The image of vertex C under the given similarity transformation is (4, 2).
To apply the given similarity transformation, we need to perform two transformations: a rotation of 90 degrees counterclockwise about the origin (denoted by R) and a dilation by a factor of 2 (denoted by D2). We perform the transformations in order: first the rotation, then the dilation.
The image of a point (x, y) after a rotation of 90 degrees counterclockwise about the origin is (-y, x).
Thus, the image of C after the rotation is:
C' = (-(-2), 1) = (2, 1)
To find the image of C' after the dilation by a factor of 2, we multiply each coordinate by 2:
C" = (22, 21) = (4, 2)
Therefore, the image of vertex C under the given similarity transformation is (4, 2).
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The sum of my digits is 14. their difference is 4. I am less than 60. What number am I?
The width of a rectangle is 15 feet more than the length. The perimeter is 290 feet. Find the length and width.
Answer:
The length = 65 The width = 80
Step-by-step explanation:
w = 15^2 = 290
225 =290
290-225 =80
w=80
80 - 15 = 65
l = 65
65+65+80+80=290
Answer:
Length: 65
Width: 80
Step-by-step explanation:
Lets turn it into an algebraic expression. x is the length.
length width
x x+15
2x + 2(x+15) = 290
2x +2x +30 =290
4x = 260
x = 65
65+15 = 80
Juanita is an accident reconstruction expert. She measured a 70-foot chord from the outer rim of the yaw mark on the road surface. The middle ordinate measured 9 feet in length. The drag factor of the road surface was determined to be 1.13. What is the minimum speed that the car was traveling when the skid occurred? Record your answer to the nearest tenth.
The minimum speed at which the car was traveling is 52.9 miles per hour.
To find the minimum speed at which the car was traveling during the skid, we can use the formula for calculating skid speed:
Skid speed = (Chord length x Chord length x Drag factor) / (2 x Middle ordinate)
Plugging in the given values:
Chord length = 70 feet
Middle ordinate = 9 feet
Drag factor = 1.13
Skid speed = (70 x 70 x 1.13) / (2 x 9)
Skid speed = 1391 / 18
Skid speed ≈ 77.3 feet per second
To convert the speed to miles per hour, we can multiply it by 3600/5280
= 77.3 x (3600/5280)
≈ 52.9 miles per hour
Therefore, the minimum speed at which the car was traveling is 52.9 miles per hour.
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Overnight, a pipe cracked and started to leak into a basement. The graph shows the depth of the water in relation to time.
The water rises 10 inches each hour. The water is 4 inches deep is the water after four hours. It will take 8 hours for the water to reach a depth of 80 inches.
A pipe cracked overnight and started to leak into a basement.
The graph represents the depth (d) of the water over time (t).
As per the given graph, the required solution would be as:
Take two points (1, 10) and (5, 50) in the given graph
The linear function will be :
d - 10 = (50-10)/(5-1)(t - 1)
d - 10 = (40/4)(t - 1)
d = 10(t - 1) + 10
d = 10t - 10 + 10
d = 10t
Here slope of the given function is 10, which means 10 inches the water rise each hour.
The value of time (t) = 4 hr corresponds to the depth of water (d) is
d = 10(4) = 40
So, the water is 40 inches deep is the water after four hours
The value of depth of water (d) = 80 in corresponds to the time (t) is
80 = 10t
t = 80/10 = 8
So, It will take 8 hours for the water to reach a depth of 80 inches
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A ) find the perimeter of the plot land
B) find the area of the plot land without the building and parking lot
The perimeter of the plot land is 78.49 units and the area of the plot land without the building and parking lot is 210 square units
Finding the perimeter of the plot landFrom the graph, the vertices of the land are
A = (0, 20), B = (25, 19), C = (20, 2) and D = (5, 0)
Calculate the distance between adjacent vertices
So, we have
AB = √[(0 - 25)² + (20 - 19)²] = 25.02
BC = √[(20 - 25)² + (2 - 19)²] = 17.72
DC = √[(20 - 5)² + (2 - 0)²] = 15.13
AD = √[(0 - 5)² + (20 - 0)²] = 20.62
The perimeter of the plot land is
P = 25.02 + 17.72 + 15.13 + 20.62
P = 78.49 units
Finding the area of the plot landThis is calculated as
Area = Plot land - Building - Parking lot
Using the vertices, we have
Area = 1/2 * |0 * 19 + 25 * 2 + 20 * 0 + 5 * 20 - (20 * 25 + 19 * 20 + 2 * 5 + 0 * 0)| - [1/2 *(15 - 7 + 17 - 7) * (15 - 10)] - [(18 - 10) * (10 - 5)]
This gives
Area = 295 - 45 - 40
So, we have
Area = 210
Hence, the area is 210 square units
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A recent concert sold $916 worth
of tickets. Students were charged
$1.25 and adults were charged
$2.25. If 560 people attended, how
many adults attended the concert?
How many students?
Answer:
250 students and 310 adults
Step-by-step explanation:
so if students are charged 1.25 and adults are charged 2.25 and 560 people attended if you divided from it should equal
100 people questioned, 37 say they eat fruits, 33 say they eat vegetables, 9 say they eat cheese and fruits, 12 eat cheese and vegetables, 10 eat fruits and vegetables, 12 eat only cheese, and 3 report they eat all three offerings. How many people surveyed eat cheese? How many do not eat any of the offerings?
Answer:
Done
Step-by-step explanation:
To solve the problem, we can use a Venn diagram to visualize the information provided in the question.
Let's draw three overlapping circles to represent the three groups of people: those who eat fruits, those who eat vegetables, and those who eat cheese.
We know that:
- 37 people eat fruits, so we write "37" in the circle representing fruits.
- 33 people eat vegetables, so we write "33" in the circle representing vegetables.
- 9 people eat both cheese and fruits, so we write "9" in the overlap between the cheese and fruits circles.
- 12 people eat both cheese and vegetables, so we write "12" in the overlap between the cheese and vegetables circles.
- 10 people eat both fruits and vegetables, so we write "10" in the overlap between the fruits and vegetables circles.
- 12 people eat only cheese, so we write "12" in the part of the cheese circle that does not overlap with the other circles.
- 3 people eat all three offerings, so we write "3" in the intersection of all three circles.
Here's what the Venn diagram looks like:
```
Cheese
+----9----+----3----+----12---+
| | Cheese | | |
| Fruits +----6----+--4 | |
| | | | |
+----10---+----3----+----8---+---+
| Vegetables |
+------------+
9 24 15
```
To find out how many people eat cheese, we add up the numbers in the cheese circle: 9 + 3 + 12 = 24. So, 24 people eat cheese.
To find out how many people do not eat any of the offerings, we need to add up the numbers in the regions that are not part of any circle: the region outside of all circles, and the region in the center of the Venn diagram. These regions add up to 9 + 15 = 24. So, 100 - 24 = 76 people do eat at least one of the offerings.
If anyone can help me on this please
true or false if two squares have equal side length then they are congruent
Find the area of the given shapes.
Area of a Triangle - Pre-Algebra
A
48 units2
B
24 units2
C
54 units2
D
30 units2
The area of the triangle given at the end of the answer is of:
B. 24 units².
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
Considering the image presented for this problem, the dimensions for the triangle are given as follows:
b = 12, h = 4.
Hence the area is given as follows:
A = 0.5 x 4 x 12
A = 24 units².
This means that option B is the correct option in the context of this problem.
Missing InformationThe triangle is given by the image presented at the end of the answer.
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A 30-year-old earns an average income and plans to retire in 35 years. The employee plans to begin making $6,000 annual contributions into an IRA.
Which type of IRA is best for the employee, and why?
The Roth IRA is the best choice because the employee will pay less in taxes during employment than in retirement.
The Traditional IRA is the best choice because the employee will pay less in taxes during employment than in retirement.
The Roth IRA is the best choice because the employee will pay more in taxes during employment than in retirement.
The Traditional IRA is the best choice because the employee will pay more in taxes during employment than in retirement.
The IRA that is best is C. The Roth IRA is the best choice because the employee will pay more in taxes during employment than in retirement.
Why is the Roth IRA best ?When contributing to a Roth IRA, one must use after-tax dollars, resulting in taxes being paid on the money prior to it being deposited into the account. Withdrawals made from a Roth IRA that meet the necessary qualifications are completely exempt from taxation, thus employees will not be required to pay any taxes on the amount withdrawn during their retirement period.
It is probable that an employee's retirement income tax bracket will be higher than their current bracket, given the anticipated increase in their income and tax rate.
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Which statement is true about the functions f(x) = -15x2 + 32 and g(x) = -17x2 + 5x + 32?
The true statement is that f(x) and g(x) have the same y-intercept. Option C.
Function problemBoth f(x) and g(x) have the same y-intercept. We can see this by setting x = 0 for both functions.
For f(x), we get:f(0) = -15(0)^2 + 32 = 32
For g(x), we get:g(0) = -17(0)^2 + 5(0) + 32 = 32
The other statements are not necessarily true. f(x) and g(x) do not necessarily have the same zeros, as the coefficients and constants in the functions are different.
The maximum value of f(x) and g(x) would depend on the vertex of each function, which may or may not be the same.
Finally, neither f(x) nor g(x) are odd functions, as they do not satisfy the property of f(-x) = -f(x) or g(-x) = -g(x) for all x.
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URGENT
A box contains 18 large marbles and 16 small marbles. Each marble is either green or white. 7 of the large marbles are green, and 7 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is large or green? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
p(large or green) = 0.794
Step-by-step explanation:
A box contains 18 large marbles and 16 small marblesEach marble is either green or white7 of the large marbles are green, and 7 of the small marbles are whiteIf a marble is randomly selected from the box, we need to find the
probability that it is small or green
1. Find P(large) ⇒ P(l)
2.Find P(green) ⇒ P(g)
3. Find P(large and green) ⇒ P(l and g)
4. Use the rule P(large or green) = P(l) + P(g) - P(l and g)
∵ The box contains 18 large marbles and 16 small marbles
∴ The total number of marbles = 18 + 16 = 34
∴ P(l) = 18/34
∵ There are 7 large green marbles
∵ There are 18 large marbles
∴ P(l and g) = 7/34
7 large green marbles9 small green marblesnumber of green marbles = 7+9 = 16∴ P(g) = 16/34
∵ P(large or green) = P(l) + P(g) - P(l and g)
∴ P(large or green) = 18/34 + 16/34 - 7/34
∴ P(large or green) = 27/34
= 0.7941176471
If a marble is randomly selected from the box, then the probability that it is large or green is 0.794
Find the area of the shaded region.
f(x)=x4-12x³ +48x², g(x) = 44x+105
340-
(-1,61)
(5,325)
co.
8
Q
Polestarp
Answer:
To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:
x^4 - 12x^3 + 48x^2 = 44x + 105
x^4 - 12x^3 + 48x^2 - 44x - 105 = 0
We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:
x = -1.932, x = 0.695, x = 4.149
Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.
The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:
A = ∫3^4 [g(x) - f(x)] dx
A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx
A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx
We can integrate term by term using the power rule:
A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4
A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]
A = 347.2
Therefore, the area of the shaded region is approximately 347.2 square units.
help please Find the base angles of the figure below.
A) 130°
B) 65°
C) 25°
D) 50°
Answer:
c
Step-by-step explanation:
The two angles on the bottom are equal.
All 3 angles equal 180 degrees.
We know one angle is 130.
The other two are 180-130= 50 combined.
Since those angles are equal, divide by two.
50/2= 25 degrees each.
how do u find the answer to this pls help
59P₂ = (Type a whole number.)
The value of permutation expression ₅₉P₂ is 3422.
What is permutation?A permutation is an arrangement of objects in a definite order.
To find the value of ₅₉P₂, we use the formula below
Formula:
Pₐ = (n!)/(n-r)!...................... Equation 1Where:
Pₐ = ₅₉P₂n = 59r = 2! = FactorialSubstitute these values into equation 1
₅₉P₂ = 59!/(59-2)! ₅₉P₂ = (59×58×57!)/(57!) ₅₉P₂ = 3422Learn more about about permutation here: https://brainly.com/question/29595163
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Question 7 (5 points)
Graph f(x)=(x-4) (x+4)
x²-8x+12
A graph that represent the system of quadratic equations is shown in the image attached below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
By expanding the bracket, we have:
f(x) = (x - 4)(x + 4)
f(x) = x² - 4x + 4x - 16
f(x) = x² - 16
Since the leading coefficient (value of a) in the given quadratic function y = x² - 8x + 12 is positive 1, we can logically deduce that the parabola would open upward and the y-intercept is given by the ordered pair (0, 12).
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17. Find the circumference given KL= 4.6 in. Round to the nearest tenth.
The circumference of the circle 48.4 inches.
How to find the circumference of a circle?The circumference of a circle is the perimeter of the circle. Therefore, let's find the circumference of the circle as follows:
length of arc = ∅ / 360 × 2πr
where
∅ = central angler = radiusTherefore, let's find the radius
length of arc = 35 / 360 × 2 × 3.14 × r
4.6 = 219.8 / 360 r
4.6 = 0.61055555555 r
divide both sides by 0.61
r = 4.6 / 0.6
r = 7.7 inches
Therefore,
circumference = 2 × 3.14 × 7.7
circumference = 48.356
circumference = 48.4 inches
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What is the value of x?
Answer:
Step-by-step explanation:
A cross section is taken from a sphere.Which of the following is true?
Option A is correct: the cross-section of a sphere must be a circle.
When a sphere is cut by a plane, the resulting cross-section will always be a circle, regardless of the orientation or angle of the cut. This is because all cross-sections of a sphere have the same shape and size as a great circle, which is a circle that passes through the center of the sphere and divides it into two equal halves.
Option B is not correct because an ellipse is not a possible cross-section of a sphere.
Option C is not correct because the cross-section of a sphere can only be a circle, not an ellipse.
Option D is not correct because a line is not a possible cross-section of a sphere. A line can only be a cross-section of a cylinder or a cone, but not a sphere.
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got the answer but said that it was wrong still?
19. What is the tangent of ?
5√/11
11
O 5√11
O 6√11
√11
5
Hello,
tan = opposite/ adjacent
[tex]tan0 = \frac{5}{\sqrt{11} } = \frac{5\sqrt{11} }{11}[/tex]
it's the first answer
The table shown below provides statistical data on the bowling scores for David and Elise.
Bowling Score Data
David
145
Interquartile Range 30
Mean
Elise
120
20
David claims that his scores were more consistent than Elise's scores. Which statement is
MOST likely true about David's claim?
t
David claims that his scores were more consistent than Elise's scores. Which statement is
MOST likely true about David's claim?
David's claim is correct because his mean score is greater than Elise's mean score.
David's claim is correct because the interquartile range for his scores is greater than the interquartile range
for Elise's scores.
David's claim is incorrect because his mean score is greater than Elise's mean score.
David's claim is incorrect because the interquartile range for his scores is greater than the interquartile
Answer:
Step-by-step explanation:
Let's set David's score to D, and Aaron's score to A. If so, we get the equation that satisfies the constraints:
D = 3*A-5, D + A = 215
Set D in terms of A:
D = 215 - A
Input it into the equation:
215 - A = 3*A - 5 -> add 5 and A to both sides to set numbers to the left and variables to the right
215 + 5 = 3* A + A ->
220 = 4A -> divide by 4
220/4 = A ->
55 = A -> substitute A into D + A = 215
D + 55 = 215 -> subtract 55 from both sides
D = 215 - 55 = 160
So, out final answer is:
D = 160, A = 55
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 36 and a standard deviation of 3. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 33 and 39? Do not enter the percent symbol. ans = %
Answer:
According to the empirical rule (also known as the 68-95-99.7 rule), for a bell-shaped distribution, approximately:
- 68% of the data falls within one standard deviation of the mean.
- 95% falls within two standard deviations of the mean.
- 99.7% falls within three standard deviations of the mean.
In this case, the mean number of phone calls answered by each receptionist is 36, and the standard deviation is 3.
To calculate the percentage of daily phone calls numbering between 33 and 39, we need to find the proportion of data within one standard deviation of the mean in either direction.
The range of interest (33 to 39) is within one standard deviation of the mean, so approximately 68% of the data will fall within this range.
Therefore, the approximate percentage of daily phone calls numbering between 33 and 39 is 68%.
Find the area under the curve
from 1 to 2.
thank you guys sm
2.883
I used Desmos graphing calculator to find this answer.
Find the surface area of the triangular prism.
3,360 m2
1,662 m2
6,720 m2
1,872 m2
The total surface area of the triangular prism is is 1872 square meters
Finding the surface area of the triangular prismFrom the question, we have the following parameters that can be used in our computation:
The triangular prism
The surface area of the triangular prism from the net is calculated as
Surface area = sum of areas of individual shapes that make up the of the triangular prism
Using the above as a guide, we have the following:
Area = 1/2 * 12 * 16 * 2 + 35 * (20 + 16 + 12)
Evaluate
Area = 1872
Hence, the surface area is 1872 square meters
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help me find an answer?
Answer:
The solution is (-2, 0).
ABCD is a square and AB = 5cm. What is the perimeter and the area of rectangle EFGH if AE=AH=FC=GC = 2cm square
The perimeter and the area of rectangle EFGH are 24 cm and 35 square cm
Calculating the perimeter and the area of rectangle EFGHFrom the question, we have the following parameters that can be used in our computation:
Side length, AB = 5 cm
Extension AE=AH=FC=GC = 2cm
Using the above as a guide, we have the following:
Dimension of the rectangle = 5 cm By (5 + 2) cm
So, we have
Dimension of the rectangle = 5 cm By 7 cm
The perimeter is then calculated as
P = 2 * (5 + 7) = 24 cm
The area is calculated as
A = 5 * 7 = 35 square cm
Hence, the perimeter and the area of rectangle EFGH are 24 cm and 35 square cm
See attachment for figure
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C) John, a meteorologist, recorded the temperatures from Monday to Frida and the mean temperature of five days was 40°F. The temperatures recorded on four consecutive days were 40°F, 39°F, 44°F, and 40°F. What temperature was recorded on the fifth day?
Average is the total sum of the given values divided by the number of values.
The average low temperature for the week is -3°F.
We have,
It is the total sum of the given values divided by the number of values.
We have,
Temperatures for one week:
Day Temperature
Sunday −5 °F
Monday −8 °F
Tuesday −6°F
Wednesday −8°F
Thursday −3 °F
Friday 2° F
Saturday 7° F
The average of the low temperature:
= [ -5 + (-8) + (-6) + (-8) + (-3) + 2 + 7 ] / 7
= (-5 - 8 - 6 - 8 - 3 + 2 + 7) / 7
= -30 + 9 / 7
= -21 / 7
= -3
Thus,
The average low temperature for the week is -3°F.
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complete question:
Christopher recorded the low temperature each day for 1 week and recorded his results in this table.
Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Low −5 °F −8 °F −6 °F −8°F −3 °F 2° F 7° F
What is the average low temperature for the week?
Guests are filling out RSVP cards for Maria's wedding. They must choose which type of entree they would prefer for dinner. The choices are chicken, beef, or vegetarian dinners. Abigail chooses an entree; on the other side of town, Zeke also chooses. Are these two events dependent or independent?
These two events are independent because the outcome of both doesn't affect each other.
What is an independent and dependent events?An independent event is the type of event that occurs when the outcome of one event does not affect the outcome of the second event it is compared with.
A dependent event is the type of event that it's outcome affects the outcome of the second event it is compared with.
That Abigail chose an entree in a town different from Zeke doesn't affect her ability to attend the wedding.
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My sallary was first increased by 10% and then decreased by 10%.find the net change in my salary.
Hello,
x = departure's sallary
increasing a value by 10% means multiplying it by 1,1decreasing a value by 10% means multiplying it by 0,9x*1,1*0,9 = 0,99x
multiplying by 0,99 is equivalent to decreasing by 1%the net change in my salary is 1%
