Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.
T=
U=
V=
W=
Answers
The coordinates of the vertices after a rotation 270° counterclockwise around the origin is
T' = (-8, -4)
U' = (-8, -6)
V' = (-3, -9)
W' = (-3, -7)
The coordinates of T = (4, -8)
The coordinates of U = (6, -8)
The coordinates of V = (9, -3)
The coordinates of W = (7, -3)
The rule of rotating 270 degree clockwise around the origin is
P(x, y) = P'(y, -x)
The coordinates of T' = (-8, -4)
The coordinates of U' = (-8, -6)
The coordinates of V' = (-3, -9)
The coordinates of W' = (-3, -7)
Hence, The coordinates of the vertices after a rotation 270° counterclockwise around the origin is
T' = (-8, -4)
U' = (-8, -6)
V' = (-3, -9)
W' = (-3, -7)
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Related Questions
Direct or Inverse variation
3y=x
{(2,6),(3,9),(5,15)}
{(1,16),(2,8),(4,4)}
Answers
The answers are as follows -
Relation 3y=x represents direct variation.Relation {(2,6),(3,9),(5,15)} represents direct variation.Relation - {(1,16),(2,8),(4,4)} reflects inverse relation.What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
Given are the following relations -
3y = x
{(2,6),(3,9),(5,15)}
{(1,16),(2,8),(4,4)}
We can write -
x = 3y
as
y = (1/3)x
m = 1/3
Relation 3y=x represents direct variation.
For the relation - {(2,6),(3,9),(5,15)}, we can write -
We can write it as -
y = 3x
Relation {(2,6),(3,9),(5,15)} represents direct variation.
For the relation - {(1,16),(2,8),(4,4)} , as [x] increases, [y] decreases, so it is a inverse relation.
Therefore -
Relation 3y=x represents direct variation.Relation {(2,6),(3,9),(5,15)} represents direct variation.Relation - {(1,16),(2,8),(4,4)} reflects inverse relation.To solve more questions on proportional relationship, visit the link below-
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Murphy and Nikita can fill their swimming pool with one hose in 10 hours. If they use another hose to help fill the pool, the pool
can be filled in 4 hours. How long would it take the other hose to fill the pool working alone? Round to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
so you just have to round where it came from
Miguel took his son to college in boulder, colorado, 300mi from their hometown. on his way home, he was slowed by a snowstorm so that his speed was 10mph less than when he was driving to boulder. his total driving time was 11hr. how fast did miguel drive on each leg of the trip?
Answers
Miguel drove at a speed of 60 mph in the first part of the trip and at a speed of 50 mph in the second part of the trip.
Let the speed while dropping his son to college be x mph
Therefore speed while returning is (x - 10) mph
The distance is 300 mi
Speed = Distance/Tie
or, Time = Distance/Speed
Hence the time taken during the first part of the journey = 300/x hrs
and,
Time taken for the next part of the journey
= 300/(x - 10) hrs
It is given that the total time taken was 11 hrs
Hence we get
300/x + 300/(x - 10) = 11
or, (300x - 3000 + 300x) / x(x - 10) = 11
or, (600x - 3000) / (x² - 10x) = 11
or, 600x - 3000 = 11x² - 110x
or, 11x² -710x + 3000 = 0
Applying the shreedharacharya rule gives us
x = (710 ± √(710² -132000)/22)
x = 50/11 or x = 60
If x = 50/11 then x - 10 will be negative.
hence x = 60
Therefore Miguel drove at a speed of 60 mph in first half and 50 mph in second half.
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A collector of rare books has a first-edition book worth $262, which he anticipates will grow in
value at a rate of 15% per year. How much will this book be worth 10 years from now?
If necessary, round your answer to the nearest cent.
Que
ans
2
Answers
The increase is compounded so 15% increase after 1 year, 15 x 15 % after 2 years, and so on. 15% = a multiplier of 1.15. And so after 10 years: 1.15 x 1.15 x ... x 1.15 (10 times). This is the same as 1.15^10. Multiply this by the starting amount, gives book value after 10 years as 262 x 1.15^10 = $1,059.94
The worth of the book after 10 years is $1061.1
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
First edition book worth = $262
Rate of increase per year = 15%
The worth of the book after t years can be given by the expression.
= 262 x [tex]1.15^{t}[/tex]
Now,
The worth of the book when t = 10.
= 262 x [tex]1.15^{10}[/tex]
= 262 x 4.05
= $1061.1
Thus,
The book is worth $1061.1 after 10 years.
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SOS PLEASE HELP QUICKLY WILL MARK BRAINLYIST 15 POINTS
The equations of two parallel lines are given below. Write an equation that gives the relationship between h and k.
Y=3/Kx + 14
y = H/2x + 3
Answers
Answer:
See below
Step-by-step explanation:
The equations are in form y = mx + b where m = slope
if the lines are parallel then the slopes are equal :
3/K = H/2 Done.
How can you write the equation of the
line?
(: before the lady in the video shows
you :)
y 5x = 3
y = 3x - 5
y = -5x + 3
y + 3 = -5x
Answers
Part 1) y = 3x -5
Part 2) y = 2x + 7
Step by step
Part 1 - they gave you slope of 3 and y intercept of -5
Your equation set up is y= mx + b
M is slope and b is y intercept so
y = 3x - 5
Part 2 - they give you (-1, 5) and slope (m) 2
Your formula is y - y1 = m (x - x1)
y - 5 = 2 (x - -1)
Distribute
y - 5 = 2x + 2
Add 5 to both sides to solve for y
y -5 +5 = 2x +2 +5
Combine
y = 2x + 7 is your answer
Ibram got a job selling bags of peanuts at the local fairground. He is paid a fixed amount of $340 per week plus $0.84 per item sold. This is represented by the equation P = 0.84 + 340 where P is the amount he is paid for the week and n is the number of bags of peanuts he sold. How much will Ibram be paid if he sells 380 bags of peanuts? If Ibram sells 380 bags of peanuts, he will earn S How many bags of peanuts did Ibram sell if he earned $1,087.60? for the week. If Ibram has earned $1,087.60, he sold bags of peanuts.
Answers
Answer:
Assuming the bags sold were for 1 week period.
1. $659.20 for 1 week and 380 bags of peanuts
2. 890 bags
Step-by-step explanation:
The equation is missing the variable, n (the number of bags sold). I'll take the liberty to add it after the $0.84/bag term, where it belongs:
P = 0.84n + 340
The 340 is $340/week. n must be in units of "bags/week."
1. How much will Ibram be paid if he sells 380 bags of peanuts?
P = $0.84n + $340
n = 380 bags (we will assume in 1 week).
P = $0.84n + $340
P = $0.84(380) + $340
P = $659.20
2. How many bags of peanuts did Ibram sell if he earned $1,087.60?
P = $0.84n + $340
P = $1087.60
$1087.60 = $0.84n + $340
$1087.60 - $340 = $0.84n
$0.84n = $1087.60 - $340
$0.84n = $747.60
n = 890 bags ( ! - I'm impressed)
A horse that weighs 1 1/4 tons carries a 110-pound person, a 15-ounce water bottle, and a 16 1/2-pound basket. What is the total weight of the horse, riders, and items?
Answers
Answer:
143.75
Step-by-step explanation:
11/4+110+15+16 1/2=143.75
a stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3.3 ft/s. how rapidly is the area enclosed by the ripple increasing at the end of 6.4 seconds?
Answers
In 139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.
What is area of circle?
For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much fabric is required to completely cover a circular table, for example. We can determine the boundary length, or the circle's circumference, using the area formula.
Here area of circle
=> A= π[tex]r^2[/tex]--------> 1
Differentiating 1 with respect to to time then
=> [tex]\frac{dA}{dt}= 2\pi r\frac{dr}{dt}[/tex]
If the radius is increasing at a constant rate 3.3ft/sec then after 6.4 seconds, radius is
=> 6.4*3.3=21.12 ft.
We know [tex]\frac{dr}{dt}= \frac{3.3ft}{sec}[/tex] and so ,
=> [tex]\frac{dA}{dt}[/tex] = 2*[tex]\pi[/tex]*21.12*3.3=139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec.
Hence In 139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.
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Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he
has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period.
a. What will the new principal be when he begins making loan payments?
b. How much interest will he pay over the life of the loan?
Answers
a) The new principal (principal + capitalized interest) when Rich begins making loan payments will be $9,425.10.
b) The total interest that Rich will pay over the life of the loan is $4,914.20.
How is interest on student loans determined?The interest on student loans is based on simple interest.
The only interest capitalized is the interest during the non-payment period if the student does not pay the interest.
Some students elect to pay the interest during the non-payment period to reduce the capitalized interest and principal during the payment period.
Capitalization refers to the addition of interest to the principal amount.
Period of student loan = 10 years
The amount of the federal unsubsidized student loan = $7,900
Interest rate = 4.29%
Capitalized interest during the non-payment time = $1,525.10 ($7,900 x 4.29% x 4.5)
New principal when Rich begins making loan payments = $9,425.10 ($7,900 + $1,525.10)
Total interest for loan = $4,914.20 ($7,900 x 4.29% x 14.5)
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A handicapped ramp is being constructed for the front entrance of First National Bank in Springfield. ADA guidelines requires a rise angle from the foot of the ramp (point furthest from the entrance) not to exceed 4.8 degrees. This means the vertical to horizontal ratio cannot exceed 1:12. If the handicapped ramp must start 15 feet away from the front entrance, contractors estimate the rise to be about 3 feet.
Part A: Explain thoroughly whether or not these ramp dimensions meet the ADA guidelines.
Part B: If the rise estimate does not meet ADA requirements, provide a measurement that would meet the guidelines.
Answers
a. The ramp dimensions of 15 feet away and 3 feet above do not meet the ADA guidelines.
b. A measurement that would meet the guidelines is the ramp starting 39 feet away, with a height of 3 meters.
How to verify if the ramp meets the guideline?The verification if the ramp meets the guidelines is made with the slope of the ramp, which is the ratio of the vertical distance of the ramp by the horizontal distance of the ramp, obtained dividing these two measures.
The measures are given as follows:
Vertical distance: The rise of 3 feet.Horizontal distance: 15 feet.Hence the ratio is given as follows:
3/15 = 1/5.
The ratio is greater than the threshold of 1/12, hence the ramp does not meet the guideline.
Keeping the vertical distance, the adequate horizontal distance is obtained multiplying the vertical distance by 13, as the ratio would be of 1/13, hence:
13 x 3 = 39 feet.
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if f represents the number of lots of fliptop pens to produce and t represents the number of lots of tiptop pens to produce, the linear programming model for this problem is:
Answers
The linear programming model for this problem is Max 1000F + 1000T
Given that,
If the quantity of flip top pens to be produced is f and the quantity of tiptop pens to be produced is t, then
Number of lots of Flip top pens to produce = F
Number of lots of Tip top pens to produce = T
Therefore, The linear programming formulation is given by:
Max 1000F + 1000T
s.t.
Plastic: 3F + 4T <= 39
Ink Assembly: 5F + 4T <= 45
Molding time: 5F + 2T <= 37
F, P >= 0
Hence, the linear programming model for this problem is Max 1000F + 1000P
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Simplify by expressing fractional exponents instead of radicals 8 sqrd x^2 y^4
Answers
After the use of fractional exponents give us the value 8√(x²y⁴) is 2³(x²y⁴)¹/₂.
Exponent:
Exponent is refers the way of writing the words, "raised to the power". And it is used to show that a number has been raised to a certain power.
Given,
Here we have the expression 8√(x²y⁴).
Now, we need to simplify the fractional exponents.
When we rewritten the expression like the following,
=> 8√(x²y⁴)
While we looking at these expression we know that, the number 8 can be written as the multiple of 2,
So, it can be written as,
=> 8√(x²y⁴) = 2³√(x²y⁴).
So, in the simplified form it can be written as,
=>8√(x²y⁴) = 2³(x²y⁴)¹/₂.
Therefore, the simplified form is 2³(x²y⁴)¹/₂.
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the sum of two nonzero real numbers is 44 times their product. what is the sum of the reciprocals of the two numbers?
Answers
The sum of the reciprocal of the two numbers is 44.
Let a and b be the two number
It is given that the sum of the number is equal to 44 times their product.
So from this, we get an equation:
a + b = 44 ab -------(1)
Now we have to find the sum of the reciprocal of the two numbers.
1/a + 1/b = b + a/ ab
= a + b / ab -------(2)
As from equation (1) we have
a + b/ ab = 44
Now put this value in equation (2) we get
1/a + 1/ b = 44
Therefore the sum of the reciprocal of the two numbers is 44.
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Which function matches the table? Number of Days Rented 1 2 3 4 Rental Cost ($) 12 17 22 27 A. f(x) = 5x B. f(x) = 5 + 5x C. f(x) = 7 + 5x D. f(x) = 12 + 5x
Answers
Then the equation that represents the total rent will be y = 5x + 7. Then the correct option is C.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The table is given below.
Number of Days Rented Rental Cost ($)
1 12
2 17
3 22
4 27
At x = 1, the value of y is 12.
12 = m + c ...1
At x = 2, the value of y is 17.
17 = 2m + c ...2
Subtraction equation 1 from equation 1, then we have
2m - m = 17 - 12
m = 5
Then the value of 'c' is given as,
17 = 2 x 5 + c
17 = 10 + c
c = 7
Then the equation that represents the total rent will be y = 5x + 7. Then the correct option is C.
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I need help like asap !!!
only numbers and decimal points
Answers
Answer:
a = 4.52 km
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (7.2)² = a² + (5.6)²
→ 51.84 = a² + 31.36
→ a² = 51.84 - 31.36
→ a = √20.48
→ [ a = 4.52 km ]
Hence, value of a is 4.52 km.
A line has a slope of -2/3 and passes through the point (-3,8). What is the equation of the line?
A. y = -2/3 x + 6
B. y = -2/3 x + 8
C. y = 6x - 2/3
D. y = 8x - 2/3
Answers
Answer:
A
Step-by-step explanation:
the graph of a lnear function passes through the point (-2, -7). When the input increses by 3 the value of the function increses by 8. what is the equation that models the function
Answers
The equation that models the function is y = 8/3(x) - 5/3.
Given:
The graph of a linear function passes through the point (-2, -7).
When the input increases by 3 the value of the function increases by 8.
(x,y) = (x+3,y+8)
(-2,-7) = (-2+3,-7+8)
= (1,1)
slope between (1,1) and (-2,-7) is m = -7-1/-2-1
= -8/-3
m = 8/3.
substitute m in y = mx + c
y = 8/3(x)+c
substitute (-2,-7)
-7 = 8/3(-2) + c
-7*3 = -16 + 3c
-21+16 = 3c
-5 = 3c
c = -5/3
y = 8/3(x) - 5/3.
Therefore the equation that models the function is y = 8/3(x) - 5/3.
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An engineering technician makes $25 an hour for the first 40 hours she works
during a week and $32 an hour for each hour over 40 hours. Which piecewise
equation models her total weekly pay y in dollars as it relates to the number
of hours x that she has worked during the week?
O A. y=
O C. y =
(25x
132(x-40)+1000
OB. y=-
OD. y=
[25x
132x+1000
(25x
(32(x-40)
(25x
132x
0≤x≤ 40
x> 40
0≤x≤ 40
x> 40
0≤x≤ 40
x> 40
0≤x≤ 40
X> 40
SUBMIT
Answers
The Piecewise Function be
25x when x < 40
y =
1000+32(x-40) when x > 40
Given, an engineering technician makes $25 an hour for the first 40 hours she works.
and $32 an hour for each hour over 40 hours.
Let the number of hours be x and her total weekly pay in dollars be, y
then the piecewise function,
25x when x < 40
y =
1000+32(x-40) when x > 40
Hence, the piecewise function be
25x when x < 40
y =
1000+32(x-40) when x > 40
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Martina purchased a prepaid phone card for 45.50$ calls cost 10 cents a minute using this card. The credit, C (in dollars) , left on the card after it is used for x minutes of calls is given by the following function
Answers
Answer:
Credit (C) = $45.50 - 0.10x
Step-by-step explanation:
Since you are wanting the credit (C) that is the y variable.
The prepaid phone card starts off with a balance of $45.50.
Every minute a call is made $0.10 is deducted (subtracted) from the card.
The unknown number or 'x' represents the number of minutes the calls lasted.
Which of the following rational functions is graphed below?
Answers
Answer:
C
Step-by-step explanation:
In the graph, you can see an asymptote is happening for x=-5, so look for an equation that divides by 0 for x=-5. That is clearly C, for x=-5 the denominator is 0.
a school is organizing a weekend trip to a nature preserve. for each student, there is a $60 charge, which covers food and lodging. there is also a $40 charge per student for the bus. the school must also pay a $30 cleaning fee for the bus. if the total cost of the weekend is $4,030, how many students will be going on the trip?
Answers
Using the concept of linear equation in one variable, it is concluded that the total number of students who will go on the trip are 40.
What is a linear equation in one variable?An equation that contains only one variable and has its degree one is called a linear equation in one variable. The general form of linear equation in one variable is ax + b = 0, where a and b are real numbers and a ≠ 0.
Given that food and lodging charge per student = $ 60
Charge per student for bus = $ 40
And the amount paid for the cleaning fee for the bus = $ 30
Let the total number of students who are going on the trip = x
Now, the Total charge for food and lodging = $60x
The total charge for bus fare = $ 40x
Given that total cost paid = $ 4030
Hence, $60x + $40x + $30 = $4030
$100X = $4030 - $30
$100X = $4000
x = 40
Hence, the total number of students who will go on a trip is 40.
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plss need help with this
Answers
Answer:
The solution is (-2, 4).
How do you write 5 11/16 and 7 24/25 as a decimal?
Answers
Answer:
5 11/16 as a decimal = 5.6875
7 24/25 as a decimal is 7.96
Step-by-step explanation:
Answer:
5 11/16 = 5.6875
7 24/25 = 7.97
Step-by-step explanation:
you keep the whole numbers then you turn the fractions into decimals so to do that you divide 100 by the denominator and whatever the answer is you multiply it by the numerator to get your answer, 100 divided by 16 is 6.25 and 6.25 multiplied by 11 is 68.75 but since the 5 is already the whole number you basically just forget the decimal in 68.75 ( I hope that makes sense)
And for 7 24/25 you do 100 divided by 25 and that’s 4 so now you multiply 24 by 4 and that’s 96 so that goes after the decimal so it’s 7.96 (I hope that helped and all made sense.)
Need help
Solve 4(x-5) = 18
Answers
Answer:
x = 19/2 or 9.5
Step-by-step explanation:
a) Distribute.
(4)(x) + (4)(−5) = 18
4x + −20 = 18
4x − 20 = 18
b) Add 20 to both sides.
4x − 20 + 20 = 18 + 20
4x = 38
c) Divide both sides by 4.
4x/4 = 38/4
x = 19/2 or 9.5
Answer:
9.5 or 19/2
Step-by-step explanation:
4 ( x - 5 ) = 18
Step 1 : Divide 4 on both sides.
x - 5 = 18/4
x - 5 = 4.5
Step 2 : Add 5 on both sides.
x = 4.5 + 5
x = 9.5
Value of x in fraction = 95/10 = 19/2
Value of x in decimal = 9.5
just confused,, brainliest?
Answers
Answer:
14
Step-by-step explanation:
Question For Middle School........
[tex]1.what \: is \: the \: value \: of \: pie \: (\pi)[/tex]
Answers
what is the slope that passes through (-10,17) (-9,17)
Answers
Answer: m=0
Step-by-step explanation: (-10,17) & (-9, 17) are 2 points away from each other on the x-axis, there is no difference in y. Therefore the answer is zero.
Step by step with slope formula
y2 - y1 over x2 - x1
17 - 17 over -9 - -10
0 over 1 = 0/1 slope
When numerator of the fraction is 0, the slope is 0. This will happen if the y value of both points is the same. The graph would be a horizontal line with no y value.
A salesman earns 9% commissions on all the merchandise that he sells.last month he sold $3000 worth of merchandise.how much commissions in dollars did he earn last month
Answers
The commission earned by selling the merchandise worth $3000 is $270
The percentage of the commission earned by the salesman is 9%
The worth of the merchandise is $3000
A sales commission is typically an amount paid to an employee upon completion of a task for the sale of a specified quantity of goods or services.
Therefore, the commission earned can be found using the formula,
Commission = SP x CP
where SP is the selling price and
CP is the commission percentage.
Let us substitute the known values in the above equation, we get
Commission = 3000 x 9%
= 3000 x 9/100
= 30 x 9
= $270
Therefore, the commission earned is $270
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What is the area of a triangle if the vertices are at
A(-11, 4)
B(-7, 8)
C(-4, 4)
Answers
Answer:
14 square units
Step-by-step explanation:
You want the area of the triangle whose vertices are the points A(-11, 4), B(-7, 8), C(-4, 4).
Area formulaThe area of a triangle is given by the formula ...
A = 1/2bh
where b is the base of the triangle, and h is the height, the1 perpendicular distance to the opposite vertex.
DimensionsThe diagram shows one side is the horizontal line AC. The length of that is the difference of the x-coordinates of the end points:
b = -4 -(-11) = 7
The opposite vertex, B, has a y-coordinate of 8, so the height of the triangle is ...
h = 8 -4 = 4
ApplicationWe now have the information we need to use the area formula:
A = 1/2(7)(4) = 14 . . . . square units
The area of ∆ABC is 14 square units.
__
Additional comment
You can use the diagram and count grid squares to find the dimensions of the triangle.