Hello! I need some help with this homework question, please? The question is posted in the image below. Q5
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
We can determine the domain and range of the function, knowing that the domain is the interval of values in x and the range is the interval of values in y.
Therefore:
[tex]\begin{gathered} D=\lbrack-5,5\rbrack \\ R=\mleft[-5,\frac{25}{17}\mright] \end{gathered}[/tex]When a function is inverted, the domain and range are inverted, therefore:
[tex]\begin{gathered} D=\mleft[-5,\frac{25}{17}\mright] \\ R=\lbrack-5,5\rbrack \end{gathered}[/tex]Which means that the inverted function goes from -5 to 25/17 in x and from -5 to 5 in y.
In addition to this we must take into account that when the inverse function is done, in most cases a reflection is made in y = x.
The only graph that meets all of the above is graph A
Related Questions
Simplify the following expression.2(0.5x - 3)2-[?]x2 – [ ]x + [ ]-
Answers
1st blank = 0.25
2nd blank = 3
3rd blank = 9
Explanation:[tex]\begin{gathered} \text{Given: (0.5x - 3)}^2 \\ \\ To\text{ simplify the expression we expand} \end{gathered}[/tex]Using distributive property:
[tex]\begin{gathered} (0.5x-3)^2\text{ = (0.5x - 3)(0.5x - 3)} \\ =\text{ 0.5x (0.5x - 3) - 3(0.5x - 3)} \\ =\text{ 0.5x(0.5x) -3(0.5x) -3(0.5x) - 3(-3)} \end{gathered}[/tex][tex]\begin{gathered} =0.25x^2\text{ - 1.5x - }1.5x\text{ + 9} \\ =0.25x^2\text{ - 3.0}x\text{ + 9} \\ =0.25x^2\text{ - 3x + 9} \\ \\ \text{first balnk = 0.25} \\ \text{second blank =3} \\ \text{third blank = 9} \end{gathered}[/tex]A ball is thrown from an initial height of 4 feet with an initial upward velocity of 23 ft/s. The ball's height h (in feet) after 1 seconds is given by the following.h=4+231-167Find all values of 1 for which the ball's height is 12 feet.Round your answer(s) to the nearest hundredth.(If there is more than one answer, use the "or" button.)Please just provide the answer my last tutor lost connection abruptly.
Answers
Answer
t = 0.59 seconds or t = 0.85 seconds
Step-by-step explanation:
[tex]\begin{gathered} Given\text{ the following equation} \\ h=4+23t-16t^2\text{ } \\ h\text{ = 12 f}eet \\ 12=4+23t-16t^2 \\ \text{Collect the like terms} \\ 12-4=23t-16t^2 \\ 8=23t-16t^2 \\ 23t-16t^2\text{ = 8} \\ -16t^2\text{ + 23t - 8 = 0} \\ \text{ Using the general formula} \\ t\text{ }=\text{ }\frac{-b\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ \text{let a = -16, b = 23, c = -8} \\ t\text{ = }\frac{-23\pm\sqrt[]{(23)^2\text{ - 4}\cdot\text{ }}(-16)\text{ x (-8)}}{2(-16)} \\ t\text{ = }\frac{-23\pm\sqrt[]{529\text{ - 512}}}{-32} \\ t\text{ = }\frac{-23\pm\sqrt[]{17}}{-32} \\ \text{t = -23+}\frac{\sqrt[]{17}}{-32}\text{ or -23-}\frac{\sqrt[]{17}}{-32} \\ t\text{ = -23 }+\text{ 4.12/-32 or t = }\frac{-23\text{ - 4.12}}{-32} \\ t\text{ = }0.59\text{ seconds or t =0.85 seconds} \end{gathered}[/tex]Therefore, t = 0.59 seconds or t = 0.85 seconds
Which of the following graphs is a polynomial function with intercepts of(-2,0), (1, 0), and (4, 0)711-15 4NO C.O D.
Answers
Explanation
We are given the following:
We are required to determine which of the following graphs is a polynomial function with intercepts of
(-2,0), (1, 0), and (4, 0).
This can be achieved by looking for the graph that crosses the x-axis at the points -2, 1 and 4.
Hence, the answer is option C.
Jackson deposited $160 a month into an account earning 7.2% compounded monthly for 12 years. He left the accumulated amount for another 3 years at the same interest rate. How much total interest did he earn?
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Using the formula for the compound interest, we have:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{ A:amount,P:principal,r:rate,n: number of times interest is compounded per year,t:time in years.} \\ A=160(1+\frac{0.072}{12})^{12\cdot15}\text{ (Replacing the values)} \\ A=160(1+0.006)^{180}\text{ (Dividing and multiplying)} \\ A=160\cdot2.935\text{ (Adding and raising the result to the power of 180)} \\ A=469.63\text{ (Multiplying)} \\ \text{Interest}=\text{ Amount - Principal=469.63}-160=309.63 \\ \text{The answer is \$309.63} \end{gathered}[/tex]triangle HXI can be mapped onto troangle PSL by a reflection If m angle H = 157 find m angle S
Answers
From the information provided, the triangle HXI can be mapped onto triangle PSL. This means the vertices of the reflected image would now have the following as same measure angles;
[tex]\begin{gathered} \angle H\cong\angle P \\ \angle X\cong\angle S \\ \angle I\cong\angle L \end{gathered}[/tex]Measure of angle S cannot be determined from the information provided because there is insufficient information given to determine the measure of angle X, hence the angle congruent to it (angle S) likewise cannot be determined.
gB - N³B = d what does B equal?
Answers
Answer:
[tex]b \: = \frac{d}{(g - {n}^{3} )} [/tex]
Jeremy Sold x tickets for a fundraiser. Kelly sold twice as many tickets as Jeremy Altogether. Jeremy and Kelly sold 192 tickets which equation could be used to determine how many tickets Jeremy sold?
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If x represents Jeremy's sold tickets, then the expression 2x + x represents the part Kelly sold twice as many tickets as Jeremy.
If the sold 192 tickets together, then the expression is 3x = 192.
Hence, the answer is B.The tax on a property with an assessed value of $63,000 is $550. Using a proportion, findthe tax on a property with an assessed value of $94,000. Round to two decimal places
Answers
Answer:
$820.63
Explanation:
For two different properties, we have the following:
• Assessed Value = $63,000
,• Tax = $550
• Assessed Value = $94,000
,• Tax = $x
Using a proportion, we have:
[tex]\begin{gathered} \frac{63,000}{94,000}=\frac{550}{x} \\ \text{Cross multiply} \\ 63,000x=94,000\times500 \\ x=\frac{94,000\times500}{63,000} \\ x=\$820.63 \end{gathered}[/tex]The tax on a property with an assessed value of $94,000 is $820.63 (correct to 2 decimal places).
AB is a median of a triangle true or false
Answers
To answer this question, first we need to understand the definition of a median of a triangle.
A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex.
AB is a segment drawn from the vertex A, to the point B, but B is not the midpoint of the base of this triangle(the midpoint divides the segment into two equal parts, and since one part is 7 and the other is 8, B is not the midpoint
find the perimeter of the triangle whose vertices are (-10,-3), (2,-3), and (2,2). write the exact answer. do not round.
Answers
We have to calculate the perimeter of a triangle of which we know the vertices.
The perimeter is the sum of the length of the three sides, which can be calculated as the distance between the vertices.
The vertices are V1=(-10,-3), V2=(2,-3), and V3=(2,2).
We then calculate the distance between each of the vertices.
We start with V1 and V2:
[tex]\begin{gathered} d_{12}=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ d_{12}=\sqrt[]{(-3-(-3))^2+(2-(-10)^2} \\ d_{12}=\sqrt[]{(-3+3)^2+(2+10)^2} \\ d_{12}=\sqrt[]{0^2+12^2} \\ d_{12}=12 \end{gathered}[/tex]We know calculate the distance between V1 and V3:
[tex]\begin{gathered} d_{13}=\sqrt[]{(y_3-y_1)^2+(x_3-x_1)^2} \\ d_{13}=\sqrt[]{(2-(-3))^2+(2-(-10))^2} \\ d_{13}=\sqrt[]{5^2+12^2} \\ d_{13}=\sqrt[]{25+144} \\ d_{13}=\sqrt[]{169} \\ d_{13}=13 \end{gathered}[/tex]Finally, we calculate the distance between V1 and V3:
[tex]\begin{gathered} d_{23}=\sqrt[]{(y_3-y_2)^2+(x_3-x_2)^2} \\ d_{23}=\sqrt[]{(2-(-3))^2+(2-2)^2} \\ d_{23}=\sqrt[]{5^2+0^2} \\ d_{23}=5 \end{gathered}[/tex]Then, the perimeter can be calcualted as:
[tex]\begin{gathered} P=d_{12}+d_{13}+d_{23} \\ P=12+13+5 \\ P=30 \end{gathered}[/tex]Answer: the perimeter is 30 units.
the sum of three consecutive integers is 219. find The largest of the three integers.
Answers
Let n be the lesser number of the three. Therefore,
[tex]n+(n+1)+(n+2)=219[/tex]Solving for n,
[tex]\begin{gathered} \Rightarrow3n+3=219 \\ \Rightarrow3n=216 \\ \Rightarrow n=72 \end{gathered}[/tex]Then, the three numbers are 72, 73, and 74. The answer is 74
When a scientist conducted a genetics experiments with peas, one sample of offspring consisted of 953 peas, with 746 of them having red flowers. If we assume, as the scientist did,
that under these circumstances, there is a 3 / 4 probability that a pea will have a red flower, we would expect that 714.75 (or about 715) of the peas would have red flowers, so the result
of 746 peas with red flowers is more than expected.
a. If the scientist's assumed probability is correct, find the probability of getting 746 or more peas with red flowers.
b. Is 746 peas with red flowers significantly high?
c. What do these results suggest about the scientist's assumption that 3 / 4 of peas will have red flowers?
a. If the scientist's assumed probability is correct, the probability of getting 746 or more peas with red flowers is
Answers
a. 74.99% probability of getting 746 or more peas with red flowers.
b. Since Z < 2, 746 peas with red flowers is not significantly high.
c. Since 746 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.
Given,
953 peas in sample with 746 of them having red flower
Scientist's assumption;
Since there is a 3/4 chance that a pea will have a red blossom, we would anticipate 714.75 (or roughly 715) of the peas to do so; hence, the finding of 746 peas with red flowers is higher than we had anticipated.
Here,
Binomial distribution:
Probability of x successes on n trials, with p probability.
Normal distribution:
In a normal distribution with mean μ and standard deviation σ, the z-score of a measure X is given by:
Z = (X - μ) / σ
If np ≥ 10 and n (1 - p) ≥ 10 , the binomial distribution can be approximated to the normal with:
μ = np
σ = [tex]\sqrt{np(1-p)}[/tex]
Here,
n = 953 and p = 3/4 = 0.75
Lets see,
μ = np = 953 x 0.75 = 714.75
σ = [tex]\sqrt{np(1-p)}[/tex] = [tex]\sqrt{714.75 . (1 - 0.75)}[/tex] = √714.5 = 26.73
a. The probability of getting 746 or more peas with red flowers.
Using continuity correction, this probability is P(X ≥ 746 - 0.5) = P(X ≥ 745.5) , which is 1 subtracted by the p-value of Z when X = 745.5.
Then:
Z = (X - μ) / σ = (745.5 - 714.75) / 26.73 = 30.75 / 26.73 = 1.150
The p value of z score 1.150 is 0.2501
1 -0.2501 = 0.7499
0.7499 = 74.99% probability of getting 746 or more peas with red flowers.
b. Is 746 red-flowering peas noticeably high
Since Z < 2, 746 peas with red flowers is not significantly high.
c. What do these findings say about the researcher's prediction that 3/4 pea plants will have red flowers?
Since 746 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.
Learn more about normal distribution here;
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You pick a card at random.
1 2 3 4
What is P(factor of 24)?
Write your answer as a percentage rounded to the nearest tenth
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Answer:
100%
Step-by-step explanation:
All of the numbers are factors of 24. So, picking a factor of 24 is guaranteed, so the probability is 1.
This is equal to 100%.
help meeeeeeeeee pleaseee !!!!!
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The values for the composition of the functions are:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3x² + 15
How to Evaluate the Composition of Functions?To evaluate the composition of a function, the first thing to do is to evaluate the inner function, then use the output as an input to evaluate the outer function of the composition.
Given the following functions:
f(x) = x² + 5
g(x) = 3x
We are required to find (f o g)(x) and (g o f)(x).
To find (f o g)(x), replace g(x) for x in the outer function f(x):
(f o g)(x) = (3x)² + 5
(f o g)(x) = 9x² + 5
To find (g o f)(x), replace f(x) for x in the outer function g(x):
(g o f)(x) = 3(x² + 5)
(g o f)(x) = 3x² + 15
Learn more about composition of functions on:
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suppose that the time required to complete a 1040r tax form is normally distributed with a mean of 100 minutes and a standard deviation of 15 minutes. what proportion of 1040r tax forms will be completed in less than 77 minutes? round your answer to at least four decimal places.
Answers
The proportion of 1040r tax forms completed in less than 77 minutes = 0.06301
How to find the proportion of the tax forms?
The time required to complete a 1040r tax form = normally distributed
Mean = [tex]\mu[/tex] = 100 minutes
Standard deviation = [tex]\sigma[/tex] = 15 minutes
The proportion of 1040r tax forms completed in less than 77 minutes is given by ,
P( X< 77 ) = P ( Z < [tex]\frac{77-100}{15}[/tex] )
= P( Z < - 1.53 )
=0.06301
Cumulative probability in the normal distribution =0.06301 or 6.301%
What is normal distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.The natural and social sciences frequently utilize normal distributions to describe real-valued random variables whose distributions are unknown, which is why normal distributions are essential in statistics. Not all symmetrical distributions are normal, but all normal distributions are symmetrical.Natural occurrences frequently resemble the normal distribution.A bell curve is another name for a normal distribution.To learn more about normal distribution, refer:
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What is the solution to x^2 – 9x < –8?A. x < 1 or x > 8B. x < –8 or x > 1C. 1 < x < 8D. –8 < x < 1
Answers
INFORMATION:
We have the next inequality
[tex]x^2-9x<-8[/tex]And we must find its solution
STEP BY STEP EXPLANATION:
To solve it, we must:
1. Move all terms aside
[tex]x^2-9x+8<0[/tex]2. Factor x^2-9x+8
[tex](x-8)(x-1)<0[/tex]3. Solve for x
[tex]x=8\text{ or }x=1[/tex]4. From the values of x, we have these 3 intervals to test
[tex]\begin{gathered} x<1 \\ 18 \end{gathered}[/tex]5. Choose a test point for each interval
For the interval x < 1:
[tex]\begin{gathered} \text{ Using x }=0, \\ 0^2-9(0)<-8 \\ 0<-8 \end{gathered}[/tex]which is false. So, the interval is discarded.
For the interval 1 < x < 8:
[tex]\begin{gathered} \text{ Using x }=2, \\ 2^2-9(2)<-8 \\ -14<-8 \end{gathered}[/tex]which is true. So, the interval is maintained
For the interval x > 8:
[tex]\begin{gathered} \text{ Using x = 9,} \\ 9^2-9(9)<-8 \\ 0<-8 \end{gathered}[/tex]which is false. So, the interval is discarded.
Finally, the solution would be the interval that was maintained: 1 < x < 8.
ANSWER:
C. 1 < x < 8
Answer:
C. 1 < x < 8
Step-by-step explanation:
x² - 9x < -8
we will suppose some values for x to check which values will satisfy this inequality:
for x = 1
1(1-9) < -8 which is wrong
for x = 2
2(2-9) < -8 this is satisfying the inequality
for x = 8
8(8-9) < -8 which is wrong
let's take any negative value now,
let x = -2
-2(-2-9) < -8 which is wrong
thus x is the positive value which will always be greater than 1 and less than 8 for the given inequality.
To beA train started from City A to City B at 13:30. The train travelledat an average speed of 180 miles per hour. If the distancebetween City A and City B is 756 miles, at what time did thetrain arrive at City B? Give your answer in a 24-hour clockformat, such as 19:00. DEnter the answer
Answers
Remember that
the speed is equal to divide the distance by the time
speed=d/t
solve for t
t=d/speed
we have
d=756 miles
speed=180 miles per hour
substitute
t=756/180
t=4.2 hours
4.2 hours=4 hours +0.20 hours
Convert 0.20 hours to minutes
Multiply by 60
0.20 h=0.20*60=12 minutes
so
4.2 hours=4 h 12 min
therefore
A train started from City A to City B at 13:30.
13:30+ 4h 12 min=17:42 hrs
35* 35. Which of the following values for r suggests that one variable causes another? A. -0.7 B. O C. 0.9 D. None of the above
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The correlation coefficient r indicates if two variables are or not dependent. If r is close to 1, then one variable causes the other one. From the options, a value of 0.9 suggests that one variable causes another
Mrs. Smith has 12 times as many markers as colored pencils. The total number of markers and colored pencils is 78. How many markers does Mrs. Smith have?ok...answers given so far are not helpful in explaining process.
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Let:
x = Colored markers
y =
What is the y-intercept of the line that passes through the point (4,-9) with a slope of -1/2
Answers
Answer:
The y-intercept b for the derived equation is;
[tex]b=-7[/tex]Explanation:
Given that the line passes through the point (4,-9) and has a slope of -1/2;
[tex]\begin{gathered} \text{slope m=-}\frac{1}{2} \\ \text{ point (4,-9)} \end{gathered}[/tex]Applying the point-slope form of linear equation;
[tex]y-y_1=m(x-x_1)[/tex]substituting the slope and the given point;
[tex]\begin{gathered} y-(-9)=-\frac{1}{2}(x-4) \\ y+9=-\frac{1}{2}x+\frac{4}{2} \\ y+9=-\frac{x}{2}+2 \\ y=-\frac{x}{2}+2-9 \\ y=-\frac{x}{2}-7 \end{gathered}[/tex]Comparing it to the slope intercept form of linear equation;
[tex]y=mx+b[/tex]where;
m = slope
and b = y-intercept
Therefore, the y-intercept b for the derived equation is;
[tex]b=-7[/tex]Question 3 4.5 pts At the honor roll party, students had the choice of cheese or pepperoni pizza and coke or sprite. Of the 125 students that made the honor roll 64% had cheese pizza. There were 48 students that had cheese pizza and a coke. 5 more students chose to have a Coke rather than Sprite. Complete the table below.
Answers
The table would look like this;
We are told that Of the 125 students that made the honor roll 64% had cheese pizza.
64% of 125 is 80 students, therefore, 80 students in total had cheese pizza.
Let's fill that in.
We now know that those who had pepperoni pizza are 125 - 80 = 45 in number.
There were 48 students that had cheese pizza and a coke, let's fill that in too, we have.
This means that the number of students that had a cheese and sprite is 80 - 48 = 32 students.
We are also told that 5 more students chose to have a coke than a sprite.
Let the total number that chose coke be x.
Then the total who chose sprite would be x - 5.
But these total must add up to 125.
So;
[tex]\begin{gathered} x+x-5=125 \\ 2x-5=125 \\ 2x=130 \\ x=\frac{130}{2}=65 \\ x-5\text{ = 60} \end{gathered}[/tex]Therefore, 65 students took coke in total and 60 took sprite, let's fill that in too.
We can now fill in the pepperoni column.
For pepperoni and coke, we subtract 48 from 65 to obtain 17
For pepperoni and sprite, we subtract 32 from 60 to obtain 28
ii. The joint relative frequency of the students who had a sprite and pepperoni pizza.
From the table, the joint relative frequency of those who had a sprite and a pepperoni pizza is
[tex]\begin{gathered} \frac{28}{45} \\ \end{gathered}[/tex]i.e 28/45 or 0.6 of those who had pepperoni pizza, took sprite.
determine if the following equations represent a linear function if so write it in standard form Ax+By=C9x+5y=102y+4=6x
Answers
9x + 5y = 10
is a linear equation because all variables are raised to exponent 1.
This equation is already written in standard form (A = 9, B = 5, C = 10)
2y + 4 = 6x
is a linear equation because all variables are raised to exponent 1.
Subtracting 2y at both sides:
2y + 4 - 2y= 6x - 2y
4 = 6x - 2y
or
6x - 2y = 4
which is in standard form (A = 6, B = -2, C = 4)
May someone please help me solve this and explain? thanks:)
Answers
Given:
Mean,
[tex]\mu=46[/tex]Standard deviation,
[tex]\sigma=7[/tex]To find: The indicated values
Explanation:
The values are calculated as follows,
[tex]\begin{gathered} \mu-3\sigma=46-3(7) \\ =46-21 \\ =25 \\ \mu-2\sigma=46-2(7) \\ =46-14 \\ =32 \\ \mu-\sigma=46-7 \\ =39 \\ \mu=46 \\ \mu+\sigma=46+7 \\ =53 \\ \mu+2\sigma=46+2(7) \\ =46+14 \\ =60 \\ \mu+3\sigma=46+3(7) \\ =46+21 \\ =67 \end{gathered}[/tex]Final answer: The values are,
[tex]\begin{gathered} \mu-3\sigma=25 \\ \mu-2\sigma=32 \\ \mu-\sigma=39 \\ \mu=46 \\ \mu+\sigma=53 \\ \mu+2\sigma=60 \\ \mu+3\sigma=67 \end{gathered}[/tex]Type the correct answer in each box. Use numerals instead of words.Consider the quadratic equation x2 + 10x + 27 = 0.Completing the square leads to the equivalent equation (x +__ )^2 = __
Answers
Given:
[tex]x^2+10x+27=0[/tex]Required:
To complete the square that leads to the equivalent equation (x +__ )^2 = __.
Explanation:
Consider
[tex]\begin{gathered} x^2+10x+27=0 \\ \\ x^2+10x+25+2=0 \\ \\ x^2+10x+25=-2 \\ \\ x^2+5x+5x+25=-2 \\ \\ x(x+5)+5(x+5)=-2 \\ \\ (x+5)(x+5)=-2 \\ \\ (x+5)^2=-2 \end{gathered}[/tex]Final Answer:
[tex](x+5)^{2}=-2[/tex]Which pair of numbers are not opposites?
47 and- 47
74 and -74
|4| and -4
47 and |-47|
Answers
FOR THE PAIRS TO BE OPPOSITE IT MEANS THE NUMBERS SHOULD ALSO CONTRAST IN SIGNS.
47 AND -47 ARE OPPOSITE
74 AND - 74 ARE OPPOSITE
|4|=4 AND -4 ARR OPPOSITE
47 AND |-47|=47 ARE NOT OPPOSITE BECAUSE THEY BOTH HAVE THE SAME SIGNS.
THE LAST OPTION IS THE ANSWER.
find the product of 1/1728.
Answers
The answer is 12
Because 12x12x12 = 1728
a bottle of juice is 2/3 full the bottle contains 4/5 cup of juice write division problem that represents the capacity of the bottle
Answers
Answer:
x = ( 6 / 5 )y
Step-by-step explanation:
Identify the equaiton.
let x = bottle;
let y = cups;
( 2 / 3 )x = ( 4 / 5 )y;
Multiply both sides by ( 3 / 2 ).
( 3 / 2 )( 2 / 3 )x = ( 3 / 2 )( 4 / 5 )y;
x = ( 12 / 10 )y;
Write the fraction in its simplest form.
x = ( 6 / 5 )y;
It takes 1 + ( 1 / 5 ) of a cup to fill the bottle.
Ethan found the spinner shownbelow and planned to use it for agame.2332453235After studying the spinner beforeusing it, Ethan correctly concludedthat the spinner was-A least likely to land on 2B least likely to land on 5C most likely to land on 3D most likely to land on 2
Answers
we have that
the number 3 appears 4 times
so
answer is
option C most likely to land on 3
please help this is for my study guide thanks! (find volume) (don't round)
Answers
100,000π ft³
1) Let's find the volume of that Cylinder using this formula:
[tex]V=\pi r^2h[/tex]Note that the volume is the area of the base (a circle) times the height
2) Also, notice that in the picture we have the diameter, the radius is half the Diameter:
[tex]\begin{gathered} V=\pi\cdot(50)^2\cdot40 \\ V=100000\pi^{} \end{gathered}[/tex]3) So the volume is 100,000π ft³
ABC with coordinates (1.3), B.4.5), and C15,2), what are the coordinates of ABC after the glide reflection described by t (-1,1) R y-axis?
Answers
Answer:
A'(0,4)
B'(-3,6)
C(-4,3)
Step-by-step explanation:
A glide reflection is the combination of a translation with a rotation.
In this question:
T(-1,1): This means that the translation is given by:
(x,y) -> (x-1,y+1)
Rotation: Around the y-axis. This means that:
(x,y) -> (-x,y)
The triangle has the following coordinates:
A(1,3), B(4,5), C(5,2)
Applying the translation:
(x,y) -> (x-1,y+1)
A(1,3) -> (1-1,3+1) = (0,4)
B(4,5) -> (4-1,5+1) = (3,6)
C(5,2) -> (5-1, 2+1) = (4,3)
Rotation over the y-axis:
(x,y)->(-x,y)
A'(0,4)
B'(-3,6)
C(-4,3)
