Answer:
-8 = x
Step-by-step explanation:
-15 = 2x + 1
-1 - 1 Subtract 1 from both sides
-16 = 2x Divide both sides by 2
-8 = x
To make sure this answer is correct, plug it into the equation to see if it works.
-15 = 2(-8) + 1 Multiply
-15 = -16 + 1 Add
-15 = -15
Solve x^2 + 5x+6 = 0
Answer:
X=-2or,-3
Step-by-step explanation:
X^2+5x+6=0
or,x^2+(2+3)x+6=0
or,x^2+2x+3x+6=0
or,x(x+2)+3(x+2)=0
or,(x+3) (x+2)=0
Either,
x+3=0 x+2=0
or,x=-3 or,x=-2
Therefore,the value if x is -2 or -3 .
I HOPE IT WILL HELP YOU
Find the missing length, c, in the right triangle below. Round to the nearest tenth, if necessary. a. 76.3 in. b. 5.5 in. c. 3.5 in. d. 8.7 in.
Answer:
i think it's c.)3.5 i may be wrong
Step-by-step explanation:
Martin uses 5/8 Of a gallon of paint to cover 4/5 Of a wall.What is the unit rate in which Martin paints in walls per gallon
Answer:
32/25 walls per gallon.
Step-by-step explanation:
Martin uses 5/8 Of a gallon of paint to cover 4/5 Of a wall
Hence 1 gallon would be 4/5÷5/8=
4/5 × 8/5= 32/25 walls per gallon.
Find all solutions of the equation in the interval [0, 2π).
Answer:
x = pi/6
x = 11pi/6
x = 5pi/6
x =7pi/6
Step-by-step explanation:
2 sec^2 (x) + tan ^2 (x) -3 =0
We know tan^2(x) = sec^2 (x) -1
2 sec^2 (x) +sec^2(x) -1 -3 =0
Combine like terms
3 sec^2(x) -4 = 0
Add 4 to each side
3 sec^2 (x) = 4
Divide by 3
sec^2 (x) = 4/3
Take the square root of each side
sqrt(sec^2 (x)) = ±sqrt(4/3)
sec(x) = ±sqrt(4)/sqrt(3)
sec(x) = ±2 /sqrt(3)
Take the inverse sec on each side
sec^-1 sec(x) = sec^-1(±2 /sqrt(3))
x = pi/6 + 2 pi n where n is an integer
x = 11pi/6 + 2 pi n
x = 5pi/6 + 2 pi n
x =7pi/6 + 2 pi n
We only want the solutions between 0 and 2pi
In a data distribution, the first quartile, the median and the means are 30.8, 48.5 and 42.0 respectively. If the coefficient skewness is −0.38
a) What is the approximate value of the third quartile (Q3 ), correct to 2 decimal places.
b)What is the approximate value of the variance, correct to the nearest whole number
Answer:
a) The third quartile Q₃ = 56.45
b) Variance [tex]\mathbf{ \sigma^2 =2633.31}[/tex]
Step-by-step explanation:
Given that :
[tex]Q_1[/tex] = 30.8
Median [tex]Q_2[/tex] = 48.5
Mean = 42
a) The mean is less than median; thus the expression showing the coefficient of skewness is given by the formula :
[tex]SK = \dfrac{Q_3+Q_1-2Q_2}{Q_3-Q_1}[/tex]
[tex]-0.38 = \dfrac{Q_3+30.8-2(48.5)}{Q_3-30.8}[/tex]
[tex]-0.38Q_3 + 11.704 = Q_3 +30.8 - 97[/tex]
[tex]1.38Q_3 = 77.904[/tex]
Divide both sides by 1.38
[tex]Q_3 = 56.45[/tex]
b) The objective here is to determine the approximate value of the variance;
Using the relation
[tex]SK_p = \dfrac{Mean- (3*Median-2 *Mean) }{\sigma}[/tex]
[tex]-0.38= \dfrac{42- (3 *48.5-2*42) }{\sigma}[/tex]
[tex]-0.38= \dfrac{(-19.5) }{\sigma}[/tex]
[tex]-0.38* \sigma = {(-19.5) }{}[/tex]
[tex]\sigma =\dfrac {(-19.5) }{-0.38 }[/tex]
[tex]\sigma =51.32[/tex]
Variance = [tex]\sigma^2 =51.32^2[/tex]
[tex]\mathbf{ \sigma^2 =2633.31}[/tex]
This area model represents the product of 27 and another number. What is the
other number?
20
600
160
210
56
60
38
Answer:
The other number is 25
See explanation below
Step-by-step explanation:
The question is incomplete. Since we were not given the area or the answer to the multiplication of the two numbers, I would show you how to multiply two 2-digit numbers using the area model.
Let's assume we want to find the area model of 27 and 25.
We would write the multiplicands(the two digit numbers) in expanded form as tens and ones.
So, 27 becomes 20 and 7
25 becomes 20 and 5.
Then draw a box that is 2 by 2 grid ( 2 rows and 2 columns)
Then multiply the 1st column by the 1st row, 2nd column by 2nd row. Afterwards sum the values obtained together.
For the question: 25×27
20×20, 20×5, 20×7, 5÷7
400, 100, 140, 35
Their sum = 400 + 100+ 140 +35
= 675
See attachment for diagram.
In this question only one of the numbers is given. The area of the two numbers wasn't given.
Assuming the area of the two numbers was given and one if the numbers was also given, we would apply area model of division.
Example: Area of the both numbers = 675, the other number given = 27. Find the other number.
The area model of solving division is gotten from finding the area of a rectangle.
Since Area of a rectangle = Length × Width
Then the the value of length would be greater than value of breadth.
675÷27 = 25
So break it down to 20 and 5. Hence You divide first by 20 in first column. Then divide the remainder (135) by 5 in second column.
See diagram for explanation
Please help! Correct answer only, please! Which of the following is a Hamiltonian Circuit, beginning at vertex A, for the given graph? A. ADBCA B. ABCDA C. ACBDA D. all of the above
Answer: d) all of the above
Step-by-step explanation:
A Hamiltonian circuit is where you follow the path of the circuit touching EVERY VERTEX only ONE time.
Notice that each path given allows every vertex to be touched and each vertex is touched only once.
Therefore, all the options given are valid paths for a Hamiltonian circuit.
Consider the probability that at least 91 out of 155 students will pass their college placement exams. Assume the probability that a given student will pass their college placement exam is 59%.Approximate the probability using the normal distribution. Round your answer to four decimal places.
Answer:
0.5616 = 56.16% probability that at least 91 out of 155 students will pass their college placement exams.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 155, p = 0.59[/tex]
So
[tex]\mu = E(X) = np = 155*0.59 = 91.45[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{155*0.59*0.41} = 6.12[/tex]
Probability that at least 91 out of 155 students will pass their college placement exams.
Using continuity correction, this is [tex]P(X \geq 91 - 0.5) = P(X \geq 90.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 90.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{90.5 - 91.45}{6.12}[/tex]
[tex]Z = -0.155[/tex]
[tex]Z = -0.155[/tex] has a pvalue of 0.4384
1 - 0.4384 = 0.5616
0.5616 = 56.16% probability that at least 91 out of 155 students will pass their college placement exams.
Help me do it please, I'm stuck.
Answer:
2/1
Step-by-step explanation:
So you want to find a point where the line crosses a intersection near perfectly, point A (1,3) and then a second point, B (2,5)
and then you count up from point a, on the Y axis until you are even with the second point, that number is your RISE
it is 2
then you just count over to point B from that spot where you counted up. RUN TO IT
1
so it is 2/1 or just 2
((point (0,1) would have worked too))
What is the factorization of the trinomial below?
x^3- 12x^2 + 35x
Answer:
Step-by-step explanation:
x • (x - 5) • (x - 7)
Answer:
x(x-5)(x-7)
Step-by-step explanation:
x³ - 12x² + 35x
x(x² - 12x + 35)
x(x-5)(x-7)
(1,6) and (2,3) are on line?
Answer:
y = - 3x + 9 or (y - 6) = - 3(x - 1)
Step-by-step explanation:
I'm assuming you are looking for the equation of the line.
First, let's find the slope of the line, which we use equation (y1-y2) / (x1-x2)
x1: 1 x2: 2
y1: 6 y2: 3
(6-3) / (1-2) = 3 / -1 = -3
The slope of the line is -3.
The equation for slope-intercept form is y = mx + b, where m is slope and b is the y - intercept.
y = -3x+b
Now substitute a set of points in (any coordinates work). I'll use (1, 6)
6 = -3(1)+b
6 = - 3 + b
b = 9
So our equation in slope intercept form is y = - 3x + 9
You can also write this in point slope form, (y-y1) = m (x-x1) m is still slope
(y - 6) = - 3(x - 1)
An Archer shoots an arrow horizontally at 250 feet per second. The bullseye on the target and the arrow are initially at the same height. If the target is 60 feet from the archer, how far below the bullseye (in feet) will the arrow hit the target
Answer:
1.84feetStep-by-step explanation:
Using the formula for finding range in projectile, Since range is the distance covered in the horizontal direction;
Range [tex]R = U\sqrt{\frac{H}{g} }[/tex]
U is the velocity of the arrow
H is the maximum height reached = distance below the bullseye reached by the arrow.
R is the horizontal distance covered i.e the distance of the target from the archer.
g is the acceleration due to gravity.
Given R = 60ft, U = 250ft/s, g = 32ft/s H = ?
On substitution,
[tex]60 = 250\sqrt{\frac{H}{32}} \\\frac{60}{250} = \sqrt{\frac{H}{32}}\\\frac{6}{25} = \sqrt{\frac{H}{32}[/tex]
Squaring both sides we have;
[tex](\frac{6}{25} )^{2} = (\sqrt{\frac{H}{32} } )^{2} \\\frac{36}{625} = \frac{H}{32} \\625H = 36*32\\H = \frac{36*32}{625} \\H = 1.84feet[/tex]
The arrow will hit the target 1.84feet below the bullseye.
Answer:
8.7
Step-by-step explanation:
on edge . You're welcome
Between what two integers is square root 54?
Answer:
7 and 8
Step-by-step explanation:
54 is between 7^2 = 49 and 8^2 = 64.
The square roots have the same relationship.
49 < 54 < 64
√49 < √54 < √64
7 < √54 < 8
Olivia invested $2,400 in an account paying an interest rate of 4.6\% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $3,550 ?
Answer:
8.5
Step-by-step explanation:
For continuous compounding, the account value formula is ...
A = Pe^(rt)
where P is the invested amount, r is the annual interest rate, and t is the number of years. We want to find t when ...
3550 = 2400e^(.046t)
ln(355/240) = 0.046t
t = ln(355/240)/0.046 ≈ 8.5
It will take 8.5 years for the value to reach $3550.
A single card is drawn at random from a standard 52 card check. Work out in its simplest form
Answer:
1/52
Step-by-step explanation:
Want Brainliest? Get this correct , Which of the two functions below has the smallest minimum y-value?
Answer:
B. g(x)
Step-by-step explanation:
g(x) is a function of odd degree, so will tend toward negative infinity as an extreme value.
f(x) is an even-degree function with a positive leading coefficient. Its minimum value is -2.
g(x) has the smallest minimum value
No-Toxic-Toys currently has $400,000 of equity and is planning an $160,000 expansion to meet increasing demand for its product. The company currently earns $140,000 in net income, and the expansion will yield $70,000 in additional income before any interest expense.
The company has three options: (1) do not expand, (2) expand and issue $160,000 in debt that requires payments of 9% annual interest, or (3) expand and raise $160,000 from equity financing. For each option, compute (a) net income and (b) return on equity (Net Income ÷ Equity). Ignore any income tax effects. (Round "Return on equity" to 1 decimal place.)
Answer:
Down below
Step-by-step explanation:
1. It does not expanda. Net income= $100,000 (as given in the question)
b. Return on equity= (net income)/(shareholder’s equity)
Shareholder’s equity= $400,000
Thus return on equity= 100000/400000 = 0.25 or 25%
2. It expands and issue $160,000 in debt
a. Net income= $100000 + 50000 – 12800 (debt interest 8% of $160000)
= $137,200
b. Return on equity= (net income)/(shareholder’s equity)
= 137200/400000
=0.343 or 34.3%
3. It expands and raises equity of $160000
a. Net Income= $100000 + 50000
= $150000
b. Return on equity= (net income)/(shareholder’s equity)
= 150000/(400000 + 160000)
Where ($560,000) 400000 + 160000 is shareholder’s equity
= 0.27 or 27%
Circle V is shown. Line segment T V is a radius with length 14 feet. In circle V, r = 14ft. What is the area of circle V? 14Pi feet squared 28Pi feet squared 49Pi feet squared 196Pi feet squared
Answer: The area of circle V is 196π ft² (196Pi feet squared)
Step-by-step explanation:
From the equation for area of a circle,
A = πr²
Where A is the area of the circle
r is the radius of the circle
In Circle V, the radius, r of the circle is 14 feet
That is,
r = 14ft
Hence, Area is
A = π × (14ft)²
A = π × 14ft × 14ft
A = 196π ft²
Hence, the area of circle V is 196π ft² (196Pi feet squared)
Answer:
The answer is D on Edge 2020
Step-by-step explanation:
I did the Quiz
Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Stacy spins the pointer 120 times and records the results. The pointer lands 30 times on a section numbered 2, 19 times on 3, 25 times on 4, 29 times on 5, and 17 times on 6.
Write a probability model for this experiment, and use the probability model to predict how many times Stacy would spin a 6 if she spun 50 times. Give the probabilities as decimals, rounded to 2 decimal places.
Spinning 2:
Spinning 3:
Spinning 4:
Spinning 5:
Spinning 6:
Stacy would spin a 6 approximately
times in 50 tries.
Answer:
To compute the probabilities, just divide the number of times a number was landed by the total amount of outcomes.
Spinning 2: 30/120 = 0.25
Spinning 3: 19/120 = 0.16
Spinning 4: 25/120 = 0.21
Spinning 5: 29/120 = 0.24
Spinning 6: 17/120 = 0.14
Stacy would spin a 6 approximately 0.14*50 = 7 times in 50 tries.
What is the length of a football
Answer: 10.5 to 11.5 inches
Answer:
10.5 to 11.5 inches
Step-by-step explanation:
Please answer this correctly
Answer:
left, if looking from person's point of view
Step-by-step explanation:
Answer:
It would be A
Step-by-step explanation:
If you cut off the overlapping cubes, you get the image on A.
The time it takes for a planet to complete its orbit around a particular star is called the? planet's sidereal year. The sidereal year of a planet is related to the distance the planet is from the star. The accompanying data show the distances of the planets from a particular star and their sidereal years. Complete parts? (a) through? (e).
I figured out what
(a) is already.
(b) Determine the correlation between distance and sidereal year.
(c) Compute the? least-squares regression line.
(d) Plot the residuals against the distance from the star.
(e) Do you think the? least-squares regression line is a good? model?
Planet
Distance from the? Star, x?(millions of? miles)
Sidereal? Year, y
Planet 1
36
0.22
Planet 2
67
0.62
Planet 3
93
1.00
Planet 4
142
1.86
Planet 5
483
11.8
Planet 6
887
29.5
Planet 7
? 1,785
84.0
Planet 8
? 2,797
165.0
Planet 9
?3,675
248.0
Answer:
(a) See below
(b) r = 0.9879
(c) y = -12.629 + 0.0654x
(d) See below
(e) No.
Step-by-step explanation:
(a) Plot the data
I used Excel to plot your data and got the graph in Fig 1 below.
(b) Correlation coefficient
One formula for the correlation coefficient is
[tex]r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}[/tex]
The calculation is not difficult, but it is tedious.
(i) Calculate the intermediate numbers
We can display them in a table.
x y xy x² y²
36 0.22 7.92 1296 0.05
67 0.62 42.21 4489 0.40
93 1.00 93.00 20164 3.46
433 11.8 5699.4 233289 139.24
887 29.3 25989.1 786769 858.49
1785 82.0 146370 3186225 6724
2797 163.0 455911 7823209 26569
3675 248.0 911400 13505625 61504
9965 537.81 1545776.75 25569715 95799.63
(ii) Calculate the correlation coefficient
[tex]r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{9\times 1545776.75 - 9965\times 537.81}{\sqrt{[9\times 25569715 -9965^{2}][9\times 95799.63 - 537.81^{2}]}} \approx \mathbf{0.9879}[/tex]
(c) Regression line
The equation for the regression line is
y = a + bx where
[tex]a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\= \dfrac{537.81\times 25569715 - 9965 \times 1545776.75}{9\times 25569715 - 9965^{2}} \approx \mathbf{-12.629}\\\\b = \dfrac{n \sum xy - \sum x \sum y}{n\sum x^{2}- \left (\sum x\right )^{2}} - \dfrac{9\times 1545776.75 - 9965 \times 537.81}{9\times 25569715 - 9965^{2}} \approx\mathbf{0.0654}\\\\\\\text{The equation for the regression line is $\large \boxed{\mathbf{y = -12.629 + 0.0654x}}$}[/tex]
(d) Residuals
Insert the values of x into the regression equation to get the estimated values of y.
Then take the difference between the actual and estimated values to get the residuals.
x y Estimated Residual
36 0.22 -10 10
67 0.62 -8 9
93 1.00 -7 8
142 1.86 -3 5
433 11.8 19 - 7
887 29.3 45 -16
1785 82.0 104 -22
2797 163.0 170 - 7
3675 248.0 228 20
(e) Suitability of regression line
A linear model would have the residuals scattered randomly above and below a horizontal line.
Instead, they appear to lie along a parabola (Fig. 2).
This suggests that linear regression is not a good model for the data.
A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard deviation of 1.12 liters. How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval
Answer:
At least 832 teenargers must be interviewed.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval
At least n teenargers must be interviewed.
n is found when M = 0.1.
We have that [tex]\sigma = 1.12[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.1 = 2.575*\frac{1.12}{\sqrt{n}}[/tex]
[tex]0.1\sqrt{n} = 2.575*1.12[/tex]
[tex]\sqrt{n} = \frac{2.575*1.12}{0.1}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.575*1.12}{0.1})^{2}[/tex]
[tex]n = 831.7[/tex]
Rounding up
At least 832 teenargers must be interviewed.
Find the area of the shape shown below.
2
4
2
N.
2
units
Answer: 10units^2
Step-by-step explanation:
You can find the area of the trapezoid by multiplying the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then dividing by 2.
The larger base is 2+2+4=8
so
A=(2+8)*2/2
=10
you decided to save $100 at the end of each month for a year and deposit it in a bank account that earns an annual interest rate of 0.3%, compounded monthly. Use the formula for an annuity, F, to determine how much money will be in the account at the end of the 6th month, rounding your answer to the nearest penny.
Answer:
1.8
Step-by-step explanation:
Please help me i dont know how to do this
Answer:
26
Step-by-step explanation:
About 19% of the population of a large country is hopelessly romantic. If two people are randomly selected, what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic?
(a) The probability that both will be hopelessly romantic is
0.0361.
(Round to four decimal places as needed.)
(b) The probability that at least one person is hopelessly romantic is
0.3439.
(Round to four decimal places as needed.)
Answer:
a)
The probability that both will be hopelessly romantic is
P(X = 2) = 0.0361
b)
The probability that at least one person is hopelessly romantic is
P( X>1) = 0.3439
Step-by-step explanation:
a)
Given data population proportion 'p' = 19% =0.19
q = 1-p = 1- 0.19 =0.81
Given two people are randomly selected
Given n = 2
Let 'X' be the random variable in binomial distribution
[tex]P(X=r) =n_{C_{r} } p^{r} q^{n-r}[/tex]
The probability that both will be hopelessly romantic is
[tex]P(X= 2) =2_{C_{2} } (0.19)^{2} (0.81)^{2-2}[/tex]
P(X = 2) = 1 × 0.0361
The probability that both will be hopelessly romantic is
P(X = 2) = 0.0361
b)
The probability that at least one person is hopelessly romantic is
P( X>1) = 1-P(x<1)
= 1 - ( p(x =0)
= [tex]1- 2_{C_{0} } (0.19)^{0} (0.81)^{2-0}[/tex]
= 1 - (0.81)²
= 1 -0.6561
= 0.3439
The probability that at least one person is hopelessly romantic is
P( X>1) = 0.3439
9 m
11 m
6 m
4 m
Find the area of this figure.
Answer: 30 for addition and 2376 for multipaction
Step-by-step explanation: Depending on how what algebraic expression.
A triangle has vertices A( -3, 4), B(6, 4) and C(2, -3). The triangle is translated 4 units down and then rotated 90° clockwise. What will be the coordinates of A’’ after both transformations?
Answer:
The coordinates of point A after both transformations becomes (0, 3)
Step-by-step explanation:
Translation 4 units down is equivalent to -4 units in the y direction, therefore, we have;
A(-3, 4), B(6, 4), and C(2, -3) becomes
A(-3, 4 - 4), B(6, 4 - 4), and C(2, -3 - 4) which is A(-3, 0), B(6, 0), and C(2, -7)
Rule on operation on coordinates due to rotation of a triangle 90° clockwise is as follows;
For vertex coordinate, (x, y), we change it to (y, -x)
Therefore, we have the coordinates of the point A(-3, 0) after a rotation of 90° clockwise becomes A(0, 3).
40 POINTS!!!! Which sequence of transformations will result in an image that maps onto itself?
Answer:
Option C.
Step-by-step explanation:
Let a point (x, y) has a sequence of transformations,
Option A).
Reflects across x-axis then the coordinates will be,
(x, y) → (x, -y)
Then reflects across the y-axis,
(x, -y) → (-x, -y)
Image (x, y) gets changed to (-x, -y) therefore, point (x, y) doesn't map onto itself.
Option B).
(x, y) rotate 90° counter clockwise about the origin.
(x, y) → (-y, x)
Then reflect across x-axis,
(-y, x) → (y, x)
Since coordinates of the image and the actual are not same therefore, image doesn't map itself.
Option C).
(x, y) when reflected across x-axis,
(x, y) → (x, -y)
Then reflected over the x-axis,
(x, -y) → (x, y)
In this option point (x, y) maps onto itself after these transformations.
Option D).
(x, y) rotated 90°counterclockwise about the origin
(x, y) → (-y, x)
Then translated up by 2 units.
(-y, x) → (-y, x+2)
Therefore, (x, y) gets changed after these transformations and doesn't maps itself.
Option (C) will be the answer.
Answer:
you have it correct the answer is option c
Step-by-step explanation: