Final answer:
Transformations in mathematics involve translating, rotating, or reflecting figures, resulting in images that maintain their shape but may change position, orientation, or both. Examples include translations that shift figures, rotations that pivot them around a point, and reflections that create mirror images.
Explanation:
When a figure is translated, rotated, or reflected, its image undergoes specific transformations. In a translation, every point of the figure moves the same distance in the same direction, resulting in a figure that maintains its shape and orientation but changes its position. A rotation involves turning the figure around a fixed point known as the center of rotation, changing the direction of the figure while preserving its shape and size. Finally, a reflection is akin to looking into a mirror, where the figure is flipped over a line known as the axis of reflection, creating a mirror image that maintains the shape and size of the original figure but reverses its orientation.
These transformations can be visually represented and understood using diagrams, such as those involving ray diagrams for reflections. For example, in the reflection of an object in a mirror, light rays hitting the mirror generate new rays that appear to originate from a point behind the mirror, creating a virtual image. This conceptual understanding helps to explain how images are formed through various transformations, highlighting the precision and predictability of geometric operations.
What would my final balance be if I put $650 in the bank for 60 months with an interest rate of 6%?
George is putting trim around his rectangular deck, including the gate. He will need 48 feet of trim to do the entire deck. If the deck is 14 feet long, how wide is the deck?
We need to convert the given information to meaningful mathematical equation.
Statement: "George is putting trim around his rectangular deck, including the gate. He will need 48 feet of trim to do the entire deck.", it means
[tex] Perimeter \; of\; the\; rectangle=48\; feet [/tex]
Assuming ' L ' as length of the rectangle & ' W ' as the width of the rectangle, the perimeter of rectangle is given by the below formula.
[tex] Perimeter \; of\; the\; rectangle\; =\; 2(L+W) [/tex]
We know "the deck is 14 feet long", which means...
[tex] L=14 \; feet [/tex]
Substituting 14 for L and 48 for Perimeter of rectangle in the formula above, we can set up and equation in terms of W.
[tex] 2(L+W)=Perimeter \; of\; the\; rectangle\\ 2(14+W)=48\\ Divide \; 2\; on\; both\; sides, \; we\; get...\\ \\ \frac{2(14+W)}{2}=\frac{48}{2} \\ Simplifying\; fraction\; on\; both\; sides\\ \\ 14+W=24\\ Subtracting\; 14\; on\; both\; sides\\ \\ 14+W-14=24-14\\ Combine\; like\; terms\\ \\ W=10 [/tex]
Conclusion:
The width of the deck is 10 Feet
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What is the length of GE? Explain how you determined the length or show your work.
Karim sent a chain email to 10 of his friends. The number of people who got the email increases by a factor of 1.4 every week. Write an expression that best represents the
number of people who got the email after three weeks.
Final answer:
The number of people who got the email after three weeks can be calculated using the formula: F = 10 * (1.4)^t, where F represents the number of people, 10 represents the initial number of friends, 1.4 represents the factor of increase, and t represents the number of weeks. After substituting t = 3, we find that approximately 27 people will have received the email after three weeks.
Explanation:
To represent the number of people who got the email after three weeks, we can use the formula:
F = 10 * (1.4)^t
Where:
F represents the number of people who got the email10 represents the initial number of friends Karim sent the email to1.4 represents the factor by which the number of people increases each weekt represents the number of weeksSubstituting t = 3 into the formula, we can calculate the number of people who got the email after three weeks.
F = 10 * (1.4)^3 = 10 * 2.744 = 27.44
Therefore, after three weeks, approximately 27 people will have received the email.
The correct expression is:
(B) [tex]\(10 \cdot 1.4^6\)[/tex]
Sure, let's break it down step by step:
1. Initial number of people who received the email: Karim sent the email to 10 friends, so initially, [tex]\(10\)[/tex] people received it.
2. Factor by which the number of recipients increases each week: The number of recipients increases by a factor of [tex]\(1.4\)[/tex] each week.
3. Number of people who received the email after 1 week: To find this, we multiply the initial number of recipients by the factor for 1 week, which is [tex]\(10 \times 1.4 = 14\).[/tex]
4. Number of people who received the email after 2 weeks: Now, we take the number of recipients after 1 week (14) and multiply it by the factor for another week, [tex]\(1.4\)[/tex], giving us [tex]\(14 \times 1.4 = 19.6\)[/tex]. Since we can't have a fraction of a person, we round this up to the nearest whole number, which is [tex]\(20\).[/tex]
5. Repeating this process for 6 weeks: We continue this process for each additional week until we reach the 6th week.
6. General formula for the number of recipients after [tex]\(n\)[/tex] weeks: After [tex]\(n\)[/tex] weeks, the number of recipients can be calculated using the formula:
[tex]\[10 \times 1.4^n\][/tex]
So after 6 weeks, the expression becomes:
[tex]\[10 \times 1.4^6\][/tex]
7. Final Answer: The correct choice is (B) [tex]\(10 \times 1.4^6\).[/tex]
The correct question is:
Karim sent a chain email to 10 of his friends. The number of people who got the on: il increases by a factor of 1.4 every week.
Which expression gives the number of people who got the email after 6 weeks?
Choose 1 Anwer:
(A) [tex]$(10 \cdot 1.4)^6$[/tex]
(5) [tex]$10 \cdot 1.4^6$[/tex]
(c) [tex]$10+1.4 \cdot 6$[/tex]
(D) [tex]$(10+1.4) \cdot 6$[/tex]
PLEASE HELP ME!!!!!!!!!!!!!ASAP!!!!!!!!!!!
The Charts Are in order for each Question
1.What is the median value of the data set shown on the line plot?
Enter your answer in the box.
2.A grocery store received two shipments of watermelon. Each watermelon in a shipment was weighed, then a line plot was made of all of the weights in a shipment. What statement about the two plots’ distributions is true?
A.There is no overlap between the two distributions.
B.The degree of overlap between the two distributions is moderate.
C.The degree of overlap between the two distributions is low.
D.The degree of overlap between the two distributions is high.
For each pair of shapes decide whether they are congruent similar or neither
what is 13 divide to 83.2
PLEASE HELP ME! IM GETTING TIMED!!
A cake in the shape of a circus tent is used as a centerpiece at a celebration. The cake consists of a cylinder and a cone. The cylinder has a diameter of 12 inches and a height of 14 inches. The cone has a height of 6 inches. What is the volume of the cake? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi. Show your work.
MAKE SURE TO SHOW YOUR WORK?
Explain how the suffix -less affects the meaning of the spelling words expressionless and fearless. (explain plz) FAST !!!
Lisa goes to school 7 hours per day, works 3 hours per day, and sleeps for 8 hours per day. What is the ratio of hours Lisa works to hours Lisa sleeps?
The ratio of hours Lisa works to hours Lisa sleep is 3: 8.
what is the ratio?
The comparison of two quantities is known as a ratio. which could be easily determined by dividing one value by other which also indicates the percentage.
Given Lisa works 7 hours per day, works 3 hours per day, and sleeps for 8 hours per day. Therefore, the ratio of hours Lisa works to hours Lisa sleeps is the work hour of Lisa divided by hours of sleep per day.
Hence, the required ratio is 3: 8.
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There are y children in an orphanage and they shared $x among themselves. If each of them got $7 there were $4 left.If there were $5 more,each would get $8.
(a) Write the pair of simultaneous linear equation connecting x and y.
(b) Hence, find
(i) x
(ii) y
What is the value of the 6 in 34.967
jan typically earns $435 each week of which 78.30 withheld for taxes. what percent of jan's earnings are withheld each week solve
A theater can seat 720 people. The number of rows is 6 less than the number of seats in each row. How many rows of seats are there?
If eight people sat at a round dinner table and each person had to shake everyone else’s hand once how many handshakes will take place
A power line extends from a light pole 43 meters to the ground and makes an angle of 30 degrees with the ground. To the nearest tenth of a meter, how tall is the light pole?
simplify 3/8+1/6 help
HELP 11190 POINTS
The dot plot shows the number of visitors. Determine the median of the data set.
A) 56
B) 61
C) 62
D) 68
Solution:
we are given with a dot plot where we can see that the number of visitors.
we have been asked to find the median of the data set.
From the data plot , we can write the data set as below
56,56,56,56,58,58,60,62,62,62,63,65,65,68,68.
Here the data set is already arranged in the ascending order.
Now if the number of data points in the data set is odd then middle number is the median.
If the number of data points in the data set is even then the sum of middle two divided by 2 gives the median.
Here the number of data points in the data set is odd.
So the median is 8th value from any side.
Hence the median of the given data set is 62.
(a) What’s the name of the 3D shape this net represents? (For example, square prism, rectangular prism, triangular prism, cube, rectangular pyramid, triangular pyramid, square pyramid…). Write your answer below.
(b) What’s the surface area of this tent? Show all work and write your answer below.
Answer:the answer is square pyramid
Step-by-step explanation:
Coco buys a very large rectangular chocolate bar and decides that each day, she
will cut the largest possible square off of the bar and eat it. When the remaining
part of the chocolate bar is a square, she will eat all that is left. The table shows
the area, in square centimeters, of the square Coco eats on each day. If Coco
finishes the chocolate bar on Day 6, what was the length of the longer side of the
chocolate bar when Coco bought it?
Table is included need answer ASAP.
Answer: 39
Step-by-step explanation:
On each of the six days Coco ate a square piece of chocolate with side length 15 cm, 15 cm, 9 cm, respectively. Then find the slope versus. 15*15+9*1=236. Then you have to do 236-200=36. Later 36+3, since there were three numbers to get 39.
Enter the missing numbers in the boxes to complete the table of equivalent ratios of lengths to widths. Length (cm) Width (cm) 6 9 36 48 15
Choose the correct product of (3x + 8)2. 9x2 − 64 9x2 + 64 9x2 + 48x + 64 9x2 − 48x + 64
Answer: The correct answer is 9x^2 + 48^x + 64
Step-by-step explanation:
The correct answer is 9x^2 + 48^x + 64
Malinda’s pair of ski boots and skis have a mass of 6 kilograms. What is the mass of one ski boot and one ski
A container is 25ft × 50ft.If you have to draw using the scale 1 inch:5ft,what are the dimensions of the container that you will draw?
Jarrod helped his teachers pack textbooks into boxes for the summer. He packed 8 boxes of science textbooks with 16 books per box. He also packed math textbooks with 12 books per box.
If x represents the total number of boxes he packed, which of the following equations can be used to find the total number of books that Jarrod packed into boxes?
A.
y = 128x + 12
B.
y = 12(x - 8) + 128
C.
y = 12x + 128
D.
y = 128(x - 8) + 12
Final answer:
The correct equation to represent the total number of books Jarrod packed is B. y = 12(x - 8) + 128, which acknowledges he packed 8 boxes of science books and the remaining boxes were for math books.
Explanation:
Jarrod packed 8 boxes of science textbooks with 16 books per box, which totals to 8 × 16 = 128 books.
For the math textbooks, if x represents the total number of boxes packed, then Jarrod would have packed (x - 8) boxes of math textbooks since he already packed 8 boxes of science textbooks.
Each math textbook box contains 12 books, so the number of math books packed is 12 × (x - 8). The total number of books that Jarrod packed is the sum of both science and math books, which is given by 128 + 12 × (x - 8).
The correct equation that represents this word problem is B. y = 12(x - 8) + 128, where y is the total number of books packed and x is the total number of boxes packed.
What value of x would make rq tangent to Circle P at point Q?
The value of x cannot be negative, hence the value of x would make rq tangent to Circle P at point Q is 6
From the given circle geometry, since the line PQ is perpendicular to QR, hence the triangle PQR is a right-angle triangle.Given the following from the geometry;
Adjacent side = QR = 12Opposite side = PQ = 9Hypotenuse side = PR = 9 + xUsing the pythagoras theorem;
[tex]c^2=a^2+b^2\\(9+x)^2=9^2+12^2\\81+18x+x^2=81+144\\x^2+18x+81-225=0\\x^2+18x-144=0\\[/tex]
Factorize the result to have;
[tex]x^2+24x-6x-144=0\\x(x+24)-6(x+24)=0\\(x-6)(x+24) =0\\x=6 \ and \ -24\\[/tex]
Since the value of x cannot be negative, hence the value of x would make rq tangent to Circle P at point Q is 6
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The following table represents the sample space of rolling two number cubes.
1 2 3 4 5 6
1 1-1 1-2 1-3 1-4 1-5 1-6
2 2-1 2-2 2-3 2-4 2-5 2-6
3 3-1 3-2 3-3 3-4 3-5 3-6
4 4-1 4-2 4-3 4-4 4-5 4-6
5 5-1 5-2 5-3 5-4 5-5 5-6
6 6-1 6-2 6-3 6-4 6-5 6-6
How many favorable outcomes are there for the event "rolling exactly one even number"?
The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours.
What is the speed of the motorboat?
A) 225 miles per hour
B) 25 miles per hour
C) 75 miles per hour
D) 50 miles per hour
Answer:
Option D.,50 miles per hour
Step-by-step explanation:
The graph shows the distance covered by motor boat at = y, ( in miles )
The certain amount of time on = x ( in hours )
The slope of the given line will represent the speed of the motorboat.
The given line passes through two points ( 0, 25 ) and ( 4, 225 )
Therefore, slope of the line = [tex]\frac{y-y'}{x-x'}[/tex]
= [tex]\frac{225-25}{4-0}[/tex]
= [tex]\frac{200}{4}[/tex]
= 50
The speed of the motorboat is 50 miles per hour.
Godfrey just got a new credit card that offers both an introductory APR and a standard APR. If the standard APR is 11.2%, which of the following rates would most likely be the introductory APR?
Answer: 1.2-apex
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A cell phone company has a basic monthly plan of 40$ plus $0.45 for any minutes uses over 700. Before receiving this statement, John saw he was charged a total of $48.10. Write and solve an equation to determine how many minutes he must have used during the month. Write an equation without decimals.
There are 18 minutes John must have used during the month.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
A cell phone company has a basic monthly plan of 40$ plus $0.45 for any minutes uses over 700.
Before receiving this statement, John saw he was charged a total of $48.10.
Let the time he must have used during the month = x
So, We can formulate the equation as;
⇒ $48.10 = $40 + $0.45 x
Solve for x as;
⇒ 48.10 - 40 = 0.45x
⇒ 8.10 = 0.45x
⇒ x = 8.10 / 0.45
⇒ x = 18
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