So here are the rules of horizontal asymptotes:
Degree of Numerator > Degree of Denominator: No horizontal asymptoteDegree of Numerator = Degree of Denominator: [tex]y=\frac{\textsf{leading coefficient of numerator}}{\textsf{leading coefficient of denominator}}[/tex]Degree of Numerator < Degree of Denominator: y = 0Looking at the rational function, since the degree of the numerator is 2 and the degree of the denominator is 1 (and 2 > 1), this means that this function has no horizontal asymptote.
Apply the distributive propertyto create an equivalent expression. 1/2(6e-3f-3/4)
3e - [tex]\frac{3}{2}[/tex] f - [tex]\frac{3}{8}[/tex]
multiply each of the terms in the parenthesis by [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex] (6e - 3f - [tex]\frac{3}{4}[/tex] )
= 3e - [tex]\frac{3}{2}[/tex] f - [tex]\frac{3}{8}[/tex]
Answer:
[tex]3e-\frac{3}{2}f-\frac{3}{8}[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{1}{2}(6e-3f-\frac{3}{4})[/tex]
To find an equivalent expression, we need to use the distributive property, that is, we have to multiply [tex]\frac{1}{2}[/tex] with each term that's inside the parenthesis.
[tex]\frac{1}{2}(6e-3f-\frac{3}{4})\\\frac{6e}{2}-\frac{3f}{2}-\frac{3}{2(4)}\\ 3e-\frac{3}{2}f-\frac{3}{8}[/tex]
Therefore, the equivalent expression is
[tex]3e-\frac{3}{2}f-\frac{3}{8}[/tex]
Remember that when we multiply fractions, we have to do it in a linear way, that is, numerators multiply each other, and denominators multiply each other. That means you CAN'T multiply a numerator with a denominator.
Find the measure of
<D = 360 - (80 + 115 + 100)
<D = 360 - 295
<D = 65
Answer
<D = 65°
(-4-7i)-(5-6i)
Simplify.
Answer is: −4−7i−(5−6i) = −9−i
The given complex expression is (-4-7i) - (5-6i). The simplification would give −9−i.
What are complex numbers?Any complex number can be written as
z = a + ib
The given complex expression is
(-4-7i) - (5-6i)
The simplification will be
= −4−7i−(5−6i)
= −9−i
Therefore, The simplification would give −9−i.
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4,divided by 3,476 i need helping hand
Efren leaves home at 9am and walks 4 miles per hour. His brother, gregory leaves half an hour later and runs 8.5 miles per hour in the same direction as efren. Predict the time at which gregory will catch up to efren
Answer:
Gregory will catch up Efren after 26 minutes 40 seconds.
Explanation:
Distance traveled = Speed x Time
Speed of Efren = 4 mi/h
Speed of Gregory = 8.5 mi/h
Let the time of catch up be t hours.
Time of journey of Efren before catch up = (t+0.5)hours, since he starts before half hour.
Distance traveled by Efren = 4 x (t+0.5) miles
Time of journey of Gregory before catch up = t hours.
Distance traveled by Gregory = 8.5 x t miles
If they catch up the distance traveled by them is same, so equating both distances.
4 x (t+0.5) = 8.5 x t
4.5t = 2
t = 0.44 hours =26.67 minutes = 26 minutes 40 seconds.
So Gregory will catch up Efren after 26 minutes 40 seconds.
Gregory will catch up to Efren approximately at 9:56am.
To find out when Gregory will catch up to Efren, we need to set up an equation based on their speeds and the time they travel.
Calculate the head start distance: Efren leaves at 9am and walks at 4 miles per hour.
Gregory leaves at 9:30am, so Efren has a 0.5-hour head start. Distance head start = speed × time = 4 miles/hour × 0.5 hours = 2 milesDetermine their relative speed: Gregory runs at 8.5 miles per hour while Efren walks at 4 miles per hour.
Relative speed = Gregory's speed - Efren's speed = 8.5 miles/hour - 4 miles/hour = 4.5 miles/hourCalculate the time for Gregory to catch up: We need to divide the head start distance by their relative speed.
Time = Distance / Relative speed = 2 miles / 4.5 miles/hour ≈ 0.444 hours (which is roughly 26.67 minutes)Find the catch-up time: Gregory leaves at 9:30am, so add the catch-up time to this.
Catch-up time ≈ 9:30am + 26.67 minutes ≈ 9:56amTherefore, Gregory will catch up to Efren at approximately 9:56am.
Eva brick makes and sells her own cranberry apple juice in jug a s
A cylinder has a radius of 12 cm and height of 16 cm. What volume for the solid/
The volume of a cylinder is given by the multiplication of the base area and the height.
The base is a circle, so its area is given by
[tex] A = \pi r^2 = 144\pi [/tex]
If we then multiply this by the height, we have
[tex] V = A\cdot h = 144\pi \cdot 16 = 2304\pi[/tex]
Are my answers correct? Precalculus!!
Answer:
Unfortunately, your answer is not right.
Step-by-step explanation:
The functions whose graphs do not have asymptotes are the power and the root.
The power function has no asymptote, its domain and rank are all the real.
To verify that the power function does not have an asymptote, let us make the following analysis:
The function [tex]y = x ^ n[/tex] , when x approaches infinity, where does y tend? Of course it tends to infinity as well, therefore it has no horizontal asymptotes (and neither vertical nor oblique)
With respect to the function [tex]y= \frac{1}{x}[/tex] we can verify that if it has asymptote horizontal in y = 0. Since when x approaches infinity the function is closer to the value 0.
For example: 1/2 = 0.5; 1/1000 = 0.001; 1/100000 = 0.00001 and so on. As "x" grows "y" approaches zero
Also, when x approaches 0, the function approaches infinity, in other words, when x tends to 0 y tends to infinity. For example: 1 / 0.5 = 2; 1 / 0.1 = 10; 1 / 0.01 = 100 and so on. This means that the function also has an asymptote at x = 0
The question involves precalculus, a High School or College level Mathematics topic, focusing on the accuracy and reasonableness of answers related to engineering principles. Students must consider significant figures, units of measure, and logical consistency within their mathematical processes.
Explanation:The student's question pertains to the subject of Mathematics, specifically within the realm of Precalculus, which is typically taught at the High School or College level. The inquiry involves reviewing the process of answering questions in mathematics and science as it relates to engineering. This includes checking whether an answer is reasonable in terms of units, magnitudes, and mathematical consistency. For instance, in the context of a precalculus class, students are expected to pay close attention to significant figures, units of measure, and ensuring answers are logically consistent with the problem presented.
The data set provided from Susan Dean's spring precalculus class can be used as an example for various statistical calculations. When dealing with such data, students need to organize it in a clear format, identify central tendencies (like mean, median, mode), and ensure that final answers are expressed with the proper significant figures and units. These practices are crucial for nd are rerced in a variety of STEM courses.
When it comes to the review questions mentioned, while specific questions are not provided, it is clear that students are encouraged to identify all correct answers to demonstrate their understanding of how mathematics and science connect with engineering. This holistic approach reflects real-world problem-solving where multiple solutions or considerations often exist.
You and three friends start a small business the total income is 1,820 and the total expenses are 360 you share the profit evenly how much do each of you get
Answer:
Each of them get 365.
Explanation:
Total income = 1820
Total expense = 360
Total profit = Total income - Total expense = 1820 - 360 = 1460
Number of persons sharing the profit = 4
Profit got by each person = Total profit/ number of persons sharing profit
= 1460/4 = 365
So each of them get 365.
What are the domain and range of the function below?
Answer:
Domain ={0,infinity)
Range = (-infinity, 4]
Step-by-step explanation:
Given a graph with curve which has y intercept 4.
It passes x axis at 4 and extends fully
The domain is the set of values x can take
In the graph horizontal axis is x axis.
Hence from the graph we see that x can take values from 4 including 4 upto infinity.
Hence domain is x>=4
For range, we consider the values of y as per graph.
WE find that y is not taking values >4
Hence Range = (-infty, 4]
Answer:
[tex]Domain=[0,\infty)[/tex]
[tex]Range=(-\infty,4][/tex]
Step-by-step explanation:
We need to find the domain and range of the function.
Domain : It is the set of input values or x values. In a graph, domain of the function represented by the x-axis.
Range : It is the set of output values or y values. In a graph, range of the function represented by the y-axis.
From the given graph it is clear that it is defined for [tex]0\le x<\infty[/tex] and [tex]-\infty <y\le 4[/tex].
We have closed circle at (0,4). It means, 0 is included in the domain and 4 is included in the range.
[tex]Domain=[0,\infty)[/tex]
[tex]Range=(-\infty,4][/tex]
Therefore, [tex]Domain=[0,\infty)[/tex] and [tex]Range=(-\infty,4][/tex].
Misty and Yesenia have a group of Base Ten Blocks. Misty has six more blocks than Yesenia. Yesenia's blocks represent 17. Together they have 22 blocks, and the total numbers of blocks represent 85. What blocks could each girl have? What is the value?
Answer:
Yesenia has qty 1 of 10s and qty 7 of 1s
Misty has qty 6 of 10s and qty 8 of 1s
Step-by-step explanation:
Note that there are two different types of blocks: 1s and 10s. Let x represent the number of 10s and y represent the number of 1s.
Value of the blocks Number of blocks
Yesenia: 1x + 7y 8
Misty:
Total: 8x + 5y 22
Start with the number of blocks that Misty has: 22 - 8 = 14
Next, how many 1s can be added to Yesenia's to make 5? 15 - 7 = 8
How many blocks are left over from Misty's 14? 14 - 8 = 6
********************************************************************************************
Fill in the information:
Value of the blocks Number of blocks
Yesenia: 1x + 7y 8
Misty: 6x + 8y 14
Total: 8x + 5y 22
The domain of y = 1/x - 10 is all real numbers except x = 10
TRUE or FALSE?
TRUE
because if we substitute the value of x = 10 to the equation, then we have quotient with divide by zero!
[tex]y=\dfrac{1}{x-10}\to f(x)=\dfrac{1}{x-10}\\\\f(10)=\dfrac{1}{10-10}=\dfrac{1}{0}\ !!!![/tex]
3/4(8x-4)=7x-5x+6
Solve this answer
If cosx is approximately 0.9511, what is the measurement of x to the nearest degree? Approximately, what is the sine of the angle that is complementary to x?
Answer:
Using the calculator angle whose cos is 0.9511 is 18 degrees
Sine of the complementary angle = 0.9511 also
Step-by-step explanation:
The sine of the complementary angle( which is 90-18 = 72 degrees) is same value 0.9511
Answer: 18 degrees and 0.9511
Step-by-step explanation:
18°; 0.9511
Cos-1(0.9511) = 18°
The complement of 18° is 72°. The sine of 72° is the cos of 18°, which is 0.9511.
Divide using synthetic division, and write a summary statement in fraction form. 2x5-x4+3x2-x+5/x-1
we are given
[tex]\frac{2x^5-x^4+3x^2-x+5}{x-1}[/tex]
Here , we have
[tex]dividend=2x^5-x^4+3x^2-x+5[/tex]
[tex]divisor=x-1[/tex]
now, we can use synthetic division
so, we get
[tex]Quotient=2x^4+x^3+x^2+4x+3[/tex]
[tex]Remainder=8[/tex]
now, we can write in fraction form
[tex]\frac{2x^5+x^4+3x^2-x+5}{x-1}=(2x^4+x^3+x^2+4x+3)+\frac{8}{x-1}[/tex]............Answer
To divide using synthetic division, arrange the polynomial in descending order, set up the synthetic division table, find the root of the divisor, perform the synthetic division, and read the coefficients of the quotient. In this case, the quotient is 2x^3 + x^2 + 4x + 3 with a remainder of -1.
Explanation:
To divide using synthetic division, you need to follow these steps:
Arrange the polynomial in descending order.Set up the synthetic division table and write down the coefficients of the polynomial.Find the root of the divisor and put it in the divisor column.Perform the synthetic division by bringing down the first coefficient, multiplying it by the root, and adding it to the next coefficient. Repeat this process until you reach the last coefficient.The last number in the synthetic division table is the remainder.The other numbers in the table form the coefficients of the quotient.In this case, the polynomial is 2x5 - x4 + 3x2 - x + 5, and the divisor is x - 1. Using synthetic division, we divide the coefficients:
+--+--+--+--+--+--+The coefficients in the bottom row of the synthetic division table are 2, 1, 4, 3. Therefore, the quotient is 2x3 + x2 + 4x + 3, and the remainder is -1.
Learn more about Dividing PolynomialsLearn more about Synthetic Division here:https://brainly.com/question/28824872#SPJ3Writing a Polynomial Function of a Graph:
use the fact that the graph passes through (0,36) to find the coefficient a in f(x)=a(x+3)(x+1)(x-2)(x-3)
a=???
we can see that
zeros are at x=-3 , x=2 , x=3
now, we can set up function
[tex]f(x)=a(x+3)(x-2)(x-3)[/tex]
now, we can select any one point and then we can find 'a'
(0,36)
x=0 and f(x)=36
we can plug it and then we can find 'a'
[tex]36=a(0+3)(0-2)(0-3)[/tex]
[tex]a=2[/tex]
now, we can plug it back
and we get
[tex]f(x)=2(x+3)(x-2)(x-3)[/tex]
now, we can multiply it
we get
[tex]f(x)=2x^3-4x^2-18x+36[/tex]............Answer
Math help please? giving 100 points. This is my last question i have and i'm just wanting some explanations on this since i was gone for a week during school. I came back and this whole part is quite confusing and i would be way too thankful for some help!
3. AB≅CE
4.CE≅AC
5.transitive property of congruence
6. definition of a isosceles triangle
What is 6,000 in a whole number multiplied by ten
Multiplying a number by 10 simply means to add a 0 at the end of the number, or to shift the decimal separator one unit to the right. So, for example,
[tex] 3 \cdot 10 = 30,\ -152 \cdot 10 = -1520,\ 25.467 \cdot 10 = 254.67 [/tex]
So, in your case, you have to add a 0 at the end of 6000, obtaining
[tex] 6000 \cdot 10 = 60000 [/tex]
On his fruit stand, Mr. Roberts has 13 papayas 23 fruit stares 35 mangoes and 19 strawberries. What is the ratio of the number of mangoes to the total number of pieces of fruit?
Answer: [tex]\frac{7}{18}[/tex] = 7:18
Step-by-step explanation:
[tex]\frac{35(mangos)}{13(papayas)+23(stares)+35(mangos)+19(strawberries)} = \frac{35(mangos)}{90(total fruit)}[/tex]
[tex]\frac{35}{90}[/tex] ÷ [tex]\frac{5}{5}[/tex] = [tex]\frac{7}{18}[/tex]
Debi walks laps around the mall for exercise during the winter months. The table represents the number of steps recorded on her meter as she walks laps around the mall one day. Which statement is true about the graph of the line representing Debi’s data?
a. Debi walks 1,875 steps per lap around the mall.
b. One lap around the mall is equal to about 2,425 steps.
c. One lap around the mall is equal to 4,300 steps.
d. Debi walks 6,175 steps per lap around the mall.
Laps / Steps
0 / 1,875
1 / 4,300
2 / 6,725
3 / 9,150
4 / 11,575
Answer:
The correct option will be: b. One lap around the mall is equal to about 2,425 steps.
Step-by-step explanation:
Here, we will just find the slope of the line representing Debi’s data. For that, we will take any two data from the table in form of point like [tex](x,y)[/tex]
Lets take two points as [tex](0, 1875)[/tex] and [tex](2, 6725)[/tex]
Formula for finding the slope is: [tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] are two given points.
Here, [tex]x_{1}= 0 , y_{1}= 1875 , x_{2}=2 , y_{2}=6725[/tex]
So, plugging these values into the above formula, we will get......
[tex]m= \frac{6725-1875}{2-0}=\frac{4850}{2}=2425[/tex]
That means, one lap around the mall is equal to about 2,425 steps.
Answer:
One lap around the mall is equal to about 2,425 steps.
Step-by-step explanation:
What is the LCM of 8x2y2 and 10x2y3?
A.40x2y3
B.40x4y5
C.80x2y3
D.80x4y6
The multiples of 8 are: 0, 8, 16, 24, 32, 40, 48, ...
The multiples of 10 are: 0, 10, 20, 30, 40, 50, ...
LCM(8, 10) = 40
LCM(x²y², x²y³) = x²y³
Therefore
LCM(8x²y², 10x²y³) = 40x²y³The LCM of 8x²y² and 10x²y³ is Option A: 40x²y³.
Identify the LCM of the numerical coefficients.
For 8 and 10, the LCM =40.
Determine the highest power of each variable present in the terms,
For x2 from both terms, the highest power is [tex]x^2[/tex].
For y2 and y3, the highest power is [tex]y^3.[/tex]
Therefore, the LCM of [tex]8x^2y^2[/tex] and [tex]10x^2y^3[/tex]is [tex]40x^2y^3[/tex].
The correct answer is Option A: [tex]40x^2y^3.[/tex]
question help brucebruce is taking a taxi to the airport. The taxi charges an initial fee of $44 and then $22 per mile. Write an algebraic expression for the cost of a taxi ride of m miles. Then evaluate the expression to find how much aa 55-mile taxi ride would cost brucebruce. Write an algebraic expression for the cost of a taxi ride of m miles. Choose the correct answer below. A. 44mminus−22m b. 22plus+44m c. 44plus+22m your answer is correct.D. 22m upper aa 55-mile taxi ride would cost brucebruce $ nothing.
Answer:
y = 44+22m
Step-by-step explanation:
Given that a taxi has a minimum charge of 44 dollar upto 1 mile and adds 22 for every additional 1 mile.
If a person travels 1 miles his charges are 44 dollar
If he travels >1 miles charges are 4 dollar +22(extra miles )
Let y be the charges and m be the no of miles.
Then the equation for y in terms of m would be
y =44+22m
is the correct answer.
What is the base 5 representation of the number 219?
The easiest way to do this is to start with the power of 5 that is just under 219.
125 would be the closest power of 5
Now subtract 125 from 219 = 94
=====================
The highest power of 5 closest to 94 is 25. You have to multiply 25 * 3 to get a number close enough to 94 that leaves a remainder under 25
94 - 75 = 19
=======================
19 - 3 * 5 = 4 Same argument as above.
Answer
219_10 = 1334_5
Answer:
1334/5
Step-by-step explanation:
Options are
A. 110
B. 410
C. 502
D. 775
Answer:
502
Step-by-step explanation:
4560/x=100/11
(4560/x)*x=(100/11)*x - we multiply both sides of the equation by x
4560=9.09*x - we divide both sides of the equation by (9.09) to get x
4560/9.09=x
501.6=x
x=501.6
why hello there
Your answer is c i was gonna give a better answer but the other dude did it
Does this table represent a function ?why or why not ?
(C) is correct answer. The values in the table assign to each x only one y value.
Answer:
c is the best answer for the question
Step-by-step explanation:
Find the area of the rectangle below by multiplying its length and width.
(7x-1) units
(3x-2) units
Hello!
When multiply binomials together, we should use the FOIL method.
The FOIL method is an acronym for First, Outer, Inner, and Last.
First, let's set up the expression.
(7x - 1)(3x - 2)
Now, we can multiply in accordance with the FOIL method.
First: 7x · 3x = 21x²
Outer: 7x · -2 = -14x
Inner: -1 · 3x = -3x
Last: -1 · -2 = 2
Now, we simplify the inner terms.
21x² - 14x - 3x + 2
21x² - 17x + 2
Therefore, the area of the rectangle is 21x² - 17x + 2.
The area of the rectangle is (21x² - 17x + 2) units².
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
Given the length of the rectangle is (7x-1) units, while its breadth is (3x-2) units. Therefore, the area of the rectangle is,
Area of rectangle = (7x-1) units × (3x-2) units
= 21x² - 14x - 3x + 2
= 21x² - 17x + 2 units²
Hence, the area of the rectangle is (21x² - 17x + 2) units².
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At the start of 2014 Tim's house is worth ?100000. The value of the house increase by 10% every years work out the value of his house at the start 2018
Answer:
Worth of Tim's house in 2018 = 146410 $
Explanation:
Worth of house in 2014 = $100000
Raise in worth per year = 10 % = 0.1
Worth of house in 2015 = 100000 + 0.1 * 100000 = 110000 $
Worth of house in 2016 = 110000 + 0.1 * 110000 = 121000 $
Worth of house in 2017 = 121000 + 0.1 * 121000 = 133100 $
Worth of house in 2018 = 133100 + 0.1 * 133100 = 146410 $
So, worth of Tim's house in 2018 = 146410 $
Easy Method;
No of years considering = 4
Initial worth = $100000
Rate of increase = 0.1
Final worth [tex]=100000(1+0.1)^4=146410$[/tex]
Worth of Tim's house in 2018 = 146410 $
The value of Tim's house at the start of 2018 will be $ 146,410.
Given that at the start of 2014 Tim's house is worth $ 100000, and the value of the house increase by 10% every year, to determine the value of his house at the start of 2018 the following calculation must be performed:
100,000 x 1.10 ^ (2018 - 2014) = X 100,000 x 1.10 ^ 4 = X 100,000 x 1,4641 = X 146,410 = X
Therefore, the value of Tim's house at the start of 2018 will be $ 146,410.
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At a peanut butter factory, the daily production cost, C, for j jars of peanut butter is modeled by the graph below. What are the domain and range of the function C(j)?
A. Domain: All Real Numbers
Range: C>5,000
B.domain: all real numbers
Range: C>2,500
C.domain: J>0
Range:C>5,000
D.domain:j>0
range:C>2,500
Answer:
Option D
Step-by-step explanation:
From the graph we find that the graph runs only in the I quadrant.
Hence x,y are positive only
Next is y intercept = 2500 and y increases continuously after that.
This implies y >=2500
Hence range is C>2500
Domain is the no of jars of peanut butter.
Hence j>0
In other words, 2500 is the fixed cost even when there is no production and cost cannot be less than 2500 at any time.
Production can be any number of jars from 0 onwards.
Hence option D
Please help answer ASAP
First of all, we need to do the expression in parenthesis first.
(4% - 2.25%) = 1.75%
Now, we convert the percent into an integer.
1.75% = 0.0175
Then, we multiply 44.5 by 0.0175
and we get 0.77875.
We have to round the number to the nearest cent.
0.77875 is roughly 0.78
So the answer is $0.78.
Calculate The Mean from the data given below: x f 0 1 1 13 2 20 3 40 4 40 5 13 6 7
Answer: 12.6
Step-by-step explanation:
(0 + 11 + 13 + 2 + 20 + 3 + 40 + 4 + 40 + 5 + 13 + 6 + 7)/13
= 164/13
= 12.6