Use the translation (x,y)=(x+5,y-9). What is the image of C(4,-2)?
A. (9,-7)
B. (9,-11)
C. (9,7)
Answers
The correct answer is B. (9, -11).
The translation (x,y)=(x+5,y-9) moves every point 5 units to the right and 9 units down. So, to find the image of C(4,-2), we need to add 5 to the x-coordinate and subtract 9 from the y-coordinate.
Image of C(4,-2) = (4+5,-2-9) = (9,-11)
Therefore, the answer is B. (9,-11).
Using the translation (x, y) = (x + 5, y - 9), we will apply this rule to the point C(4, -2) to find its image.
The new x-coordinate will be: 4 + 5 = 9
The new y-coordinate will be: -2 - 9 = -11
So, the image of C(4, -2) is (9, -11).
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Related Questions
Find the value of x in the triangle below:
Answers
Answer:
x=12
Step-by-step explanation:
turn into and equation because angles in a triangle add up to 180°
so
6x-19+3x+7+84=180
collect like terms
9x+72=180
solve to find 'x'
9x=108
x=12
What is a rule for the translation of ARST to AR'S'T' ? Select all that apply.RSГуRISतकT-2이erA. T-7,3)B. 7 units down; 3 units rightC. 7 units right; 3 units downD. T7.-3
Answers
Given :
R'S'T' is the image of RST
we will find the rule of translation using the coordinates of :
\(\begin{gathered} R=(-4,5) \\ R^{\prime}=(3,2) \end{gathered}\)So, the rule will have the form :
\(\begin{gathered} R\rightarrow R^{\prime} \\ (x,y)\rightarrow(x+h,y+k) \end{gathered}\)\(\begin{gathered} 3=-4+h\rightarrow h=7 \\ 2=5+k\rightarrow k=-3 \end{gathered}\)So, the answer is :
T(7,-3)
7 units right ; 3 units down
dots are spaced one unit apart, horizontally and vertically. what is the number of square units enclosed by the polygon?
Answers
The number of square units enclosed by the polygon is 18.
First, count the number of dots that are enclosed by the polygon (including those on the boundary). There are 14 such dots.Next, count the number of dots on the boundary of the polygon. There are 8 dots on the boundary.Each of the dots on the boundary corresponds to a line segment of the polygon.
So, the perimeter of the polygon is 8 units (the length of each of these line segments).Now, we can use Pick's theorem to find the area of the polygon. Pick's theorem states that A = i + b/2 - 1, where A is the area of the polygon, i is the number of dots inside the polygon, and b is the number of dots on the boundary of the polygon.
So, plugging in the values we have: A = 14 + (8/2) - 1 = 14 + 4 - 1 = 17
Therefore, the area of the polygon is 17 square units.However, we have to remember that the dots are spaced one unit apart, horizontally and vertically.
Therefore, each square that is enclosed by the polygon has an area of 1 square unit. We counted 17 such squares, so the total area enclosed by the polygon is 17 square units.
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During a rainstorm 2inches of rain fell in 5hours at that rate how many hours will It take for 20 inches of rain to fall
Answers
Answer:
You would get 8in of rain Hope this Helped
Step-by-step explanation:
what is the perimeter of the garden?
Answers
D) 20 ft.
If the area of a square garden is 25 square feet, it means that the length of each side of the square is the square root of 25, which is 5 feet.
To find the perimeter of the square garden, we need to add up the lengths of all four sides. Since all sides of a square are equal, we can simply multiply the length of one side by 4 to get the perimeter.
Perimeter = 4 x length of one side
Perimeter = 4 x 5 ft
Perimeter = 20 ft
Therefore, the perimeter of the square garden is 20 feet.
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Find the definite integral using its geometric interpretation. Sketch the graph of the integrand. So g(x) dx, where q (u) = 160-18|-6 Enter the greater value of the x-intercept of g (2), rounded to the nearest hundredth,
Answers
The greater value of the x-intercept of g(2) rounded to the nearest hundredth is 14.89.
What is a definite integral?
To find the definite integral using its geometric interpretation, we need to sketch the graph of the integrand and calculate the area under the curve between the given limits.
First, let's sketch the graph of the integrand function, g(x). The integrand is given as g(x) = 160 - 18|x - 6|. We'll break it down into two cases based on the absolute value:
For x ≤ 6:
In this case, |x - 6| = -(x - 6) = -x + 6. Therefore, g(x) = 160 - 18(-x + 6) = 160 + 18x - 108 = 18x + 52.
For x > 6:
In this case, |x - 6| = x - 6. Therefore, g(x) = 160 - 18(x - 6) = 160 - 18x + 108 = -18x + 268.
Now let's plot the graph of g(x):
The graph of g(x) consists of two line segments: one with a positive slope of 18 starting at (0, 52) and passing through (6, 160), and the other with a negative slope of -18 starting at (6, 160) and passing through (14.89, 0).
To find the definite integral of g(x) dx between x = -6 and x = 2, we need to calculate the area under the curve bounded by these limits. Since the area below the x-axis represents negative values, we'll subtract the area of the triangle below the x-axis from the area of the trapezoid above the x-axis.
The area of the trapezoid is given by:
A = [(b1 + b2) * h] / 2,
where b1 is the length of the longer base, b2 is the length of the shorter base, and h is the height.
In this case, the longer base is the segment from (6, 160) to (14.89, 0), which has a length of 8.89 units. The shorter base is the segment from (0, 52) to (6, 160), which has a length of 6 units. The height is the difference between the y-coordinates of the two bases, which is 160 - 0 = 160 units.
Therefore, the area of the trapezoid is:
A = [(8.89 + 6) * 160] / 2 = 1758.4 square units.
Now let's calculate the area of the triangle below the x-axis. The base of the triangle is 6 units, and the height is 52 units.
Therefore, the area of the triangle is:
A = (6 * 52) / 2 = 156 square units.
To find the definite integral, we subtract the area of the triangle from the area of the trapezoid:
Definite integral = Area of trapezoid - Area of triangle
= 1758.4 - 156
= 1602.4 square units.
Since the question asks for the greater value of the x-intercept of g(2), let's find the x-coordinate of the point
We know that g(x) = 18x + 52 for x ≤ 6, and g(x) = -18x + 268 for x > 6.
For x ≤ 6:
Setting g(x) = 0, we have:
18x + 52 = 0
18x = -52
x = -52/18 ≈ -2.89
For x > 6:
Setting g(x) = 0, we have:
-18x + 268 = 0
18x = 268
x = 268/18 ≈ 14.89
Since we're interested in the greater value of the x-intercept, the x-coordinate of the point where g(2) intersects the x-axis is approximately 14.89 (rounded to the nearest hundredth).
Therefore, the greater value of the x-intercept of g(2) rounded to the nearest hundredth is 14.89.
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A polygon has vertices A(3,3), B(3,6) , and C(9,3). Find the area of the polygon
Answers
The area of the given polygon is 9 square units.
To find the area of the polygon with vertices A(3,3), B(3,6), and C(9,3), we can use the formula for the area of a triangle. Since the given points form a triangle, we can calculate the area of this triangle and consider it as the area of the polygon.
First, we need to find the base and height of the triangle. The base can be determined as the distance between points A and C, which is the horizontal distance between their x-coordinates. In this case, the base is 9 - 3 = 6 units.
Next, we find the height of the triangle, which is the vertical distance between point B and the line formed by points A and C. In this case, the height is the difference between the y-coordinate of point B and the y-coordinate of point A, which is 6 - 3 = 3 units.
Now, we can calculate the area of the triangle using the formula:
Area = (base * height) / 2
Area = (6 * 3) / 2 = 9 square units
Therefore, the area of the given polygon is 9 square units.
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PLEASE HURRY 20 POINTS I NEED THIS REALLY REALLY SOON
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create an inequality in standard form that represents the restaurant owner’s desired revenue.
Type the correct answer in each box. Use numerals instead of words.
blank x^2 blank + x + blank ≥
Answers
The desired revenue for the restaurant owner can be represented by an inequality in standard form: x^2 + x + c ≥ 0, where x represents the number of $1 increases and c is a constant term.
To calculate the hourly revenue from the buffet after x $1 increases, we multiply the price paid by each customer by the average number of customers per hour. Let's assume the price paid by each customer is p and the average number of customers per hour is n. Therefore, the total revenue per hour can be calculated as pn.
The number of $1 increases, x, represents the number of times the buffet price is raised by $1. Each time the price increases, the revenue per hour is affected. To represent the desired revenue, we need to ensure that the revenue is equal to or greater than a certain value.
In the inequality x^2 + x + c ≥ 0, the term x^2 represents the squared effect of the number of $1 increases on revenue. The term x represents the linear effect of the number of $1 increases. The constant term c represents the minimum desired revenue the owner wants to achieve.
By setting the inequality greater than or equal to zero (≥ 0), we ensure that the revenue remains positive or zero, indicating the owner's desired revenue. The specific value of the constant term c will depend on the owner's revenue goal, which is not provided in the question.
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pls help this is past due and I have no idea on how to do it
Answers
Answer:
42.3
Step-by-step explanation:
Substitute in values\(3.6\times (3)+4.5\times (7) = 10.8+31.5=42.3\)The maximum number of students in a classroom
is 26. If there are 16 students signed up for the
art class, how many more students can join the
class without exceeding the maximum?
Answers
Answer:
10 students
Step-by-step explanation:
The maximum number is 26 and 16 have already signed up so in order to know how many can join without exceeding the maximum. You subtract 16 from 26. which then leaves you with 10
60,192 visitors/minute = _____ visitors/day
Please show ur work
Answers
Answer: 86,676,480 Visitors!
Step-by-step explanation:
There are 1,440 minutes per day and if there are 60,192 visitors per day, by multiplying 1,440 by 60,192 you would get 86,676,480.
A barge traveled 30 miles up a river in 5 hours What was the average rate of travel, in miles
per hour, of the barye?
Answers
Answer:
6 miles per hour
does this help??
Step-by-step explanation:
Average speed = distance/time = 30/5 = 6 miles/hour
Match each step in the process of solving square root of 6y= saque root of 36+2y. With its justification
Answers
Answer:
y=9 - division property of equality
6y=36+2y - squaring property of equality
4y=36 - subtraction property of equality
Step-by-step explanation:
Answer:
y = 9 > division property of equality
6y = 36 + 2y > squaring property of equality
4y = 36 > subtraction property of equality
Step-by-step explanation:
edg 2021
A home run is hit in such a way that the baseball just clears a wall 20 m high, located 120 m from home plate. The ball is hit at an angle of 37
∘
to the horizontal, and air resistance is negligible. (Assume that the ball is hit at a height of 1.0 m above the ground.) (a) Find the initial speed of the ball. m/s (b) Find the time it takes the ball to reach the wall. 5 (c) Find the velocity components of the ball when it reaches the wall. \begin{tabular}{l|l} x-component. & m/s \\ recomponent & m/s \end{tabular} Find the speed of the ball when it reaches the wall.
Answers
The initial speed of the ball can be determined using the range equation for projectile motion. The horizontal distance traveled by the ball is given by:
Range = (Initial velocity) * (Time of flight)
In this case, the range is 120 m and the angle of projection is 37 degrees. The time of flight can be calculated using the equation:
Time of flight = (2 * Initial velocity * sin(angle)) / g
where g is the acceleration due to gravity (approximately 9.8 m/s^2). Plugging in the given values, we can solve for the initial velocity:
120 m = (Initial velocity) * [(2 * sin(37)) / 9.8]
Solving this equation will give us the initial velocity of the ball.
The time it takes for the ball to reach the wall can be found using the horizontal component of the velocity. Since air resistance is negligible, the horizontal velocity remains constant throughout the motion. The horizontal distance traveled by the ball is 120 m, and the horizontal velocity is given by:
Horizontal velocity = Initial velocity * cos(angle)
By dividing the horizontal distance by the horizontal velocity, we can find the time it takes for the ball to reach the wall.
To find the velocity components of the ball when it reaches the wall, we can use the equations for projectile motion. The horizontal component of the velocity remains constant and is equal to the initial horizontal velocity. The vertical component of the velocity can be calculated using the equation:
Vertical velocity = Initial velocity * sin(angle) - (g * time)
where time is the time it takes for the ball to reach the wall (found in part.
Using the given values, we can calculate the horizontal and vertical components of the velocity.
The speed of the ball when it reaches the wall can be found by calculating the magnitude of the velocity vector at that point. This can be calculated using the equation:
Speed = sqrt((Horizontal velocity)^2 + (Vertical velocity)^2)
Calculating this will give us the speed of the ball when it reaches the wall.
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which is the equation of a parabola with focus (-5,3) and vertex (-5,6)
Answers
Answer:
(y−6)=(-1/12)*(x+5)² i think
Step-by-step explanation:
A car drives at a speed of 90km/h for 2 hours and 20 minutes.
How far does the car drive
Answers
The car drives a distance of 210 kilometers.
To find the distance the car drives, we can use the formula:
Distance = Speed × Time
The given speed is 90 km/h. However, we need to convert the time of 2 hours and 20 minutes into hours.
Since there are 60 minutes in an hour, 20 minutes is equal to 20/60 = 1/3 hours. Therefore, the total time is 2 hours + 1/3 hours = 2 1/3 hours.
Now we can calculate the distance:
Distance = 90 km/h × 2 1/3 hours
To multiply a whole number by a mixed fraction, we convert the whole number to a fraction with the same denominator as the mixed fraction:
Distance = 90 km/h × 7/3 hours
Simplifying:
Distance = (90 × 7) km / (3 hours)
Distance = 630 km / 3
Distance = 210 km
Therefore, the car drives a distance of 210 kilometers.
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Jeff has two sticker-printing machines. Each machine can print 42 stickers per minute. On day 1, only the first machine was used, and it printed 89 stickers. On the following day, the first machine printed for x minutes and the second machine printed for y minutes. Which expression shows the total number of stickers printed by both machines during these two days? (1 point) a 131x + 42y b 42 + 89x + y c 89 + 42x + 42y d 89x + 84y
Answers
Answer:
c 89+42x+42y
Step-by-step explanation:
On day 1 :
First Machine= 89 stickers
Second Machine= none
On day 2 :
First Machine= ? stickers ( if in 1min = 42stickers
x min=?
( x min/1 min × 42stickers)
=42x stickers.
Second Machine=?stickers ( if in 1min = 42stickers
y min=?
( y min/1 min × 42stickers)
=42y stickers.
Total = 89 + 42x + 42y
factorize 4x^3 -8x^2- 12x
Answers
Answer:
Step-by-step explanation:
4x³ - 8x² - 12x = 4x ( x² - 2x - 3)
= 4x (x² + x - 3x - 3*1)
= 4x [ x(x + 1) - 3(x +1)]
= 4x [ (x +1) (x - 3)]
= 4x (x + 1)(x-3)
Answer:4x^3 -8x^2- 12x
Taking common4 x
4X(x²-2x-3)
Doing middle term factorization
4x(x²-3x+x-3)
4x(x(x-3)+1(x-3))
4x(x-3)(x+1) is your answer
Step-by-step explanation:
What is the volume of the rectangular pyramid
Answers
Answer:
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Finding the Volume of a Rectangular Pyramid
Your overall formula for finding the volume of these multi-faceted shapes is V = (l x w x h) / 3. Basically, your first step is finding the area of the base by multiplying length by width. Once you determine the area of the base, multiply that by the height.
Answer:
Finding the Volume of a Rectangular Pyramid
Your overall formula for finding the volume of these multi-faceted shapes is V = (l x w x h) / 3. Basically, your first step is finding the area of the base by multiplying length by width. Once you determine the area of the base, multiply that by the height.
Step-by-step explanation:
What's the missing angle?
Answers
Answer:
125 and 55
Step-by-step explanation:
The total angle degree of (2x+3) and (x-6) is 180. So, you add both, and set the equation equal to 180 degrees.
2x+3+x-6=180
3x-3=180
3(x-1)=180
x-1=60
x=61
Substitute that for your angles, and you get your answers.
Given the parent graph
f(x) = 4^x
explain all transformations to the parent
graph given the new functions
f(x) =-1/3 • 4x
Answers
Using translation concepts, it is found that the new function was reflected over the x-axis and vertically compressed by a factor of 3.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The functions are given as follows:
Parent: \(f(x) = 4^x\).Translated: \(f(x) = -\frac{1}{3} \times 4^x\).The translated function was multiplied by -1/3, hence it was reflected over the x-axis(multiplication by negative number) and vertically compressed by a factor of 3(fraction of 1/3).
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let x1 and x2 be two independent random variables with respective variances σ21 = k and σ22 = 2. given that the variance of y = 3x2 −x1 is 25, find k.
Answers
The value of k is 7.
We know that the variance of a linear combination of independent random variables can be calculated using the following formula:
Var(\(a_{X}\) + \(b_{Y}\)) = \(a^{2}\) * Var(X) + \(b^{2}\) * Var(Y)
In this case, we have Y = 3\(X_{2}\) - \(X_{1}\), so we can substitute this into the formula:
Var(3\(X_{2}\) - \(X_{1}\)) = \(3^{2}\) * Var(\(X_{2}\)) + \((-1)^{2}\) * Var(\(X_{1}\))
Given that Var(Y) = 25, and Var(\(X_{1}\)) = k, and Var(\(X_{2}\)) = 2, we can solve for k:
25 = 9 * 2 + 1 * k
25 = 18 + k
k = 25 - 18
k = 7
Therefore, the value of k is 7.
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Suppose you had been in charge of designing the study. What sample size would be needed to construct a margin of error of 2% with 95% confidence
Answers
Answer:
A sample size of 2401 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).
The margin of error is given by:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
95% confidence level
So \(\alpha = 0.05\), z is the value of Z that has a p-value of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).
What sample size would be needed to construct a margin of error of 2% with 95% confidence?
This is M for which n = 0.02.
Supposing we have no estimate for the true proportion, we use \(\pi = 0.5\).
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}\)
\(0.02\sqrt{n} = 1.96*0.5\)
\(\sqrt{n} = \frac{1.96*0.5}{0.02}\)
\((\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2\)
\(n = 2401\)
A sample size of 2401 is needed.
Multiply 2.89x 23.2 =
Answers
289 x 232 = 67048
67.048
67.048
Y=x-12, y=14 what is x I need someone to answer fast please
Answers
Answer:
x = 26
Step-by-step explanation:
If Y= x - 12 and Y = 14
Then we input the value of y which gets us the equation of: 14 = x - 12
Now we add 12 on both sides to isolate the variable.
We ADDED 12 because we needed a way to cross out the - 12 on the right side. Now the equation would be 14+12 = x
Easily we can find that 26=x
Find the missing measurements in triangle ABC. If angle C has 35 degrees, and the side length of BC is 9, what are the missing measurements?
Answers
The missing measurements are m∡B =55, AB = 5.2 and AC = 7.3
How to determine the missing measurementsThe complete question is added as an attachment
From the given figure, we get,
m∡B = 180 - (90 + 35) --- sum of angles in a triangle
m∡B =55
use Law of Sines to find AB and AC:
sin(35) = AB/9
So, we have
AB = sin(35) * 9
Evaluate
AB = 5.2
Next, we have
AC^2 = 9^2 - 5.2^2
AC^2 = 53.96
Take square roots
AC = 7.3
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adian picks apples at the rate of 11 apples every minute. how many apples would he pick in 36 minutes
Answers
Answer:
Adian would pick 396 apples in 36 minutes.
Step-by-step explanation:
Therefore, in 1 minute, Adian picks 11 apples.
In 36 minutes, he will pick:
11 apples/minute x 36 minutes = 396 apples.
Therefore, Adian would pick 396 apples in 36 minutes.
Answer:
396 apples
Step-by-step explanation:
adian picks apples at the rate of 11 apples every minute
So in order to find out how many he picks in 36 minutes we just multiply 36 by 11
36 x 11 = 396 apples in 36 minutes
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The temperature increase 12 Fahrenheit between 9 AM and noon decreased 9 Fahrenheit between noon and 6 PM
Answers
Complete question :
The temperature increased 12 degrees between 9 am and noon. it decreased 9 degrees between noon and 6 pm. write an expression with three terms to show the change in temperature. let the first term represent the temperature at 9am.
Answer:
(t + 12 - 9)°F
Step-by-step explanation:
Let the temperature at 9:00 am = t
Temperature increase between 9:00 am and noon = 12 degrees
Temperature at noon = t + 12
Temperature decreased between noon and 6:00 pm
Temperature at 6:00 pm :
(t + 12) - 9
Hence final temperature at 6:00 pm :
(t + 12 - 9)
If 1 1/2 sections are 3/4 mile long, how long is each section?
Answers
Answer:
1/2 mile
Step-by-step explanation:
.75 mile /1.5 sections = .5 mile/section
In one area along the interstate, the number of dropped wireless phone connections per call follows a Poisson distribution. From four calls, the number of dropped connections is 2 0 3 1 (a) Find the maximum likelihood estimate of 2. (b) Obtain the maximum likelihood estimate that the next two calls will be completed without any ac- cidental drops.
Answers
The solution involves calculating the likelihood function, maximizing it, and using the estimated value to find the probability of no dropped connections in the next two calls.
(a) To find the maximum likelihood estimate of λ, the mean number of dropped connections per call, we need to use the Poisson distribution to calculate the likelihood function L(λ) for the given data. The Poisson distribution is given by:
P(X = x | λ) = (λ^x * e^(-λ)) / x!
where X is the random variable representing the number of dropped connections per call, λ is the parameter representing the mean number of dropped connections per call, and x is the observed number of dropped connections in a call.
The likelihood function for four calls with observed numbers of dropped connections 2, 0, 3, and 1 can be expressed as:
L(λ) = P(X = 2 | λ) * P(X = 0 | λ) * P(X = 3 | λ) * P(X = 1 | λ)
= (λ^2 * e^(-λ)) / 2! * (e^(-λ)) / 0! * (λ^3 * e^(-λ)) / 3! * (λ^1 * e^(-λ)) / 1!
= (λ^6 * e^(-4λ)) / 6
Taking the derivative of L(λ) with respect to λ, setting it equal to zero, and solving for λ.
d/dλ [L(λ)] = d/dλ [(λ^6 * e^(-4λ)) / 6]
= [(6λ^5 * e^(-4λ) - 4λ^6 * e^(-4λ)) / 6]
Setting this derivative equal to zero, we get:
2λ - 3λ^2 = 0
λ = 0 or λ = 2/3
Since λ = 0 is not a valid solution for a Poisson distribution, the maximum likelihood estimate of λ is λ = 2/3.
Therefore, the maximum likelihood estimate of the mean number of dropped connections per call is 2/3.
(b) To obtain the maximum likelihood estimate that the next two calls will be completed without any accidental drops, we can use the estimated value of λ = 2/3 to calculate the probability of no dropped connections in each of the next two calls, using the Poisson distribution:
P(X = 0 | λ = 2/3) = (2/3)^0 * e^(-2/3) / 0! = e^(-2/3) ≈ 0.5134
P(both calls have no drops | λ = 2/3) = P(X = 0 | λ = 2/3)^2 ≈ 0.2637
Therefore, the maximum likelihood estimate that the next two calls will be completed without any accidental drops is approximately 0.2637.
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