Answer:
3.0 kg
Step-by-step explanation:
Momentum before collision = momentum after collision
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
(1.0 kg) (5.0 m/s) + m (-2.0 m/s) = (1.0 kg) (-4.0 m/s) + m (1.0 m/s)
5.0 kg m/s + m (-2.0 m/s) = -4.0 kg m/s + m (1.0 m/s)
9.0 kg m/s = m (3.0 m/s)
m = 3.0 kg
The length of a rectangle is 6 yards longer than its width and
If the perimeter of the rectangle is 72 yards, find its length and width.
Let...
length=x+6
width=x
x+x+x+6+x+6=72
4x+12=72
4x=60
x=15
x+6=21
answer: length=21 and width=15
To solve for the length and width of the rectangle, we first need to understand the formulas and relationships involved:
- The perimeter (P) of a rectangle is the total distance around its boundary, which is calculated by adding together twice the length (L) and twice the width (W): `P = 2L + 2W`.
- We have two pieces of information to work with:
1. The length is 6 yards longer than the width, which we can express as `L = W + 6`.
2. The perimeter is 72 yards, so `P = 72`.
With these equations, we can set up our system to solve for the length and width:
1. Substitute the expression for L from the first piece of information into the perimeter formula:
`P = 2(W + 6) + 2W`
2. Plug in the value for the perimeter:
`72 = 2(W + 6) + 2W`
3. Distribute the 2 through the parentheses:
`72 = 2W + 12 + 2W`
4. Combine the W terms:
`72 = 4W + 12`
5. Isolate the W term by subtracting 12 from each side:
`72 - 12 = 4W`
`60 = 4W`
6. Divide by 4 to solve for W:
`W = 60 / 4`
`W = 15`
Now that we have the width, we can use the first equation to solve for the length:
`L = W + 6`
`L = 15 + 6`
`L = 21`
So, the width (W) is 15 yards and the length (L) is 21 yards.
Which shows a difference of squares? 10 y squared minus 4 x squared 16 y squared minus x squared 8 x squared minus 40 x + 25 64 x squared minus 48 x + 9
Answer:
16y² - x² shows a correct difference of squares.
Step-by-step explanation:
Following are the given options from which we have to chose which represents the difference of squares.
A) 10y² - 4x²
B) 16y² - x²
C) 8x² - 40x+25
D) 64x² - 48x+9
Difference of square is given by:
a² - b² = (a + b) (a - b)
If we analyze the expressions from the choices given in the question. We should figure out that option B) should be the right answer that shows a difference of squares. i.e. 16y² - x² shows a correct difference of squares. All other options do not represent the difference of perfect squares.
As in option A) 10y² - 4x²
10y² is not a complete square of any number. Hence, option A) is incorrect.
As in option C) 8x² - 40x+25
Neither of the terms in the expression as shown in option C can be a perfect square. Hence, option C) is incorrect.
As in option D) 64x² - 48x+9
The term 48x+9 in the expression as shown in option D can not be a perfect square. Hence, option D) is incorrect.
Lets take the expression 16y² - x² of option B) and solve it.
First simplify the terms separately to associate them as perfect squares as shown below:
⇒ 16y² = (4y)² Equation (1)
⇒ x² = (1x)² Equation (2)
Now, take the difference of Equation (1) and Equation (2).
⇒ 16y² - x²
⇒ (4y)² - (1x)² Equation (3)
So,
Equation (3 )shows a difference of squares. It can also be represented as factorizing the difference of two perfect squares such as (4y - x) (4y + x).
Which is
(4y - x) (4y + x) = 16y² - x²
= (4y)² - (1x)²
So, option B) i.e. 16y² - x² shows a correct difference of squares.
Keywords: difference of square
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Answer:
the correct answer would be
16y² - x²
Consider the following system of equations:
Equation 1: 3x + y = 5
Equation 2:5x – 4y = -3
What is the solution to this system?
(To answer this question, we need to know the value of y.)
O (1.8)
O (1,2)
O (1,1)
O (1.3)
Answer:
x=1, y=2. (1, 2).
Step-by-step explanation:
3x+y=5
5x-4y=-3
---------------
4(3x+y)=4(5)
5x-4y=-3
----------------------
12x+4y=20
5x-4y=-3
---------------
17x=17
x=17/17
x=1
3(1)+y=5
y=5-3
y=2
you want to limit the amount of television you watch to an average of at most two hours per week do an eight week. How many hours acts of television must you watch in the eighth week to meet your goal.
PLEASE SHOW YOUR WORK
Answer:
16 hours acts of television we must watch in eighth weeks to meet your goal.
Step-by-step explanation:
This problem requires us to determine the total hours we spend on watching television in eight week if we spend two hours watching television each week. This problem can easily be solved by multiplying 2 hours with number of week that is 8 week.
= 8 * 2 = 16
Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
Write the formula to calculate the height, h.
The formula to calculate the height (h) of a cone, given its volume (V) and radius (r), is [tex]\(h = \frac{3V}{\pi r^2}\)[/tex]. This formula isolates the height by multiplying both sides of the volume formula by [tex]\(3/\pi r^2\).[/tex]
To isolate the height (h) in the volume formula of a cone ([tex]\(V = \frac{1}{3}\pi r^2 h\)[/tex]), we can rearrange the formula to solve for h.
Starting with the given formula:
[tex]\[ V = \frac{1}{3}\pi r^2 h \][/tex]
To find h, we can multiply both sides of the equation by [tex]\(3/\pi r^2\)[/tex] to isolate h:
[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]
Therefore, the formula to calculate the height (h) of a cone, given its volume (V), radius (r), is:
[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]
This formula allows you to determine the height of a cone when you know its volume and radius.
the average cost of jeans in the us is around $50. if the cost of jeans increases by 2% per year, what will be the cost of jeans in 25 years? what did jeans cost 20 years ago?
$ 82.03 in 25 yrs
$ 74.30 in 20 yrs
Step-by-step explanation:
Every year, the cost of the jeans increases by 2% which is equivalent to 0.02 in decimal points. The get the cost of the jean for every year we are multiplying the principle cost by;
100 % + 2% = 102% OR 1.02 in decimal
This increase occurs 25 time for 25 years. Therefore;
1.02 ^ 25 * 50
= 1.641 * 50
= $ 82.03
To get the price in 20 years;
1.02 ^ 20 * 50
= 1.486 * 50
= $ 74.30
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How can you express 5 1/3 + (-7 2/3) as the sum of its integer and fractional parts
Answer:
-7/3
Step-by-step explanation:
-7 2/3=-23/3
5 1/3=16/3
-----------------
16/3+(-23/3)
16/3-23/3
-7/3
Final answer:
To express 5 1/3 plus (-7 2/3), separate and add the integers to get -2, then add the fractions to find -1/3, resulting in the final expression -2 1/3.
Explanation:
To express the sum of 5 1/3 and (-7 2/3) as the sum of its integer and fractional parts, we need to perform the following steps:
First, separate the integers from the fractions: 5 + 1/3 and -7 + (-2/3).Now, add the integers: 5 + -7 = -2.Next, add the fractions: 1/3 + (-2/3). Recall that subtracting a negative is the same as adding a positive, so this becomes 1/3 - 2/3 = -1/3.Combine the integer and fractional results to get the final expression: -2 1/3.Our intuition about addition and subtraction of fractions can be helpful in visualizing the mixing of different pie pieces to form a whole, and understanding how changing the sign affects the direction of the operation.
Let a = x2 + 4. Use a to find the solutions for the following equation:
(x2 + 4)2 + 32 = 12x2 + 48
Which of the following are solutions for x?
The solutions for x are -2, 0, 2
Solution:
Given that,
[tex]\text { Let } a = x^2 + 4[/tex]
Given equation is:
[tex](x^2 + 4)^2 + 32 = 12x^2 + 48[/tex]
[tex](x^2 + 4)^2 + 32 = 12(x^2 + 4)[/tex]
[tex]\text { Subtsitute } a = x^2 + 4 \text{ in above equation }[/tex]
[tex]a^2 + 32 = 12a\\\\a^2 -12a + 32 = 0[/tex]
[tex]\text{ Let us factorize the above equation }\\\\\text{ Splitting the middle term -12a as -4a - 8a we get, }[/tex]
[tex]a^2 -4a - 8a + 32 = 0[/tex]
Taking "a" as common term from first two terms and taking "-8" as common from last two terms
[tex]a(a-4)-8(a - 4) = 0[/tex]
[tex]\text{Taking (a - 4) as common term, }\\\\(a - 4)(a - 8) = 0[/tex]
[tex]\text{Equating to zero we get, }\\\\(a - 4) = 0 \text{ or } (a - 8) = 0\\\\a = 4 \text{ or } a = 8[/tex]
[tex]\text{Now substitute the value of a = 8 and a = 4 in: }\\\\a = x^2 + 4[/tex]
[tex]\text{ For a = 8: }\\\\a = x^2 + 4\\\\8 = x^2 + 4\\\\x^2 = 4\\\\x = \pm2\\\\x = +2 \text{ or } -2[/tex]
[tex]\text{For a = 4: }\\\\a = x^2 + 4\\\\4 = x^2 + 4\\\\x = 0[/tex]
[tex]\text{Thus solutions of } x \text{ are: }\\\\x = 0 \text{ or } x = 2 \text{ or } x = -2[/tex]
At a meeting with 25 businessmen, twelve businessmen drank coffee, and ten businessmen drank tea. Five businessmen drank both coffee and tea. How many businessmen drank neither coffee nor tea?
Answer:
Step-by-step explanation:
25 total people
5 drank coffee and tea
tea drinkers only : 10 - 5 = 5
coffee drinkers only : 12 - 5 = 7
total people who drank anything : 7 + 5 + 5 = 17
number of people who drank neither : 25 - 17 = 8 <=====
Evaluate the expression of 9! - 4! (5!)
Answer:
360,000.
Step-by-step explanation:
9! - 4! (5!)
= 9*8*7*6*5*4*3*2*1 - 4*3*2*1 * 5*4*3*2*1
= 5*4*3*2*1 ( 9*8*7*6 - 4*3*2*1)
= 120( 3024 - 24)
= 120 * 3000
= 360,000
Michelle receives 32K per year as an assistant fast food manager. Her benefits include health insurance, paid holidays, retirement contributions, and a 2-week paid vacation each year. Because she wears a uniform, Michelle calculates that she saves $2,500 on clothing costs per year. She constructed this table to show the value of each benefit. What is her annual salary, including benefits?
Michelle's annual salary, including benefits, is $43,330.
Explanation:To calculate Michelle's annual salary, we need to add up her base salary and the value of her benefits. Based on the information given, her base salary is $32,000 per year. In addition, her benefits include health insurance, paid holidays, retirement contributions, and a 2-week paid vacation, as well as saving $2,500 on clothing costs. Let's calculate the value of these benefits:
Health insurance: This benefit is not given a specific value, so we will assume a typical cost of $5,000 per year. (Note: This is an assumption and may vary depending on the specific circumstances).Paid holidays: Assuming 10 paid holidays per year, at an average daily rate of $100, the value of this benefit is $1,000.Retirement contributions: Assuming a 5% contribution from Michelle's salary, the value of this benefit is $1,600.2-week paid vacation: Assuming Michelle's base salary is $32,000 per year, the value of a 2-week paid vacation is $1,230 (($32,000/52)*2).Savings on clothing costs: As given, Michelle saves $2,500 on clothing costs per year.Now let's add up the base salary and the value of the benefits:
Base salary: $32,000
Health insurance: $5,000
Paid holidays: $1,000
Retirement contributions: $1,600
2-week paid vacation: $1,230
Savings on clothing costs: $2,500
Total annual salary, including benefits: $43,330
Karen has $1.70 in coins. Karen has 8 coins, all of which are quarters or dimes.
So can someone help me with these 3 parts?
Answer:
Karen has 6 quarters and 2 dimes
Step-by-step explanation:
Let
x ----> the number of quarter coins Karen has
y ----> the number of dimes coins Karen has
Remember that
[tex]1\ quarter=\$0.25\\1\ dime=\$0.10[/tex]
we know that
Equation that represent the amount of coins Karen has
[tex]x+y=8[/tex]
isolate the variable y
[tex]y=8-x[/tex] ----> equation A
Equation that represent the value of coins Karen has
[tex]0.25x+0.10y=1.70[/tex] ----> equation B
Solve the system of equations by substitution
substitute equation A in equation B
[tex]0.25x+0.10(8-x)=1.70[/tex]
solve for x
[tex]0.25x+0.80-0.10x=1.70[/tex]
[tex]0.25x-0.10x=1.70-0.80[/tex]
[tex]0.15x=0.90[/tex]
[tex]x=6[/tex]
Find the value of y
[tex]y=8-x[/tex] ----> [tex]y=8-6=2[/tex]
therefore
Karen has 6 quarters and 2 dimes
What is 20% as an whole number
Final answer:
20% does not directly convert into a whole number; it represents a fractional part of a whole. If you look at the percent as a part of some quantity, you calculate 20% of that quantity to find the represented part. However, 20% by itself is 0.20 in decimal form, not a whole number.
Explanation:
What is 20% as a whole number?
When talking about percentages, it's important to understand that a percent is a way of expressing a fractional amount as part of a whole divided into 100 parts. For example, 5% means 5 out of 100.
In the case of 20%, you are looking at 20 out of 100. As a whole number, however, percentages less than 100% do not directly convert since they represent a part of a whole, not the whole itself. 20% can be represented as 0.20 in decimal form, which still does not constitute a whole number. The closest concept related to whole numbers would be if you had some quantity that you wish to find 20% of; you would then calculate 20% of that number to find the part it represents. But the 20% by itself remains a fraction, not a whole number.
9 - 4(7x - 8x) = x - 3
Answer:
.2 or 1/5
Step-by-step explanation:
sorry for bad picture
There are 20 cars in my building's parking lot. All of the cars are red or white. Also, all the cars are either 2-door or 4-door. 12 of them are red, 15 of them are 4-door, and 4 of them are 2-door and white. How many of the cars are 4-door and red?
Answer:
11 cars
Step-by-step explanation:
There are 20 cars in my building's parking lot, 15 cars are 4-door, then
[tex]20-15=5[/tex] cars are 2-door.
5 cars are 2-door, 4 of them are 2-door and white, then
[tex]5-4=1[/tex] car is 2-door and red.
12 cars are red, 1 car is 2-door and red, then
[tex]12-1=11[/tex] cars are 4-door and red.
(1/3) are red = 30 *1/3 = 10 are red
So...20 are white
50% are 4 door = 15 are 4 door
So....15 are 2 door
8 are 2 door and white.....so 12 are 4 door and white since we have 20 white total
And since 15 are 4 door and 12 of these are white...then 3 must be 4 door and red
ORRRRMake a two-way table as follows:
RED WHITE
2-DOOR 7 8
4-DOOR 3 12
TOTALS 10 20
So, it looks like you have 3 cars that are red and have 4 doors.
Simplify negative 2 and 1 over 9 – negative 4 and 1 over 3.
Answer:The answer can be calculated by doing the following steps;
Step-by-step explanation:
Answer:
the Answer should be 2 2/9
Step-by-step explanation:
I can assure you i i worked this problem out and i'm 100% sure :) Hope i helped some of ya'll! :>
For a large batch of cupcakes, the robots use 1/5 of a gallon of milk. They pour it into two separate cups , each the same size. How much milk goes into each measuring cup?
Answer:
12.8oz.
Step-by-step explanation: 128 oz in a gallon/5/2
Malachy and Paul win some money and share it in the ratio 4:5. Malachy gets £44. How much did Paul get?
Answer:
I believe the answer is 55.
Step-by-step explanation:
Because if Malachy gets 44 and the ratio is 4:5 it would only make sense if Paul got 55.
Can someone please help!
Answer:
(x, y ) → (- y, - x )
Step-by-step explanation:
Consider the coordinates of corresponding vertices of the 2 triangles, that is
A(1, 7 ) → D(- 7, - 1 )
Note the coordinates of D are the negative reversals of A
Thus (x, y ) → (- y, - x )
What is the reason for each step in the solution of the equation? 18x-2x=4x. Match the reasons with each step in the equation
The correct answer is:
The equation simplifies to [tex]\(x = 0\)[/tex] after combining like terms and isolating [tex](x\), resulting in \(x\)[/tex] being zero.
the equation [tex]\(18x - 2x = 4x\)[/tex] step by step:
1. Original equation:
[tex]\[ 18x - 2x = 4x \][/tex]
2. Combine like terms on the left side:
[tex]\[ 16x = 4x \][/tex]
Explanation: We add or subtract coefficients of like terms. Here,[tex]\(18x - 2x\) simplifies to \(16x\).[/tex]
3. Subtract [tex]\(4x\)[/tex] from both sides:
[tex]\[ 16x - 4x = 0 \][/tex]
Explanation: We want to isolate [tex]\(x\)[/tex] on one side. Subtracting [tex]\(4x\)[/tex] from both sides ensures the equation remains balanced.
4. Simplify:
[tex]\[ 12x = 0 \][/tex]
Explanation: After subtracting, we simplify the expression [tex]\(16x - 4x\) to \(12x\).[/tex]
5. Divide both sides by [tex]\(12\)[/tex]:
[tex]\[ \frac{12x}{12} = \frac{0}{12} \] \[ x = 0 \][/tex]
Explanation: To solve for [tex]\(x\), we divide both sides by the coefficient of \(x\), which is \(12\).[/tex]
Therefore, the solution to the equation [tex]\(18x - 2x = 4x\) is \(x = 0\)[/tex]. This means [tex]\(x\)[/tex] is zero, satisfying the equation.
The value of x in the expression 2x+3=13 is
A. 8
B.5
C.4
D.3
Answer:
the anwer of youre question is B.5 .
factory workers make $15 per hour and work 40 hours per week. how much should the Radcliff Company budget for salary each week if they have 250 workers?
Answer:
123,000
Step-by-step explanation: 40×15=600
For 1 worker
600×250=123,000
For all 250 workers
Is -x+4y=-2 a direct variation?
Answer:
No
Step-by-step explanation:
Direct variation: two variables, one variable is a constant multiple of another variable
y = k x .... k constant
-x+4y=-2
4y = x - 2
y = 1/4 x -1/2 ..... y = k x + b y is not a simple multiple of x
in th fig , d is the mid point of ab and cd is perpendicular to ab. prove abc is congurence to bcd.
Statement Reason
-------------------------------------------------------------------------------------
1. CD=DC Reflexive Property
2. D-midpoint of AB Given
3. AD=BD Definition of Midpoint
4. CD⊥AB Given
5. m<CDA=m<CDB Definition of Perpendicular Lines
6. ΔACD≅ΔBCD SAS
Solve the equation.
9x + 33 = -30
Answer:
x=-7
Step-by-step explanation:
Subtract 33 from -30 (because subtraction is the opposite of addition.
that's leaves 9x=-63
you want to isolate the variable so divide -63 by 9 (since division is the opposite of multiplication)
x=-7
What is the probability that a registered voter voted in the election?
Answer:
0.4714
Step-by-step explanation:
The diagram shows:
3,371,556 registered voters which did not vote;3,006,202 registered voters which voted in the election.Then the total number of registered voters is
[tex]3,371,556+3,006,202=6,377,758[/tex]
Thus, the probability that a registered voter voted in the election is
[tex]\dfrac{3,006,202}{6,377,758}\approx 0.4714[/tex]
The probability that a registered voter participated in the election can vary significantly. In the U.S. 2020 Presidential Election, 77 percent of registered voters voted. However, it's vital to consider the full context, including the total and voting-age populations, and understand that turnout rates can vary by factors like age.
Explanation:The probability that a registered voter voted in the election depends on various factors such as the year, voters' ages and other socioeconomic factors. In the U.S., for instance, in the 2020 Presidential Election, 77 percent of registered voters cast their vote. However, it's vital to keep in mind that while this data is significant, it doesn't give full context without considering factors such as the eligible voting-age population or the total population.
Furthermore, it's useful to understand the concept of a 90 percent confidence level when interpreting statistics related to voter turnout. In this context, the statement 'We estimate with 90 percent confidence that between 56.4 percent and 63.6 percent of all students are registered voters.' suggests that there's a 90 percent probability that the actual percentage of registered voters among all students falls between the specified range.
On a related note, the age group also influences voter turnout. For instance, in 2016, 51 percent of eligible voters between the ages of eighteen and twenty-four registered, but only 39 percent of them voted. Conversely, 75 percent of eligible voters aged from sixty-five to seventy-four registered, and of these, 68 percent voted. Hence, the probability of a registered voter voting in the election can vary quite a bit based on age, among other factors.
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Simplify x + 4 – 5x – 2.
Answer: -4x+2
Step-by-step explanation: Simplify the expression.
Hope this helps you out! ☺
Jim went to a carnival with $25.00. He bought some food for $3.75. Jim wants to spend the rest of his money on tickets for rides, r, which cost $1.25 each. Which represents, r, the number of tickets Jim can purchase?
(A) r is < than equal to 17
(B) r is > greater than equal to 17
(C) r is < less than equal to 20
(D) r is > greater than equal to 20
Answer:
(A) [tex]r[/tex] is < than equal to 17
Step-by-step explanation:
Total amount Jim had for the carnival =$25.00
Amount spent on food = $3.75
Amount left with him = [tex]\$25.00-\$3.75=\$21.25[/tex]
Jim plans to sped rest on tickets for rides.
Cost of each ride ticket = $1.25
Given: [tex]r[/tex] represents the number of ride tickets bought.
Using unitary method
If 1 ride ticket cost = $1.25
Cost of [tex]r[/tex] ride tickets in dollars will be = [tex]1.25r[/tex]
Amount spent on rides must be less than or equal to the total amount left with Jim which is =$21.25.
So, we have:
⇒ [tex]1.25r\leq 21.25[/tex]
Dividing both sides by 1.25.
⇒ [tex]\frac{1.25r}{1.25}\leq \frac{21.25}{1.25}[/tex]
∴ [tex]r\leq 17[/tex]
Thus, the inequality representing te number of tickets Jim can purchase is given by:
[tex]r\leq 17[/tex]
If a reflection takes triangle CAT to C'A'T', what is A'C'?
triangle CAT with vertex A at negative 2 comma 1, vertex T at negative 1 comma 4 and vertex C at 0 comma 0, side AT has a measure of 3 units, side TC has a measure of 4 units, and side AC has a measure of 5 units
3
4
5
Cannot be determined
Answer:
The length of A'C' will also be 5 units.
Step-by-step explanation:
If a reflection takes triangle CAT to C'A'T', what is A'C'?
Starting with ΔCAT triangle as shown in figure (a).
Reflections are said to be Isometries as it does preserve the distances.
If the shape or triangle ΔCAT reflected it will remain the same size. As a result, the reflected image would be 'congruent' to the original object.
Lets suppose, ΔCAT is reflected across y axis.
The rule for reflection of the point (x,y) across the y-axis is actually the point (-x,y).
Reflect a point across the y-axis, the y-coordinate will remain the same, but the x-coordinate will be transformed into its opposite (the sign of x-coordinate will be changed).
C(0, 0) → C'(0, 0)
A(-2, 1) → A'(2, 1)
T(-1, 4) → T(1, 4)
length of Side AT = 3 units
length of Side TC = 4 units
length of Side AC = 5 units
As reflections are said to be Isometries as it does preserve the distances.
So, if ΔCAT reflected is reflected across y axis. ΔC'A'T' preserves the distances. The length of each segment of the preimage would be equal to its corresponding side in the image as shown in figure (a).
So, the length of A'C' will also be 5 units.
Keywords: reflection, transformation, triangle
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Answer:
The length of A'C' will also be 5 units.
Step-by-step explanation:
Triangle ABC was dilated with the origin as the center of dilation to create triangle A'B'C'. The triangle was dilated using a scale factor of 14.
The coordinates of the vertices of triangle ABC are given. You can use the scale factor to find the coordinates of the dilated image.
Enter the coordinates of the vertices of triangle A'B'C' below.
(Decimal values may be used)
pls answer ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]A'(-0.25,0.75)\\\\B'(1.75,-0.25)\\\\C'(-1,-0.25)[/tex]
Step-by-step explanation:
A Dilation is defined as a transformation in which the image and the pre-image have the same shape, but their sizes are different.
When the scale factor is greater than 1, the image obtained after the dilation is greater than the pre-image and it is an "Enlargement".
When the scale factor is is between 0 and 1, the image obtained after the dilation is smaller than the pre-image and it is an "Reduction".
In this case you know that the triangle ABC was dilated by this scale factor:
[tex]scale\ factor=\frac{1}{4}[/tex]
With the origin as the center of dilation.
Since:
[tex]0<\frac{1}{4}<1[/tex]
It is a Reduction.
You can identify that the vertices of the triangle ABC are:
[tex]A(-1,3)\\\\B(7,-1)\\\\C(-4,-1)[/tex]
So you need to multiply the coordinates of each vertex of the triangle ABC by [tex]\frac{1}{4}[/tex], in order to get the coordinates of the triangle A'B'C. Then, you get:
[tex]A'=(\frac{1}{4}(-1),\frac{1}{4}(3))=(-0.25,0.75)\\\\B'(\frac{1}{4}(7),\frac{1}{4}(-1))=(1.75,-0.25)\\\\C'(\frac{1}{4}(-4),\frac{1}{4}(-1))=(-1,-0.25)[/tex]
The coordinates of the vertices of triangle A'B'C' include the following;
A' (-1/4, 3/4).
B' (7/4, -1/4).
C' (-1, -1/4).
What is dilation?In Mathematics and Euclidean Geometry, dilation is a type of transformation that is used for altering the dimensions of a geometric figure, but not its shape.
In this scenario and exercise, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin as follows:
Ordered pair A (-1, 3) → (-1 × 1/4, 3 × 1/4) = Ordered pair A' (-1/4, 3/4).
Ordered pair B (7, -1) → (7 × 1/4, -1 × 1/4) = Ordered pair B' (7/4, -1/4).
Ordered pair C (-4, -1) → (-4 × 1/4, -1 × 1/4) = Ordered pair C' (-1, -1/4).
Read more on dilation here: brainly.com/question/20482938
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Missing information;
Triangle ABC was dilated with the origin as the center of dilation to create triangle A'B'C'. The triangle was dilated using a scale factor of 1/4.
The coordinates of the vertices of triangle ABC are given. You can use the scale factor to find the coordinates of the dilated image.
Enter the coordinates of the vertices of triangle A'B'C' below.
(Decimal values may be used)