Answers
The value of the rational function R(x) can be found by changing the sign of the denominator of the function to get;
R(x) = (-4·x³ - 6·x² + 12·x + 22)/(x² - 4)
What are rational functions?Rational functions are functions of the form; R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials.
The specified function is; R(x) = f(x) - g(x)
Where;
f(x) = (-4·x³ - 6·x² + 14·x + 23)/(x² - 4)
g(x) = (-2·x - 1)/(-x² + 4)
Therefore, we get;
-g(x) = -(-2·x - 1)/(-x² + 4) = (-2·x - 1)/(x² - 4)
f(x) - g(x) = (-4·x³ - 6·x² + 14·x + 23)/(x² - 4) + (-2·x - 1)/(x² - 4)
f(x) - g(x) = (-4·x³ - 6·x² + 14·x + 23 + (-2·x - 1))/(x² - 4)
f(x) - g(x) = (-4·x³ - 6·x² + 12·x + 22)/(x² - 4)
Therefore;
R(x) = f(x) - g(x) = (-4·x³ - 6·x² + 12·x + 22)/(x² - 4)
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Related Questions
Which linear function represents a slope of ? A two column table with five rows. The first column, x, has the entries, 3, 6, 9, 12. The second column, y, has the entries, negative 11, 1, 13, 25. A coordinate plane with a straight line with a positive slope passing through (0, 3), (4, 4), and (8, 7). A two column table with five rows. The first column, x, has the entries, negative 5, negative 1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8. A coordinate plane with a straight line with a positive slope passing through (2, 0), (3, 4), and (4, 8)
Answers
The linear function which represents a slope of -3 as required in the task content is; A two column table with five rows. The first column, x, has the entries, negative 5, negative 1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8.
Which answer choice has a slope of -2?It follows that the task requires that a linear function whose slope, i.e rate of change is -2 is to be determined.
Since slope is the rate of change in y with respect to x;
The required linear function is; A two column table with five rows. The first column, x, has the entries, -5, -1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8 so that we have;
Slope = (24 - 32) / (-1 -(-5)) = -8 / 4 = -2.
Remarks: The complete question is such that the required slope is -2.
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Answer: the second option
Step-by-step explanation:
i took the assignment
Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2,700 grams and a standard deviation of 900 grams, while babies born after a gestation period of 40 weeks have a mean weight of 3,000 grams and a standard deviation of 465 grams. If a 33-week gestation period baby weighs 2,225 grams and a 40-week gestation period baby weighs 2,525 grams, find the corresponding z-scores. Which baby weighs less relative to the gestation period?
a. The 33-week gestation period baby weighs _____ standard deviations _____ the mean.
b. The 40-week gestation period baby weighs _____ standard deviations _____the mean.
(Round to two decimal places as needed.)
c. Which baby weighs relatively less?
A. The baby born in week 40 does since its z-score is smaller.
B. The baby born in week 40 does since its z-score is larger.
C. The baby born in week 33 does since its z-score is larger.
D. The baby born in week 33 does since its z-score is smaller.
Answers
Answer:
the answers have been provided below
Step-by-step explanation:
Population z score is given as (x-μ)/sd For a 32 to 35 week gestation period
μ= 2700
Sd = 900grams
x = 2225
z = (2225-2700)/900
z = -0.527
For a 40 week gestation period.
μ = 3000
Sd = 465grams
x = 2525
z = (2525-3000)/465
Z = -1.022
In answer to the question:
a. The 33-week gestation period baby weighs 0.53 standard deviations below the mean.
b. The 40-week gestation period baby weighs 1.02 standard deviations below the mean.
c. -1.022 < -0.527. the 40 weeks gestation baby weighs less.
A. The baby born in week 40 does since its z-score is smaller.
The graph shows the relationship between time and the distance a train travels.
What is the slope of the line?
?
Distance (mi)
200
150
100
50
0
ہے
Time (h)
3
Answers
Answer:
50
Step-by-step explanation:
i got it correct on the iready quiz
The graph of the line does not change except only in the y - intercept. The slope of the line remains same.
What is the general equation of the straight line? What is a mathematical function, equation and expression?straight line equation : The general equation of a straight line is -y = mx + c
[m] : slope of line.
[c] : y - intercept
function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is a graph that shows the relationship between time and the distance a train travels.
From the graph, we can write the coordinates as -
(1, 60) and (2, 120)
So, we can write the slope of the line as -
m = (120 - 60)/(2 - 1)
m = 60/1
m = 60
Therefore, the slope of the line given in the graph will be 60 miles/hr.
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Hailey drew a scale drawing to represent her favorite park. The drawing is rectangular. The longer sides measure 28.5 centimeters and the shorter sides measure 16.5 centimeters. Hailey decides she wants the drawing to be smaller. She will reduce it by a scale factor of 1/4. What will be the measure of the longer sides? Select from the drop-down menu to correctly complete the statement. The measure of the longer sides will be Choose... cm.
Answers
The new length of the longer side after application of a scale factor of 1/4 is; 7.125 ft
How to interpret Scale factors?A scale factor is defined as the ratio between the scale of a given original object and a new object. This will be indicative of its' representation but of a different size. Thus, it could represent an enlargement or a reduction.
Now, we are given that the length of the sides are;
Length of longer sides = 28.5 cm
Length of shorter side = 16.5 cm
Thus, if the scale factor is 1/4, then it means that;
New length of longer side = 1/4 * 28.5
New length = 7.125 ft
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I give Brainlest !!!!!!!
Answers
Answer:
40,000
Step-by-step explanation:
circumference of the back wheel=9 feet, front wheel=7 feet. On a certain distance the front wheel gets 10 revolutions more than the back wheel. What is the distance?
Answers
The distance would be 315 feet which is a certain distance the front wheel gets 10 revolutions more than the back wheel.
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
Given that the circumference of the back wheel=9 feet, the front wheel=7 feet. At a certain distance, the front wheel gets 10 revolutions more than the back wheel.
Both wheels must move at the same distance. If the number of revolutions taken by the back wheel is x, then the number of revolutions taken by the front wheel is x+10.
Because the distance traveled is the same as:
⇒ 9x = 7(x+10)
⇒ 9x = 7x+70
⇒ 9x - 7x = 70
⇒ 2x = 70
⇒ x = 35
We obtain x = 35 revolutions.
So the total distance traveled is 35×9=315 feet or 45×7=315 feet.
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A cream is sold in a 34-gram container. The average amount of cream used per application is 1 and two ninths grams. How many applications can be made with the container?
Answers
Answer:
Total cream = 34g
One application = 1 8/9 =(9+8)/9 = 17/9
Total applications = total cream/one application = 34/(17/9) = 34*9/17 = 18 applications
Step-by-step explanation:
How do I find percent change, so confused, please help.
Answers
Because when you change them into decimal they numbers are .4 & .33 then you subtract them from each other which would be .07 then convert. Please do double check this though
If a data set has many extremely small data values, than the median will be________the mean.
A. the same as
B. larger than
C. equal to
D. smaller than
Answers
if a data set has many extremely small data values,than the median will be the same as the mean
Artificial grass sells for $10.98 per square yard final cost to buy and install 69.2 square yards if the seller charges $5.15 per square yard for labor round to the nearest cent
Answers
Answer:
$1,116.19.
Step-by-step explanation:
Given that artificial grass sells for $ 10.98 per square yard, to determine the final cost to buy and install 69.2 square yards if the seller charges $ 5.15 per square yard for labor, round to the nearest cent, the following calculation must be performed:
69.2 x (10.98 + 5.15) = X
69.2 x 16.13 = X
1,116,196 = X
Thus, the cost to purchase and install 69.2 square yards of artificial grass is $ 1,116.19.
85% de 1560 90% de 158 138% de 1610 50% de 230
Answers
b. 142.2
c. 2221.8
d. 115
Yesterday, Jack drove 20 miles in his car. Today, Jack drove 15 miles in his car. What is the percent decrease of the time spend driving the car?
Answers
The percentage change will be 25%.
What is the percentage?According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.
Using these estimates, we can calculate the per cent decrease in the time spent driving as follows:
The initial time spent driving was 0.5 hours.
The final time spent driving was 0.375 hours.
The decrease in time spent driving was 0.5 - 0.375 = 0.125 hours.
The per cent decrease in time spent driving is,
P = (0.125/0.5) x 100%
P = 25%.
Therefore, we can estimate that the per cent decrease in the time Jack spent driving his car is 25%.
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help .........thanks
Answers
b= -5
a= -4
-5+4(-4)=
-5-16= -21
2.) xz-z
x= -2
z= -5
(-2)•(-5) -(-5)=
10+5=15
At the craft store, Rudy bought a bag of green and red marbles. The bag contained 60 marbles, and 60% of them green. How many green marbles did Rudy receive?
Answers
Answer:
36 green marbles
Step-by-step explanation:
If 60% of the 60 marbles in the bag are green, then the number of green marbles can be calculated as:
Green marbles = 60% x 60 marbles
To simplify this calculation, we can convert 60% to a decimal by dividing by 100:
Green marbles = 0.60 x 60 marbles
Green marbles = 36 marbles
Therefore, Rudy received 36 green marbles.
Answer: 36
Step-by-step explanation:
60 is 6/10 of 100 so if you are taking a percent of 60 just multiply the percentage by 6/10. 6/10 of 60 is 36
What is the slope and y-intercept of the line whose equation is y + 4x =
8?
Answers
Answer:
The slope is -4 and the y-intercept is 8.
Step-by-step explanation:
y+4x=8
y=8-4x
y=-4x+8
y=mx+b where m=slope and b=y-intercept.
Hello!
The equation of this line is written in slope-intercept form (y=mx+b)
Where
m is the slope
b is the y-intercept
m is 4
b is 8
Hope it helps!
If you have any questions, feel free to ask! :)
~An excited gal
\(MagicalNature\) here to help
Sean partially filled a container with water. The container was shaped like 10 pointsa box and had dimensions of 9 inches long, 8 inches wide, and 10 incheshigh. If w represents the height of the water (in inches), and the volume V(in cubic inches) of the water is given by the formula V = 72 w, whichquantity is the independent variable?The height of the containerThe volume of the containeroThe height of the water in the containeroThe volume of the water in the container
Answers
Given data:
V = 72w
Dimension = 9 inches long , 8 inches wide and 10 inches high.
Volume = long x wide x hight
Now, by the given question volume is given by
V = 72 w , that means height of the water in container changes.
And volume depend upon the height of the water contained.
Thus, the height of the container is the independent variable.
The answer is , height of the container is independent.
alg 2 - transformations of functions. need asap
(brainliest + 15 pts)
Answers
Answer:
\(y = f(x - 1) + 2\)
Step-by-step explanation:
Let's say that the dotted graph is y.
See f(3) = 0 or (3,0). Let's call that the point of interest. Notice that our point of interest has to move to the right by 1 unit to get to the dotted graph. so
\(y = f(x - 1)\)
And it has to go up by two units so
\(y = f(x - 2) + 2\)
Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made in a time period. The folllowing table gives the type of defect and the number of lenses with that defect. Assume categories are mutually exclusive.
Defect Type Frequency
Scratch 5734
Right shaped - small 4654
Flaked 1554
Wrong axis 1594
Chamfer wrong 1829
Crazing, cracks 1387
Wrong shape 1718
Wrong PD 1822
Spots and bubbles 1291
Wrong height 1602
Right shape - big 1538
Lost in lab 975
Spots/bubbles - intern 997
a) Find the probability that a randomly selected defect from the table will be in the categor "Crazing, cracks" or the category "Right shaped - small".
Give your answer as a fraction.
Give your answer rounded to three decimal places.
b) Find the probability that a randomly selected defect is not in the category "Crazing, cracks".
Given your answer as a fraction.
Give your answer rounded to three decimal places.
Answers
The probabilities for this problem are given as follows:
a) Crazing, cracks or Right shaped - small: (4654 + 1387)/26695 = 0.226.
b) Not Crazing cracks: (26695 - 1387)/26695 = 0.948.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of outcomes for this problem is given as follows:
5734 + 4654 + 1554 + 1594 + 1829 + 1387 + 1718 + 1822 + 1291 + 1602 + 1538 + 975 + 997 = 26695.
The probability for item a is given as follows:
(4654 + 1387)/26695 = 0.226.
The probability for item b is given as follows:
(26695 - 1387)/26695 = 0.948.
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Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Answers
developing:
a low GDP
an economy based on agriculture
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
What is the intermediate step in the form (x+a)^2=b as a result of complementing the square for the following equations
Answers
The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.
To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.
Add the square of half of the coefficient of x to both sides of the equation:
x² + 2x + (2/2)² = 319 + (2/2)²
x² + 2x + 1 = 320
The left-hand side of the equation can now be factored as a perfect square:
(x+1)² = 320
This is the equation in the form (x+a)²=b, where a=1 and b=320.
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The complete question is as follows:
What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?
x² + 2x = 319
The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
Answers
The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
In this problem
Applying proportion
we have
4/10=x/28
solve for x
x=(4/10)*28
x=11.2
therefore
answer is 11 booksGiven the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
Answers
A has the larger standard devlation.
What is standard devlation?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
We are given two plots of normal distributions A and B.
The mean of a normal distribution is located at the center of the plot.
Since the centers of both of the normal distributions A and B seems to be aligned, therefore, they both seems to have equal means.
The standard deviation basically determines the shape of the distribution.
As you can see, the normal distribution A is more spread out and thus has a larger standard deviation than normal distribution B.
Therefore, the two correct options are
• The means of A and B are equal.
• A has larger standard deviation.
Complete question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
Select all that apply:
A has the larger mean.
B has the larger mean.
The means of A and. Q jual.
A has the larger standard devlation.
B has the larger standard deviation.
The standard deviations of A and B are equal.
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Need to find the Step by step how to do this problem?
Answers
Answer:
y=10x+125
Step-by-step explanation:
rise over run, so y goes up by 10 each time and x goes up by one each time so that's your X, your b is where it starts at zero so if you did -1 for x you get zero but you have to do that with the y also so 135-10=125, 125 is where your y starts and that's your b
The quantity r varies jointly with t and u and inversely with s when t= -12, u= -7, and s= -4, r= -126. Find r when t= -8, u= 8, and s= -6.
Write your answer in exact form.
Answers
Answer:
r = 64
Step-by-step explanation:
r = (k*t*u)/s
Where,
k = constant of proportionality
t = -12,
u= -7,
s= -4,
r= -126.
r = (k*t*u)/s
-126 = (k*-12*-7)/-4
-126 * -4 = 84k
504 = 84k
k = 504/84
k = 6
Find r when t= -8, u= 8, and s= -6.
r = (k*t*u)/s
= (6*-8*8) / -6
= -384 / -6
= 64
r = 64
Find the length of CD.
E
2
D
A1 B
The length of CD is
5
C
unit(s).
Answers
The length of CD can be found to be 7. 21 units .
How to find CD ?The length of CD can be found by using the distance formula which is :
= √ [ ( x ₂ - x ₁ ) ² + ( y ₂ - y ₁ ) ² ]
Given the points, ( 3, - 2 ) and ( 7, - 8 ).
The length of CD is :
= √ [ ( 7 - 3 ) ² + ( - 8 - (- 2 ) ) ² ]
= 7. 21
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angeliquw is buyinh towels for her aparetment. she finds some green twowels that cost $8 each and bule towels that cost 10$ each. many of each towel can she purchase?
Answers
She can purchase 3 blue towels and 5 green towels.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units
Let's say you go to the store to buy six apples.
You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.
Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.
We are aware of the quantity of apples and the amount of money in the aforesaid problem.
According to our question-
8 x 5 = 40
10 x 3 = 30
40 + 30 = 70
Hence, She can purchase 3 blue towels and 5 green towels.
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Select all the expressions equivalent to (0.5p+7)+(0.3p-6)
Answers
Answer:0.8p+1 and 1+0.8p
Step-by-step explanation:
0.5p+0.3p=0.8p
7-6=+1
0.8p+1
and
Swap both numbers
(0.5p+7)+(0.3p-6)=1+0.8p
3/4+(1/3÷1/6)-(-1/2) is equal to?
Answers
Simplifying the fraction gives 13/ 4
What are fractions?A fraction is a part of a whole.
The number is usually expressed as a quotient, with the numerator is divided by the denominator
A simple fraction is made up of two integers.
A complex fraction is made up of a fraction in the numerator or denominator
In a proper fraction, the numerator is less than the denominator
Given the fraction;
3/4+(1/3÷1/6)-(-1/2)
Expand the bracket
3/ 4 + ( 1/ 3 × 6/ 1) + 1/ 2
Thus gives;
3/ 4 + (6/ 3) + 1/ 2
3/ 4 + 2 + 1/ 2
Find the LCM
3 + 8 + 2/ 4
13/ 4
Thus, simplifying the fraction gives 13/ 4
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PLEASE HELP ME OUT WITH THIS I AM TIMED I HAVE 5 MIN LEFT
Answers
Answer:
From what I've seen, the answer should be 28. Also, let me know if I'm wrong.
Answer:
28
Step-by-step explanation:
Which ordered pair is in the solution set of the system of linear inequalities?
y > 3/2x - 1
y < 3/2x - 1
O (-5,2)
O (2, 2)
O (5,2)
O no solution
Answers
Answer:
No solution is the correct answer for this inequality.
Step-by-step explanation:
equation 1 equal to y > \(\frac{3x}{2}\) -1
equation 2 equals to y < \(\frac{3x}{2}\) -1
and can be written as
\(\[\frac{3}{2}x - 1 < \frac{3}{2}x - 1\]\)
which clearly shows there is no solution
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