Identify a transformation of the function f(x) = |x| by observing the equation of the function g(x) = |x|- 2.
The base graph has been shifted right 2 units.
The base graph has been shifted down 2 units.
The base graph has been shifted left 2 units.
The base graph has been shifted up 2 units.
Answers
The base graph has been shifted down 2 units.
g(x) = f(x) -2 and that -2 is outside the f(x) notation, so it's an up/down transformation. -2 says "move it down 2 units."
A transformation of the function f(x) = |x| by observing the equation of the function g(x) = |x|- 2 is option B; The base graph has been shifted down 2 units.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
Right shift by c units:
y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k:
\(y = k \times f(x)\)
Horizontal stretch by a factor k:
\(y = f\left(\dfrac{x}{k}\right)\)
We have g(x) = f(x) -2 and that -2 is outside the f(x) notation,
Thus, it's an up/down transformation -2 says "move it down 2 units."
Therefore, The base graph has been shifted down 2 units.
Hence, A transformation of the function f(x) = |x| by observing the equation of the function g(x) = |x|- 2 is option B.
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Related Questions
HELPPPP PLEASEEEEEEE!!!!
Answers
Answer:
Depends on the range of x
Step-by-step explanation:
Does that make sense to you
Please explain how to write this in the horizontal model and the 3 other questions. Thank you! Sample Problem (remember the real"problem will be similar but could be presented differently Lau and LauLLC(LLLLC)builds swimming builds custom swimming pools in Boise,Idaho.LL LLC uses material reguisition forms and direct labor time tickets to trace direct materials and direct labor costs to specific jobs. Manufacturing overhead is applied to all jobs based on a percent of direct labor costs At the beginning of the second month of operations, the company had the following balances: oRaw Materials $75,000 Work in ProcessWIP) $140,000 Finished Goods -0- During the second month of operations (June 201XX),the company recorded the following transactions. aPurchased S225.000 in raw materials bssued the S150.000 of raw materials to production.of which S125.000 were direct materials cRecorded the following labor costspaid in cash) S60.000 in direct labor S40,000 in construction supervisorssalaries S26,000 in administrative salaries dRecorded the following actual manufacturing overhead costs oConstruction insurance 10,000 oConstruction equipment depreciation S55,000 Pool permits and inspections 9,000 eRecorded the $18.000 in selling and administrative costs. fApplied manufacturing overhead to jobs using 175%of direct labor costs gCompleted 16 pools at a total cost of S352,000.One1of these pools costingS22,000 is still waiting for final inspection and customer approval so the sale has not been finalized. hRealized sales revenue of S525.000 on the sale of the 15 pools that were sold Closed the Manufacturing Overhead account balance to Cost of Goods Sold. Required Questions: 1Draw the following t-accounts or colurmns and enter their beginning balances:Raw Materials WIP.Finished Goods,MOHCOGS if you find it helpful to draw SG&A Sales Revenue and Cash that is okay but not required). 2Record the transactions listed above and calculate the ending balances for all accounts 3)How much is manufacturing overhead over or underapplied? 4What isthe adiusted ending balance for CostofGoods Sold
Answers
(3) Add: Under applied overhead 34,000
(4) Adjusted cost of goods sold 364,000
1 and 2 RAW MATERIAL INVENTORY
Beginning balance 75,000
a 225,000 150,000 b, Ending Balance 150,000
WORK IN PROGRESS INVENTORY
Beginning balance 140,000
b 125,000 352,000 g
c 60,000
f 105,000
j Ending Balance 78,000
FINISHED GOODS INVENTORY
Beginning balance -
g 352,000 330,000 h
Ending Balance 22,000
FACTORY OVERHEAD
b 25,000
c 40,000 105,000 f
d 74,000
Ending Balance 34,000
COST OF GOODS SOLD
h 330,000
Ending Balance 330,000
Factory overhead applied on the basis of direct labor cost .
Hence applied overhead = 60,000 x 175% = $105,000Step: 2
3)
Computation of under /(over) applied OH
Actual OH($) Applied OH ($) Under /(over) applied OH ($)
139,000 105,000 34,000
Actual manufacturing overhead:
$
Indirect material 25,000
Indirect Labour 40,000
Other manufacturing overhead 74,000
139,000
4)
Cost of goods sold (Unadjusted) 330,000
Add: Under applied overhead 34,000
Adjusted cost of goods sold 364,000
Actal manufacturing overhead is more than applied overhead,it means factory overhead under applied and it will be added in unadjusted cost of goods sold to ascertain adjused cost of goods sold.
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the glass gauge on a cylindrical coffee maker shows there are 45 cups left when the coffee maker is 36% full. How many cups of coffee does it hold when its full?
Answers
Answer:
125 cups
Step-by-step explanation:
45 is 36% of what number?
45 = 0.36n
n = 45 / 0.36
n = 125
Select the correct answer. which sum or difference is modeled by the algebra tiles? a. (-x2 2x 3) − (x2 − 2x − 1) = -2x2 2 b. (-x2 2x 3) − (-x2 2x 1) = -2x2 2 c. (-x2 2x 3) (-x2 2x 1) = -2x2 2 d. (-x2 2x 3) (-x2 − 2x − 1) = -2x2 2
Answers
The sum or difference modeled by the algebraic tiles is (-x²+2x+3) + (-x²-2x-1) = -2x²+2
How to determine the sum or difference?From the complete question, we have the following expressions:
(-x²+2x+3) and (-x²-2x-1)
Add both expressions
(-x²+2x+3) + (-x²-2x-1)
Expand
-x²+2x+3 -x²-2x-1
Collect the like terms
-x² -x² + 2x - 2x + 3 -1
Evaluate the like terms
-2x²+2
Hence, the sum or difference modeled by the algebraic tiles is (-x²+2x+3) + (-x²-2x-1) = -2x²+2
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4225x^4-130x^2-3+36y^2-81y^4
Answers
Answer:
=4225x4−81y4−130x2+36y2−3
Step-by-step explanation:
What are the lengths of AD, DB, AE, and EC? Measure and record them.
Answers
18 of the 23 tables at Paul's Italian Restaurant are full. What is the ratio of the number of full tables to the number of empty tables?
Write your answer as two numbers separated by a colon (for example, 2:3).
Answers
Answer: 18:23
Step-by-step explanation:
Question Progress
Homework Progress
16/32 Marics
Toby goes on holiday to Geneva, Switzerland.
In Geneva, Toby sees a watch costing 193.75 CHF (Swiss Francs).
In Manchester, an identical watch costs £145.
Given that £1 = 1.55 CHF
a) In which city is the watch cheaper?
b) By how much is it cheaper (in £)?
Answers
So I was cheaper in Switzerland
Find the equation of a line containing the given points. Write the equation in slope-intercept form (-2, -5) and (-5, -8)
Answers
Answer
\(y=x-3\)Explanation
The equation in slope-intercept form is:
\(y=mx+b\)where m is the slope and b is the y-intercept.
Additionally, the slope m can be calculated using the change between two points as it is a line and will be the same in all points:
\(m=\frac{y_2-y_1}{x_2-x_1}\)Considering the two points given, we can assume that point one is (-2, -5) and point two is (-5, -8). Replacing these values we get:
\(m=\frac{-8-(-5)}{-5-(-2)}\)Simplifying:
\(m=\frac{-8+5}{-5+2}=\frac{-3}{-3}=1\)Then, replacing the slope calculated in the equation we get:
\(y=(1)x+b\)Next, we have to choose one of the given points to replace in the equation and solve for b. For example, choosing (-2,-5):
\(-5=(1)(-2)+b\)\(-5=-2+b\)\(b=-5+2\)\(b=-3\)Finally, our equation is:
\(y=x-3\)what are the values of a b and c in the quadratic equation 0=-15 9x^2 13
Answers
-15,9,13 are the quadratic equation values of a,b and c is 231.3.
How do you solve a quadratic equation for B and C?The equation for the quadratic function is f(x) = a * x2 + b * x + c. The center figure, the one right next to the x, is the b-value. Both a and c are numbers, just like the other letters. Any number may be used for each of them. They provide information about the graph of the quadratic function when taken together.
Graphs, A quadratic function is one that has the formula f(x) = ax2 + bx + c, where a, b, and c are all integers with a not equal to zero. T
Our ability to solve any quadratic equation is aided by the quadratic formula. First, we change the equation's form to read as ax2+bx+c=0, where a, b, and c are the coefficients.
As a result, we enter these coefficients into the formula:
(-b(b2-4ac))/(2a).
(-b(b2-4ac))/(2a).
-9(9-4*-15*13)/2*-15
-9(9-780)/-30 = -9(-771)/-30 =6939/-30 = -231.3.
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Complete question:
What are the values of a, b and c in the quadratic equation 9x² -15x + 13 = 0?
If angle m tyr = (8x+6) m angle (8x-6) and m angle tyw = 120 what is angle m wyr
Answers
Using the sum of the angles in a triangle, The measure of angle m wyr is 54 degrees.
To find the measure of angle m wyr,
we can use the fact that the sum of the angles in a triangle is 180 degrees.
Given,
m angle tyr = 8x + 6
m angle tyw = 120
Since angle tyr and angle tyw are part of the triangle tyr,
we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle m wyr.
m angle tyr + m angle tyw + m angle m wyr = 180
Substituting the given values:
(8x + 6) + 120 + m angle m wyr = 180
Simplifying the equation:
8x + 126 + m angle m wyr = 180
To find the measure of angle m wyr,
we need to isolate m angle m wyr,
Subtracting 126 from both sides,
8x + m angle m wyr = 180 - 126
8x + m angle m wyr = 54
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find the radius of convergence, r, of the series. [infinity] (−1)n (x − 8)n 3n 1 n = 0
Answers
The radius of convergence of the given series is `∞`.
The series is, `
\([infinity] (−1)n (x − 8)n 3n / 1` n=0\)
We can apply the ratio test to find the radius of convergence `r`.
Let,
\(`an = (−1)n (x − 8)n 3n / 1\)
`For the ratio test, we take the limit of `
\(`an = (−1)n (x − 8)n 3n / 1\).
Therefore,
\(`|an+1| / |an| = |(−1)n+1 (x − 8)n+1 3n+1 / 1| * |1 / (−1)n (x − 8)n 3n|`\)
\(`= |x − 8| lim(n → ∞) (3 / (3n+1))``\)
\(= |x − 8| * 0``\)
= 0`
Therefore, the series converges for all values of `x` and its radius of convergence,
`r = ∞`.
Hence, the radius of convergence of the given series is `∞`.
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if a typist is able to type 5 pages in 10 minutes, then by your calculations, how many hours will it take the typist to type 60 pages?
Answers
Answer:
2 hours
Step-by-step explanation:
\(\frac{5}{10}\) = \(\frac{60}{x}\) Cross multiply and solve for x
5x = 600 Divide both sides by 5
x = 120
This is 120 minutes. 120 minutes is equal to 2 hours.
Helping in the name of Jesus.
Answer:
2 hours
Step-by-step explanation:
If 5 pages in 10 minutes and 60 pages than 60/5, which is 12. 12*10=120 minutes. 120 minutes is equivalent to 2 hours.
slok and his father are sitting at the distance of 5 m on a seasaw.his father is at the distance of 2m from the fulcrum and slok weighs 20 kg.if they are balancing the seasaw , find the weight of his father
Answers
Answer:
500N
Step-by-step explanation:
his father weighs 500N
Which is not a characteristic of simple moving averages applied to time series data?
A.) smoothes random variations in tl
B.) weights each historical value equally
C.) lags changes in the data
D.) has minimal data storage requirements
E.) smoothes real variations in the data
Answers
Option (D) Has minimal data storage requirements
16. Mrs. Yokom created a scatterplot of the relationship between the number of hours her students spent studying for their tests and their test scores. After creating the scatterplot of her results, she drew in a line of best fit. 100 (6,98) 90 (4.80) 60 Number of hours studied Use the given points to find the slope of the line. (4) (4 Write an equation for the line of best fit in slope intercept form. Are there any outliers? If so, give the approximate coordinates. a. b. C. Test Scores in %
Answers
The equation for the line of best fit in slope-intercept form is:
y = 9x + 44
To find the slope of the line of best fit using the given points, we can use the formula:
slope = (change in y) / (change in x)
Let's consider the two given points: (6, 98) and (4, 80).
(change in y) = 80 - 98 = -18
(change in x) = 4 - 6 = -2
Now we can calculate the slope:
slope = (-18) / (-2) = 9
So, the slope of the line of best fit is 9.
To write the equation for the line of best fit in slope-intercept form (y = mx + b), we need to find the y-intercept (b).
Let's choose one of the given points, (4, 80), and substitute the values into the slope-intercept form equation:
80 = 9(4) + b
Simplifying, we get:
80 = 36 + b
Now, solve for b:
b = 80 - 36 = 44
Therefore, the equation for the line of best fit in slope-intercept form is:
y = 9x + 44
Regarding outliers, the given data points do not indicate any outliers as all the points seem to fall relatively close to the line of best fit. However, without additional data or information on what constitutes an outlier, it is difficult to definitively determine if there are any outliers.
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Help pls and thank uu
Answers
Answer:
f(- 4) = - 4
Step-by-step explanation:
f(- 4) with x = - 4 gives f(- 4) = - 4
Determine the truth value of each of the following complex statements.
Circle your answer or put it in red. (NOTE: LET A, B, C BE TRUE AND X, Y, Z BE FALSE)
3. B. Z 4. Xv-Y
5. CvZ 6. B-Z 7. (A v B)Z 8. (AZ) 9. B v (Y - A) 10. A) -(Z v-Y) 11.( AY) v (-Z.C) 12. -X v-B) (~Y v A) 13. (Y » C)-(B3-X) 14.(C =~A) v (Y = Z) 15.-(AC)(-XB) 16.( AY). (-Z.C) 17.-[( AZ) = (-C •-X)] 18. ~~[( AZ) = (-C •-X)] 19.-(A.-Z) v (Y = Z) 20. A. A
Answers
The truth values for the given complex statements are:
3. False
4. False
5. False
6. True
7. False
8. Undefined
9. True
10. True
11. True
12. False
13. True
14. True
15. True
16. False
17. True
18. False
19. True
20. False
To determine the truth value of each complex statement, we'll use the given truth values:
A = True
B = True
C = True
X = False
Y = False
Z = False
Let's evaluate each statement:
3. B • Z
B = True, Z = False
Truth value = True • False = False
4. X V Y
X = False, Y = False
Truth value = False V False = False
5. ~C v Z
C = True, Z = False
Truth value = ~True v False = False v False = False
6. B - Z
B = True, Z = False
Truth value = True - False = True
7. (A v B) Z
A = True, B = True, Z = False
Truth value = (True v True) • False = True • False = False
8. ~(THIS)
"THIS" is not defined, so we cannot determine its truth value.
9. B v (Y • A)
B = True, Y = False, A = True
Truth value = True v (False • True) = True v False = True
10. A • (Z v ~Y)
A = True, Z = False, Y = False
Truth value = True • (False v ~False) = True • (False v True) = True • True = True
11. (A • Y) v (~Z • C)
A = True, Y = False, Z = False, C = True
Truth value = (True • False) v (~False • True) = False v True = True
12. (X v ~B) • (~Y v A)
X = False, B = True, Y = False, A = True
Truth value = (False v ~True) • (~False v True) = False • True = False
13. (Y • C) ~ (B • ~X)
Y = False, C = True, B = True, X = False
Truth value = (False • True) ~ (True • ~False) = False ~ True = True
14. (C • A) v (Y = Z)
C = True, A = True, Y = False, Z = False
Truth value = (True • True) v (False = False) = True v True = True
15. (A • C) (~X • B)
A = True, C = True, X = False, B = True
Truth value = (True • True) (~False • True) = True • True = True
16. (A • Y) (~Z • C)
A = True, Y = False, Z = False, C = True
Truth value = (True • False) (~False • True) = False • True = False
17. ~[(A • Z) (~C • ~X)]
A = True, Z = False, C = True, X = False
Truth value = ~(True • False) (~True • ~False) = ~False • True = True
18. [(A • Z) (~C • ~X)]
A = True, Z = False, C = True, X = False
Truth value = (True • False) (~True • ~False) = False • True = False
19. (A • Z) v (Y = Z)
A = True, Z = False, Y = False
Truth value = (True • False) v (False = False) = False v True = True
20. A • ~A
A = True
Truth value = True • ~True = True • False = False
Therefore, the truth values for the given complex statements are:
3. False
4. False
5. False
6. True
7. False
8. Undefined
9. True
10. True
11. True
12. False
13. True
14. True
15. True
16. False
17. True
18. False
19. True
20. False
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Can someone please teach me long division, and please provide examples.
i haven't done long division in so long and i need to sharpen up.
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oh yea 50 points each.
Answers
Answer:
Step-by-step explanation:
Divide the tens column dividend by the divisor.
Multiply the divisor by the quotient in the tens place column.
Subtract the product from the divisor.
Bring down the dividend in the ones column and repeat.
okay so look at the image down below
What is 6×28. Please show me a picture. This is my homework. My teacher requires a picture for my homework and I love that stuff and it would really help me out. Thanks.
Answers
Answer: Im sorry i dont have a picture :( but the awnser to your problem is (168)
Step-by-step explanation:
HELLPPP How many lines in the plane are perpendicular bisectors of the segment?
O one
O two
O infinitely many
Onone
Answers
We have one line in the plane as the perpendicular bisector of the segment.
What is perpendicular bisector?This is the term that is used to refer to the line that is able to bisect another line in a right angle. This line would bisect it through the point of intersection.
We are told that when it is line in a plane, it would have one perpendicular bisector but it would be infinite if it is in space.
Hence we can conclude that We have one line in the plane as the perpendicular bisector of the segment.
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given f^-1(36)=7, what value of x makes f(x)=36
Answers
Answer:
x =7
Step-by-step explanation:
\( {f}^{ - 1} (36) = 7 \\ \\ \implies \: 36 = {f} (7) \\ \\ f(x) = 36.... (given) \\ \\ f(7) = f(x) \implies \: x = 7\)
Which represents the most effective chunking of the digit sequence 14929111776?
Answers
The most effective chunking of the digit sequence 14929111776 would depend on the purpose of chunking.
However, a possible effective chunking could be 14-92-91-11-77-6, which groups the digits into pairs or triplets based on their similarity or pattern. Another possible chunking could be 1492-911-1776, which separates the digits based on significant historical events. Ultimately, the effectiveness of chunking would depend on the context and intended use of the sequence. The most effective chunking of the digit sequence 14929111776 would be to group the numbers into smaller, manageable chunks. One possible way to chunk the sequence is: 149-29-11-17-76. This breaks the sequence into five groups, making it easier to remember and process.
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The 10th-grade class officers ordered t-shirts and sweatshirts to sell as a fundraiser. each t-shirt weighed startfraction one-half endfraction. of a pound, and each sweatshirt weighed startfraction 3 over 4 endfraction of a pound. the total weight of the contents of the box was 43 and startfraction 3 over 4 endfraction pounds. which equation written in standard form represents the number of t-shirts, t, and the number of sweatshirts, s, that were ordered? startfraction one-half endfraction t plus startfraction 3 over 4 endfraction s equals 43 and startfraction 3 over 4 endfraction startfraction 3 over 4 endfraction s equals negative startfraction one-half endfraction s plus 43 and startfraction 3 over 4 endfraction. 2t 3s = 175 3s = –2t 175
Answers
2t + 3s = 175 is the standard linear equation.
What are linear equations?
Equations of the first order are linear equations. Lines in the coordinate system are determined by linear equations. It is referred to be a linear equation in one variable when the equation only contains one homogeneous variable of degree 1. There might be more than one variable in a linear equation. Linear equations in two variables, for example, are those that have two variables in them.
Let the number of t-shirts = x = t
and the number of sweatshirts = y = s
Each t-shirt weighed 1/2 of a pound and the sweatshirt weighed 3/4 of a pound.
Total weight of t-shirt = \(\frac{1}{2}x\) pounds
Total weight of sweatshirt = \(\frac{3}{4} y\) pounds
Now, the total weight of the items in the box = \(43\frac{3}{4}\) pounds
∴ The total weight of the items = \(\frac{1}{2}x+\frac{3}{4} y\)
=> \(\frac{1}{2}x+\frac{3}{4} y=43\frac{3}{4}=\frac{4.13+3}{4}=\frac{175}{4}\)
Simplifying, we get,
2x + 3y = 175 or
2t + 3s = 175
Therefore, the equation written in standard form represents the number of t-shirts, t, and the number of sweatshirts, s, that were ordered is 2t + 3s = 175.
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The standard linear equation that represents the number of t-shirts 't' and the number of sweatshirts 's', that were ordered is 2t + 3s = 175.
What is an equation?An equation is the combination of variables, coefficients, and the constant with an arithmetic operation in between them. An equation represents a mathematical relationship between two expressions.Depending on the degree of the variables, the type of the equation is defined.For a degree 1, it is said to be a linear equation (for one or two variables).and for a degree 2, it is said to be a quadratic equation, etc.Calculation:The given data about the orders of shirts and sweatshirts by a 10th-grade class officer is as follows:
The number of t-shirts ordered by them = t
The number of sweatshirts ordered by them = s
The weight of the t-shirts = 1/2 t pounds
The weight of the sweatshirts = 3/4 s pounds
But it is given that, the total weight of the contents of the box = 43 3/4
I.e., 1/2 t + 3/4 s = 43 3/4
On simplifying, we get
(2t + 3s)/4 = 175/4
⇒ 2t + 3s = 175
Thus, the required linear equation is 2t + 3s = 175.
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Topic: Probability
Only complete question 13.
Answers
Answer:
see below
Step-by-step explanation:
Assuming the comma means and
a) P(A , E) = P(A) * P(E) = .1 * .5 = .05
b) P( A, L, E) = P(A) * P(L) *P(E) = .1 *.4* .5 = .002
C This means that it snows in Abbostford, Lehtbridge and Estevan today is .002 or .2%
Suppose c(x) = x3 -24x2 + 30,000x is the cost of manufacturing x items.Find a production level that will minimize the average cost ofmaking x items.
a) 13 items
b) 14 items
c) 12 items
d) 11 items
Answers
The correct option is B, the minimum is at 14 items.
How to find the value of x that minimizes the cost?The cost function is given by:
c(x) = x³ - 24x² + 30,000x
The average cost is:
c(x)/x = x² -48x + 30000
The minimum of that is at the vertex of the quadratic, remember that for the general quadratic:
y = ax² + bx + c
The vertex is at:
x = -b/2a
So in this case the minimum is at:
x = 24/(2*1) = 14
So the correct option is B.
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A soccer ball kicked with an initial velocity of 39 ft/sec and an angle of 44° with the ground. Find the parametric equations that model the motion. What was its maximum height?
step by step please asap
Answers
The soccer ball reaches a maximum height of approximately 34.8 feet.
How to solveThe parametric equations for the motion of the soccer ball are:
x(t) = 39*cos(44°)t ≈ 26.9t
y(t) = \(39\sin(44)*t - 16t^2\) ≈ \(22.7t - 16t^2\)
where t is the time elapsed since the ball was kicked.
To find the maximum height of the ball, we need to find the vertex of the parabolic trajectory given by y(t).
The maximum height occurs at the vertex, which is at the time t = -b/2a, where a = -16 and b = 39*sin(44°).
So, t = -b/2a ≈ 1.1 seconds.
Substituting this value of t into the equation for y(t), we get the maximum height:
y(max) = \(39*\sin(44)1.1 - 16(1.1)^2 = 34.8 feet.\)
Therefore, the soccer ball reaches a maximum height of approximately 34.8 feet.
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3x-2(x+5)=14 then x
Answers
3x -2x -10 = 14
x -10 =14
10. 10. add 10 to both sides
x = 24
:)
Answer:
x = 24
Step-by-step explanation:
3x-2(x-5)=14
remove the parentheses using distributive property
3x-2x-10=14
collect like terms
x-10=14
move constant to the right side and change the sign
x=14+10
calculate ( add the numbers together)
x = 24
A sequence of transformations is applied to ACDE to create AC'D'E'.
Select all of the sequences of transformations that could be applied to ACDE so that ACDE = AC'D'E'.
A clockwise rotation of 90 degrees and then a dilation by a scale factor of 2.
A dilation by a scale factor of 2 and then a reflection across the y-axis.
A clockwise rotation of 90 degrees and then a reflection across the y-axis.
A translation 5 units down and then a dilation by a scale factor of 2.
A translation 5 units down and then a clockwise rotation of 90 degrees.
A reflection across the y-axis and then a translation 5 units down.
Answers
The option 1 "A clockwise rotation of 90 degrees and then a dilation by a scale factor of 2", option 3 "A clockwise rotation of 90 degrees and then a reflection across the y-axis." and option 5 "A translation 5 units down and then a clockwise rotation of 90 degrees." are correct.
In the given question,
A sequence of transformations is applied to ACDE to create AC'D'E'.
We have to select all of the sequences of transformations that could be applied to ACDE so that ACDE = AC'D'E'.
Firstly we learn about Transformation
A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations. The pre-image is the shape of the object as it was originally, and the transformed shape of the object is termed the image.
We can transform an object by translation, rotation, reflection, and enlargement.
So according to explanation we can see that
Option 1 is correct because in this option we transform the ABCD by rotation of 90 degrees and then a dilation by a scale factor of 2. In this option only shape is changing.
Option 2 is not correct because in this option we used both dilation by a scale factor of 2 and then a reflection across the y-axis. In this option shape and size both changes.
Option 3 is also correct because in this option we rotate 90 degree in clockwise direction and then a reflection across the y-axis. So there only change the position.
Option 4 is not correct because there is a translation by 5 units down and then a dilation by a scale factor of 2. It will change the shape and direction both.
Option 5 is correct because there is a translation by 5 units down and then a clockwise rotation of 90 degrees. It will change only shape.
Option 6 is not correct because there is reflection across the y-axis and then a translation 5 units down.
Hence, the option 1,3 and 5 are correct.
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What scale factor was applied to the first diamond to get the resulting image?
(21 points)
Answers
The scale factor was applied to the first diamond is 2.5
How to determine the scale factorFrom the question, we have the following parameters that can be used in our computation:
The diamonds
The scale factor is calclated as
scale factor = Diamond 2/Diamond 1
Substitute the known values in the above equation, so, we have the following representation
scale factor = 1.5/0.6
Evaluate
scale factor = 2.5
Hnce, the scale factor is 2.5
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