Given:
Consider triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form triangle A'B'C'.
To find:
The transformation that can be used to map each point (x,y) on Triangle ABC to its corresponding point on Triangle A'B'C'.
Solution:
If a figure rotated 90 degrees counterclockwise, then
[tex](x,y)\to (-y,x)[/tex]
[tex]P(x,y)\to P_1(-y,x)[/tex]
If a figure translated 3 units up, then
[tex](x,y)\to (x,y+3)[/tex]
[tex]P_1(-y,x)\to P'(-y,x+3)[/tex]
If triangle ABC is rotated 90 degrees counterclockwise and then translated 3 units up to form triangle A'B'C', then the rule of transformation is
[tex](x,y)\to (-y,x+3)[/tex]
Therefore, the required rule of transformation is [tex](x,y)\to (-y,x+3)[/tex].
Note: Option are not in proper form.
All the points of the triangle ABC(assuming it is in first quadrant) of the form (x,y) turns (-x,y+3) after applying considered transformations.
How does rotation by 90 degrees changes coordinates of a point if rotation is with respect to origin?Let the point be having coordinates (x,y).
Case 1: If the point is in first quadrant:Subcase: Clockwise rotation:
Then (x,y) → (x, -y)
Subcase: Counterclockwise rotation:
Then (x,y) → (-x, y)
Case 2: If the point is in second quadrant:Subcase: Clockwise rotation:
Then (x,y) → (-x, y)
Subcase: Counterclockwise rotation:
Then (x,y) → (x, -y)
Case 3: If the point is in third quadrant:Subcase: Clockwise rotation:
Then (x,y) → (x, -y)
Subcase: Counterclockwise rotation:
Then (x,y) → (-x, y)
Case 4: If the point is in fourth quadrant:Subcase: Clockwise rotation:
Then (x,y) → (-x, y)
Subcase: Counterclockwise rotation:
Then (x,y) → (x, -y)
Case 5: For points on axesYou can take that point in any of the two surrounding quadrants. Example, if the point is on positive x axis, then it can taken as of first quadrant or fourth quadrant.
Case 6: On originNo effect as we assumed rotation is being with respect to origin.
Since no quadrant is specified, we assume triangle is fully in first quadrant. That means all points (x,y) will turn (-x,y) after counter clockwise rotation.
Now translation of 3 units up means all y coordinates will be increased by 3, thus, all (x,y) points of triangle first become (-x,y) then (-x, y+3).
Thus, all the points of the triangle ABC(assuming it is in first quadrant) of the form (x,y) turns (-x,y+3) after applying considered transformations.
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Parker owns a food truck that sells tacos and burritos. He sells each taco for $3.25 and each burrito for $7. Yesterday Parker made a total of $552 in revenue from all burrito and taco sales and there were twice as many burritos sold as there were tacos sold. Write a system of equations that could be used to determine the number of tacos sold and the number of burritos sold. Define the variables that you use to write the system.
Answer:
let t= the number of tacos sold
let b= the number of burritos sold
3.25t+7b=552
b=2t
Step-by-step explanation:
Since there were twice as many burrito sold as tacos sold, there were more burritos sold, so if we multiply by 2 the number of tacos sold, we will get the number of burritos sold, meaning b=2t.
The system of equation should be considered as the 3.25t+7b=552 and the value of b should be equivalent to 2t.
Calculation of the equation:here we assume that
t= the number of tacos sold
And, b= the number of burritos sold
As per the situation, the equation be like
3.25t+7b=552
b=2t
So,
put b value in the first equation
3.25t + 14t = 552
t = 3.01
And, b = 1.51
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help please
25 + 2v = 47, v = ?
Answer:
11
Step-by-step explanation:
2v = 47-25
2v = 22
v = 11
A hiker climbed up from the bottom of a mountain. His elevation increased at a rate of 40 feet each hour. Which equation models the change in his elevation at 3 hours.
O A.3(-40)=120
O B.(-3)(-40)=120
O C. 3•40=120
O D.3(-40)=120
Answer:
I believe it is C
Step-by-step explanation:
Answer:
Its C
Step-by-step explanation:
A-P-E-X
Two triangles have the same height. The base of one
triangle is twice that of the other. Find the difference in
their areas.
[tex]\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}[/tex]
They both have same height,
let the height of both triangles be = x
let the base one triangle = y
then the base of another trainlgle = 2y
Area of triangle = 1/2 X B X H
Area of Triangle 1
[tex] \frac{1}{2} \times y \times x \\ = > \frac{xy}{2} [/tex]
Area of Triangle 2
[tex] \frac{1}{2} \times 2y \times x \\ = > \frac{2xy}{2} \\ = > xy[/tex]
Difference in the area =
[tex]xy - \frac{xy}{2} \\ = > \frac{2xy - xy}{2} \\ = > \frac{xy}{2} [/tex]
Hence Area of Triangle 1 is half the area of Triangle 2
Difference of 1/2 area.
Answer:
[tex]\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}∣ANSWER∣
They both have same height,
let the height of both triangles be = x
let the base one triangle = y
then the base of another trainlgle = 2y
Area of triangle = 1/2 X B X H
Area of Triangle 1
\begin{gathered} \frac{1}{2} \times y \times x \\ = > \frac{xy}{2} \end{gathered}21×y×x=>2xy
Area of Triangle 2
\begin{gathered} \frac{1}{2} \times 2y \times x \\ = > \frac{2xy}{2} \\ = > xy\end{gathered}21×2y×x=>22xy=>xy
Difference in the area =
\begin{gathered}xy - \frac{xy}{2} \\ = > \frac{2xy - xy}{2} \\ = > \frac{xy}{2} \end{gathered}xy−2xy=>22xy−xy=>2xy
Hence Area of Triangle 1 is half the area of Triangle 2
Difference of 1/2 area.
[/tex]
Step-by-step explanation:
side it
siso,;-):-(
HAIIIIIII PLS HELPPPPPP
dis is confusing -_-
Miguel has $30. He spends $8.00 on a movie ticket, $3.85 for snacks and $1.00 for bus fare each way.
How much money does Miguel have left?
Miguel has_____dollars left
Answer:
$16.5
Step-by-step explanation:
$30-$8-$3.85-$1-$1 = $16.5
Alice needs twice as many yards of ribbon as Quincy. how many rolls of ribbon does Alice need? explain your answer i like your cut g
Answer: Twice the length of 322 yards is 644. If I divide by 15 I get 42 r14. Alice needs to buy 43 rolls of ribbon. I like your cut G !
Step-by-step explanation:
9/4 ÷ 3/8
HELP ME PLS
Answer:
the answer is 6 u welcome
3. The product of two rational numbers is 15. If one of the numbers is - 10, find the other.
Answer: -1.5
because one of the numbers is - 10 => the other is 15/-10 = -1.5
Step-by-step explanation:
Is X +3 a factor of 2X squared minus 2X -12
Answer: No, x+3 is not a factor of 2x^2-2x-12
========================================================
Explanation:
Let p(x) = 2x^2 - 2x - 12
If we divide p(x) over (x-k), then the remainder is p(k). I'm using the remainder theorem. A special case of the remainder theorem is that if p(k) = 0, then x-k is a factor of p(x).
Compare x+3 = x-(-3) to x-k to find that k = -3.
Plug x = -3 into the function
p(x) = 2x^2 - 2x - 12
p(-3) = 2(-3)^2 - 2(-3) - 12
p(-3) = 12
We don't get 0 as a result so x+3 is not a factor of p(x) = 2x^2 - 2x - 12
----------------------------------------
Let's see what happens when we factor p(x)
2x^2 - 2x - 12
2(x^2 - x - 6)
2(x - 3)(x + 2)
The factors here are 2, x-3 and x+2
I need to find the slope for the question: 6y-14x=2
Answer:
Step-by-step explanation:
Explain in your own words why you would use division to change a smaller unit to a bigger one . What would happen if you multiplied instead ? TOPIC IS MEASUREMENT
Answer:
you would use division to change bigger units into smaller ones as a form of cancellation
Please look at number 10. from the slope and write the equation for me
Answer:
y = 8x + 38
Step-by-step explanation:
To find the slope we set up y = mx + b and plug m (our slope) in and then plug in the point into x and y to find b (our y-intercept)
y = mx + b
y = 8x + b
6 = 8(-4) + b
6 = -32 + b
+32 +32
38 = b
So using our slope and our intercept we have our slope intercept
y = mx + b
y = 8x + 38
Hope this helps :)
Answer:
y - y1 = m(x - x1)
y - 6 = 8(x - (-4))
y - 6 = 8(x + 4)
y - 6 = 8x + 32
y = 8x + 32 + 6
y = 8x + 38
Step-by-step explanation:
First you input the given values ( m = 8 and (-4, 6)) into the point-slope equation.
After that, you multiply the 8 by the two terms inside the parentheses, giving you 8x and 32.
Then you add 6 to both sides of the equation to isolate the y.
The slope-intercept equation ends up looking like this: y = 8x + 38
Hope this helps :)
A sociologist polled a random sample of people and asked them their age and annual income. The two-way frequency table below shows the results. Annual income vs. age group Less than $50,000 At least $50,000 Total Ages 44 and under 148 68 216 Ages 45 and above 38 94 132 Total 186 162 348 Which of the following statements is true of those polled? Choose 1 answer: А A person with an annual income of less than $50,000 is more likely to be 45 years old or above. B A person in the 44 and under age group is more likely to to have an annual income of at least $50,000
Answer:
C A person with an annual income of at least \$50{,}000$50,000dollar sign, 50, comma, 000 is more likely to be 454545 years old or above
A person in the 44 and under age group is more likely to have an annual income of at least $50,000 is a correct statement.
We have given that,
A sociologist polled a random sample of people and asked them their age and annual income.
What is the annual income?
annual income is the amount of money you receive during the year into your bank account, before any deductions.
The two-way frequency table below shows the results.
Annual income vs. age group Less than $50,000 At least $50,000
Total Ages 44 and under 148 68 216 Ages 45 and above 38 94 132
Total 186 162 348
A person with an annual income of at least
[tex]=\$50000\\=$50,000dollar[/tex]
Therefore statement b is true.
A person in the 44 and under age group is more likely to have an annual income of at least $50,000.
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y-2 = -3(x + 6), write the equation of the line in slope intercept form.
Answer:
y = -3x - 16
Step-by-step explanation:
Point-slope form: y - y1 = m(x - x1)
Given: y - 2 = -3(x + 6)
Slope-intercept form: y = mx + b
To write the equation in slope-intercept form, we need to know the slope(m) and the y-intercept(b). By looking at the given equation, we can see that the slope is -3. We are also given the value of one point: (-6, 2).
To find the y-intercept, input the given values of the slope and the point into the equation format and solve for b:
y = mx + b
2 = -3(-6) + b
2 = 18 + b
Subtract 18 from both sides of the equation to isolate b:
2 - 18 = 18 - 18 + b
-16 = b
The y-intercept is -16.
Now that we know the slope and the y-intercept, we can write the equation:
y = -3x - 16
PLEASE HELP
Alex wants to paint one side of his skateboard ramp with glow-in-the-dark paint, but he needs to know how much area he is painting. Calculate the area of the isosceles trapezoid.
140 ft2
160 ft2
180 ft2
200 ft2
Answer:
D.) 200ft²
Step-by-step explanation:
The formula for the area of a trapezoid:
[tex]A=\frac{1}{2} (b_{1}+b_{2})h[/tex]
where:
[tex]b_{1}[/tex] and [tex]b_{2}[/tex] are the basesh is the heightInsert the given values:
[tex]A=\frac{1}{2}(16+24)*10[/tex]
Simplify the equation using PEMDAS. Simplify parentheses:
[tex]A=\frac{1}{2}*40*10[/tex]
Simplify multiplication:
[tex]A=\frac{1}{2}* 400[/tex]
Simplify multiplication. Use the rule [tex]\frac{a}{b}*c=\frac{ac}{b}[/tex] :
[tex]A=\frac{1*400}{2}\\\\A=\frac{400}{2}[/tex]
Simplify division:
[tex]A=200[/tex]
The area is 200ft²
:Done
The gross domestic product (GDP) of France is about $2.00 × 10 12 12 , and the GDP of Tuvalu is about $4.00 × 10 7 7 . How many times larger is the GDP of France than the GDP of Tuvalu?
Answer:
France's GDP is 50 000 times larger than Tuvalu's GDP.
Step-by-step explanation:
Given: Gross Domestic Product (GDP) of France = $2.0 x [tex]10^{12}[/tex]
Gross Domestic Product (GDP) of Tuvalu = $4.0 x [tex]10^{7}[/tex]
To determine the number of times in which the GDP of France is greater than that of Tuvalu, divide the GDP of France by the GDP of Tuvalu.
[tex]\frac{2.0*10^{12} }{4.0*10^{7} }[/tex] = [tex]\frac{2000000000000}{40000000}[/tex]
= [tex]\frac{200000}{4}[/tex]
= 50000
Therefore, France's GDP is 50 000 times larger than Tuvalu's GDP.
i can’t figure this one out
Answer:
H.
Step-by-step explanation:
the number of premiums sold in week 3 was 50
the number of premiums sold in week 2 was 25
25 times 2 is 50
Letf(x)=(x+2)2. Letg(x)=3(x+2)2. Which statement describes the graph of g(x) with respect to the graph of f(x)?
Answer:
I say two.
Step-by-step explanation:
A total of 2000 people attended a benefit concert was held to raise money for a children foundation. Student ticket cost $2 and an adult ticket cost $3. If the organizer raises a total of $5050, how many students attended the concert?
Answer:
257 kids
Step-by-step explanation:
PLEASE HELP!!!!! 2.) What is the perimeter of a polygon with vertices at (-3, 1), (5, 1), (-3, 4), (5, 4)? 30 points if you can help
Answer:
22 units.
Step-by-step explanation:
We want to find the perimeter of the polygon with vertices at: (-3, 1); (5, 1); (-3, 4); and (5, 4).
Let’s first plot the points and see what polygon we acquire. Please refer to the graph below.
As we can see, when plotting the points and connecting them, we get a rectangle.
So, we can use the perimeter formula for a rectangle, given by:
[tex]P=2(\ell+w)[/tex]
Where [tex]\ell[/tex] Is the length and [tex]w[/tex] is width.
Remember that the perimeter is simply the distance around the figure.
So, let’s find the length. We can do so by counting or by subtracting.
By counting, we can see that the length (longer side) is 8 units.
And by subtracting, we get the same length of |5-(-3)| or 8 units.
We use absolute value because distance is always positive.
Using the same process, we find the width to be 3 units.
Using subtract, we can see that this is indeed true as |1-4|=3.
So, we can now substitute the values into our formula:
[tex]P=2(8+3)[/tex]
Evaluate:
[tex]P=2(8+3)=2(11)=22\text{ units}[/tex]
So, the perimeter of the polygon is 22 units.
In (2x-3) +In (3x+4)
Answer: x=7
Step-by-step explanation: is that what you're looking for?
Decrease £40 by 70%
plz answer and ill brainlist u!
Answer:
12
Step-by-step explanation:
Answer:
£12
Step-by-step explanation:
It's asking us to find the 30% of the 40 and to do this we multiply 40 by 30 then divide it by 100
40 × 30 ÷ 100 = 12
Choose the word that correctly completes the statement. Triangle A B C is shown. Angle A C B is 45 degrees, angle C B A is 75 degrees, and angle B A C is 60 degrees. Since angle B is the largest angle, Line segment A C is the ________ side. adjacent included longest shortest
Answer:
longest
Step-by-step explanation:
was Answer Expert Verified on a different question :)
Answer:
Longest
Step-by-step explanation:
Edgen 2021
which equation repersent functions?
2x+3y=10
4x=16
2x-3=14
3y=18
14.6=2x
Answer:
y= (-2/3)x+10/3 is a function
3y=18 is a function
Step-by-step explanations
in both cases for each input x there is exactly one output y
how do i solve -3=-2x+1 by graphing?
Answer:
x = 2
Step-by-step explanation:
-3 = -2x + 1
minus 1 to the both sides
-3 -1 = -2x
-4 = -2x
divide both sides by -2
x = 2
In RST, RS=15, RT=12, and ST=17. Which angle of RST has the smallest measure?
Answer:A
Step-by-step explanation: I took the test
1. The price of a ring is directly proportional to its weight. If 10grams ring worth is
$3000, what is the weight of a ring worth $9000?
30g
your welcomeeeeeeeeeeeee
which expression is equivalent to 8c+6-3c-2
Answer:5c+4
Step-by-step explanation:
plss show the work
6 − 4v = 3 − v
Answer: = 1
Step-by-step explanation: 6−4v=3−v
Step 1: Simplify both sides of the equation.
6−4v=3−v
6+−4v=3+−v
−4v+6=−v+3
Step 2: Add v to both sides.
−4v+6+v=−v+3+v
−3v+6=3
Step 3: Subtract 6 from both sides.
−3v+6−6=3−6
−3v=−3
Step 4: Divide both sides by -3.
−3v
−3
=
−3
−3
v=1
Answer:
v=1
Answer:
V=1
Step-by-step explanation:
6 - 4v = 3 - v
move the varible
6 - 4v + v = 3
collect like terms
-3v = 3 - 6
divide both sides by -3
V = 1
A store advertises a 20% markdown on a dishwasher that normally sells for $952. a. Find the price on sale. b. The markdown is the greatest possible without the store losing money. What does this tell you about the store’s cost?
Answer:
a. $761.60
b. The store bought the dishwasher for the price they are currently selling it at. They are receiving no profit when it is on sale.
Step-by-step explanation:
give brainliest pls
If 20% is the greatest possible markdown the store can give without losing money, then the price of the dishwasher is $761.60
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that the Sales price = $952
Markdown % = 20%
The Sales price = (100 - 20)% x $952
The Sales price = 80% x $952
The Sales price = $761.60
If 20% is the greatest possible markdown the store can give without losing money, then the price of the dishwasher is $761.60
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