Answers
Rational function
A rational function is any function which can be written as the ratio of two polynomial functions.
Any function of one variable, x, is called a rational function if, and only if, it can be written in the form:
[tex]\begin{gathered} f(x)=\frac{P(x)}{Q(x)} \\ \end{gathered}[/tex]Yes, a rational function always have an aymptote.
It always have an asymptote because the denominator can never be zero.
Yes, It is possible to have holes in the graph of a rational function.
The main reason why there is a hole because if there is the same factor in the numerator and denominator, there is a hole.
Related Questions
I am having trouble with subtracting this fraction with a whole number. What is 3 2/5-4/5?
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Fractions with whole numbers are called Mixed Fractions.
To add or subtract them, first convert the mixed fraction to an improper fraction, perform the operation and then convert the result back to a mixed fraction if it's an improper fraction.
The given expression is:
[tex]3\frac{2}{5}-\frac{4}{5}[/tex]Convert the mixed fraction on the left to an improper fraction:
[tex]\begin{gathered} \frac{(3\times5)+2}{5}-\frac{4}{5}=\frac{15+2}{5}-\frac{4}{5} \\ =\frac{17}{5}-\frac{4}{5} \end{gathered}[/tex]Since the denominators are the same, add subtract the numerators:
[tex]\Rightarrow\frac{17}{5}-\frac{4}{5}=\frac{17-4}{5}=\frac{13}{5}[/tex]Convert back to a mixed fraction:
[tex]\frac{13}{5}=2\frac{3}{5}[/tex]The correct answer is 2 3/5.
Find the exact circumference and area of each circle.4 in.
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In order to find the circunference of a circle, we can use the formula:
[tex]C=2\pi r[/tex]Where r is the circle radius.
So, using r = 4, we have:
[tex]\begin{gathered} C=2\pi\cdot4 \\ C=8\pi \end{gathered}[/tex]So the circunference is 8π inches.
The area can be calculated using the formula:
[tex]A=\pi r^2[/tex]So we have:
[tex]\begin{gathered} A=\pi\cdot4^2 \\ A=16\pi \end{gathered}[/tex]Area = 16π in².
Help on math question precalculus The graph is discontinuous.Group of answer choicesTrueFalse
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It is TRUE that the graph is discontinuous
Explanation:A graph is continuous when the limit exists on its two sides.
The given graph is discontinuous and limits have been indicated on both edges of the graph.
The monthly water bill is a function of the number of gallons used. The cost is $19 60 for 20.000 gal or less Over 20.000 gal the cost is $19 60 plus $1 for each 1000 gal over 20,000 with any fraction of 1000 gal charged at a fraction of $1 On what interval is the cost constant? On what interval is the cost increasing? On what interval is the cost constant?
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Let's define the monthly water bill as a function, where:
• c ,is the number of gallons consumed that month
,• B(c), is cost of the monthly water bill
Therefore, for a consumption of 20.000 gallons or less, the monthly water bill would be:
[tex]\begin{gathered} B(c)=19.60 \\ c\le20000 \end{gathered}[/tex]For a consumption of more than 20.000 gallons,
[tex]\begin{gathered} B(c)=19.60+\frac{c-20000}{1000} \\ c>20000 \end{gathered}[/tex]Therefore:
• The cost is constant ($19.60) when the number of gallons consumed is less than or equal to 20,000 gallons
,• The cost increases if the number of gallons consumed is greater than 20,000 gallons
To raise money, a school band is selling tickets to a breakfast. The graph on the coordinate grid below shows the functional relationship between the number of tickets sold and the revenue. What is the domain of the function?a) integers from 0 to 400b) real numbers from 0 to 500c) integers from 0 to 80
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the domain of function represents the value of the function on the horizontal axis that is the x-axis,
here we can see that line is starting from origin that is (x, y) = (0, 0) and it is ending at (x,y) = (80, 400)
so x is varying from
x =0 to x = 80
so it the domain of the function
so the answer is option C
Do you think it is possible for giants exist? Consider the human femur, or thighbone. It is the strongest bone in the body. The femur of an average adult man is 48 cm long and has a diameter of 2.34 cm. It can support up to 30 times the weight of an adult. If a giant was 5 times larger than an average man, in each dimension, do you think the femur could support the giant's
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Let us assume that the top of the femur is circular. We would calculate the cross sectional area by applying the formula,
Area = πr^2
where
π = 3.14
r = radius
Given that diameter = 2.34,
radius = diameter/2 = 2.34/2
radius = 1.17
Cross sectional area = 3.14 x 1.17^2 = 4.298 cm^2
Given that the length = 48cm,
volume = 48 x 4.298 = 206.304 cm^3
206.304 cm^3 can support 30 times the weight of the adult. Thus,
ratio of volume to weight = 30
206.305/weight = 30
206.305 = 30 x weight
weight = 206.305/30 = 6.88
If the giant is 5 times larger than the average adult, it means that
radius of the giant's bone = 5 x 1.17 = 5.85
Area = 3.14 x 5.85 = 18.369
length of femur = 48 x 5 = 240
Volume of the giant's femur = 240 x 18.369 = 4408.56
This means that 4408.56 cm^3 should support 30 times the giants weight
Thus,
Weight of the giant = 5 times the weight of the adult
Weight of the giant = 5 x 6.88 = 34.4
Dividing the volume by the weight, we have
4408.56/34.4 = 128.15
This is more than 30
Now, the ratio of the giant's weight to the normal adult's weight should be 5. We have
146.952/6.88 = 128
This means that the femur can support up to 128 tims the weight of the giant. Since it is more than 30, then, the femur could support the giant's weight.
the triangle ABC is similar to Triangle d e f the measures of the side lengths are in cm which proportional can be used to find the length of EF in cm
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We were told that
traingle ABC is similar to triangle DEF
This means that the ratio of corresponding sides is equal. This means that
AB/DE = BC/EF = AC/DF
10/20 = 6/EF = 7/14
Thus, the proportion that can be used to find the length of EF is
6/EF = 1/2
400 meters to 350 meters The percent of change is
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hello
to solve this question, let's find the difference between the two numbers first
[tex]\text{change}=\text{ 400-350=50}[/tex]the percentage can be calculated as
[tex]\frac{50}{400}\times100=12.5\text{ \%}[/tex]from the calculation above, the percentage change is 12.5%
The can has a diameter of 5 inches and a height of 6.5 inches. The can's label covers the entire lateral surface of the can. How many square inches are covered by the label of the can?
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ANSWER
102.1 square inches
EXPLANATION
The can's label covers the entire lateral surface of the can.
The area (in square inches) covered by the label of the surface can be gotten by finding the lateral surface area of the can.
That is:
[tex]\begin{gathered} L\text{. S. A = 2 }\cdot\text{ }\pi\cdot\text{ r }\cdot\text{ h} \\ \text{where r = radius} \\ h\text{ = height} \end{gathered}[/tex]Since radius is half of the diameter, we have that:
r = D / 2
r = 5 / 2
r = 2.5 inches
Therefore:
[tex]\begin{gathered} LSA\text{ = 2 }\cdot\text{ }\pi\cdot\text{ 2.5 }\cdot\text{ 6.5} \\ \text{LSA = 102.1 square inches} \end{gathered}[/tex]That is the area covered by the label.
Jake records the expression below b×6 which of the following uses th3 commutarive property to represent an equivalent expression
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If we have the expression:
[tex]b\cdot6[/tex]If we apply the commutative property, we have:
[tex]b\cdot6=6\cdot b[/tex]The order of the factors in a product does not affect the result.
Answer: b*6 = 6*b
The formula for the surface area A of a cylinder with radius r and height h is given. Solve for h.[tex]a = 2\pi {r}^{2} + 2\pi {r}h [/tex]
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The formula for the surface area A of a cylinder with radius r and height h is:
[tex]A=2\pi r^2+2\pi rh[/tex]Solving for h:
[tex]\begin{gathered} A=2\pi r^2+2\pi rh \\ \Rightarrow A-2\pi r^2=2\pi rh \\ \Rightarrow\frac{A-2\pi r^2}{2\pi r}=h \\ \Rightarrow h=\frac{A}{2\pi r}-r \end{gathered}[/tex]The answer is h=(A/(2r*pi))-r
translate this sentence into an equation the product of 4 and Diego's age is 52use the variable d to represent Diego's age
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Explanation:
If Diego's age is 'd', the product of 4 and Diego's age is: 4d and that equals to 52
Answer:
The equation is 4d = 52
for a project in statistics class a pair of students decided to invest in two companies one that produced software and one that does biotechnology research Joe purchase 58 shares in the software company and 21 shares in the biotech firm which cost a total of $1,793 while Dave bought with ,$1848, 18, shares in the software company and 30 shares in the biotech firm. how much did each share cost
Answers
Answer
Price of a software company share = $11
Price of a biotech firm share = $55
Explanation
Let the cost of a share with the software company be s dollars
Let the cost of a share with the biotech research be b dollars.
Joe bought 58 software company shares and 21 biotech firm shares for $1793
58s + 21b = 1793
Dave bought 18 software company shares and 30 biotech firm shares for $1848
18s + 30b = 1848
The two equations can then be written together and solved simultaneously
58s + 21b = 1793
18s + 30b = 1848
Solving this simultaneously, we obtain
s = $11
b = $55
Hope this Helps!!!
The one-to-one functions g and h are defined as follows.g={(-8, 2), (-5, 6), (4, -8), (9, -9)}h(x) = 9x+13Find the following h^-1(-8)=h^-1(x)=(h^-1•h)(-2)
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Given
g={(-8, 2), (-5, 6), (4, -8), (9, -9)}
h(x) = 9x+13
Then for g^-1(-8):
[tex]\begin{gathered} given\text{ g(}4)=-8 \\ g^{-1}(-8)=4 \end{gathered}[/tex]for h^-1(x):
[tex]\begin{gathered} h(x)=9x+13 \\ \text{change h(x) to y} \\ y=9x+13 \\ i\text{nterchange x and y} \\ x=9y+13 \\ \end{gathered}[/tex]And solve for y:
[tex]\begin{gathered} x-13=9y+13-13 \\ x-13=9y \\ \frac{x-13}{9}=\frac{9y}{9} \\ y=\frac{x-13}{9} \\ \text{change y to }h^{-1}(x) \\ h^{-1}(x)=\frac{x-13}{9} \end{gathered}[/tex]for (h^-1 o h)(-2):
[tex](h^{-1}o\text{ h})(-2)=h^{-1}(h(-2))[/tex]So,
[tex]\begin{gathered} h^{-1}(9(-2)+13)=h^{-1}(-18+13)=h^{-1}(-5)=\frac{-5-13}{9}=\frac{-18}{9}=-2 \\ \end{gathered}[/tex]Answer:
[tex]\begin{gathered} g^{-1}(-8)=4 \\ h^{-1}(x)=\frac{x-13}{9} \\ (h^{-1}o\text{ h)(-2)=}-2 \end{gathered}[/tex]2. A square has an area of 64 square inches. It is enlarged by a scale factorof Ž. What is the length of one side of the new square?Step One Find the lengths of the sides of the original square, givenescribes theen the lengthsdes. It does notnship betweenfigures orits area.The area is 64. If the sides are n, then n x n = 64 and n=ibusStep Two Multiply the length by the scale factor.8x =The length of the new square is 12 inches.
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Following the setps we have that
[tex]\begin{gathered} n\cdot n=64 \\ n^2=64 \\ n=\sqrt[]{64}=8 \end{gathered}[/tex]the lengths of the sides of the original square is 8 inches each one. Now we are going to find the lengths of the sides of the new square following the step 2
[tex]8\cdot\frac{3}{2}=\frac{24}{2}=12[/tex]the lengths of the sides of new square is 12 inches each one.
The table below shows the radius, y, in inches, created by growing algae in x days:
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Part A
The most likely value of the correlation coefficient can be obtained by examining if there is an existing relationship between Time(x) and Radius(y) from the given table.
From the table, as time increases from 1 to 4 days, the radius increases by two times. As we progress from 4 to 7 days, this change in radius is reduced.
Hence, the correlation coefficient is 0.94
The relationship between time and radius of the algae can be explained thus: for every increase in time (days), the radius of the increases but not steadily.
Part C
The data in the table does not indicate causation. It rather shows correlation.
This is because the change in the radius of the algae is not a result of the change in time.
can you solve for me 3ax-n/5= -4
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Answer:
If you are solving for n then it would be n=15ax+20
Hope it helps
Glven: y varies directly with x and has a constant rate of change of 7. When the value of y is 12, then the value of x would be?
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Since y varies directly with x, we will be using this formula:
[tex]\text{ y = kx}[/tex]Given:
Constant rate of change = k = 7
Let's substitute k to generate the equation. We get,
[tex]\text{ y = 7x}[/tex]Let's now determine the value of x when y = 12.
[tex]\text{ y = 7x }\rightarrow\text{ x = }\frac{y}{7}[/tex][tex]\text{ x = }\frac{12}{7}[/tex]Therefore, at a constant rate of change of 7 and y varies directly with x, a value of y = 12 will have an x value of 12/7.
A football team gained 12 yards on one play and then lost 26 yards on the next. How many yards do they need to gain to get back to their starting position
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1) Gathering the data
1st play: 12 yrds
2nd play: -26yrds
2) Let's sketch this:
So they started on 0, gained 12 in the absolute value we have
They lost -26 +12 =-14
They need to gain 14 yards to get back to the starting position before the 1st play.
what is the largest number rounded to 30000
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Answer:
The largest possible number that can be rounded to 30,000 is 34,999
Explanation:
We want to find the largest number that can be rounded to 30,000.
Depending on the rounding;
To the nearest ten, the largest number is 30,004
To the nearest Hundred, the largest number is 30,049
To the nearest thousand, the largest number is 30,499
To the nearest ten thousand, the largest number is 34,999
Therefore, since the specified rounding is not given. From the above, The largest number that can be rounded to 30,000 is 34,999
Simplify:1000 ÷2500 +300
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Answer:
300 2/5 or 300.4
Explanation:
Given the expression:
[tex]1000\div2500+300[/tex]We use the order of operations (BODMAS) to evaluate this.
First, we start with the division.
[tex]\begin{gathered} 1000\div2500+300=\frac{1000}{2500}+300 \\ =\frac{2}{5}+300 \\ =300\frac{2}{5} \end{gathered}[/tex]Find the area of this trapezoid. Be sure to include the correct unit in your answer. 10 ft 13 ft 7 ft 9 ft 0 010 ft X 00 ft² S ft³ ?
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Given:
Required:
We need to find the area of given trapezoid
Explanation:
Take
[tex]\begin{gathered} a=13\text{ ft} \\ b=7\text{ ft} \\ h=9\text{ ft} \end{gathered}[/tex]The area of trapezoid is
[tex]A_T=\frac{a+b}{2}*h=\frac{13+7}{2}*9=10*9=90\text{ ft}^2[/tex]Final answer:
90 square feet
what is the area of the circle? what's the circumference? the diameter is 12 ft
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Hello
to calculate the area and circumference of a circle, we need to know the formula for that
[tex]\begin{gathered} \text{area of a circle }=\text{ }\Pi r^2 \\ circumference\text{ of a circle }=\text{ 2}\Pi r \end{gathered}[/tex]r = radius of the circle
radius = diameter / 2
diameter = 12ft
[tex]\begin{gathered} \text{radius}=\frac{diameter}{2} \\ \text{radius = }\frac{12}{2} \\ \text{radius }=\text{ 6ft} \end{gathered}[/tex]substitute the value of radius in the formula to find the area and circumference of the circle
[tex]\begin{gathered} area\text{ }=\text{ }\Pi r^2 \\ \Pi\text{ }=\text{ }\frac{22}{7} \\ \text{area}=\frac{22}{7}\times6^2 \\ \text{area}=\frac{22}{7}\times36 \\ \text{area}=\frac{792}{7} \\ \text{area}=113.14ft^2 \end{gathered}[/tex]to find the circumference of the circle, let's substitute the values into the formula
[tex]\begin{gathered} \text{circumference}=2\Pi r \\ \Pi=\frac{22}{7} \\ \text{circumference of the circle = 2}\times\frac{22}{7}\times6 \\ \text{circumference of the circle = }\frac{264}{7} \\ \text{circumference of the circle }=\text{ 37.71ft} \end{gathered}[/tex]the area and circumference of the circle is 113.14ft^2 and 37.7ft respectively
multiply decimals 9.07 × 6.5=
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ANSWER
[tex]58.955[/tex]EXPLANATION
We want to make the given multiplication.
To do this, first, write the numbers as whole numbers:
[tex]\begin{gathered} 9.07\Rightarrow907\div100 \\ 6.5\Rightarrow65\div10 \end{gathered}[/tex]Now, we have to multiply the two whole numbers and divide the final answer by 1000 (i.e. 100 * 10)
Therefore, we have:
Now, divide by 1000:
[tex]\begin{gathered} \frac{58955}{1000} \\ \Rightarrow58.955 \end{gathered}[/tex]That is the answer.
Two variables have a positive non-linear correlation. Does the dependent variable increase or decrease as the independent variable increases? Dependent variable would remain the sameCannot determine from information givenDependent variable decreasesDependent variable increases
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Since the correlation is not linear (non-linear), this means that the points tend to lie on a curve.
In addition, since the correlation is positive, we can assume that as one variable increases, the second variable also increases.
Hence, as the independent variable increases, the dependent variable also increases. (Option 4)
What should you multiply the first equation (top equation) by in order toeliminate the variable y when the two equations are added together?(2x - 5y = 71-6x - 5y = 3
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Given a simultaneous equation as shown below
[tex]\begin{gathered} 2x\text{ -5y = 7} \\ -6x\text{ -5y = 3} \end{gathered}[/tex][tex]\begin{gathered} \text{ multiply equation (1) by -1} \\ -2x\text{ + 5y = 7} \\ -6x\text{ -5y = 3} \end{gathered}[/tex]Hence the variable of y in the top equation must be multiplied by -1 in order to eliminate y
Solve the trigonometric equation for all values 0 ≤ x< 2π. sin x + 1 = 0
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
sin x + 1 = 0
Step 02:
0 ≤ x< 2π
sin (x) = - 1
x = arc sin (-1)
x = - π / 2
The answer is:
x = - π / 2 = - 90 degrees
Give the degree and leading coefficient of the following polynomial function. f(x)=x^7(7−6x^4−4x^4)
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Degree is 11
Leading coefficient is -10
Explanations:The highest value of the power of a given polynomial function is the degree of the function while the leading coefficient is the coefficient of the leading term.
Given the function
[tex]\begin{gathered} f(x)=x^7(7-6x^4-4x^4) \\ f(x)=x^7(7-10x^4) \end{gathered}[/tex]Expand the result
[tex]\begin{gathered} f(x)=7x^7-10(x^{7+4}) \\ f(x)=7x^7-10x^{11} \end{gathered}[/tex]Rearrange the resulting function according to the leading degree
[tex]f(x)=-10x^{11}+7x^7[/tex]From the resulting function, the degree of the polynomial is 11 while the leading coefficient is -10
Hi can you help me find the correct answer to this?
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Answer: x = 7,4
Choice A
To begin, we can get rid of the square root sign on the right side by squaring both sides of the equation. Squaring a square root will cancel out the square root, since they are opposite functions. Now we have the following:
(x-5)^2 = x-3
Now, we can expand the left side of the equation as follows:
(x-5)(x-5) = x-3
x^2 - 5x - 5x + 25 = x - 3
x^2 - 10x + 25 = x - 3
x^2 - 11x +28 = 0
Now, we can simply factor the left side of the equation as follows:
(x - 7)(x - 4) = 0
Now, we can set both expressions equal to 0 to find our solutinos:
x - 7 = 0
x = 7
x - 4 = 0
x = 4
x^5+3x^4-2x^3-6x^2+x+3 use synthetic division to identify all the zeros and characteristics of the function
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We want to use synthetic division in order to identify all the zeros of the following polynomial:
[tex]x^5+3x^4-2x^3-6x^2+x+3[/tex]First step: we