Add the scale factor to the x- and y-coordinates of a point on a coordinate plane with the center of dilatation at the origin.
Given,
Dilation;
Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.
We have to dilate a figure with a center of dilation;
Dilations centered at the origin;
On the coordinate plane, figures can be enlarged. The centre of dilatation is frequently used to be the origin. The points in the picture can be found by multiplying the coordinates of the preimage's points by the scale factor when distorting a figure that is centered at the origin.
That is,
On a coordinate plane with the center of dilatation at the origin, multiply the point's x and y coordinates by the scale factor.
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A woman at a point A on the hore of a circular lake with radiu 2 mi want to arrive at the point C diametrically oppoite A on the other ide of the lake in the hortet poible time (ee the figure). She can walk at the rate of 4 mi/h and row a boat at 2 mi/h. For what value of the angle hown in the figure will he minimize her travel time?
She should make a 90° turn from the starting location. Taking this viewpoint will cut down on her trip time.
What does a math angle mean?An angle is a figure in plane geometry that is created by 2 rays and lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
Briefing :Radius of lake= 2mi
walk rate= 4mi/h
boat speed= 2mi/h
cosθ=adj/hyp=d1/4
d1=4cosθ
The arc length from A to C
S=rθ
arc length is expressed as 2θ
S=2(2θ)
S=4θ=d2
d2=4θ
time= distance/speed
t1=d1/2= 4cosθ/2=2coθ
t2=d2/4=4θ/4=4
total time =t1+t2
T=2cosθ+θ
T(θ)=2cosθ+θ
T'(θ)= -2sinθ+1
0=-2sinθ+1
2sinθ=1
sinθ=1/2
T(π/6)=2.25hours
for 90 we have
T(π/2)=1.57hours
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Consider the data set 92, 100, 98, 89, 95, 100, 97. How will adding 65 to the data set affect the mean and the median?
A. The median will increase less than the mean.
B. The median will increase more than the mean.
C. The median will decrease less than the mean.
D. The median will decrease more than the mean.
The arithmetic mean is frequently used when discussing a bunch of numbers as being "average." One of three possible averages—the others being the median and the mode—is the one we're discussing here.
What is the Relationship Between Mean, Median and Mode?It would appear that the mean, median, and mode have no relationship at first glance. Measuring the center of a data collection, however, does have an empirical link.There is typically a difference between the median and the mode, and it is typically three times larger than the gap between the mean and the median, according to mathematicians.Formula below illustrates how the empirical relationship works:Mean minus Mode = 3 (Mean – Median)
For Given
Median, Mode, and Median Results: 95.85714 (Mean (Average)).
A middle value of 97
100 is the Mode (Most Popular)
Variety & Totals
Maximum to Minimum Results: 11
Total Numbers in the Set: 7
in descending order: 89, 92, 95, 97, 98, 100, 100
Ordered in decreasing order: 100,100,98,97,95,92,89
Even Numbers: 92, 98, 100, 100.
Odd Numbers: 89,95,97.
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luis thinks the slope is 1/2 explain his mistake and give the correct slope
The correct slope of the line is 5/2 and the mistake made by Luis is that he didn't correctly interpret the scale of both x and y axes.
How to find the slope of the line?To find the slope, we will divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points
By looking at the given graph, we could easily suspect that the slope is 1/2, but then we have to look at it closely to get the correct thing.
The y-axis shows that 1 unit represents 5 while for the x-axis, 1 unit represents 1.
To get the slope, we need two points on the line (w, x) and (y, z), and the slope is given by the quotient:
m = (z - x)/(y - w)
Looking at the graph we can see that the points (0, 5) and (2, 10) are on the line, and as such the slope is;
m = (10 - 5)/(2 - 0) = 5/2
The slope of the linear equation is 5/2.
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Which cost will increase or decrease with increase in production?
The variable costs will increase or decrease with an increase in production.
A variable cost could be a corporate expense that changes in the extent to how much a company produces or offers. Variable costs increment or decrease depending on a company's generation or sales volume. When production or deals increment, variable costs increment; when generation or deals decrease, variable costs decrease. Variable costs stand in differentiate from settled costs, which don't alter the extent of production or sales volume. Variable costs are a central portion in deciding a product's contribution margin, the metric utilized to decide a company's break-even or target profit level.
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what is price of $80 hoodie on 24% discount
Answer: 60.80
Step-by-step explanation:
you saved 19.20
evaluate 24 - 2³ . 2
Answer:
8
Step-by-step explanation:
solve the 2 cube first = 8
then solve the .2 with 8 = 16
then minus 24
24-8.2
24-16
8
Given:BC is congruent to DC, AB is congruent to ED, AG is congruent to EF. With the given information above, what is needed to prove that triangle ABF is congruent to triangle EDG
Answer:
To prove that triangle ABF is congruent to triangle EDG, we need to show that the three sides of triangle ABF are congruent to the corresponding three sides of triangle EDG.
Since we are given that BC is congruent to DC, AB is congruent to ED, and AG is congruent to EF, we can conclude that the three sides of triangle ABF are congruent to the corresponding three sides of triangle EDG. Therefore, triangle ABF is congruent to triangle EDG.
you roll two fair dice, a green one and a red one. (a) what is the probability of getting a sum of 6? (enter your answer as a fraction.) incorrect: your answer is incorrect. (b) what is the probability of getting a sum of 10? (enter your answer as a fraction.) (c) what is the probability of getting a sum of 6 or 10? (enter your answer as a fraction.) g
a) The Probability of getting a sum of 6 is 5/36.
b) The Probability of getting a sum of 10 is 1/12.
c) The Probability of getting a sum of 6 or 10 is 2/9.
Probability:
Probability is the branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty [Note 1][1][2]. that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2 (also written as 0.5 or 50%).
Probability = (number of desired outcomes / number of all possible outcomes)
Roll of Dice: Green and Red.
(a) The probability of totaling 6:
Number of outcomes needed = 5
Therefore,
P(sum of 6) = 5/36
b) The probability that the total is 10
Number of outcomes required = 3
Therefore,
P(sum of 10) = 3 / 36 = 1/12
c) The probability that the sum is 6 or 10:
P(sum is 6) + P(sum is 10)
(5/36) + (1/12) = (5 + 3) / 36
= 8/36 = 2/9
The events are mutually exclusive because they do not all occur at the same time.
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Diego measured the length of a pen to be 22 cm. The actual length of the pen is 23 cm. Which of these is closest to the percent error for Diego's
measurement?
4.3%
4.5%
95.7%
104.5%
Answer: 4.3%
Step-by-step explanation:
His accuracy was 22/23 which, as a percentage, is somewhere around 95-96%
To find his percentage error, you would do 1 - 22/23 (or the decimal- whichever you prefer)
1 - 22/23 ≈ 4.3% (as a decimal, it would be approximately 0.043)
If you're allowed to use a calculator, I recommend Desmos Scientific Calculator
I hope this helps!
A total of 809 tickets were sold for the school play. They were either adult tickets or student tickets. There were 59 more student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
375 Adult tickets
434 Student tickets
Step-by-step explanation:
Let A and S be the numbers of Adult(A) and Student(S) tickets sold. We are told that A+S= 809.
We also learn that A + 59 = S [59 more student tickets sold than adult tickets]
Rearrange the last expression to isolate one of the two variables, A or S. I'll isolate A:
A = S - 59
Now use this expression for A in the first equation ("substitution").
A + S = 809
(S - 59) + S = 809
2S = 868
S = 434
From A + S = 809, we can find A:
A + S = 809
A + 434 = 809
A = 375
Check: Does 375 + 434 = 809?? YES
There were 375 Adult and 434 Student tickets sold, for a total of 809 tickets.
Han's cell phone plan costs $200 to start. Then there is a $50 charge each month. What is the total cost for x months? write an equation:
Answer:
200+50x
Step-by-step explanation:
If Han's cell phone plan costs $200, Han will have to pay $200 at the start, and since Han has to pay $50 dollars each month, and x = months, we can create 50x for $50 each month. Put both of these together, and we get 200+50x.
A rectangular pool 24 meters by 16 meters is surrounded by a walkway of width x meters. At what value of x will the area of the walkway equal the area of the pool?
The value of x that the walkway will be equal to the area of the rectangular pool is 5 meters
How to find the value of x that equals the dimension of the poolArea of a rectangle is given by
length * width
Area of the pool
= 24 * 16
= 384
area of the walk way
= (24 + 2x) * (16 + 2x) - area of the pool
= 384 + 58x + 4x² - 384
= 4x² + 58x
when the area will be equal
4x² + 58x = 384
4x² + 58x - 384 = 0
solving the quadratic equation gives
x= 4.9386 OR -19.4386
ignore the negative value
x = 5 meters
at x = 5 meters the walkway will have same area with the pool
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What type of dilation is formed when the scale factor K is greater than 1?
An expansion where image size increased is formed when scale factor k is greater than 1
The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.
The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image.
The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted. Scale factor is a number by which the size of any geometrical figure can be changed with respect to its original size.
when the scale factor K is greater than 1 , The image will enlarged
Hence, An expansion will be occur.
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Hey anyone, may i have a hand for this one?
Answer:
nope
Step-by-step explanation:
Answer: Yes (depends)
Step-by-step explanation: It depends because it can only be called "a square" if all sides are parallel, I can't tell. I hoped this helped you understand a little more :)
Sophia is selling bracelets and necklaces at her stall. She sells each bracelet for $6.25 and each necklace for
$12.50. On a day she sold a total of 15 items and made $125. How many necklaces did Sophia sell?
Answer:
5 necklaces and 10 bracelets
Step-by-step explanation:
Let N and B stand for the numbers of necklaces(N) and bracelets(B) sold. The total sales would be:
Total Sales = 6.25B + 12.50N, whcu we are told amounted to $125:
$125 = 6.25B + 12.50N
We know that B + N = 15.
Rearrange this to isolate B: B = 15-N
Now use this definition of B in the first equation:
$125 = 6.25B + 12.50N
$125 = 6.25(15-N) + 12.50N
$125 = 93.75-6.25N + 12.50N
31.25 = 6.25N
N = 5 necklaces
From B+N = 15, we can find B:
B = 15 - 5
B = 10 bracelets
Check: Do 5 necklaces and 10 bracelets add up to $125??
5*($6.25) + 10*($12.50) = $62.50 + $62.50 = $125 YES
The number of bracelets and the number of necklaces if, Sophia sells each bracelet for $6.25 and each necklace for $12.50, and the total number of items sold is 15, are 10, and 5 respectively.
What is equation?
An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.
Given:
Sophia sells each bracelet for $6.25 and each necklace for $12.50,
Total number of items sold = 15,
Total income made = $125,
Write the equation as shown below,
x + y = 15
Here, x is the number of bracelets and y is the number of necklaces,
6.25x + 12.5y = 125
Solve the equations by elimination method as shown below,
y = 5 and x = 15 - 5 = 10
Thus, the number of bracelets is 10 and the number of necklaces is 5.
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What is the dilation called if scale factor is less than 1?
The dilation is known as contraction when the scale factor is less than 1
The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.
The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image.
The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted.
Scale factor is a number by which the size of any geometrical figure can be changed with respect to its original size.
when the scale factor K is greater than 1 , The image size decreased. It gets contracts
Hence, The dilation is called Contraction
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Can a figure be reflected across three lines of reflection so the
image is the original figure? Explain.
A figure cannot be reflected across three lines of reflection so the image is the original figure
What is reflection of a geometrical image? What is a mathematical function, equation and expression? reflection : A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane. function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is a statement -
"Can a figure be reflected across three lines of reflection so the image is the original figure".
No, a figure cannot be reflected across three lines of reflection so the image is the original figure. For the number of reflections equal to 3, which indicates an odd number of reflections changes the orientation of the figure.
Therefore, a figure cannot be reflected across three lines of reflection so the image is the original figure.
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When the scale factor is a greater than 1 the dilation will be a reduction?
No , When the scale factor is a greater than 1 the dilation will not be a reduction.
The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.
The initial figure is referred to as the pre-image, and the new figure that results from dilatation is known as the image.
The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted.
Scale factor is a number by which the size of any geometrical figure can be changed with respect to its original size. We multiple the scale factor to get image.
When the scale factor is greater than 1 figure size increased.
Hence , When the scale factor is a greater than 1 the dilation will be a expansion
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Solve
3(2x + 9) = 24
Solve
4x - 2 = 10x + 1
3x - 4(2x + 1) = 10
Solve
3x + 10 = 19
Answer:
x = -1/2 x = -1/2 x = -14/5 x = 3Step-by-step explanation:
1) 3(2x + 9) = 24, find x?
→ 3(2x + 9) = 24
→ 6x + 27 = 24
→ 6x = 24 - 27
→ x = -3/6
→ [ x = -1/2 ]
Hence, value of x is -1/2.
2) 4x - 2 = 10x + 1, find x?
→ 4x - 2 = 10x + 1
→ 4x - 10x = 1 + 2
→ -6x = 3
→ x = -3/6
→ [ x = -1/2 ]
Hence, value of x is -1/2.
3) 3x - 4(2x + 1) = 10, find x?
→ 3x - 4(2x + 1) = 10
→ 3x - 8x - 4 = 10
→ -5x = 10 + 4
→ [ x = -14/5 ]
Hence, value of x is -14/5.
4) 3x + 10 = 19, find x?
→ 3x + 10 = 19
→ 3x = 19 - 10
→ x = 9/3
→ [ x = 3 ]
Hence, value of x is 3.
What function equation is represented by the graph?
The function equation represented by the graph is f(x)=1/4x-3.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=10x+4. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=10 and b=4.
From the graph is possible to see the following coordinates points: (0,-3) and (4,-2). Applying the standard form for the linear equation, you can write:
-3=0*m+b (1)
-2=4*m+b (2)
-3=b (1)
-2=4m+b (2)
If b=-3, you can find m from equation 2. Then,
-2=4m-3
-2+3=4m
1=4m
m=1/4
Therefore, the linear equation represented in the graph is y=1/4b -3
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2x-6(3x+8)=-208 please help i dont know howww
Garrick and Zan are measuring the heights of seedling plants for science class.
Use the drop-down menus to complete the statements about the measured heights and the actual heights of the plants.
The complete statements are
Garrick's plant is shorter than Zan's plant, each millimetre of error results in a 11.11% percent error.Garrick's measurement was 2 millimetres off and Zan's was 12 millimetres off. Garrick's measurement was 20% off and Zan's was 12% off.How to complete the statements?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
Garrick's plant:
Actual height = 10 mmMeasured height = 8 mmZan's plant:
Actual height= 100 mmMeasured height = 88 mmGarrick's plant is shorter than Zan's plant and the difference in heights is
Actual difference = 100 mm - 10 mm = 90 mm
Measured difference = 88 mm - 8 mm = 80 mm
The percentage errors are calculated using
Percentage errors = Difference/Actual measurement * 100%
So, we have
Garrick's actual error = (10 - 8)/10 *100% = 20%
Zan's actual error = (100 - 88)/10 * 100% = 12%
Hence, Garrick's measurement was 20% off and Zan's was 12% off.
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3x - y = -9
−2x + 2y = 6
Answer:
x= -3
y= 0
Step-by-step explanation:
3x-y= -9
+y. +y
3x= -9+y
+9 +9
3x+9=y
-2x+2(3x+9)=6
-2x+6x+18=6
4x+18=6
-18 -18
4x= -12
/4. /4
x= -3
3(-3)-y=-9
-9-y=-9
+9 +9
-y=0
/-1. /-1
y= 0
hopes this helps please mark brainliest
Write an equation of the line that passes through (4,3) and is parallel and perpendicular to -4x+10
This s the answer
Answer y=(-1/4)x+10
5 years ago Patricia put 1200 in a saving account with a 1.5% interest rate. how much does she have now in her savings account now
PLEASE HELP!!!!!
The amount of money in her account after five years will be $1,292.74.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
A long time back Patricia put 1200 in a saving record with a 1.5% financing cost. Then the amount of money in her account after five years will be given as,
A = $1,200 × (1 + 0.015)⁵
Simplify the expression, then we have
A = $1,200 × (1.015)⁵
A = $1,200 × 1.07728
A = $1,292.74
The amount of money in her account after five years will be $1,292.74.
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What is the square number of 13?
Answer: If you wanted to know what 13x13, or the square of something is, then the value is 169. Or if you wanted to know the square root of 13, it would be about 3.606.
Step-by-step explanation: A square number is any number multiplied by itself = that number. For example, 12x12 = 144, which means the square root of 144 is 12, and the square number of 12 is 144.
What effect does a scale factor less than 1 have on the dimensions of the image being scaled?
A scale factor less than 1 will decrease the dimensions of the image being scaled
The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.
The resizing happens from a point called the center of dilation. It is the center of dilation from which the objects/figures are expanded or contracted.
Scale factor is a number by which the size of any geometrical figure can be changed with respect to its original size.
An image's dimension expand , when scale factor is greater than one
An image's dimension will decrease when the scale factor is less than one
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Sonya walks on a treadmill at a constant rate of 3.5 miles per hour. A graph showing the relationship between the time she walks and the distance she travels passes through the origin and through the point (1, 3.5). Name three other points that lie on the graph.
The other two points on the line are (2, 7) and (4, 14).
What is the slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.
Given, Sonya walks on a treadmill at a constant rate of 3.5 miles per hour
it is the slope.
∴ The equation of this line passing through point (1, 3.5) is,
3.5 = 3.5(1) + b.
b = 0.
So, y = 3.5x.
Now the other points can be obtained by choosing some integer values of x.
When x = 2, y = 7 ⇒ (2, 7).
When x = 4, y = 14 ⇒ (4, 14).
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Derek only had time to visit 90% of the exhibits at Aquaworld Aquarium. If Derek visited 36 exhibits, how many exhibits does the aquarium have?
Answer: 4 left
Step-by-step explanation:
36 divided by 90% = 40
40-36=4
What was Veronica’s mistake
By using the concept of distance, it can be calculated that
Veronica's mistake was that the number of animals seen per kilometer was not calculated by her. Arrangement was made on the basis of animals seen
What is distance?
Distance is the length of the path travelled by an object during its motion.
Here,
For River Edge
Number of animals seen = 8
Length of hike = 3 km
Number of Animals seen per km = [tex]8 \div3[/tex] = 2.67
For Wooden Marsh
Number of animals seen = 24
Length of hike = 8 km
Number of Animals seen per km = 24 [tex]\div[/tex] 8 = 3
For Canyon Creek
Number of animals seen = 35
Length of hike = 15 km
Number of Animals seen per km = [tex]35 \div 15[/tex] =2.33
Number of animals in ascending order are 2.33, 2.67, 3
Canyon Creek, River Edge, Marshy Land is the required arrangement from the least to the greatest.
Veronica's mistake was that the number of animals seen per kilometer was not calculated by her. Arrangement was made on the basis of animals seen
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Complete Question
Veronica went on three hikes. On each hike, she saw the following numbers of animals:
Rivers Edge 3 8
Wooded Marsh 8 24
Canyon Creek 15 35Veronica tried to order the hikes from least to greatest by number of animals seen per kilometer, but she made a mistake. Here's her work:
least greatest
8 24 35
rivers edge wooded marsh canyon creek
What was Veronica's mistake?