1.) Translation to the right increases the x-coordinate value.
... (x+10, y)
2.) Translation up increases the y-coordinate value.
... (x, y+10)
How many centimeters are in 7 meters 100cm/1m=?/7m
Determine whether AB ← → and CD ← → − are parallel, perpendicular, or neither. A(2, 8), B(−1, −2), C(3, 7), D(0, −3)
A plot of the points quickly reveals the vectors to be parallel.
Answer:
AB and CD are parallel to each other.
Step-by-step explanation:
We have to check whether the line segment AB and CD are parallel, perpendicular or nothing,
The coordinates of A, B, C , D are:
A(2, 8), B(−1, −2), C(3, 7), D(0, −3)
We calculate the slope of line segment AB and CD.
Formula:
[tex]\text{Slope} = \displaystyle\frac{y_2-y_1}{x_2-x_1}\\\text{where }(x_1,y_1), (x_2, y_2)\text{ are the coordinates of the endpoints of line segment}[/tex]
Putting the values, we get,
Slope of Line segment of AB =
[tex]\displaystyle\frac{-2-8}{-1-2} = \frac{-10}{-3}=\frac{10}{3}[/tex]
Slope of Line segment of CD =
[tex]\displaystyle\frac{-3-7}{0-3} = \frac{-10}{-3}=\frac{10}{3}[/tex]
Thus,
Slope of Line segment of AB = Slope of Line segment of CD
Hence, the two line segments AB and CD are parallel to each other.
I need help on 13-18 I don’t understand. Can you show me how to do the math??
The percent change is given by ...
... (percent change) = (new amount - old amount)/(old amount) × 100%
This can be rearranged to give a formula for the new amount. First, we'll rewrite it to a slightly different form.
... (percent change) = ((new amount)/(old amount) -1) × 100%
... (percent change)/100% = (new amount)/(old amount) -1 . . . . divide by 100%
... (percent change)/100% + 1 = (new amount)/(old amount) . . . add 1
... (old amount) × ((percent change)/100%) +1) = new amount . . . . multiply by old amount
We can now use this formula to find the new amount in each case.
13. 25 × (300%/100% +1) = 25 × 4 = 100 . . . . dollars
14. 160 × (-20%/100% +1) = 160 × 0.8 = 128 . . . . bananas
15. 56 × (-75%/100% +1) = 56 × .25 = 14 . . . . books
16. 52 × (25%/100% +1) = 52 × 1.25 = 65 . . . . companies
17. 12000 × (5%/100% +1) = 12000 × 1.05 = 12,600 . . . . miles
18. 710 × (-10%/100% +1) = 710 × 0.90 = 639 . . . . points
_____
Considering the above formula for percent change (or its "slightly different form"), you may want to reconsider your answers for problems 7–12.
How do i make this chart pie chart with percentages
A spreadsheet program, such as Google Sheets, will happily make a pie chart for you, even displaying the percentages. (See the attachment.)
To calculate the percentages, divide each of the numbers in your list by the total of those numbers, then multiply that ratio by 100%
For example, the total is 2175, so the percentage belonging to Winter is
... 234/2175 × 100% ≈ 10.75862% ≈ 10.8%
If you're constructing the pie chart by hand, the next thing you need to know is the central angle of the section of pie representing Winter. To find that, mutiply the percentage (or its corresponding fraction) by 360°.
... 10.8% × 360° ≈ 38.7°
You can plot this on your chart using a protractor.
To create a pie chart with percentages, determine the values, calculate the percentages, draw the sections, and label them accordingly.
Explanation:To create a pie chart with percentages, follow these steps:
Determine the values or categories that you want to represent in your chart.Calculate the percentage for each value by dividing it by the total sum of all values and multiplying by 100.Draw a circle and divide it into sections, one for each value. The size of each section should correspond to the calculated percentage.Label each section with the corresponding value and its percentage.For example, if you have a pie chart representing the sales distribution of three products: A, B, and C, and their respective values are 100, 200, and 300, you would calculate the percentages as follows: A: (100 / 600) * 100 = 16.67%, B: (200 / 600) * 100 = 33.33%, C: (300 / 600) * 100 = 50%. Then, you would draw the pie chart with three sections, labeling each section with the product and its percentage.
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30+86=2+5(56-8) please help
Let's solve the left side first since there's no parentheses or multiplication.
30 + 86 = 116
Now we have 116 = 2 + 5(56 - 8)
Using PEMDAS, Parentheses first.
(56 - 8) = 48
Now we have 2 + 5(48)
Using PEMDAS, Multiplication next.
5 * 48 = 240
Using PEMDAS, Addition is next.
2 + 240 = 242
The equation 116 = 242 is false, as the values do NOT equal each-other.
116 ≠ 242
Dale is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 46 feet and its width is 35 feet. Suppose each can of wood stain covers 115 square feet. How many cans will he need to cover the court?
You will need to find the area of the rectangular shaped wooden floor and divide that area by 115 square feet.
46 x 35 = 1610
1610 square feet/115 square feet
= 14 cans of wood stain
Answer:
It should be 14
Step-by-step explanation:
The graph below shows the air temperature of a location (y), in degrees Celsius, after different time intervals (x), in hours: Graph of first line going through ordered pairs 0, 40 and 2, 10. Graph of second line going through ordered pairs 2, 10 and 4, 10. Graph of third line going through ordered pairs 4, 10 and 7, 50. Which of the following statements best describes the temperature of the location?
It is decreasing in the time interval 10 < x < 50 hours.
It is decreasing in the time interval 0 < x < 2 hours.
It is increasing in the time interval 10 < x < 50 hours.
It is increasing in the time interval 0 < x < 2 hours.
Please answer ASAP!!
Answer:
it is decreasing in the time interval 0<x<2 hours.
Step-by-step explanation:
Graph of first line going through ordered pairs A(0, 40) and B(2, 10).
Graph of second line going through ordered pairs B(2, 10) and C(4, 10). Graph of third line going through ordered pairs C(4, 10) and D(7, 50).
When movement is from point A to B, change in x = 2 and change in y = -30
Hence change for unit x = -30/2 = -15 ... i
When movement is from point B to C, change in x = 2 and change in y = 0
Hence change for unit x = 0/2 = 0 ... ii
When movement is from point C to D, change in x = 3 and change in y = +40
Hence change for unit x = 40/7 = 5.71 .. iii
Hence from A to B it is decreasing, B to C it remains constant and C to D it is increasing.
x coordinate represents hours and y coordinate degrees.
Hence answer is it is decreasing in the time interval 0<x<2 hours.
Answer:
decreasing in the time interval 0<x<2 hours. or B
Step-by-step explanation:
a poster is 66.05 centimeters high and 35.4 centimeters long. what is the difference in centimeters, between the height and lenght of the poster
Please help need answers
see explanation below
(1) [tex]\frac{1}{5}[/tex] × [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{10}[/tex] = 0.2
(2) [tex]\frac{6}{25}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{24}{100}[/tex] = 0.24
(3) 2 [tex]\frac{3}{4}[/tex] = 2 +[tex]\frac{75}{100}[/tex] = 2.75
(4) 3 [tex]\frac{9}{10}[/tex] = 3 + 0.9 = 3.9
(5) 1.25 = 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]
(6) 3.29 = 3 [tex]\frac{29}{100}[/tex] = [tex]\frac{329}{100}[/tex]
(7) 0.65 = [tex]\frac{65}{100}[/tex] = [tex]\frac{13}{20}[/tex] in simplest form
(8) 5.6 = 5 [tex]\frac{6}{10}[/tex] = 5 [tex]\frac{3}{5}[/tex] = [tex]\frac{28}{5}[/tex]
(9) he is incorrect
[tex]\frac{3}{5}[/tex] × [tex]\frac{20}{20}[/tex] = [tex]\frac{60}{100}[/tex] = 0.6 ≠ 3.5
Write equivalent expressions for x^7×x^-2 and x^7/x^2. What do you notice? Explain how your results relate to the properties of integer exponents.
PLEASE HELP!!! PERFORMANCE TASK FOR MATH. WILL MARK YOU BRAINLIEST
A) If grace and Claire’s parents each invested $7,600 into a college saving account when the girls were born, how much money will each girl have for college when she turns 18? Explain.
B) Do the functions show a positive or negative correlation between time and the amount of money saved? Explain.
A.) If Grace and Claire’s parents each invested $7,600 into a college savings account when the girls were born, how much money will each girl have for college when she turns 18? Explain.
Answer/Explanation:
For Grace, I plugged in 18 for x.
Work:
y= 1000(18) + 7600
y= 18000 = 7600
y= 25600
For Claire, I had to first find the slop by using rise over run.
11600-10000/3= 800
So the formula for Claire is y= 800x + 7600 and then you just plug in 18 for x.
Work:
y= 800(18) + 7600
y= 14,400 + 7600
y= 22,000
Therefore, Grace would have $25,600 at the end of 18 years old and Claire would have $22,000 when she turns 18 years old.
I hope that helped you or anyone else!! :)
The amount of money that Grace and Claire will have for college when they turn 18 will be $25600 and $22000 respectively.
Based on the information given, the amount that Grace will make will be:
= 1000x + 7600
= 1000(18) + 7600
= 18000 + 7600
= 25600.
The amount that Claire will make will be:
= 800x + 7600.
= 14400 + 7600
= 22000
The functions show a positive correlation between time and the amount of money saved.
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PLZ HELP GEOMETRY BELOW
One of the angles formed by two intersecting lines is 30°. What is the measure of the other three angles?
20 degrees. hope i helped sorry if ididn't
Answer:
the measures are 30, 150, and 150
Step-by-step explanation:
Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu. The previous menu had D dishes. Which of the following expressions could represent how many dishes crispy clovers new menu has? D+1/5D D+20 D+20D 20D 1.2D choose two answers.
The following expressions could represent how many dishes crispy clovers the new menu has [tex]\rm D+\dfrac{1}{5}D[/tex].
Given
Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu.
The previous menu had D dishes.
How to represent the expression which models the given situation?If it has 20% more, it must mean that it is 1.2 of the previous menu (Because it is 100 percent, plus an extra 20).
Therefore,
The following expressions could represent how many dishes crispy clovers new menu has;
[tex]\rm= D (100 \ of \ the \ previous \ menu) }+ \dfrac{1}{5} \rm \times { 20 \ percent \ D \ of \ the \previous \ menu}\\\\=D+\dfrac{1}{5}D[/tex]
Hence, the following expressions could represent how many dishes crispy clovers the new menu has [tex]\rm D+\dfrac{1}{5}D[/tex].
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Larry's Lemons is a street vendor business that sells lemonade and lemon bars. A cup of lemonade sells for $2 and a lemon bar sells for $1.50. When all related business expenses are included, a cup of lemonade costs $0.25 to prepare and a lemon bar costs $0.20 to prepare.
Last Monday, one of the vendors selling Larry's Lemons sold at least $500 worth of lemonade and lemon bars and its expenses were no more than $100. At least 150 cups of lemonade were sold.
Let x be the number of cups of lemonade sold last Monday and y be the number of lemon bars sold last Monday.
Which ordered pairs representing a combination of cups of lemonade and lemon bars could have been sold last Monday and make sense in the context of the situation?
Select each correct answer.
(160,110)(160,110)
(232.5,200)(232.5,200)
(155,305.5)(155,305.5)
(150,200)(150,200)
(180,100)
We can let x and y represent cups of lemonade and numbers of lemon bars, respectively. Then the constraints are ...
x ≥ 150y ≥ 02x +1.5y ≥ 5000.25x +0.20y ≤ 100A graph is shown in the attachment, with the ordered pairs plotted. It is not feasible to sell half cups of lemonade or half lemon bars, so the second and third choices must be excluded. The point (160, 110) falls outside the feasible region, so is not a correct choice.
The correct choices are ...
(150, 200)(180, 100)Final answer:
The only ordered pairs that meet the constraints of Larry's Lemons business situation are (150,200) and (180,100), as these combinations satisfy the conditions for revenue, expenses, and minimum amount of lemonade sold.
Explanation:
To find which ordered pairs (x, y) make sense in the context of Larry's Lemons' business situation, we need to consider the given conditions and set up inequalities to express the sales and expense constraints.
The conditions are:
A cup of lemonade sells for $2 and a lemon bar for $1.50.The cost to prepare a cup of lemonade is $0.25, and a lemon bar is $0.20.The vendor sold at least $500 worth of products.The vendor's expenses were no more than $100.At least 150 cups of lemonade were sold.Revenue Constraint:
For the revenue, we need to ensure that the seller made at least $500.
2x + 1.5y ≥ 500
Expense Constraint:
For the expenses, they should not exceed $100.
0.25x + 0.20y ≤ 100
Lemonade Sold Constraint:
Since at least 150 cups of lemonade were sold:
x ≥ 150
Now we check the given ordered pairs against these constraints:
(160,110): Given the constraints, this pair is feasible because the revenue is $2(160) + $1.50(110) = $470, which does not meet the revenue condition. Therefore, it is not a correct answer.(232.5,200): This pair does not represent whole units of lemonade and lemon bars, which doesn't make sense in this context as you can't sell half a cup of lemonade or half a lemon bar.(155,305.5): Similar to the above, this also includes half units and is thus not feasible.(150,200): Meets the revenue constraint, $2(150) + $1.50(200) = $500 in sales, and the expense constraint, $0.25(150) + $0.20(200) = $92.5 in expenses. It is a correct answer.(180,100): Also meets the constraints with revenue $2(180) + $1.50(100) = $510 and expenses $0.25(180) + $0.20(100) = $85. It is a correct answer.Only the ordered pairs (150,200) and (180,100) satisfy all the conditions of the problem.
Create equations of two lines that are parallel to y=1/2x+5
Y = 1/2 + 5 , the slope of this equation is 1/2
The equations of the parallel lines must also have a slope of 1/2.
This is because parallel lines have the same value of slope.
Based on the triangles, which statement is true?
The sum of interior angles of a triangle is 180°, and a linear pair is supplementary (adds to 180°). The appropriate choice is
... G. w = 105°, because ...
_____
In short, an exterior angle is equal to the sum of the opposite interior angles.
... w = 180 - (180 - (45 + 60)) = 180 -180 +45 +60
... w = 45 +60
During the day, the temperature in Nome, Alaska rose 35 degrees. The low temperature for that day is -22 degrees. What was the high temperature for that day?
Find the periodic rate that corresponds to the given compound rate, if the rate is compounded as follows.
(Round your answers to eight decimal places.)
Compound rate = 18%
(a) quarterly
Periodic rate = ?
(b) monthly
Periodic rate = ?
(c) daily
Periodic rate = ?
(d) biweekly (every two weeks)
Periodic rate = ?
(e) semimonthly (twice a month)
Periodic rate = ?
Answer:
a) 0.045b) 0.015c) 0.00049315d) 0.00692308e) 0.0075Step-by-step explanation:
Apparently, your periodic rate is that used to compute the interest accrued each period. It seems to be the compound (annual) rate divided by the number of periods in a year: quarterly, 4; monthly, 12; daily, 365; biweekly, 26; semimonthly, 24.
_____
If you want the effective annual rate to be 18% in each case, the numbers are different. For n periods per year, those are calculated as
[tex]\sqrt[n]{1.18}-1[/tex]
A periodic rate of 0.04224664 will give an effective annual rate of 18%.
Periodic rates for a 18% compound rate compounded quarterly, monthly, daily, biweekly, and semimonthly are calculated as follows :
Quarterly periodic rate: 0.18/4 = 0.045 or 4.5%Monthly periodic rate: 0.18/12 = 0.015 or 1.5%Daily periodic rate: 0.18/365 ≈ 0.000493 or 0.0493%Biweekly periodic rate: 0.18/26 ≈ 0.006923 or 0.6923%Semimonthly periodic rate: 0.18/24 ≈ 0.0075 or 0.75%Suppose the supply function for product x is given by qxs = - 30 + 2px - 4pz.
a. how much of product x is produced when px = $600 and pz = $60?
Replace the variables with their values and do the arithmetic.
qxs = -30 +2(600) -4(60) = -30 +1200 -240
qxs = 930
930 of product x is produced.
Explanation of how to determine the quantity of product x produced when given specific prices, the quantity produced of product x is -150.
Supply Function: qxs = - 30 + 2px - 4pz
a. To determine the quantity produced when px = $600 and pz = $60, substitute these values into the supply function:
qxs = -30 + 2(600) - 4(60) = -30 + 120 - 240 = -150
Therefore, when px = $600 and pz = $60, the quantity produced of product x is -150.
Please, Help Quick! Thank you!!!
If 87 people attend a concert and tickets for adults cost $3.75, while tickets for children cost $2.75 and total receipts for the concert was $272.25, How many of each went to the concert?
Adults? Children?
The cost of an LCD TV dropped from $800 in 2012 to $700 in 2014. (i) Find the unit rate at which the cost has been decreasing. (Express your answer rounded correctly to the nearest cent!) dollars per year (ii) Construct a linear model to predict the cost of an LCD TV and use it to predict the cost of a TV in 2016. (Express your answer rounded correctly to the nearest cent!)
Given
cost of an LCD TV dropped from $800 in 2012 to $700 in 2014
Find out unit rate at which the cost has been decreasing
Proof of (1)
As given in the question
let x denote the number of year and y denote the cost of the LCD TV
Take 2012 as intial year
cost of LCD TV = $800
Thus
x = 0 , y = 800
Take 2014 as the final year.
cost of LCD TV = $700
y = 700
x =2
( as the year changes 2012 to 2014 here exit change of 2 years)
Now find out the unit rate at which the cost is decreasing.
Take two points
( 0, 800) and ( 2, 700)
[tex]unit\ rate=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
putting the above value
we get
[tex]unit\ rate=\frac{700-800}{2-0}\\unit\ rate=\frac{-100}{2}[/tex]
thus
unit rate = -50
unit rate at which the cost has been decreasing is -50.
proof of ( 2)
points are( 0, 800) and ( 2, 700)
The equation is
[tex]\left ( y - y_1 \right ) =\frac{y_2 - y_1}{x_2-x_1}(x-x_1)[/tex]
put the values in the above equation
[tex]\left ( y - 800 \right ) =\frac{700 - 800}{2-0}(x-0)[/tex]
thus the equation becomes
y = -50x+800
Thus y = -50x+800 is the linear model to perdict the cost of LCD TV.
Now find out cost of the LCD TV in 2016
As taken earlier 2012 as the intial year
find the cost of LCD TV in 2016
thus x =4
( year changes 2012 to 2016 here exit the change of 4 years)
put x = 4 in the linear model y = -50x + 800
y = -50× 4 + 800
y = -200 + 800
y = 600
The cost of the LCD TV in 2016 is $600.
Hence proved.
Final answer:
The unit rate at which the cost has been decreasing is $50/year. The predicted cost of an LCD TV in 2016 is $900.
Explanation:
(i) To find the unit rate at which the cost has been decreasing, we can use the formula:
Unit rate = (Change in cost) / (Change in time)
Here, the change in cost is $800 - $700 = $100, and the change in time is 2014 - 2012 = 2 years. Substituting these values into the formula:
Unit rate = $100 / 2 years = $50/year
So, the cost has been decreasing at a rate of $50 per year.
(ii) To construct a linear model, we can use the formula:
Cost = mx + b
Where m is the slope (unit rate) and b is the y-intercept. Substituting the values:
Cost = $50(x - 2012) + $700
Since we want to predict the cost in 2016, we substitute x = 2016:
Cost = $50(2016 - 2012) + $700
Cost = $50(4) + $700
Cost = $200 + $700 = $900
Therefore, the predicted cost of an LCD TV in 2016 is $900.
1.Factor
3x(y−4)−2(y−4)
2. Factor.
20xy−4y+35x−7
Please Help!!! I'm trying to get caught up as fast as i can but k12 has been giving me so much work I can't keep up!!
(1)
take out the common factor (y - 4 )
= (y - 4)(3x - 2)
(2)
factor by grouping (1/2 terms and 3/4 terms )
4y(5x - 1) + 7(5x - 1)
take out the common factor (5x - 1)
= (5x - 1)(4y + 7)
1. Factor out the (y-4)
(y-4) (3x-2)
2.Factor by grouping
20xy -4y +35x -7
4y(5x-1) +7(5x-1)
then factor out 5x-1
(5x-1)(4y+7)
PLS HELP 50 POINTS
write y=x-1 in function notation.
Answer:
f(x)=x-1
Step-by-step explanation:
replace y by f(x) to obtain functional notation
f(x) = x - 1
If it snows tomorrow, then my dentist appointment will be canceled. If my dentist appointment is canceled, then I will clean under my bed. Therefore, if it snows tomorrow, then I will clean under my bed. Is this a Law of Detachment?
Yes this is a Law of Detachment.
Solve for z:
2 + 8 - z = -24
Show your work
Why does this make sense? a. You use the power of a product law of exponents to combine the exponents; this law says to add the exponents. b.You use the power of a power law of exponents to combine the exponents; this law says to multiply the exponents. c. You use the product of powers law of exponents to combine the exponents; this law says to add the exponents.
Answer:
You use the product of powers law of exponents to combine the exponents; this law says to add the exponents.
Step-by-step explanation:
got it right
Answer: D
Step-by-step explanation:
please help, need answer fast!
Which of the following describes the roots of the polynomial function f(x)= (x + 2)^2(x - 4)(x + 1)^3?
–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3
–2 with multiplicity 3, 4 with multiplicity 2, and –1 with multiplicity 4
2 with multiplicity 2, –4 with multiplicity 1, and 1 with multiplicity 3
2 with multiplicity 3, –4 with multiplicity 2, and 1 with multiplicity 4
Multiplicity means multiple roots. So [tex](x + a)^n[/tex] means that the root [tex]-a[/tex] has multiplicity [tex]n[/tex].
Using the definition of multiplicity of roots, we deduce that we have:
(A) -2 with multiplicity 2, 4 with multiplicity 1, and -1 with multiplicity 3.
Multiplicity of a polynomial means how many times a particular number is a zero for a given polynomial.
In the given polynomial :
[tex]f(x)=(x+2)^{2} (x-4)(x+1)^{3}[/tex]
The roots of the equation can be found by taking the factor =0.
x+2=0 or x=-2
x-4=0
or x=4
x+1=0
or x=-1
The roots of the polynomial are -2,4,-1.
The powers of the root denotes the multiplicity of the polynomial.
The root -2 occurs 2 times ,4 occurs once ,-1 occurs 3 times.
So we say :–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3.
Option A is the right option.
Write a function with the following characteristics: 1.A vertical asymptote at x = 3 A horizontal asymptote at y = 2 An x-intercept at x=-5 2.A vertical asymptote at x=-1 An oblique asymptote at y = x + 2
1. The vertical asymptote requires the denominator have a zero at that location. The x-intercept requires the numerator have a zero at that location. The horizontal asymptote amounts to a multiplier of the function:
... y = 2(x +5)/(x -3)
2. The vertical asymptote requires the denominator have a zero at that location. The oblique asymptote is an add-on
... y = 1/(x +1) +(x +2)
... y = (x² +3x +3)/(x +1)
We can use rational functions to define functions with specific characteristics. A function with a vertical asymptote at x = 3, a horizontal asymptote at y = 2, and x-intercept at x = -5 could be written as f(x) = 2(x + 5) / (x - 3). A function with a vertical asymptote at x = -1 and an oblique asymptote at y = x + 2 can be written as f(x) = (x^2 + x - 2) / (x + 1).
Explanation:The subject here pertains to certain characteristics of functions, specifically regarding asymptotes and intercepts. In order to create a function with the required characteristics, you would typically use rational functions.
Vertical asymptotes occur when the denominator of a function is zero, horizontal asymptotes are connected to the degree of the polynomials in the function, and x-intercepts occur when the function itself equals zero.
Here's how we can write the function for each case:
A function with a vertical asymptote at x = 3, a horizontal asymptote at y = 2, and an x-intercept at x = -5 can be given as f(x) = 2(x + 5) / (x - 3). In this function, as x approaches 3, the function tends towards infinity, producing the vertical asymptote. As x approaches infinity, the function tends towards 2, leading to the horizontal asymptote. The function equals zero at x = -5, giving the x-intercept.A function with a vertical asymptote at x = -1 and an oblique (also termed a 'slant') asymptote at y = x + 2 can be given as f(x) = (x^2 + x - 2) / (x + 1). As x approaches -1, the function tends towards infinity, producing the vertical asymptote. The oblique asymptote y = x + 2 is found by performing polynomial long division on (x^2 + x - 2) by (x + 1).Learn more about Rational Functions here:https://brainly.com/question/27914791
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alexis is trying to partition segment ab in the ration 2:3 using a compass
Solution: The Steps are defined below,
Explanation:
To divide a line segment in 2:3 using compass alexis has to follow many steps:
1) Draw a line segment ab of length x.
2) Draw a line ac which makes an acute angle with the line ab.
3) Since alexis has to divide the line is 2:3, so make 2+3=5 arc of equal length of ac with the help of compass.
4) Name the fifth arc as d, so join the fifth arc with point b.
5) The draw a parallel to the line bd, and passing through the 2nd acr of ad. mark the second are as m.
6) Let the parallel line intersect at point n. Where the parallel line intersect the line ab, that point divides the line segment ab is 2:3.
By using above steps we get the figure same as the figure given below.
The line [tex]\bf ab[/tex] can be divided into the ratio [tex]2:3[/tex] with the help of a compass.
Further explanation:
Given that Alexis is trying to partition a line segment [tex]\bf ab[/tex] in the ratio [tex]2:3[/tex] with the help of compass.
There are different methods to divide a line segment in the given ratio, but we will use a simple method to divide the line [tex]\bf ab[/tex] in the ratio [tex]2:3[/tex].
Given a line segment [tex]\bf ab[/tex], which is to be divided in the ratio of [tex]2:3[/tex].
First draw any ray [tex]\bf ax[/tex] which makes an acute angle with [tex]\bf ab[/tex].
Locate [tex]5[/tex] points [tex]\bf a_{1},a_{2},a_{3},a_{4}\text{ and }a_{5}[/tex] on the ray [tex]\bf ax[/tex] such that [tex]\bf aa_{1},a_{1}a_{2},a_{2}a_{3},a_{3}a_{4}[/tex] and [tex]\bf a_{4}a_{5}[/tex] are equal, with the help of a compass.
Since, Alexis is trying to divide the line [tex]\bf ab[/tex] into the ratio of [tex]2:3[/tex], therefore, the ray [tex]\bf ax[/tex] is divided into [tex]5(2+3)[/tex] points.
Now, join the point [tex]\bf b[/tex] with the point [tex]\bf a_{5}[/tex].
From the point [tex]\bf a_{2}[/tex], draw a line parallel to [tex]\bf ba_{5}[/tex] and this can be drawn by making an angle equal to [tex]\angle\text{aa}_{5}\text{b}[/tex].
Now, consider that the line that is drawn parallel to [tex]\bf ba_{5}[/tex] intersect the given line [tex]\bf ab[/tex] at the point [tex]\bf c[/tex].
The point of intersection on the line [tex]\bf ab[/tex] is the point where it is divided into the ratio [tex]2:3[/tex] as shown in Figure 1 (attached in the end).
The above used steps are used to divide any line in the given ratio.
Therefore, the line [tex]\bf ab[/tex] can be divided into the ratio of [tex]2:3[/tex].
Learn more:
1. Learn more about angles https://brainly.com/question/1953744
2. Learn about collinear points https://brainly.com/question/5191807
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Constructions
Keywords: Alexis, compass, partition, segment, ab, ratio, 2:3, constructions, line, ray, parallel, intersection, angle, acute, geometry, line segment, acute angle.