increasing demand for oll around the world, oil investors in
2005 predicted that the price of oil would increase by $5.00 a barrel each year.
DILOIL
a. Let a represent the number of years since 2005. Write an equation that predicts the price of oil, y, using the information available in 2005.
b. Investors in 1990 did not have the benefit of the 2005 information. Write an equation that represents the prediction made in 1990, using the same variables as in
part (a). Remember that a represents the number of years since 2005.
c. Use the equations you wrote in parts (a) and (b) to determine when the cost of a barrel of oil would be the same for both price predictions.
d. In the spring of 2011, a barrel of oil was selling for about $112. Which prediction was closer? Was it a pretty good prediction?
Answers
a) The linear function for the 2005 estimate is given as follows: y = 30 + 5x.
b) The linear function for the 1990 estimate is given as follows: y = 53.75 + 2.25x.
c) They would be predicted to have the same cost in the year of 2013.
d) The 1990 prediction was closer, however it still had a large residual, hence neither was good enough.
How to define the linear functions?The linear functions are defined in the slope-intercept format, given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change for the price.b is the y-intercept, representing the initial cost in the reference year.Taking 2005 as the estimate, the function is given as follows:
y = 30 + 5x.
Taking 1990 as the estimate, the equation would be of:
y = 20 + 2.25x.
The estimate for 2005 would be of:
y = 20 + 2.25(15) = 53.75.
Hence the equation taking 2005 as the estimate would be of:
y = 53.75 + 2.25x.
The costs would be the same when:
30 + 5x = 53.75 + 2.25x.
2.75x = 23.75
x = 23.75/2.75
x = 8.63 -> + 2005 -> year of 2013.
The estimates for 2011(6 years after 2005) are given as follows:
y = 30 + 5x = 30 + 5(6) = $60.y = 53.75 + 2.25(6) = $67.25. (better estimate but not good enough).More can be learned about linear functions at https://brainly.com/question/24808124
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How do you teach regrouping to 2nd graders?
Answers
Answer:Pass out the pennies and the dimes to your students. Write a couple of problems on the board that will use regrouping. As you write them, write “ones” over the ones column. Write “tens” over the tens column. Have students take out their coins for each problem.
Step-by-step explanation:
a baseball coach uses a pitching machine to simulate pop flies during practice. the quadratic function f(x)
Answers
The time taken by the baseball in the air if the ball is not caught is 4.513 seconds.
Here we have to find the time taken by the baseball.
Given data:
The quadratic function is given:
f(x) = 16x² + 70x + 10
To find the value of x we have to formula:
x = ±b [tex]\sqrt{b^{2} - 4ac}[/tex] / 2a
from the equation we get the value of a, b, and c as:
a = -16
b = 70
c = -10
now putting in the equation we have:
x = -70 ±[tex]\sqrt{70^{2} -4(-16)(10)}[/tex] / 2(-16)
= -70 ±[tex]\sqrt{4900 + 640}[/tex] / -32
= -70 ± √5540 / -32
= - 70 ± 74.43 / -32
By calculating this we get two values:
x = -0.138 and 4.513
Time can never be negative so.
x = 4.513
Therefore the time taken is 4.513 seconds.
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At the time of her grandson's birth, a grandmother deposits 14000 in an account that pays 9.5% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?
Answers
The value of the account at the child's twenty-first birthday is 102125.44
How to determine the value of the account at the child's twenty-first birthday?We can use the compound interest formula to determine the value of the account (A) on the child's twenty-first birthday:
A = P (1 + r/n)^(nt)
Where:
P is the initial amount of money deposited in the account
r is the interest rate
n is the number of times the interest is compounded per year
t is the number of years
Given: P = 14000, r = 9.5% = 0.095, t = 21, n = 12 (i.e. 12 months per year)
Substitututing into A = P (1 + r/n)^(nt):
A = 14000 (1 + 0.095/12)^(12×21)
A = 14000 (1 + 0.095/12)^(252)
A = 102125.44
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Which of the following are solutions to the inequality below? Select all that apply.
4>q/23
q = 138
q = 46
q = 69
q = 92
Answers
We get
92>q
q can be 46 or 69 because they are both less than 92
How to get
The midpoint of GH is M(-6,-3). One endpoint is H (-4,4). Find the coordinates of endpoint G
Answers
The coordinates of point G are (-8, -10)
What is the midpoint of a line?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments
The midpoint of a line segment is the point on a segment that is at the same distance or halfway between the two ending points.
midpoint(M) = (-6, -3)
H = (-4, 4)
let the coordinates of G be (p,q)
taking the x coordinates for M, G and H
-6 = p -4/2
cross multiply
p -4 = -12
p = -12 + 4
p = -8
taking y-coordinates
-3 = q +4/2
q + 4 = -6
q = -6 -4
q = -10
coordinates of G (-8, -10)
in conclusion the coordinates of G is ( -8, -10)
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a hypothesis test was performed to decide whether houses are more prone to being lost to fire than condominiums are. the researcher looked at 1500 randomly selected houses and 1200 randomly selected condominiums over a ten year period. then, since over 30 of each were in the sample, the researcher can use a z-test for the difference between two proportions.
o False
o True
Answers
It is false, the researcher cannot use a z-test for the difference between two proportions.
A hypothesis test was performed to decide whether houses are more prone to being lost to fire than condominiums are. the researcher looked at 1500 randomly selected houses and 1200 randomly selected condominiums over a ten year period. then, since over 30 of each were in the sample, the researcher cannot use a z-test for the difference between two proportions.
z = (X - mean)/(SD/√n)
Where SD is the standard deviation and n is the number of observations.
Here, the required value is not provided. So, we cannot use the z - test.
Therefore, the researcher cannot use a z-test for the difference between two proportions, so the given statement is false.
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PLEASEEE HELP THIS IS 3 GRAFE LEVELS ABOVE ME!
Check your answer to problem 4 by solving it using a different strategy Show your work.
Answers
Answer:
you are right
n=1
Step-by-step explanation:
1/2(-3/2n+1)=3/4-n
-3/4n+1/2=3/4-n
-3/4n+2/4=3/4-4/4n
+3/4n +3/4n
2/4=3/4-1/4n
-3/4. -3/4
-1/4= -1/4n
/-1/4. /-1/4
1=n
to check i normally just pop in the value (i know no other way in all my years of school)
1/2(-3/2(1)+1)=3/4-1
1/2(-3/2+1=3/4-1
1/2(-1/2)=-1/4
-1/4= -1/4
hopes this helps please mark brainliest
Which of the following is an identity?
A. csc²x + cot²x = 1
B. (cscx + cotx)2 = 1
C. sin²x-cos²x = 1
D. sin²x sec²x + 1 = tan²x csc²x
Answers
Answer:
Step-by-step explanation:
it is D as
L.H.S.=sin²x sec²x+1
[tex]\frac{sin^2x}{cos^2x} +1\\=\frac{sin^2x+cos^2x}{cos^2x} \\=\frac{1}{cos^2x} \\=sec^2x[/tex]
again
[tex]R.H.S.=tan^2x csc^2x\\=\frac{sin^2x}{cos^2x} \times \frac{1}{sin^2x} \\=\frac{1}{cos^2x} \\=sec^2x[/tex]
L.H.S.=R.H.S.
Order the answers of these following expressions from least to greatest. -13 + 12= . -3 - (-2) + 3= . -3 + 9= . 9 + (-15)= . 13 - (-13)= .
Answers
The answers of the given expressions ordered from least to greatest is
-6, -1, 2, 6, 26
Ordering the answers of expressions from least to greatestFrom the question, we are to order the answers of the given expressions from the least to greatest
To do this, we will evaluate the expressions
Evaluating -13 + 12 =-13 + 12 = -1
Evaluating -3 - (-2) + 3-3 - (-2) + 3
-3 + 2 + 3 = 2
Evaluating -3 + 9 =-3 + 9 = 6
Evaluating 9 + (-15)9 + (-15)
9 - 15 = -6
Evaluating 13 - (-13)13 - (-13)
13 + 13 = 26
Hence, ordering the answers from least to greatest, we get
-6, -1, 2, 6, 26
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which option proves the following statement by contradiction? for all real numbers r and s, if r is rational and s is irrational, then r 2s is irrational. proof (by contradiction): suppose not. that is, suppose there are real numbers r and s such that r is rational and s is irrational and r 2s is rational. [we must show that this supposition leads logically to a contradiction.] by definition of rational,
Answers
Any whole number, fraction, or decimal that terminates or repeats is a rational number. Any number that cannot be divided into a fraction and hence does not meet the concept of a rational number is said to be irrational.
When it comes to rationality, we have
r + 2s = c/d and r = a/b.
The result of the substitution is a/b + 2s = c/d
2s= c/d-a/b=(bc-ad)/bd
s = (bc-ad)/2bd
Now that both (bc - ad) and (bd) are integers, bd is not equal to 0
As a result, the integer s is a quotient of the two integers (bc - ad) where bd is not equal to 0. So, s is rational according to the definition. This disproves the idea that s is irrational.
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Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without replacement from a standard deck. If both cards are diamonds, your friend will pay you $615. Otherwise, you have to pay your friend $37.
Step 2 of 2 :
If this same bet is made 621 times, how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values.
Answers
If this same bet is made 621 times,then we expect to lose of $4514670
Probability
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The bet is done 621 times then expected value is that we may have a loss of $4514670.if the bet is that is heart comes we will get $615 and lose $37 if not comes.
$615 if hearts come and lose $37 when not comes and bet is made 621 times. Calculate the expected win after 621 times.
There are 578 hearts in the standard deck of cards.
Probability is the chance of happening an event among all the events possible. The formula of calculating probability is as under:
Probability= number of items/ total number of items.
When two cards are chosen at random without replacement then the probability of getting two hearts is 578/52*577/51
=333,506/2652
=125.75
When two cards are chosen at random without replacement then the probability of not getting two hearts is 1-125.75
=124.75
When bet is made only 1 time expected value will be 125.75*615-124.75*37
=77,336.25 - 4,615.75
=-72720.5 means we are expecting to lose $2.05.
When bet is made 762 times then the expected value will be -72720*621= 4514670.
Then the expected value when bet is made 621 times is that we will lose $4514670 .
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The domestic price of shoes is $80. After trade the price of a pair of shoes is $60. After trade this country will import
Answers
The trade this country will import is given by the option (C) 300 pair of shoes.
The number of shoes exported will be calculated by the formula -
Import = quantity demanded - quantity supplied. The formula is based on the concept that the import of shoes will be carried out once the manufacturing is more than the demand.
The graph indicates the quantity demanded is 1000 and the quantity supplied is 1300. Keep the values in formula to find imports.
Imports = 1300 - 1000
Performing subtraction on Right Hand Side of the equation
Imports = 300
Hence, the import is 300.
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The complete question is attached in figure.
a popular brand of pen is available in 5 colors and 4 writing tips. how many different choices of pens do you have with this brand?
Answers
If a popular brand of pen is available in 5 colors and 4 writing tips. The number of different choices of pens do you have with this brand is: 20 choices.
How to find the number of different choices of pen?Using this formula to find the number of different choices of pen
Number of different choices of pen = Number of color × Number of writing tips
Where:
Number of color = 5
Number of writing tips = 4
Let plug in the formula
Number of different choices of pen = 5 × 4
Number of different choices of pen = 20 choices
Therefore the number of different choices of pen is 20 choices.
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Jada has $260 to spend on flowers for school celebration. She decides that the only flower that she wants to buy are roses and carnations. Roses cost $1.50 each and carnations cost $0.65 each. Jada buys enough roses so that each of the 75 people attending the event can take home at least one rose. Let x be the number of roses and y be the number of carnations.
a. Write an inequity to represent the constant “that every person takes home at least one rose”
b. Write an inequality to represent the cost constraints?
Answers
R ≥75 will be the inequality to symbolize the need that each individual bring home at least one rose, and for the cost requirement, it will be, 1.45R + 0.65C ≤ 200.
What is inequality?
A connection that compares two numbers or other mathematical expressions unequally is known as an inequality in mathematics. Most frequently applied when comparing two numbers on the number line that differ in size.
Given:
Jada has $200 she can use to buy flowers. Each carnation costs $0.65 and a rose costs $1.45, so 75 guests may leave with at least one rose.
Jada has a total of $200.
Let R be the number of roses Jada bought.
There will be 75 persons in all present at the event.
As a result, the cost of R roses at $1.45 each is 1.45R.
Combined with roses C: Jada bought carnations.
Currently, each carnation costs $0.65.
Cost of C carnations at $0.65 per flower, then, equals 0.65C.
Inequality will serve as a restraint that requires everyone to bring home at least one rose,
[tex]R \geq 75[/tex]
There will be inequality that represents the cost limitation.
[tex]1.45R + 0.65C \leq 200[/tex]
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For the functions f(t) = 5t and g(t) = sin(t) defined on 0≤t<[infinity], compute f * g in two different ways.a. By directly evaluating the integral in the definition of f * g.b. By computing L−1{F(s)G(s)} where F(s)=L{f(t)} and G(s)=L{g(t)}.
Answers
The laplace inverse transformation L−1{F(s)G(s)} = 5 [tex]\frac{2s}{s^{2} + 1^{2} }[/tex]
If L{f(t)} = F(s), then the inverse Laplace transform of F(s) is
L−1{F(s)} = f(t). (1)
The inverse transform L−1is a linear operator:
L−1{F(s) + G(s)} = L−1{F(s)} + L−1{G(s)}, (2)
andL−1{cF(s)} = cL−1{F(s)}, (3)
for any constant c
given functions are
f(t) =5t ,g(t) = sin(t)
L(f(t)) = F(s)
L{F(s)*G(s)} = L^-1{5tsin(t)}
=5L^-1{tsin(t)}
=5L^-1{[tex]\frac{d}{ds}[/tex] tsin(t)}
= 5 [tex]\frac{2s}{s^{2} + 1^{2} }[/tex]
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• For which of the following equations is (3, - 1) not a solution?
Answers
Therefore , x +3 =y is the equation which is not the solution of point (3,-1)
What is equation ?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. It is demonstrated that the expressions on the left and right are equivalent to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations.
Here,
The given equations are ( a) x-4= y (b) 2x -7 =y (c ) x +3 =y ( d) x/3 = -y
Thus from the given equation
We put, values in each of equation to find that values satisfy the equation or not
Thus, we found x +3 =y does not satisfy the point (3,-1)
Therefore , x +3 =y is the equation which is not the solution of point (3,-1)
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The correct question is -
For which of the following equations is (3, - 1) not a solution?
Group of answer choices - y=x-1, -3x=4y-6, 2y-3x=0, 5x+2y=-16
