The order in which the two transformations in a composite transformation affect the final answer
How to determine the composite transformation?To determine if order matters or not, I will use the following example and illustration.
Let the coordinate of point A be:
A = (2, 5)
Perform the following transformations:
Translate by (x, y + 1)Dilate by a scale factor of 2First order: Translation before dilation
The translation by (x, y + 1) would give:
A' = (2, 5 + 1)
A' = (2,6)
The dilation by a scale factor of 2 would give
A" = 2 * (2,6)
A" = (4,12)
Second order: Dilation before translation
The dilation by a scale factor of 2 would give
A' = 2 * (2,5)
A' = (4,10)
The translation by (x, y + 1) would give:
A'' = (4, 10 + 1)
A'' = (4,11)
See that the final coordinates in both orders are not the same.
Hence, the order in which the two transformations in a composite transformation affect the final answer
Read more about transformation at:
https://brainly.com/question/1548871
#SPJ1
To sell 300 notebooks and 120 pens quickly, a store decided to create two types of gift sets. one set is to include 2 notebooks and 1 pen, and the other will consist of 1 pen and 3 notebooks. the first set will be sold for $8, while the second will be sold for $11.50. it is unprofitable to sell more than 20 of any gift set. how many gift sets of each type must the store sell to obtain the biggest possible income?
The store must sell 60 of each set each to obtain the biggest possible income
How to determine the number of each gift set?The given parameters can be represented using the following table:
Set 1 Set 2 Available
Notebook 2 3 300
Pen 1 1 120
Selling price 8 11.5
Using the above data values, we have:
Objective function: Max P = 8x + 11.5y
Subject to:
2x + 3y ≤ 300
x + y ≤ 120
Next, we plot the graph of the above inequalities (see attachment)
From the attached graph, we have:
(x,y) = (60,60)
Hence, the store must sell 60 of each set each to obtain the biggest possible income
Read more about maximizing functions at:
https://brainly.com/question/16826001
#SPJ1
If triangle ABC has vertices A(1, 2), B(-1, -1), and C(0, -2), which of the following coordinates is B’ of the dilation using the scale factor 4?
Answer: B'(-4, -4)
Given : A(1, 2), B(-1, -1), C(0, -2)
"Focusing on B coordinates"
If the points are dilated with a scale factor of 4
Then new coordinates : (-1, -1) × 4 = B'(-4, -4)
Answer:
B' = (-4, -4)
Step-by-step explanation:
Dilation: A type of transformation that makes the pre-image larger or smaller without changing its shape.
Center of a dilation: a fixed point about which all points are dilated.
Given:
A = (1, 2)B = (-1, -1)C = (0, -2)Scale factor = 4For dilation when the center of dilation is the origin (0, 0), simply multiply the coordinates of the vertices of the pre-image by the given scale factor to find the image under dilation:
Therefore:
A' = (1 x 4, 2 x 4) = (4, 8)
B' = (-1 x 4, -1 x 4) = (-4, -4)
C' = (0 x 4, -2 x 4) = (0, -8)
Apply the 45º-45º-90º Triangle Theorem to find the length of the hypotenuse of the triangle.
Answer:
The sine of the angle = the length of the opposite side. the length of the hypotenuse.
The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.
The tangent of the angle = the length of the opposite side. the length of the adjacent side.
Step-by-step explanation:
Answer:
c = a√2
Step-by-step explanation:
Apply the 45º-45º-90º Triangle Theorem to find the length of the hypotenuse of the triangle.
since there is no measure, I will write you the formula:
c (hypotenuse) = a√2
Mathematics
height=1cm,base=√5cm.what is the area of isosceles triangle?
Step-by-step explanation:
what is the formula for the area of a triangle ? hmm ?
area = baseline × height / 2
in our case (it does not matter for this question, if it is an isoceles triangle or not, the formula applies to all)
area = sqrt(5) × 1 / 2 = sqrt(5)/2 cm² = 1.118033989... cm²
Answer:
[tex]\huge\boxed{\sf Area = 1.12 \ cm^2}[/tex]
Step-by-step explanation:
Given data:Height = h = 1 cm
Base = b = √5 cm
Required:Area = A = ?
Formula:[tex]\displaystyle Area = \frac{1}{2}(b)(h)[/tex]
Solution:[tex]\displaystyle Area = \frac{1}{2} (\sqrt{5} )(1)\\\\Area = \frac{\sqrt{5} }{2} \\\\Area = 1.12 \ cm^2\\\\\rule[225]{225}{2}[/tex]
A family of 4 gets 505 text messages per month. Which of the following best describes the most even way these texts can be divided?
2 family members get 124 text messages each
2 family members get 125 text messages each
2 family members get 126 text messages each
2 family members get 125 text messages each
3 family members get 126 text messages each
1 family member gets 127 text messages
3 family members get 125 text messages each
1 family member gets 126 text messages
Answer:
3 family members get 126 text messages each
1 family member gets 127 text messages
Step-by-step explanation:
If you were finding the exact division of texts, 505 texts / 4 people, you would end up with 126.25 texts.
However, you can't get 0.25 of a text. If we take back each family member's 0.25 text, they will all be left with 126 texts (with an extra text leftover)
This extra text is considered the "remainder", meaning the amount left over when a number is divided [when it doesn't go into the larger number evenly]. The only importance/relevancy of a remainder is when a value cannot be split, such as a dog or a text.
So, we can give each family member 126 texts, and then we can give one family member an additional text, so that all texts are distributed.
This means that 3 family members get 126 texts, and 1 family member gets 127 texts
hope this helps!!
Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). Explain.
Find point Z that partitions the directed line segment XY in the ratio of 2:1 where X(1, 2) and Y(7, 5). Explain.
For both problems, we can use the section formula.
1) [tex]P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}[/tex]
2) [tex]Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}[/tex]
Find the value of y in the solution to the system of equations shown.
3y = 18x + 6
y = 2x + 14
A. y = 3
B. y = 4
C. y = 20
D. y = 26
Divide by 3
y=6x+2--(1)y=2x+14--(2)Equating
6x+2=2x+144x=12x=3Now
y=6(3)+2y=18+2y=20C
Answer:
C. y = 20
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}3y = 18x + 6\\y = 2x + 14\end{cases}[/tex]
Multiply the second equation by 3:
[tex]\implies (3)y=(3)2x+(3)14[/tex]
[tex]\implies 3y=6x+42[/tex]
Subtract this from the first equation to eliminate 3y:
[tex]\begin{array}{r l}3y & = 18x+6\\-\quad3y&=6x+42\\\cline{1-2}0&=12x-36\end{array}[/tex]
Solve the resulting equation for x:
[tex]\implies 12x-36=0[/tex]
[tex]\implies 12x=36[/tex]
[tex]\implies x=3[/tex]
Substitute the found value of x into the original second equation and solve for y:
[tex]\implies y=2(3)+14[/tex]
[tex]\implies y=6+14[/tex]
[tex]\implies y=20[/tex]
What is the equation of the linear function represented by the table?
I need help on this pleas,what is 9 ÷ 1/5
Answer:
45
Step-by-step explanation:
Flip the fraction, 1/5 to 5/1, and reverse the equation to a multiplication problem.
[tex]1/5 \rightarrow 5/1\\9 \cdot 5/1 = 45[/tex]
Let me know if you have questions or concerns.
6.75 into a mixed number
Answer:
6 3/4
Step-by-step explanation:
Answer:
6 3/4
Explanation:
0.75 is the result of dividing 3 by 4, which is the previous point but inversed.
f(x)=x^2+2x-5
g(x)=2x+4
what is (f•g)(x)
The product of the functions is 2x³ + 8x² - 2x - 20. Then the correct option is C.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The functions are given below.
f(x) = x² + 2x - 5
g(x) = 2x + 4
Then the product of the functions will be given as
(f•g)(x) = f(x) × g(x)
(f•g)(x) = (x² + 2x - 5) × (2x + 4)
(f•g)(x) = 2x³ + 8x² - 2x - 20
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ1
a) At what percent rate of compound interest per annum will the compound interest on Rs 1,25,000 be Rs 91,000 in 3 years?
The rate of compounding on the investment is 20%.
What is the rate of compounding?
When an amount compounds annually, it means that both the amount invested and the interest accrued increases in value once a year.
The formula that can be used to determine the rate of compounding is: (FV / PV)^(1 /n)
Where:
FV = future value = 125,000 + 91,000 = 216,000PV = present value = 125000n = number of years - 3(216,000 / 125000)^ (1 / 3) - 1 = 20%
To learn more about future value, please check: https://brainly.com/question/18760477
#SPJ1
5x-7≥8
This is a 2-step inequality: solve for x
your work by listing each step of the
process.
Answer:
x≥3
Step-by-step explanation:
Let's solve your inequality step-by-step. 5x−7≥8
Step 1: Add 7 to both sides.
5x−7+7≥8+7
= 5x≥15
Step 2: Divide both sides by 5.
5x/5≥15/5
= x≥3
Which of these graphs represents a function?
5NW&S
4
1
43-2-1₁ 1 2 3 4 5
-2
-3
-4
-5
W.
N.
1
-5-4-3-2-1 1 2 3 4 5
JANM
-5
-2
Y.
A
X
२४
-3-2-
>
८
4
3
1
-5-4-3-2-1 1 2 3 4
-2
-3
-4
-5
>
X.
V
5
4
-2
-3
-4
5
Z.
HE
४
+X
1 2 3 4 5
Answer: W
Step-by-step explanation:
The graph must pass the vertical line test.
The domain of a function f(x) is x > 1, and the range is y< 2. what are the
domain and range of its inverse function, f '(a)?
o a. domain: * > - 2
range: y si
o
b. domain: x < -2
range: y > 1
c. domain: x > 1
range: y < -2
o d. domain: x = 1
range: y > -2
submit
Answer: Domain: x<-2 Range: y>1
Step-by-step explanation:
I don't know for sure but I am taking the test and that was the outcome of the answer.
Which value of y forms the solution of the systems defined by y=11x+1 and 11x+12y=12
A. 1
B. 1/13
C. 11
D. 11/13
Answer:
b because it can't be full number
What is the inverse of the function f(x) = 2x + 1?
Answer:
:) The Inverse of the Function f(x) = 2x + 1 is f-1(x) = x/2 - 1/2.
Step-by-step explanation:
mark me brainlist^_^
A timer is started and a few moments later a model airplane is launched from the ground. Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−10)2+95. Which of the following statements is true?
The airplane reaches its maximum height of 10 feet in 95 seconds.
The airplane reaches its maximum height of 95 feet in 10 seconds.
The airplane reaches its minimum height of 95 feet in 10 seconds.
The airplane reaches its minimum height of 10 feet in 95 seconds.
Considering the given quadratic function, the correct statement is given by:
The airplane reaches its maximum height of 95 feet in 10 seconds.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient. If a > 0, the vertex is a minimum point, and if a < 0 it is a maximum point.
In this problem, the function is:
h(t) = -(t - 10)² + 95.
Hence the vertex is (10, 95), and since a < 0, the correct statement is given by:
The airplane reaches its maximum height of 95 feet in 10 seconds.
More can be learned about quadratic functions at https://brainly.com/question/24737967
#SPJ1
A summer job as a life guard at lincoln pool pays 9.50 per hour how much willl you earn for working 6 hours
57
Step-by-step explanation:
$ 9.50 -> 1 hr
? -> 6 hrs
9.50(6) = $ 57
Two random samples were taken to determine how often people in a community listen to the local radio station each month.
The first sample surveyed 15 people as they exited the bank on Main Street. The first sample found that the mean number of hours they listened to the radio each month was 20.
The second sample surveyed every sixth person as they exited the only local grocery store until 100 people were surveyed. The second sample found that the mean number of hours they listened to the radio each month was 12.
Which statements are true? Check all that apply.
The true statements about the sample include:
The second sample is random.The second sample is likely to be more representative of the population.The second sample will give a better representation because is it larger.Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month.What is a sample?
Sampling is the selection of a subset of individuals from within a statistical population to estimate the characteristics of the whole population.
The second sample is random because in the second sample, people were surveyed at random. Every sixth person that exited the grocery store was surveyed and this selection represents an unbiased sampling method of the general population.
The options include:
Which statements are true? Check all that apply.
A) The second sample is random.
B) The second sample is likely to be more representative of the population.
C) The first sample is likely to be more representative of the population.
D) The second sample will give a better representation because is it larger.
E) The first sample will give a better representation because it is smaller.
F) Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month.
Learn more about sampling on
https://brainly.com/question/5404367
#SPJ1
The only thang i need help is area and for question 7. 8. and 9. no bots ONLY THE AREA
The area of the triangle based on the information given is 16.67 inches ²
How to calculate the triangle?It should be noted that the area of a triangle is given by the formula:
= 1/2 × base × height
In this second figure, the height will be:
= 5.9² - (3.4/2)²
= 5.9² - 1.7²
= 34.81 - 2.89
= 5.65
The area will be:
= 1/2 × base × height
= 1/2 × 5.65 × 5.9
= 16.67 inches ²
Learn more about triangles on:
brainly.com/question/17335144
#SPJ1
help me please these dot plots show hourly earnings for a sample of workers in two different
careers
career a
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
career b
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
hourly eamings (5)
what are the differences between the centers and spreads of these earning
distributions?
select two choices: one for the centers and one for the spreads
a. spreads: the hourly earnings for career b are more spread out
b. spreads: the hourly earnings for career a are more spread out.
c. centers career bhas greater median hourly earnings than career
d. centers: career a has greater median hourly earnings than career
The hourly earnings for career a are more spread out.
Career a has greater median hourly earnings than career.
What is the spread and median of the data plots?Median is the number at the center of the dataset that is arranged either in ascending order or descending order.
The median of career A is 60.
The median of career b is 40
Spread refers to the range of the dataset. Career A has a greater range than career B.
Please find attached the image of the dot plot. To learn more about median, please check: https://brainly.com/question/14746682
#SPJ1
I need help asap please? and this is for math? what is the missing angle of the triangle? the 2 angles are 55 and 90!!
Answer:
the missing angle of the triangle is 35
Step-by-step explanation:
180-90= 90-55= 35
Answer:
i agree with losesight57
Step-by-step explanation:
Sean spends 35 minutes revising for his exam. Erica spends 1 hours 15 minutes revising for her exam. Work out the total time, in minutes, spent revising by Sean and Erica. please help ASAP
The total time spent in minutes is 110 minutes
How to determine the total time?The given parameters are:
Erica = 1 hour, 15 minutesSean = 35 minutesThe total time is calculated as:
Total = Erica + Sean
So, we have:
Total = 1 hour, 15 minutes + 35 minutes
1 hour = 60 minutes
So, we have:
Total = 60 minutes + 15 minutes + 35 minutes
Evaluate the sum
Total = 110 minutes
Hence, the total time spent is 110 minutes
Read more about time at:
https://brainly.com/question/4931057
#SPJ1
can someone help me with theses answers and a explanation
The arrangement of the numbers in the ascending order will be 11, 13, and 17.
The complete question is given below.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Ali picked a three number from a hat.
The lowest number was 11.
The range was 13.
The median was 17.
The arrangement of the numbers in the ascending order. Then we have,
11, 13, and 17.
The arrangement of the numbers in the ascending order will be 11, 13, and 17.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
The first graph represent a=450-20t, which describes the relationship between gallons of water in tank and time in minutes. a. Where on the graph can we see 450? Where can we see the -20? b. What do these numbers mean in this situation?
Answer:450 is the intercept. We see it when t=0 (where the line cross the y axis). -20 is the slope
Step-by-step explanation: y = 20 is a thing no one would ever solve for but to do it, 20=450-20t -> y =20 when t=(20-450)/20. I don’t know why anyone would ever need to find this value
What type of Symmetry
Answer:
Line Symmetry, Horizontal and Vertical Lines, 90 and 180 degrees
Step-by-step explanation:
It is line symmetry because you can fold the H, and it would overlap perfectly.
Horizontal and vertical lines because if you were to place a line in the middle both horizontally and vertically it would overlap.
90 and 180 degrees because the H would still have have symmetry if you flipped it on its side or upside down.
A right triangle has a hypotenuse of 14 inches and another side that is 12 inches. What is the length of the missing side of the triangle?
Answer:
7.2111
Step-by-step explanation:
14 squared times 12 squared= squareroot ofmissing angle
Ezra has a square brick patio. he wants to reduce the width by 6 feet and
increase the length by 6 feet.
6 ft
6 ft
6 ft
6 ft
let x represent the length of one side of the square patio. write expressions
for the length and width of the new patio. then find the area of the new patio
if the original patio measures 13 feet by 13 feet.
The area of the new patio if the original patio measures 13 feet by 13 feet is 133 ft².
Ezra has a square brick patio. he wants to reduce the width by 6 feet and
increase the length by 6 feet.
What is the area of the square?The area of the square is the measure of the space occupied by it. It is equal to the product of the measure of its two sides.
We need to write the expression for the new patio and the area of the new patio if the original patio measures 13 feet by 13 feet.
let x be the measure of the side of a square.
The length increased by 6 ft, so the new length=x+6.
The width decreased by 6 ft, so the new width=x-6.
The area is the product of length and width, so the new area is
l×w = (x+6)×(x-6)
Since the original side is 13 ft, the new length is 13+6 = 19 ft, and the new width is 13-6=7 ft.
So, the area is (19 ft)×(7 ft) = 133 ft²
Hence, the area of the new patio if the original patio measures 13 feet by 13 feet is 133 ft².
To learn more about the area of the square visit:
https://brainly.com/question/22964077
#SPJ1
Sital says that 2.5cm³ is the same as 25mm³. Is she right?
Answer:
Sital is right
Step-by-step explanation:
This is because there are 10mm in a cm so therefore you would times 2.5cm by 10 to get 25mm