If a regular polygon has exteriorangles that measure approximately17.14° each, how many sides doesthe polygon have?
Answers
To answer this question we will set and solve an equation.
Recall that the exterior angle of an n-gon has a measure of:
[tex]\frac{360^{\circ}}{n}.[/tex]Let n be the number of sides that the polygon that we are looking for has. Since the regular polygon exterior angles with a measure of approximately 17.14 degrees, then:
[tex]\frac{360^{\circ}}{n}\approx17.14^{\circ}.[/tex]Therefore:
[tex]n\approx\frac{360^{\circ}}{17.14^{\circ}}[/tex]Simplifying the above result we get:
[tex]n\approx21.[/tex]Answer: 21 sides.
Related Questions
3.2 Hangalakani works as a builder for 6,5 hours per day excluding 30 minutes tea break 1 hour lunch. He starts working at 07:30 am 2.1 Determine the time of the day Hangalakani leaves work for home 312.2 Hangalakani calculated that 245,37 bags of cement are required for the job His manager states that they need to purchase 246 bags Explain why the manager's statement is correct.
Answers
Hangalakani leaves his work for home at 3.30 PM .
Hangalakani starts his work at 7.30 am.
He works for 6.5 hours.
He then takes a lunch break for 1 hour .
He then takes tea break for about 30 minutes = 0.5 hour
Total time spent at work = 6.5 + 1 + 0. 5 = 8 hours.
So if he starts work at 7.30 then he will end at
7.30 am + 8 hours = 3.30 pm in the afternoon .
Now the manager says that they need 246 bags while Hangalakani calculated they need 245.37 bags of cement.
The manager is correct because bags of cement are not sold as a part or decimal . The number of bags that can be bought must be a whole number.
To learn more about work visit:
https://brainly.com/question/28265361
#SPJ9
Hello, May I please get some assistance with this homework question? I posted an image below. Question A has already been answered, but do need help with the other questions. Q2 (part b)
Answers
ANSWER
• (g o f)(x) = ,16x² + 24x + 9
,• B., the domain of g o f is all real numbers
EXPLANATION
The composition is,
[tex](g\circ f)(x)=g(f(x))[/tex]This means that, to find the composition, we have to replace x with f(x) in the function g(x),
[tex]g(f(x))=(f(x))^2[/tex]Now, replace f(x) with its expression,
[tex]g(f(x))=(4x+3)^2[/tex]We can expand this binomial squared to write it in standard form. The composition is,
[tex](g\circ f)(x)=16x^2+24x+9[/tex]As we can see, this is a polynomial function. Therefore, the domain is all real numbers.
connie is packing for a trip. she has 16 pairs of shoes. if she has room to pack 7 pairs, how many ways can she choose which shoes to take?
Answers
Combinatorics
If Connie had only 7 pairs of shoes and she has room for 7 pairs of shoes, then she has only one way to take her shoes.
If she had 8 pairs of shoes, then she can select any group of shoes that leaves one pair out. This makes 8 possible ways to choose.
When the number of pairs of shoes goes up, then the counting gets more complex. That is when combinatorics is a useful tool.
If we have a total of n elements to select m, where the order of selection is not important, then the total number of selections is given by:
[tex]C_{n,m}=\frac{n!}{(n-m)!\cdot m!}[/tex]Where the sign (!) is the factorial of a number.
Connie has n=16 pairs of shoes and she will take m=7 from them, thus the number of possible ways or combinations is:
[tex]\begin{gathered} C_{16,7}=\frac{16!}{(16-7)!\cdot7!} \\ C_{16,7}=\frac{16!}{(9)!\cdot7!} \end{gathered}[/tex]Expanding the factorial down to match the greatest factorial in the denominator:
[tex]C_{16,7}=\frac{16\cdot15\cdot14\cdot13\cdot12\cdot11\cdot10\cdot9!}{(9)!\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex]Simplifying and calculating:
[tex]C_{16,7}=\frac{57,657,600}{5,040}=11,440[/tex]Connie can choose in 11,440 ways the shoes to choose
What is the product of the complex numbers below?(3 - 2i)(1 + 7i)A.-11 + 19iB.17 + 19iC.-11 - 23iD.17 - 23i
Answers
Solution:
Given:
[tex](3-2i)(1+7i)[/tex]To find the product, we multiply the terms in the second parentheses by each term in the first parentheses.
Thus, we have
[tex]\begin{gathered} 3(1+7i)-2i(1+7i) \\ open\text{ parentheses,} \\ 3+21i-2i-14i^2 \\ but\text{ i}^2=-1 \\ thus,\text{ we have} \\ 3+21i-2i-14(-1) \\ collect\text{ like terms,} \\ (3+14)+i(21-2) \\ \Rightarrow17+19i \end{gathered}[/tex]Hence, the product of the complex numbers is
[tex]17+19i[/tex]The correct option is B
the recursive rule is a1=__and a n-1 for n> __.the explicit rule is a n= ___(__)n-1
Answers
We are required to find both the recursive rule and the Explicit rule for the values given in the table.
Recursive rule:
To get the recursive rule, we need to find the common ratio.
The common ratio (r) is found by dividing the 2nd term by the 1st term, or the 3rd term by the 2nd term, or the 4th term by the 3rd term, and so on.
We can generalize and say the common ratio is also the division of the nth term by the (n-1)th term.
Let us put these facts into mathematical expressions:
[tex]\begin{gathered} Let,_{}_{} \\ a_1=\text{first term} \\ a_2=\text{Second term} \\ a_3=\text{third term} \\ \text{...} \\ a_n=\text{nth term} \\ \\ \text{common ratio (r)=}\frac{a_1}{a_2}=\frac{a_3}{a_2}=\frac{a_4}{a_2}\ldots=\frac{a_n}{a_{n-1}} \\ \\ \text{if a}_1=1,a_2=3_{} \\ \therefore r=\frac{a_2}{a_1}=\frac{3}{1}=3 \end{gathered}[/tex]Thus, we can now write the recursive formula as:
[tex]\begin{gathered} \frac{a_n}{a_{n-1}}=\text{common ratio (r)} \\ \\ \therefore\frac{a_n}{a_{n-1}}=3 \\ \\ \therefore a_1=1,a_n=3a_{n-1}\text{ for n}\ge1 \end{gathered}[/tex]Explicit rule:
To get the rule, we need to recognize the pattern:
[tex]\begin{gathered} \text{when n = 1} \\ a_1=1=3^0 \\ \\ \text{When n = 2} \\ a_2=3=3^1 \\ \\ \text{When n= 3} \\ a_3=9=3^2 \\ \\ \text{When n= 4} \\ a_4=27=3^3 \\ \\ \text{When n = 5} \\ a_5=81=3^4 \end{gathered}[/tex]We can see a pattern developing and from that, we can generalize:
[tex]\begin{gathered} a_1=3^0 \\ a_2=3^1 \\ a_3=3^2 \\ a_4=3^3 \\ a_5=3^4 \\ \ldots \\ a_n=3^{n-1} \end{gathered}[/tex]Thus, the explicit rule is:
[tex]\begin{gathered} a_1=1 \\ a_n=1\times3^{n-1} \end{gathered}[/tex]which of the following is not a polynomial identityA) x²+y²=x²+2xy+y²B) x³+y³=(x+y) (x²-xy+y²)C) (x+y)² = x²+2xy+y²D) x²-y²= (x+y) (x-y)
Answers
The first option:
A)
x² + y² = x² + 2xy + y²
is not a polynomial identity because the right side of the equation corresponds to a binomial squared, which is given by:
(x + y)² = x² + 2xy + y²
and what you have left side of the given expression is x² + y² and not (x + y)² which is totally different.
Hence, x² + y² = x² + 2xy + y² is not a polynomial identity
coupon A:$18 rebate on a $95 bicycle couponB:15% off of a $95 bicycle
Answers
Coupon A gives the lower price,is $3.75 less than the price with coupon b
Explanation
Step 1
get the final price
a) Coupon A
$ 18 rebate on a $95 bycicle
so, the final price is
[tex]\begin{gathered} \text{final price=original price-discoutn} \\ \text{ final price=\$95 -\$18} \\ \text{ final price(a)=\$77} \end{gathered}[/tex]b) 15% off of a $95 bucycle
fint, the value for 15% of $95
[tex]15\text{ percent=}\frac{\text{15}}{100}=0.15[/tex]so, to know the value for 15% of $95,do:
[tex]\text{discount}=0.15\cdot95=14.25[/tex]the discount for coupon b is $14.25,
hence the final price is
[tex]\begin{gathered} \text{ Final price=\$95 -\$14.25} \\ \text{ Final price=80.75} \end{gathered}[/tex]Hence,
[tex]\text{ Final price(B)=\$ 80.75}[/tex]Step 2
compare the prices(difference)
[tex]\begin{gathered} \text{Price(a)}=77 \\ \text{Price(b)}=80.75 \\ \text{pric e(b)-price(a)=80.75-77=3.75} \end{gathered}[/tex]I hope this helps you
find the constamt of proportionality (r) in the equation y=rx
Answers
To find the constant of proportionality of the equation y = rx, from the values of the given table, just calculate the quotient r = y/x, where x and y can be any pair of values of the table.
For x = 3 and y = 30:
r = 30/3
r = 10
Hence, the constant of proportionality is
r = 10
drag two number lines to the box where the shade parts best compare 1/6 and 1/4
Answers
Given the fractions 1/6 and 1/4
We need to compare between them
The two number lines will be:
By comapring between them : 1/6 < 1
two hundred million thirty five
Answers
The given number is two hundred million thirty five.
As you can observe, this number has hundred millions, tens, and units. Specifically, it has 2 hundred million, 3 tens and 5 units. We write each part as a sum, as follows
[tex]200,000,000+30+5[/tex]Then we add, so the number is
[tex]200,000,035[/tex]WILL GIVE BRAINLYEST 100 POINTS !!!! A student is painting a brick for his teacher to use as a doorstop in the classroom. He is only painting the front of the brick. The vertices of the face are (−6, 2), (−6, −7), (6, 2), and (6, −7). What is the area, in square inches, of the painted face of the brick?
144 in2
108 in2
72 in2
42 in2
Answers
The area, in square inches, of the painted face of the brick is; 144 in²
How to find the area of a square with coordinates?The area of a square is given by;
A = L²
where;
L is the length of the side of the square
The sides of a square all have the same length, and as such we just need to find the length of one side.
The length of the side of the square here is the distance between two vertices, which can be calculated as
L = √[(x₂ - x₁)² + (y₂ - y₁)²]
However, to avoid long process, since it is a square, we can use subtraction of coordinates to get the side length which is gotten by using the first 3 coordinates;
Horizontal length = (6 + 6) = 12
Thus;
Area = L² = 12² = 144 in²
Read more about area of square coordinates at; https://brainly.com/question/14698897
#SPJ1
Situation:Holly wants to save money for anemergency. Holly invests $1,000 in anaccount that pays an interest rate of6.25%
Answers
Given data:
Amount of money invested, P = $1000
Interest rate, r = 0.0625
Total money in the account, A = 5500
Now, to find the years use simple interest rate formula that is
[tex]A=P(1+rt)[/tex]Therefore, t will become
[tex]t\text{ = (A/P}-1\text{)/r}[/tex]Putting the values we get,
[tex]t=(\frac{5500}{1000}-1)\text{ / 0.0625}[/tex][tex]\begin{gathered} t=(5.5-1)\text{ / 0.0625} \\ t=\frac{4.5}{0.0625} \\ t=72 \end{gathered}[/tex]Thus, it will take 72 years for the account to reach 5500.
what is slope of the line parallel to the given line(I know the steps no explanation just need work:)
Answers
Given the equation of the line :
[tex]4x-3y=-12[/tex]To find the slope, solve the equation for y:
[tex]\begin{gathered} 4x-3y=-12 \\ -3y=-4x-12 \end{gathered}[/tex]Divide both sides by -3 :
[tex]\begin{gathered} \frac{-3y}{-3}=\frac{-4x}{-3}-\frac{12}{-3} \\ \\ y=\frac{4}{3}x+4 \end{gathered}[/tex]So, the slope of the given line = 4/3
And the slope of the line parallel to the given line = 4/3
Because the parallel line have the same slopes
So, the answer is : slope = 4/3
Over the past 7 days, Ms.Burge found that the temperature outside had dropped a total of 28 degrees. What is the average temperature per day?
Answers
Remember that the average or mean is the ratio between the sum of all numbers involve and the total number of items there.
In this case, the total is 28 degrees, and the total number of days is 7, we just have to divide.
[tex]\bar{x}=\frac{28}{7}=4[/tex]Therefore, the average temperature per day is 4 degrees.mean=100 sd=20 determine the probability that random student scores below 70 on the pax test. above 112 on the pax test, and random student scores between 85 and 115 on the pax test
Answers
For this problem, we are given the mean and standard deviation of a certain test. We need to determine a probability of a random sample to be in a few values.
The first value we need to determine is the probability of the random sample being below 70. The first step we need to take is to determine the z-score of this value, which can be calculated with the following expression:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]For the value of 70, we have:
[tex]Z=\frac{70-100}{20}=\frac{-30}{20}=-1.5[/tex]Now we need to find this value on the z-table, which is:
[tex]P(Z<-1.5)=0.0668[/tex]Therefore we can determine that the probability of a value to be below 70 is 6.68%.
Now we need to determine the probability of a value above 112. We need to determine the z-score once again:
[tex]Z=\frac{112-100}{20}=\frac{12}{20}=0.6[/tex]The z-table only tells us values below the z-score, so we need to subtract the result from 1, which is shown below:
[tex]P(Z>0.6)=1-P(Z<0.6)=1-0.7275=0.2725[/tex]The probability of the value being greater than 112 is 27.25%.
Now we need to find the probability of the score to be between 85 and 115. We need to find both Z-scores:
[tex]\begin{gathered} Z(85)=\frac{85-100}{20}=\frac{-15}{20}=-0.75\\ \\ Z(115)=\frac{115-100}{20}=\frac{15}{20}=0.75 \\ \end{gathered}[/tex]So we need to find the two values on the Z-table and subtract them. We have:
[tex]P(-0.75The probability of the random value being between 85 and 115 is 54.68%.Stefan can pick forty bushels of apples in12 hours. One day his friend Gabriellahelped him and it only took 6.67 hours.Find how long it would take Gabriella todo it alone.
Answers
Stefan picks up 40 bushels of apples in 12 hours.
With the helo of gabriela they do so th 6.67 hours. We can represent this in the following table:
Bulshels of apples Hours
40 6.67
We need to multiply these number by 2, so that we can know how much time it would take for Gabriella to pick 40 alone.
Bulshels of apples Hours
40 6.67
80 13.34
Now, since picking 80 together takes 13.34 hours, and we know that tefan picks up 40 in 12 hours, the other 40 where picked up by Gabriella in:
[tex]13.34-12=1.34[/tex]Answer: 1.34 Hours
I
3. (5 points) Herman and Rosie need to wash the walls on the side of the school. Herman
has a power washer, which could complete the job in 10 hours. Rosie has a manual
scrubber, which could complete the job in 15 hours. in
they work together, how many hours
will it take them to clean the wall?
Answers
Answer:
It would take them 6 hours. Six hours is 3/5 of Herman’s required time. 6 hours is 2/3 of Rosie’s, so 3/5 +2/5= the project being complete.
The hotel room tax in Junction City is calculated using the function T(x) =0.06x + 4.5, where x = the cost in dollars of the room and T(x) = the tax in dollars. What is the tax on a room that costs $120?
Answers
Since the tax on the room is given by the function:
T(x)=0.06x+45
And x(cost in dollars of the room) is given= $120, you just have to subtitue x=120 on the function
T(120)=0.06(120)+4.5
T(120)=7.2+4.5
T(120)=11.7
So, the tax in dollars would be $11.7
The function y =30+5x represents the cost y (in dollars) of having your dog groomed and buying x for extra services . can u please just do C (graph the function using six values of it's domain
Answers
Problem
The function y =30+5x represents the cost y (in dollars) of having your dog groomed and buying x for extra services . can u please just do C (graph the function using six values of it's domain
Solution
Part a
For this case a linear function is given by: y = mx+b
If we compare the function y =30 +5x we can see that we have the sam efunctional form and we can conclude that yes is a linear function with m = 5 and b =30
Part b
For this part since we have a linear function the domain is given by:
D= [0,1,2,3,4,5}
Then the domain is discrete
Part c
For this case we have the following solution:
A telemarketers computer selects phone numbers at random. The telemarketer has recorded the number of respondents in each age bracket for one evening in the following table. What is the probability that the next respondent will be between 18 and 25? Enter a fraction or round your answer to four decimal places, if necessary.Under-18 =1818-25=2526-35=4636-45=56Over 45=54
Answers
The probability P of an event e can be found using the formula:
[tex]P(an\text{ event e occurring\rparen= }\frac{Number\text{ of occurrence of an event}}{Total\text{ number of occurrence}}[/tex]Required: The probability that the next respondent will be between 18 and 25
Number of respondents between the ages of 18 and 25 = 25
Total number of respondents :
[tex]\begin{gathered} =\text{ 18 + 25 + 46 + 56 + 54} \\ =\text{ 199} \end{gathered}[/tex]Hence, the probability of a selecting a respondents in the age range 18 to 25 is:
[tex]\begin{gathered} P\text{ = }\frac{25}{199} \\ =\text{ 0.125628} \\ \approx\text{ 0.1256} \end{gathered}[/tex]Answer: 0.1256
I need help with this question my answer was 2 but I for sure
Answers
Given
Distance = 30 km
Time = 1 1/2 hours = 3/2 hours
Find
rate in km per hour
Explanation
we need to find the rate in km per hour.
as we now the rate is also called a speed
so , speed = distance/time
[tex]\begin{gathered} rate=\frac{distance}{time} \\ \\ rate=\frac{30}{\frac{3}{2}} \\ \\ rate=\frac{30\times2}{3} \\ \\ rate=\frac{20km}{h} \end{gathered}[/tex]Final Answer
Therefore, the rate of ship is 20km/hr
so , the correct option is 1.
23 pointsThe length of a rectangular box is 1 inch longer than twice the width (x).The height is 5 inches.which is the volume (y) function
Answers
y = 5x ( 2x + 1)
Explanations:Let the width of the rectangular box be x
Let the length be L
Let the height be H
Let the volume be y
The length of the rectangular box is 1 inch longer than twice the width (x)
L = 2x + 1
The Height is 5 inch
H = 5
The volume of a rectangular box is:
Volume = Length x Width x Height
y = LHx
y = (2x + 1) (5) (x)
y = 5x (2x + 1)
A and B are mutually exclusive events P(A) =0.60 and P(B)=0.30 what is P (A or B)
Answers
We know that for any number of mutually exclusive events, we have the formula:
[tex]P(A_1\cup A_2\cup A_3\cup\ldots)=P(A_1)+P(A_2)+P(A_3)+\cdots[/tex]In this case, we have that P(A)=0.60 and P(B)=0.30, then:
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)=0.60+0.30=0.90 \\ P(A\cup B)=0.90 \end{gathered}[/tex]Therefore, P(A or B) =0.90
Can you please help me with this , choices (Add,divided,exponent, multiply, square roots, subtract and N/A)
Answers
a) in term
b)subtraction
c) N/A
d) 4
Explanation
a term is a single mathematical expression , it can be a number, a variable or a combination, the terms are separated by the symbols + or -
for example:
in
[tex]ax^2+bx+c[/tex]there are 3 expression , so
Step 1
check the expression
[tex]\frac{6(5-3)^3}{12}[/tex]it has only a term ( a fractions)
so
a)the number of terms is : 1
Step 2
b)first thing to do to term 1
PEMDAS means the order of operations for mathematical expressions involving more than one operation. It stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.so
we need to P ( break the parenthesis)
to do that,
do the SUBTRACTION
[tex]\begin{gathered} \frac{6(5-3)^3}{12} \\ \frac{6(5-3)^3}{12}=\frac{6(2)^3}{12} \\ \frac{6\cdot2^3}{12} \end{gathered}[/tex]
Step 3
c) as there is not term 2
N/A
Step 4
simplify the expression: folloing the PEMDAS order
[tex]\begin{gathered} \frac{6\cdot2^3}{12}\text{ } \\ \text{Exponents} \\ \frac{6\cdot2^3}{12}\text{ =}\frac{6\cdot8}{12}\text{ } \\ \text{ Mulitiplication} \\ \frac{6\cdot8}{12}\text{ =}\frac{48}{12} \\ \text{Division} \\ \frac{48}{12}=4 \\ 4 \end{gathered}[/tex]so
d) 4
i hope this helps you
The vertex of this parabola is at (-2,5). Which of the following could be its equation? (-2,5) -5 O A. y = 3(x-2)2-5 O B. y = 3(x-2)2 + 5 O C. y= 3(x+ 2)2-5 BE E EIE O D. y=3(x + 2)2 + 5 anter
Answers
The base equation of a parabola is F(X) = X^2 + C
if we make F(X+2) it means the chart will move 2 units to the left
on the other hand, if the make F(X) + 5, it means the chart will displace 5 units upwards
As a result, from the given chart, our equation would be: y = 3(x+2)^2 + 5
the answer to this equation no steps needed for me just needed a,b,c or d
Answers
Solution
- The solution steps are given below:
[tex]\begin{gathered} y\propto\frac{1}{x^2} \\ \\ \therefore y=\frac{k}{x^2} \\ where,\text{ }k\text{ is the constant of proportionality} \\ \\ when\text{ }x=1,y=\frac{7}{4} \\ \\ \frac{7}{4}=\frac{k}{1^2} \\ \\ \therefore k=\frac{7}{4} \\ \\ \text{ Thus, we can say} \\ y=\frac{7}{4x^2} \\ \\ \text{ Thus, when }x=3,\text{ we have:} \\ y=\frac{7}{4(3^2)} \\ \\ y=\frac{7}{4\times9} \\ \\ \therefore y=\frac{7}{36} \end{gathered}[/tex]Final Answer
The answer is
[tex]y=\frac{7}{4x^2};y(3)=\frac{7}{36}\text{ \lparen OPTION C\rparen}[/tex]One type of dog treat, Barker, contains 3 oz and sells for $1.95. DogYum contains 3.25 and sells for $2.10.Which is less expensive, per ounce?A. DogYum is less expensive, per ounceB. Barker is less expensive, per ounce
Answers
Solution
- We are told that dog treats, Barker and DogYum cost $1.95 for 3 oz and $2.10 for 3.25 oz respectively and we are required to find out which is more expensive per ounce.
- In order to find the more expensive dog treat, we need to find the cost per ounce for each item. The cost per ounce is given by the formula below:
[tex]\frac{\text{Cost of dog treat (In Dollars)}}{\text{Weight of dog treat (In Oz)}}[/tex]- The dog treat with the larger cost per oz is the more expensive item.
- Thus, let us calculate the cost per oz for both items.
DogYum:
[tex]\begin{gathered} \frac{\text{Cost of DogYum}}{\text{Weight of DogYum}}=\frac{2.10}{3.25}=0.646 \\ \\ \text{Thus, the cost per oz of the DogYum treat is \$0.646/oz} \end{gathered}[/tex]Barker:
[tex]\begin{gathered} \frac{\text{ Cost of Barker}}{\text{Weight of Barker}}=\frac{1.95}{3}=0.65 \\ \\ \text{Thus, the cost per oz of the Barker treat is \$0.65/oz} \end{gathered}[/tex]- We can observe that Barker is marginally more expensive than DogYum. We can confirm this by simply subtracting the cost per oz for both treats.
[tex]\text{Barker - DogYum}=0.65-0.646=0.004[/tex]Final Answer
The answer is:
DogYum is less expensive, per ounce
i need help with question 36 (make sure to read the the information above the graph)
Answers
Given:
[tex]\begin{gathered} x+2y>6 \\ -2x+3y\leq6 \end{gathered}[/tex]Required:
To solve the given inequality by graphing.
Explanation:
The graph of the above inequality is,
Now, the solution is shaded in the graph.
Final Answer:
The solution by using the graph is,
Find the composition of transformations thatmap ABCD to EHGF.Reflect over the [? ]-axis, then translate(x+[ ], y+[ ]).Note: Enter x ory for axis.BсGH2DE124-3-2-10Enter
Answers
Let's complete the transformation from ABCD to EHGF.
Let's first determine the coordinates of the two figures.
Figure ABCD:
A : -5, 2
B : -3, 4
C : -2, 4
D : -1, 2
Figure EHGF:
E : 4, 1
H : 2, 3
G : 1, 3
F : 0, 1
Reflecting ABCD over the y - axis, we get:
P (x, y) = P' (-x, y)
For ABCD:
A : -5, 2 = A' : 5, 2
B : -3, 4 = B' : 3, 4
C: -2, 4 = C' : 2, 4
D: -1, 2 = D' : 1, 2
Let's now complete the translation,
(x + S), (y + T)
Where,
S = translation at x-axis
T = translation at y-axis
We get,
A' : 5, 2 = E : 4, 1 → S, T = 4 - 5, 1 - 2 = -1, -1
B' : 3, 4 = H : 2, 3 → S, T = 3 - 4, 3 - 4 = -1, -1
C' : 2, 4 = G : 1, 3 → S, T = 1 - 2, 3 - 4 = -1, -1
D' : 1, 2 = F: 0, 1 → S, T = 0 - 1, 1 - 2 = -1, -1
Therefore, we can say that the translation is (x + _, y + _) = (x + (-1), y + (-1)) = x - 1, y - 1
3x - 4y = 10Add a Com6x + y = 38andMediac-9% +12y = -30Save9x - 3y = 48These systems are said to be equivalent. Both of the equations in the secondsystem came from the first system somehow,Two questions: How was the first equation is the second system formed fromthe first system? And how was the second equation in the second systemformed from the first system?
Answers
First solution
[tex]\begin{gathered} \text{The first equation in the second system (Equation 2.1),} \\ \text{was formed by multiplying (Equation 1.1) by -3} \end{gathered}[/tex][tex]\begin{gathered} \text{proof:} \\ -3\text{ (3x - 4y= 10) = -9x + 12y = -30} \end{gathered}[/tex]Second solution
The second equation in the second system (Equation 2.2) was formed by adding both equations in the first system.
That is;
(Equation 2.2) = (Equation 1.1) + (Equation 1.2)
[tex]\begin{gathered} \text{proof:} \\ 3x\text{ -4y = 10 } \\ +\text{ 6x + y = 38} \\ (3x+6x)\text{ + (-4y+y) = 10+38} \\ 9x\text{ -3y = 48} \end{gathered}[/tex]