Answer: Option A
Step-by-step explanation:
Given the parent function [tex]f(x)=x^5[/tex], it can be transformated:
If [tex]f(x)=x^5-k[/tex], then the function is shifted k units down.
If [tex]f(x)=a(x^5)[/tex] and [tex]a > 1[/tex] it is vertically stretched it, but if [tex]0 < a < 1[/tex] it is vertically compressesd.
If [tex]f(x)=-(x^5)[/tex], then the function is reflected over the x-axis.
Then, if the function given is reflected over the x-axis, it is vertically streteched by a factor o 2 and it is shifted down 1 units, the function that results after this transformations is:
[tex]g(x)=-2(x^5)-1[/tex]
[tex]g(x)=-2x^5-1[/tex]
For a us census clock based on the 2000 census, the birth light would flash every 10 seconds, the death light every 16 seconds, the immigration light every 81 seconds, and the emigration light every 900 seconds, to indicate gains and losses in population.
A. If the birth and death lights flashed at the same time, how many seconds would pass before they flashed together again?
Show work
Answer:80
Step-by-step explanation:
Let's pretend we start a stopwatch when the birth and death light flash together. The birth light will flash at 10 seconds, 20 seconds, 30 seconds, etc. The death light will flash at 16 seconds, 32 seconds, 48 seconds, etc.
So the trick here is to find the least common multiple (LCM) of 10 and 16. To do that, we write the prime factorization of each:
10 = 2×5
16 = 2⁴
The LCM must include all these prime factors without any duplicates. So the LCM = 2⁴×5 = 80. We can check our answer by dividing:
80 / 10 = 8
80 / 16 = 5
So 80 is indeed a multiple of both 10 and 16.
By using the concept of HCF and LCM, the result obtained is
The birth and death light will flash again after 80 seconds.
What is HCF and LCM of two numbers?
HCF means Highest Common Factors. HCF of two numbers a and b is the highest number which divides both a and b
LCM means Lowest Common multiple. LCM of two numbers a and b is the lowest numbers which is divisible by both a and b
HCF and LCM can be calculated by division method and prime factorization method.
Also there is an important formula relating HCF and LCM
HCF [tex]\times[/tex] LCM = Product of two numbers
Here,
The birth light would flash every 10 seconds,
The death light every 16 seconds,
The immigration light every 81 seconds,
The emigration light every 900 seconds,
They will flash again after LCM (10, 16)
Now,
10 = [tex]2 \times 5[/tex]
16 = [tex]2 \times 2 \times 2 \times 2[/tex]
LCM of 10 and 16 = [tex]2 \times 2 \times 2 \times 2 \times 5[/tex] = 80
The birth and death light will flash again after 80 seconds.
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Please HELP with inequality and graph. !!!!!!
Answer:
A. | x+1 | > 6none of the aboveStep-by-step explanation:
4. The graph is showing you x < -7 ∪ 5 < x. The difference between the end points is 12, suggesting that the inequality will be of the form | f(x) | > 6. We want the expression for f(x) to be zero at the midpoint of the excluded interval, which is (-7+5)/2 = -1. The inequality that matches this requirement is ...
| x+1 | > 6 . . . . . . . matches choice A
__
7. The graph shows a domain of x-values less than 3, so the domain in interval notation is (-∞, 3).
The graph shows the range of y-values from -∞ to -1, including -1. In interval notation, the range is (-∞, -1].
None of the answer choices match ...
Domain (-∞, 3), range (-∞, -1].
(Your computer might say C is correct, but it is not. Talk to your teacher about this question.)
A flagpole stands in the middle of a flat, level field. 50 feet away from its base, a surveyor measures the angle to the top of the flagpole as 48 degrees. How tall is the flagpole? Round to the nearest hundredth of a foot
Answer:
55.53 feet.
Step-by-step explanation:
We have been given that a flagpole stands in the middle of a flat, level field. 50 feet away from its base, a surveyor measures the angle to the top of the flagpole as 48 degrees.
We can see from attached photo that flagpole, the surveyor forms a right triangle with respect to ground.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(48^{\circ})=\frac{h}{50}[/tex]
[tex]\text{tan}(48^{\circ})*50=\frac{h}{50}*50[/tex]
[tex]1.110612514829*50=h[/tex]
[tex]h=1.110612514829*50[/tex]
[tex]h=55.53062574[/tex]
[tex]h\approx 55.53[/tex]
Therefore, the height of the flagpole is approximately 55.53 feet.
Soldering is accomplished by quickly heating metal parts. Solder is a metal that is melted to join metallic surfaces together. Common solder formulations based on tin and lead are listed below. The fraction represents percentage of tin first, then lead, totaling 100%.
Tin/Lead Melting Point (°C)
40/60 230 °C
50/50 214 °C
60/40 190 °C
63/37 183 °C
95/5 224 °C
With the same soldering iron, assuming the soldering iron’s highest temperature is 204 degrees Centigrade, would you be able to make the repair if you had solder made of 50/50?
Answer:
No.
Step-by-step explanation:
50/50 solder is shown to melt at 214 °C. If the soldering iron only heats to 204 °C, it cannot melt the solder. The solder will only be melted if it is heated to a temperature at or higher than its melting point.
An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 3 tan(3θ) − 1 = 0 (b) Find the solutions in the interval [0, 2π).
[tex]3\tan3\theta-1=0[/tex]
[tex]3\tan3\theta=1[/tex]
[tex]\tan3\theta=\dfrac13[/tex]
Recall that the tangent function has a period of [tex]\pi[/tex] so that
[tex]3\theta=\tan^{-1}\dfrac13+k\pi[/tex]
for any integer [tex]k[/tex]. Then
[tex]\theta=\dfrac13\tan^{-1}\dfrac13+\dfrac{k\pi}3[/tex]
We get 6 solutions in the interval [0, 2π) for [tex]0\le k\le5[/tex],
[tex]\theta\approx0.107[/tex]
[tex]\theta\approx1.154[/tex]
[tex]\theta\approx2.202[/tex]
[tex]\theta\approx3.249[/tex]
[tex]\theta\approx4.296[/tex]
[tex]\theta\approx5.343[/tex]
Thirty-five points on the line!!!
A bag contains five plain muffins and six blueberry muffins. Without looking, Sherman selects a muffin, hands it to his sister and then selects a second muffin for himself. What is the probability that Sherman gets a plain muffin, and his sister gets a blueberry muffin?
A. 30/121
B. 3/11
C. 5/11
D. 5/6
Your answer would be B) 3/11, hope this helps!
Remember there are 11 muffins in the bag
Answer:
The answer is B. 3/11
What’s is the median for this number
8,9,3,1,2,6,5,7,4,0,10
Answer:
To find the median, set the numbers in order and the median is the number in the middle. If there was an even number of number then you would the two middle numbers and average it.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
So the median in this case would be 5
Answer: 6
Step-by-step explanation:
Median means the middle. You cross out a number from each side until you get one number and it’s 6. If there was uneven amount of numbers, and you were left with two numbers you add them and divide of how many numbers there are
write in y = mx + b form (1) -x-5y = 21. (2) -2x - 5y = 25
1. -x-5y=21
-5y=x+21
y= -1/5x-21/5
2.-2x-5y=25
-5y=2x+25
y= -2/5x-5
HELP PLEASE I do not know what to do i can only add photos of the answers i need help fast thank you
Answer:
f(x) = 3 if x ≤ -2
= 1 if x > -2 ⇒ attached figure
Step-by-step explanation:
* Lets explain how to answer the question
- For the part of the graph on the left side (2nd quadrant)
- There is a horizontal line start from x = -∞ and stop at x = -2
- The end of the line is black dot means x = -2 belongs to the function
- The horizontal line drawn at y = 3
∴ The equation of the horizontal line is y = 3
∴ The function represents this part of graph is y = 3 if x ≤ -2
- The other part of the graph is also horizontal line start from
x = -2 to x = ∞
- The end of the line is white dot means x = -2 does not belong
to the function
- The horizontal line drawn at y = 1
∴ The equation of the horizontal line is y = 1
∴ The function represents this part of graph is y = 1 if x > -2
* f(x) = 3 if x ≤ -2
= 1 if x > -2
- The answer is attached
اقعى2اعلاع2ىخث
قرهغىع24عغع2ر
Use the graph below to determine the number of solutions the system has. x = - 4 y = - x - 1
Answer:
Final answer is given by x=-4, y=3
Step-by-step explanation:
Question says to use the given graph to determine the number of solutions the system where given system is x = - 4, y = - x - 1
Graph is missing but we can still find the solution.
plug first equation x=-4 into other equation y=-x-1
y=-x-1
y=-(-4)-1
y=4-1
y=3
Hence final answer is given by x=-4, y=3
or we can also write that as (-4,3)
If point (x, y) is reflected over the y-axis, the resulting point is (-x, y)
Answer:
That is correct
Step-by-step explanation:
If its reflecting over the y axis only the x is becoming opposite. the x becomes -x, so (x, y) is reflected over the y-axis, the resulting point is (-x, y)
A reflection over the y-axis in mathematics results in changing the sign of the x-coordinate of a point, while the y-coordinate remains the same. This is a property associated with even functions, which are symmetric around the y-axis. The process is a transformation involving a change in direction.
Explanation:In mathematics, a point's reflection over the y-axis is represented as (-x, y). When you reflect a point across the y-axis, the x-coordinate changes its sign while the y-coordinate stays the same. For example, if we start with point (2,3), its reflection would be at point (-2,3) across the y-axis.
Notably, this reflection is a property of even functions, which are symmetric around the y-axis. To visualize this, you can plot specific values for (x,y) data pairs and observe the symmetry.
The reflection process can be seen as a transformation involving a change in direction represented by unit vectors. In a plane, it’s customary that the positive direction on the x-axis is denoted by the unit vector i and the positive direction on the y-axis by the unit vector j. The reflection over the y-axis turns the x components in the opposite direction, hence -x.
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What is the area of the base in the figure below
Answer:
[tex]A=9\pi\ square\ units[/tex]
Step-by-step explanation:
we know that
The base of the cylinder is a circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=6/2=3\ units[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (3)^{2}[/tex]
[tex]A=9\pi\ units^{2}[/tex]
BBBBBBBBBBBBBBBBB
the answer is B
Convert 6 hours 36 minutes to decimal hours.
A)6.52 hours
B)6.55 hours
C)6.58 hours
D)6.6 hours
E)6.62 hours
Answer:
D. 6.6 hours
Step-by-step explanation:
100/60= 1.66
Multiply 1.66 times 36 and get 6.6 hours
Hope this helps!
The hour equivalent in decimal to 6 hours 36 minutes is,
D) 6.6 hours
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
What is the measure of each integer step in a clock?A clock can be thought of as a circle having 12 steps and we know that circle is 360°,
So, the measure of each integer step of a clock is 30°.
We know, One hour is equivalent to 60 minutes.
Given, We have 6 hours and 36 minutes.
Therefore, The hour equivalent to 36 minutes is,
= 36/60.
= 3/5.
= 0.6 hours.
Therefore, 6 hours and 36 minutes is equal to 6.6 hours.
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Find the value of b in the graph of y=3x+b if it is known that the graph goes through the point: N(0,5)
Answer:
I believe b is 5.
Step-by-step explanation:
When you place the points in the values, you get 5=3(0)+b. When you simplify it, you get 5=b. I really hope this is correct, I apologize if it isn't! I hope this helps! :)
I think it’s five too
Factor 60y-90-20x to identify the equivalent expressions.
Answer:
10(6y-9-2x)
Step-by-step explanation:
60y-90-20x
We can factor out 10 from each term
10(6y-9-2x)
Answer:
10(6y-9-2x)
Step-by-step explanation:
i dont know how to say it bit this is 100% true
Ugh like terms. Help
Answer:
-4y - 7x^3 + 2
Step-by-step explanation:
So first lets combine the y terms together, doing this we get:
-4y + 1 - x^3 - 3x^3 + 1 - 3x^3
Now lets combine the terms with x^3 together
-4y + 1 - 7x^3 + 1
Lastly, lets add the constants
-4y - 7x^3 + 2
a rectangle is 6 units "wide" and x -8 use long it has the same area of a triangle with a height of 7 units and a base of x minus 3 years what is the area of the rectangle
Answer:
42 square units
Step-by-step explanation:
The area of the rectangle is the product of its length and width:
area = 6(x -8)
The area of the triangle is half the product of its base and height:
area = (1/2)(x-3)·7
These two areas are equal, so we have ...
6(x -8) = (1/2)(x -3)(7)
6x -48 = 3.5x -10.5 . . . . eliminate parentheses
2.5x = 37.5 . . . . . . . . . . . add 48 -3.5x
x = 15 . . . . . . . . . . . . . . . divide by 2.5
The area of the rectangle is ...
area = 6(15 -8) = 42 . . . . square units.
A dumpster, in the shape of a right rectangular prism, has a length of 10 feet, a width of 5.5 feet, and a height of 4 feet. It is completely full of yard waste that weighs, on average, 7.5 pounds/cubic foot. What is the weight of the yard waste to the nearest pound? Enter the number only.
Answer:
The weight of the yard waste = 1650 pounds
Step-by-step explanation:
* Lets revise the rule of the volume of the prism
- The rectangular prism has 6 rectangular faces
- Its base shaped a rectangle of dimensions length and width
- The volume of the rectangular prism = Area of its base × its height
∵ Area of the rectangle = length × width
∴ The volume of the prism = length × width × height
* Now lets solve the problem
∵ The length of the rectangular prism = 10 feet
∵ The width of it = 5.5 feet
∵ The height of it = 4 feet
∴ Its volume = 10 × 5.5 × 4 = 220 feet³
- The prism is completely full of yard waste
∴ The volume of the yard waste = the volume of the prism
∴ The volume of the yard waste = 220 feet³
- The average weighs of it is 7.5 pounds/cubic foot
∴ The weight of the yard waste = the average of weight × the volume
∴ The weight of the yard waste = 7.5 × 220 = 1650 pounds
please help
Use numerals instead of words. If necessary, use / for the fraction
Answer:
1
Step-by-step explanation:
Factor and cancel common factors from numerator and denominator.
[tex]\displaystyle\frac{2y^3-y^2+2y-1}{y^3-y^2+y-1}\times\frac{2y^2-3y+1}{4y^2-4y+1}\\\\=\frac{(y^2+1)(2y-1)\times (2y-1)(y-1))}{(y^2+1)(y-1)\times (2y-1)^2}=\frac{(y^2+1)(2y-1)^2(y-1)}{(y^2+1)(2y-1)^2(y-1)}\\\\=1[/tex]
The figure below shows three right triangles joined at their right-angled vertices to form a triangular pyramid. Which of the following to length of XX?
Answer:
d) 9 inches
Step-by-step explanation:
By the Pythagorean theorem:
WZ² = 15² -12.5² = 68.75
WX² = 13² -12.5² = 12.75
Then the length of XZ can be found from ...
XZ = √(WZ² +WX²) = √81.5 ≈ 9.028 . . . . closest to 9 inches (choice D)
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Find the associated radius of convergence R. f(x) = 6(1 − x)−2
I guess the function is
[tex]f(x)=\dfrac6{(1-x)^2}[/tex]
Rather than computing derivatives of [tex]f[/tex], recall that for [tex]|x|<1[/tex], we have
[tex]g(x)=\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]
Notice that
[tex]g'(x)=\dfrac1{(1-x)^2}[/tex]
so that [tex]f(x)=6g'(x)[/tex]. Then
[tex]f(x)=6\displaystyle\sum_{n=0}^\infty nx^{n-1}=6\sum_{n=1}^\infty nx^{n-1}=6\sum_{n=0}^\infty(n+1)x^n[/tex]
also valid only for [tex]|x|<1[/tex], so that the radius of convergence is 1.
How do you verify this trigonometric identity? cos^2 θcot^2 θ = cot^2 θ - cos^2 θ
Replace cos^2(θ) with 1-sin^2(θ), and cot(θ) with cos(θ)/sin(θ).
cos^2(θ)cot^2(θ) = cot^2(θ) - cos^2(θ)
(1 -sin^2(θ))cot^2(θ) = . . . . . replace cos^2 with 1-sin^2
cot^2(θ) -sin^2(θ)·cos^2(θ)/sin^2(θ) = . . . . . replace cot with cos/sin
cot^2(θ) -cos^2(θ) = cot^2(θ) -cos^2(θ) . . . as desired
I am desperate! 95 points for correct answer!!!!!
1543 pages is $77.40, 7361 pages is $368.30 using a linear equation with $250 in budget how many pages can you print. Please write steps!
Answer:
[tex]\boxed{\text{4995 pages}}[/tex]
Step-by-step explanation:
The question is asking you to find the equation of a straight line that passes through two points
Let x = the number of pages
and y = the cost
Then the coordinates of the two points are (1543, 77.40) and (7361, 368.30).
(a) Calculate the slope of the line
[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = & \dfrac{368.30 - 77.40}{7361 - 1543}\\\\& = & \dfrac{290.90}{58.18}\\\\ & = & 0.05000\\\end{array}[/tex]
In other words, the cost is 5¢ per page.
(b) Calculate the y-intercept
[tex]\begin{array}{rcl}y & = & mx + b\\368.30 & = & 0.05 \times 7361 + b\\368.30 & = & 368.05 + b\\b & = & 0.25\\\end{array}[/tex]
(c) Write the equation for the line
y = 0.05x + 0.25
That is, the cost is 25¢ plus 5¢ per page
(d) Calculate the pages you can print for $250
[tex]\begin{array}{rcl}y & = & 0.05x + 0.25\\250 & = & 0.05x + 0.25\\249.75 & = & 0.05x\\x & = & 4995\\\end{array}\\\text{ You can print }\boxed{\textbf{4995 pages}}[/tex]
The figure below shows the graph of your equation, with slope 0.05 and y-intercept at (0,0.25).
It looks as if you could print 5000 pages, but you must pay that 25¢ (5 pages worth) up-front, so you can print only 4995.
Answer:
4995 pages
Step-by-step explanation:
The question is asking you to find the equation of a straight line that passes through two points
Let x = the number of pages
and y = the cost
Then the coordinates of the two points are (1543, 77.40) and (7361, 368.30).
(a) Calculate the slope of the line
In other words, the cost is 5¢ per page.
(b) Calculate the y-intercept
(c) Write the equation for the line
y = 0.05x + 0.25
That is, the cost is 25¢ plus 5¢ per page
(d) Calculate the pages you can print for $250
The figure below shows the graph of your equation, with slope 0.05 and y-intercept at (0,0.25).
It looks as if you could print 5000 pages, but you must pay that 25¢ (5 pages worth) up-front, so you can print only 4995.
Subtract and simplify
23 ft 7 in
- 13 ft 11 in
18 gal 2 qt
- 5 gal 3 qt
21 yd 1 ft 7 in
- 12 yd 2 ft 9 in
Answer:
9 ft 8 in12 gal 3 qt8 yd 1 ft 10 inStep-by-step explanation:
There are several different ways you can work problems like this. The method you may prefer may be different from the one I prefer. At least, they include ...
You can treat the smaller units as a fraction of the larger unit: 23 7/12 -13 11/12. Then subtracting mixed numbers proceeds in any of the usual ways. You may even be able to use a calculator for this.You can "subtract by adding": 8 inches added to the subtrahend makes it 14 ft 7 in; then adding 9 ft makes it 23 ft 7 in. The difference is then seen to be 9 ft 8 in.You can subtract the different units separately, then "make change" or "borrow" as required. 23'7" -13'11" = 10'(-4)" = 9'8". (This is probably the method I prefer.) An on-line calculator may be able to handle the mixed units to your satisfaction (see attached).___
1. There are 12 inches in a foot.
23 ft 7 in - (13 ft 11 in) = (23 -13) ft (7 -11) in = 10 ft (-4) in = 9 ft 8 in
__
2. There are 4 quarts in a gallon.
18 gal 2 qt - (5 gal 3 qt) = (18 -5) gal (2 -3) qt = 13 gal (-1) qt = 12 gal 3 qt
__
3. There are 3 feet in a yard and 12 inches in a foot.
21 yd 1 ft 7 in -(12 yd 2 ft 9 in) = (21 -12) yd (1 -2) ft (7 -9) in
= 9 yd (-1) ft (-2 in)
= 8 yd 2 ft (-2) in
= 8 yd 1 ft 10 in
points (1,3) and (5,3) lie on line r. what is the slope of the line that is parallel to r?
First we must find out the slope of the points
The equation for slope is
[tex]\frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex]
Let's plug in our points
[tex]\frac{3 - 3 }{5 -1 } = \frac{0}{4}[/tex]
Our slope is 0
When lines are parallel, that means we have they have the same slope
So a line that is parallel to r would have a slope of 0!
5 boys gathered leaves. Each boy filled 2/3 of his bag with leaves. How many bags of leaves in all did the 5 boys collect?
Answer:
3 1/3 bags
Step-by-step explanation:
5 × 2/3 = (5×2)/3 = 10/3 = 3 1/3
The total quantity of leaves gathered is equivalent to 3 1/3 full bags.
What are the constants in this expression?
x-3+2/3-y/2
A. 1 and -3
B. -3 and 2/3
C. -3 and -y/2
D. 2/3 and -1/2
Answer:
B. -3 and 2/3
Step-by-step explanation:
One way to see the constants is to set the variables to zero. What's left is ...
-3 + 2/3
These are the constants in the expression.
Answer:
c
Step-by-step explanation:
Find the value of b in the graph of y=3x+b if it is known that the graph goes through the point: O(3,8)
Answer:
b= -1
Step-by-step explanation:
y=3x+b
8= 3(3)+b
b= -1
The value of b in the equation y = 3x + b that passes through (3, 8) is -1
From the question, we have the following parameters that can be used in our computation:
The equation of the graph
Where, we have
y = 3x + b
Also, we have the point
(3, 8)
This means that
x = 3 and y = 8
When these values are substituted into the equation, we have
8 = 3 * 3 + b
This gives
8 = 9 + b
Evaluate the like terms
b = -1
Hence, the value of b is -1
b. 64x3 - 125
Factor sum or difference of cubes
Answer:
(4x -5)(16x^2 +20x +25)
Step-by-step explanation:
The factoring of the difference of cubes is something you might want to memorize, or keep handy:
(a³ -b³) = (a -b)(a² +ab +b²)
Here, the minus sign in the middle tells you this is a difference. The power of x is a clue that this might be the difference of cubes. Your knowledge of cubes of small integers tells you ...
64 = 4³125 = 5³so you can recognize this as ...
(4x)³ - 5³ . . . . . the difference of cubes.
___
Since you are familiar with the factorization above, you can easily write down the factoring of this expression using a=4x, b=5.
(4x -5)(16x² +20x +25)
_____
For "completeness", here is the factorization of the sum of cubes:
a³ +b³ = (a +b)(a² -ab +b²)
Note the linear factor (a +b) has the same sign as the sign between the cubes. The sign of the middle 2nd-degree term (ab) is opposite that.
The point (-7,4) is reflected over the line x=-3. Then the resulting point is reflected over the line y=x. Where is the point located after both reflections
Answer:
(4, 1)
Step-by-step explanation:
Since the first reflection is over the vertical line x=-3, the y-coordinate remains the same. The x-coordinate of A' will make the point (-3, 4) on the line of reflection be the midpoint between A and A':
(-3, 4) = (A +A')/2
2(-3, 4) -A = A' = (-6-(-7), 8 -4) = (1, 4)
The reflection over the line y=x simply interchanges the two coordinate values:
A'' = (4, 1)
The point (-7,4) upon reflection over the lines x = -3 and y = x would be at point; (4,1).
According to the question;
We are required to determine where the point is located after both reflections.For the first reflection;
The first reflection is over the vertical line defined at, x=-3. Consequently, the y-coordinate remains constant.However, the x-coordinate of P' will make the point (-3, 4) on the line of reflection be the midpoint between A and A':
(-3, 4) = (P +P')/2 2(-3, 4) -P = P' = (-6-(-7), 8 -4) = (1, 4)For the second reflection;
The reflection over the line y=x simply interchanges the x- and y- coordinate values:Ultimately, the point P'' = (4, 1)
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