The triangle JLK is transformed to J''K''L'' by a rotation of 90° anticlockwise and a translation of -2 units
What is Rotation?The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.
90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
Given data ,
Let the triangle be represented as ΔJKL
Now , the coordinates of the triangle JKL is
J ( 2 , -4 ) , K ( 5 , -4 ) and L ( 2 , -2 )
And , the transformed triangle be represented as Δ J''K''L
Now , the coordinates of the triangle J''K''L'' is
J'' ( 2 , 2 ) , K'' ( 2 , 5 ) and L'' ( 0 , 2 )
The triangle JKL is first rotated by an angle of 90° counterclockwise rotation: (x,y) becomes (-y,x) to form J'K'L'
So , substituting the values in the equation , we get
The coordinates of the triangle J'K'L' is
J' ( 4 , 2 ) , K' ( 4 , 5 ) and L' ( 2 , 2 )
Now , when the triangle is translated -2 units to up , we get
So , the coordinates of the triangle J''K''L'' is
J'' ( 2 , 2 ) , K'' ( 2 , 5 ) and L'' ( 0 , 2 )
Hence , the transformed triangle is going through a rotation of 90° counterclockwise and a translation of -2 units
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Answer:
Either
90 degree rotation about point 0 composition translation of 0 units x, negative 2 units y
or
90 degree rotation about point 0 composition translation of negative 2 units x, 0 units y
Step-by-step explanation:
The answer above is correct.
Simplify the expression.
768x^8y^5
O A. 42³y32²
O B. 2xy² √2x
OC. 4x²y3y
O D. 4x²y3x²y
Answer:
4y^4√3x^2y
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
An oil spill spreads 25 square meters every $\frac{1}{6}$
hour. What is the area of the oil spill after 2 hours?
Answer:
Step-by-step explanation:
Area = l x w
Area = 25 x 12
Area = 350sqm²
When a projectile is at the top of its path What is its Y direction velocity?
When a projectile is at the top of its path, its vertical velocity that is Y direction velocity is 0 m/s. At this point, the projectile has reached its maximum height and is changing direction from moving upward to moving downward.
What is vector?A vector is a matrix that has only one row or one column. A row vector is a matrix with only one row. Example Because it only contains one row, the matrix is a row vector. A column vector is a matrix with only one column. We can express a vector as a matrix since it is simply a collection of integers. This is why vectors may be written in matrix notation. A vector is a quantity linear array. A matrix is a two-dimensional array of values. Tensors are three-dimensional and higher-dimensional arrays that exist. A matrix may be seen as both a series of column vectors and a sequence of row vectors.
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a management dilemma defines the research question. (True or False)
Answer:
False
Step-by-step explanation:
39 · 89 · 89 · 53 · 74
39
·53
·74
·89
Multiply.
39 * 89 * 89 * 53 * 74 * 39 * 53 * 74 * 89
= 16,493,560,000,000,000
A number that is greater than 2 1/3 and less then 2 2/5
Answer: 2 21/60
Step-by-step explanation:
2 21/60 is greater than 2 and 1/3 because is you multiply each number by 20, you would get 2 20/60. If you take 2/5 and multiply each by 12, you would get 24/60. This means that 2 21/60, 2 22/60, and 2 23/60 would be greater than 2 1/3 and less than 2 2/5.
Pls help asap ! . . . . . . . . . . .
The solution is (6, 32) and it means that the total cost of 6 kites from 2 different businesses is $32.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
From the graph of two lines,
The intersection point is the solution to the two lines system of equations.
Now,
The intersection point = (6, 32)
This means,
x = 6 and y = 32
x = number of kites
y = total cost of the kites
Thus,
The solution is (6, 32).
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random samples of size 49 are taken from a population that has 400 elements, a mean of 170, and a variance of 196. the distribution of the population is unknown. the mean and the standard error of the distribution of sample means are .
The mean and the standard error of the distribution of sample means are 170 and 1.876 respectively.
As per the given data random samples of size 49 are taken from a population that has 400 elements.
N = 400
n = 49
The mean of the data is 170.
[tex]$ \mu_{\bar{x}}=\mu=170 \\[/tex]
The variance of the data is 196
If the sample size is more than 5 %. of the entire population, a finite population correlation factor (fpc) is multiplied with standard error,
Finite population correlation factor = [tex]$\sqrt{\frac{N-n}{N-1}} \\[/tex]
Finite population correlation factor = [tex]$\sqrt{\frac{400-49}{400-1}} \\[/tex]
Finite population correlation factor (fpc) = [tex]$\sqrt{\frac{351}{399}} \\[/tex]
Finite population correlation factor (fpc) = [tex]\sqrt{0.8797} \\[/tex]
Finite population correlation factor (fpc) = 0.937923
Finite population correlation factor(fpc) [tex]$& \simeq[/tex] 0.938
The standard error of the mean,[tex]$\sigma_\bar{x}$[/tex] [tex]$=\frac{\sqrt{196}}{\sqrt{49}} \times \mathrm{fpc}$[/tex]
[tex]$\sigma_\bar{x}$[/tex] [tex]$& =\frac{14}{7}(0.938) \\[/tex]
[tex]$\sigma_\bar{x}$[/tex] = 1.876
Therefore the mean and the standard error of the distribution of sample means are 170 and 1.876.
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you're given a six sided die. you're told that rolling an even number is as likely as rolling an odd number. you're told that rolling a 1, 2, or 3 is as likely as rolling a 4, 5, or 6. you're told that rolling a 1 is as likely as rolling a 6. is the probability of rolling a 3 equal to the probability of rolling a 4?
P(A) is the likelihood that a six-sided die will produce an even number when rolled (2, 4, or 6).
P(B) is the likelihood that a six-sided dice will land on four.
P(A) = 3/6 = 1/2
P(B) = 1/6
The probability of rolling an even number followed by a four, or P(C), equals P(A) * P(B) = 1/2*1/6 = 1/12 = 0.083 since events A and B are independent of one another.
With a six-sided die, there is a roughly 0.83*100 or 8.3% probability of rolling an even number (2, 4, or 6), followed by a four.
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The number of visitors at the aquarium was 3 times the number of visitors at the art museum. There were 1,500 visitors at the aquarium. Solve the equation 3m = 1,500 to find the number of visitors m at the art museum.
Answer:
m=500
Step-by-step explanation:
do 1,500 divided by 3
a small apartment has a 11ft by 11ft bedroom, a 4ft by 6ft bathroom, and a single multi-use 15ft by 16ft living room/kitchen. what is the total square footage (area) of the apartment?
The total square footage (area) of the apartment is 385 square feet.
The total square footage, also known as the area, of an apartment is a measure of how much space the apartment has.
First, let's find the area of the 11ft by 11ft bedroom. To do this, we multiply the length and the width of the room. In mathematical terms, the area of a rectangle is equal to the length times the width. So, for the bedroom, the area is
=> 11ft * 11ft = 121 square feet.
Next, let's find the area of the 4ft by 6ft bathroom. The formula for the area of a rectangle is still the same, so the area of the bathroom is
=> 4ft * 6ft = 24 square feet.
Finally, we'll find the area of the multi-use living room/kitchen, which is 15ft by 16ft. The area of this room is
=> 15ft * 16ft = 240 square feet.
Now that we have the area of each room, we can add them together to find the total area of the apartment. So, the total area is
=> 121 square feet + 24 square feet + 240 square feet = 385 square feet.
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If 5 sweaters cost 47.45$, how much would 7 sweaters cost?
Answer:
$66.43
Step-by-step explanation:
47.45$ divided by 5
9.49*7
=66.43
what is the answer?
My teacher never explained this to me
The value of sinθ for the condition is 0.822.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given the identity cos²θ + sin²θ = 1
and cosθ = 0.57 where 0 < θ < π/2
the value of θ varies from 0 to π/2 which means θ is in the first quadrant.
substitute the value in identity,
cos²θ + sin²θ = 1
(0.57)² + sin²θ = 1
sin²θ = 1 -0.3249
sinθ = √0.6751
sinθ = 0.8216
or sinθ = 0.822
Hence the value of sinθ is 0.822.
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Here is your graph from the previous screen.
A new restaurant charges `\$7` for each burrito, and a `\$5` delivery fee.
Describe how the graph of this new restaurant's burrito delivery would be the same and how it would be different.
The new graph would have the same intercept, however it would always assume lesser values than the old graph due to the new slope being less than the old slope.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the price per burrito.The intercept b represents the delivery fee.Hence the two functions are given as follows:
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If m∠ABF=(7b−24)°
and m∠ABE=2b°
, find m∠EBF
.
The measure angle EBF is (5b-24)°.
What are adjacent angles?Adjacent angles are those angles that are always placed next to each other in such a way that they share a common vertex and a common side but they do not overlap each other.
Give that, m∠ABF =(7b-24)° and m∠ABE =2b°.
From the figure,
m∠ABF =m∠ABE + m∠EBF
(7b-24)°=2b° + m∠EBF
m∠EBF = 7b-24-2b
m∠EBF = (5b-24)°
Therefore, the measure angle EBF is (5b-24)°.
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13 with work please and thank you
The required simplified value of x for the given similar triangles is given as x = 5.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
Here,
From the similar triangle property,
The ratio of sides is equal for similar triangles so,
12/[12-8] = 15/x
12/4 = 15/x
x = 15/3
x = 5
Thus, the required simplified value of x for the given similar triangles is given as x = 5.
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consider that in 2019 u.s. household income had a mean of $64,000, a standard deviation of $12,000, and a frequency distribution that was mound-shaped and symmetric. determine the z-score for someone with an income of $40,000. group of answer choices -3.00 -2.00 2.00 3.00
A z-score of -2 means that the income of $40,000 is 2 standard deviations below the mean income of $64,000.
The z-score is a standard measure of how many standard deviations a data point is away from the mean. To determine the z-score, we need to use the formula:
z = (x - μ) / σ
Where x is the data point of interest ($40,000), μ is the mean ($64,000), and σ is the standard deviation ($12,000).
Substituting the values:
z = (40000 - 64000) / 12000
z = -2
Therefore, the z-score for someone with an income of $40,000 is -2.
In conclusion, a z-score of -2 means that the income of $40,000 is 2 standard deviations below the mean income of $64,000.
Hence, the correct answer is B.
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--The given question is incorrect; the correct question is
"Consider that in 2019, U.S. household income had a mean of $64,000, a standard deviation of $12,000, and a frequency distribution that was mound-shaped and symmetric. Determine the z-score for someone with an income of $40,000.
A. -3.00
B. -2.00
C. 2.00
D. 3.00"--
Select the correct answer. What is the simplest form of the ratio 11 : 16? A. 1 : 6 B. 5 : 8 C. 11 : 16 D. 22 : 32
Answer:
C. 11:16
Step-by-step explanation:
It is C, it can't go simpler bcs of 11
Which inequality is equivalent to IX-41 <9?
O-9> x-4 <9
O-9 < x-4<9
O x-4 <-9 or x-4 <9
O x-4>-9 or x-4 < 9
The correct compound inequality is:
x - 4 < 9 or x - 4 > -9
Which inequality is equivelnt to |x - 4| < 9?We want to find a compound inequality equal to the absolute value one below:
|x - 4| < 9
We can break it into two ones, these are:
x - 4 < 9
x - 4 > -9
Solving these two we will get:
x < 9 + 4 = 13
x > -9 + 4 = -5
Then the compound inequality is:
x < 13
x > -5
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4. Factor the expression completely.
6×3- 4×2 – 16x
A. 0
B. 2x(3×2 – 2x – 8)
C. 2x(3x + 4)(x – 2)
D. 4x(2x + 1)(x – 4)
E. 2x(2×2 + 7x – 4)
6x³ - 4x² - 16x
To factorize the expression first factor out the GCF out
The GCF in the expression is 2x
2x( 3x² - 2x - 8)
Next, Factorize the terms in the bracket
To factorize write - 2x as a difference
2x( 3x² + 4x - 6x - 8)
Factor out x from the expression
2x [ x( 3x + 4) - 6x - 8 ]
Next factor out - 2 from the expression
2x [ x ( 3x + 4) - 2( 3x + 4) ]
Factor out 3x + 4 from the expression
The final answer : 2x( 3x + 4)( x - 2)
Letter C
based on the data you graphed, what type(s) of cancer appear to have a positive correlation with smoking rates?
The calculation for the correlation coefficient for the data graphed was 0.99 which is indicative of a strong positive correlation between smoking rates and lung cancer.
The data graphed showed a positive correlation between smoking rates and lung cancer. The correlation coefficient for the data was 0.99, which is very close to 1. This indicates a strong positive correlation between smoking rates and lung cancer. The formula for calculating the correlation coefficient is r = (NΣxy - (Σx)(Σy)) / √[(NΣx2 - (Σx)2)(NΣy2 - (Σy)2] where r is the correlation coefficient, N is the number of data points, Σx is the sum of all x-values, Σy is the sum of all y-values, Σxy is the sum of the products of the x and y values, and Σx2 and Σy2 are the sums of the squares of the x and y values respectively. The calculation for the correlation coefficient for the data graphed was 0.99 which is indicative of a strong positive correlation between smoking rates and lung cancer.
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John paid $75.75 for 3 shirts and jayda paid $108.00 for 4 shirts. Who paid less per shirt
Answer:John
Step-by-step explanation: John got 3 shirts each for 25.25
Jayda got 4 shirts each for 27
WILL GIVE BRAINLIST!!
The secant-tangent rule which is a relationship between a secant and a tangent of a circle indicates that we have;
(a) [tex]\overline{BC}[/tex]² = [tex]\overline{CD}[/tex] × [tex]\overline{CF}[/tex]
(b) The length of the tangent [tex]\overline{BC}[/tex], found based on the secant-tangent rule is 12 inches
What is a tangent to a curve?A tangent to a curve at a point is the line that touches the curve at the specified point and has the same slope as the curve at the point.
(a) The relationship between the lengths of the segments formed by the secant and the tangent is indicated by the secant-tangent rule which can be presented as follows;
[tex]\overline{BC}[/tex]² = [tex]\overline{CD}[/tex] × [tex]\overline{CF}[/tex]
Therefore, the relationship between the segments is that the square of the length of the tangent is equivalent to the product of the length of the secant and the external segment of the secant
(b) Where the length of the secant (segment) [tex]\overline{CD}[/tex] = 16 inches, and the length of the external segment of the secant, [tex]\overline{CF}[/tex] = 9 inches, therefore, according to the secant-tangent rule, we get;
[tex]\overline{BC}[/tex]² = 16 × 9 = 144
[tex]\overline{BC}[/tex] = √(144) = 12
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Which of the following terms does NOT apply to rhombus ABCD? Square Kite Parallelogram Trapezoid
Answer: 4) Trapezoid.
Step-by-step explanation:
#1 A rhombus has four equal sides, has opposite angles that are equal, and opposite sides that are parallell.
#2 A rhombus is close to three quadrilaterals that apply to a rhombuses terms, parallel sides, equal sides, equal angles, or opposite angles that are equal are: square, kite, and parallelograms that have the following.
#3 A Trapezoid, however, has four different lengths and different angles. Only one pair of sides from a trapezoid are parallel.
Your welcome, I hope this much information will help you. Good day/night. If the answer incorrect, or there are errors in this explanation, please let me know. Thank you.
if the station stocks 600 gallons at the start of the week, what is the probability that thry sell more than 250 gallons
The exact probability cannot be determined without additional information such as the average daily sales rate.
To find the probability of selling more than 250 gallons, we need to find the cumulative distribution function (CDF) of the number of gallons sold, which is the probability of selling a certain amount or less. Since the amount sold follows a Poisson distribution with an average of 200 gallons, the CDF can be calculated using the Poisson cumulative distribution function formula:
P(X <= x) = e^(-μ) * (μ^x) / x!
Where μ is the average number of gallons sold and x is the amount sold. To find the probability of selling more than 250 gallons, we subtract the CDF for 250 gallons or less from 1. This gives us the probability of selling more than 250 gallons.
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An artist is building a pedestal out of wood that will be used to display a piece of sculpture. She plans to cover the pedestal with tile.
How much tile will it take to cover the pedestal?
PLEASE HELP
The amount of tile that would be used to cover the pedestal is equal to the area of the pedestal
What is area of an object?The area of an object is the amount of two-dimensional space it occupies.
It is a measure of the size of a surface and is typically expressed in square units, such as square meters or square inches.
The area can be determined for various shapes including squares, rectangles, circles, triangles, and more complex shapes.
for a rectangle it is calculated by the formula
length * width
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Amy's company makes solid balls out of scrap metal for various industrial uses. Her current task is to make a batch of aluminum balls with radius 4.5 in. If she
has a total of 76.302 in
of aluminum, how many balls can she make?
Use 3.14 for I, and do not round your answer.
The number of aluminium balls with a radius of 4.5 in will be 200.
What is the volume of the sphere?The amount of space that a sphere can occupy is measured by its volume. The three-dimensional shape of a sphere lacks vertices and edges.
Given that Amy's company makes solid balls out of scrap metal for various industrial uses. Her current task is to make a batch of aluminium balls with a radius of 4.5 in. The total volume of the aluminium is 76302 cubic inches.
The number of spheres with a radius of 4.5 inches will be calculated as:-
Number = ( Total volume of aluminium) / ( Volume of the small sphere)
The volume of small sphere = ( 4 / 3 ) πr³
The volume of small sphere = ( 4 / 3 ) π x 4.5³
The volume of the small sphere = 381.7 cubic inches
Number = ( Total volume of aluminium) / ( Volume of the small sphere)
Number = 76302 / 381.7
Number = 200
Hence, the number of spheres will be 200.
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a salesperson is paid $300 per week plus 15% commission on her weekly sales of x dollars. find a linear function that represents her total weekly pay w in terms of x.
Answer:
w = 300 + 0.15x
Step-by-step explanation:
Let x = weekly sales
Since there is a fixed remuneration of $300, that will be a constant in the linear equation
15% = 15/100 = 0.15 in decimal
15% commission on x dollars of sales = 0.15x
Therefore total weekly pay, w, in terms of x
w = 300 + 0.15x
the sum of a certain infinite geometric series is $2$. the sum of the squares of all the terms is $3$. find the common ratio.
The common ration between the sum of a certain infinite geometric series is 2. the sum of the squares of all the terms is 3 is ( r,a) = ( 1/7, 12/7)
That means { a/ 1-r} = 2
a^2/1-r^2 = 3
2a/ 1+r = 3
2(2-2r)/ 1+r = 3
4-4r= 3+ 3r
7r + 1
r= 1/7
2a/ 8/7 = 3
7a= 12
a= 12/7
so( r,a) = ( 1/7, 12/7)
What is infinite geometric series?
An infinite geometric series is the sum of an infinite geometric sequence. This series would have no last term. The general form of the infinite geometric series is a1 + a1r + a1r2 + a1r3+…, where a1 is the first term and r is the common ratio.
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please help me. it’s a practice assignment and i don’t know what to do.
The population will be 40 thousnd after 22.5 years,and 60 thousand after 34.4 years.
How to estimate the number of years?First, we want to estimate the number of years that takes to reach 40 thousand, to estimate that we need to look at the graph.
We can see that when y = 40, the value of x is between 20 and 25 (almost in the middle)
So here we estimate that the answer is 22.5
b) Now we want to estimate it using the equation
p(x) = 18*e^(0.035*x)
We want to find how many years it takes to reach a population of 60 thousand, then we need to solve:
p(x) = 18*e^(0.035*x) = 60
e^(0.035*x) = 60/18
Using the natural logarithm in both sides:
ln( e^(0.035*x)) = ln(60/18)
0.035*x = ln(60/18)
x = ln(60/18)/0.035 = 34.4
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