The coordinates of the image of the vertices of the polygon are A''(x, y) = (1, - 2), B''(x, y) = (2, - 2), C''(x, y) = (0, - 1), D''(x, y) = (- 1, - 2) and E''(x, y) = (- 2, - 1).
What are the images of the vertices of a polygon by using rigid transformations?
Rigid transformations are transformations applied on geometric loci such that Euclidean distances in such constructions are conserved. Translations and dilations are common examples of rigid transformations.
If we know that A(x, y) = (- 6, 0), B(x, y) = (- 3, 0), C(x, y) = (0, - 3), D(x, y) = (- 3, - 6) and E(x, y) = (- 6, - 3), then the coordinates of the image are determined below:
Translation
A'(x, y) = (- 6, 0) + (9, - 6)
A'(x, y) = (3, - 6)
B'(x, y) = (- 3, 0) + (9, - 6)
B'(x, y) = (6, - 6)
C'(x, y) = (0, - 3) + (9, - 6)
C'(x, y) = (9, - 9)
D'(x, y) = (- 3, - 6) + (9, - 6)
D'(x, y) = (6, - 12)
Dilation
A''(x, y) = (1 / 3) · (3, - 6)
A''(x, y) = (1, - 2)
B''(x, y) = (1 / 3) · (6, - 6)
B''(x, y) = (2, - 2)
C''(x, y) = (1 / 3) · (0, - 3)
C''(x, y) = (0, - 1)
D''(x, y) = (1 / 3) · (- 3, - 6)
D''(x, y) = (- 1, - 2)
E''(x, y) = (1 / 3) · (- 6, - 3)
E''(x, y) = (- 2, - 1)
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The perimeter of a pool is 150 m. The rectangle at the right is a
scale drawing of the pool. The length of each square on the grid
represents 1 cm. Draw another scale drawing of the pool using the
scale 25 m to 2 cm. Explain why your drawing is accurate. Is it accurate?
The we can draw a rectangle with length = 2 cm and width = 4 cm.
According to the statement
We have to find that the dimensions of the another rectangle.
So, For this purpose, we know that the
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
From the given information:
The perimeter of a pool is 150 m. The rectangle at the right is a scale drawing of the pool. The length of each square on the grid represents 1 cm. Draw another scale drawing of the pool using the scale 25 m to 2 cm.
Then
From the given rectangle,
Length of the rectangle = 5 cm
Width of the rectangle = 10 cm
Ratio of length : width = 1 : 2
Perimeter of the rectangle = 2(l + b)= 150 cm
l + b = 75 -----(1)
Since, l : b = 1 : 2
b = 2l ------(2)
From equations (1) and (2),
l + 2l = 75
3l = 75
l = 25 m
Width 'b' = 2(25) = 50 m
Now we have to draw a rectangle with a scale = 25 : 2
Therefore, Scale factor = 25/l = 25/2
Scale factor = l = 2cm
Then Similarly,
50/ w= 50/2
w = 4cm
Now we can draw a rectangle with length = 2 cm and width = 4 cm.
So, The we can draw a rectangle with length = 2 cm and width = 4 cm.
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Find the coordinates of the vertices of the figure after the given transformation.
reflection across the x-axis
H(−4, 3), I(−1, 5), J(−4, 0)
The coordinates of the vertices of the figure after the given transformation are H' (−4, -3), I'(−1, -5), J(−4, 0)
How to find the coordinates of the vertices of the figure after the given transformation?The coordinates of the vertices of the figure are given as:
H(−4, 3), I(−1, 5), J(−4, 0)
The transformation is given as:
A reflection across the x-axis
The rule of reflection across the x-axis is
(x, y) = (x, -y)
When the above rule is applied on the coordinates of the vertices of the figure, we have:
H' (−4, -3), I'(−1, -5), J(−4, 0)
Hence, the coordinates of the vertices of the figure after the given transformation are H' (−4, -3), I'(−1, -5), J(−4, 0)
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question 13 about the width being turned into feet
The width of the banner is 8 feets
The banner is in the shape of a rectangle
The length of the banner or the rectangle is 20 feet
the length of the banner or the rectangle is 2.5 times the width
So here we need to find out the value of width of the banner or the rectangle in feets
Let us assume the width of the banner or the rectangle to be x feets
So, the length of the banner or the rectangle would become 2.5 x
by solving this simple linear equation 20 = 2.5x
[tex]\frac{20}{2.5}[/tex] = x
so the value of x appears to be 8 feets
hence, the width of the banner is 8 feets
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A student discovers that, in the triangle shown here, the equation conclude from this fact? m² + n²/p² = 1 holds true. What can she conclude from this fact
m² + n²/p² = 1 is not equation of triangle
Solution :
Triangle :
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted. Equilateral triangle.
Pythagorean triples are any three positive integers that completely satisfy the Pythagorean theorem. The theorem states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the right triangle.
m² + n²/p² = 1
Pythagorean triples are a set of 3 positive numbers that fit in the formula of the Pythagoras theorem which is expressed as, a2 + b2 = c2, where a, b, and c are positive integers. Here, 'c' is the 'hypotenuse' or the longest side of the triangle and 'a' and 'b' are the other two legs of the right-angled triangle. The Pythagorean triples are represented as (a,b, c). The most popular example of Pythagorean triples is (3, 4, 5). We can verify that 3, 4 and 5 satisfy the equation a2 + b2 = c2. Let us see how! 32 + 42 = 52 ⇒ 9 + 16 = 25. Observe the right-angled triangle given below which shows the Pythagorean triples, 3, 4, and 5.
triangle triplet :
3,4,5
let's try to prove this by using pre define triplet triangle
m= 3
n=4
p=5
3*3+4*4/5*5= 1
9+16/25= 1
9*25 +16/25 =1
225+16/25=1
9.64[tex]\neq[/tex] 1
this
m² + n²/p² = 1 is not equation of triangle
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What is the relationship between the 5s in 5,519 help please
Consider the functions f(x)=-3x=3 and g(x)=-3x+4 find f(8)
evaluate the expression
Answer:
16
Step-by-step explanation:
Step 1. Plug the numbers into the equation
Step 2. Solve using PEMDAS
[tex]\frac{6 ( 6 + 2)}{3}[/tex]
[tex]\frac{6 ( 8 )}{3}[/tex]
[tex]\frac{48}{3}[/tex]
16
Answer:
6(a+c)÷b
6(6+2)÷3
6×8÷3
48÷3
16 Ans
Step-by-step explanation 16is the answer
the driving distance between phoenix and los angeles is 599kilometers. the driving distancce between pheonix and chicago is approximately 2.3 x 10^3. a. which city is nearer to pheonix, los angeles, or chicago
Answer:
Los Angeles
Step-by-step explanation:
If you convert the scientific notation of Chicago (2.3x10³) to regular notation, that would be 2,300 km. Which is further out than LA.
Create your own math problem referring to real life problems.pls help i need it now thank you.
Answer: $40
Step-by-step explanation: Bob has $100 he gives $15 to each of his 4 friends how much money does he have left?
The function graphed above is:
Increasing on the interval(s)
Decreasing on the interval(s)
Answers in bold
Increasing on the interval (-2.5, 0)Decreasing on the interval (-∞, -2.5) U (0, ∞)Each answer is in interval notation.
=================================================
Explanation:
The graph is increasing when the curve goes uphill when moving to the right.
This occurs on the interval -2.5 < x < 0 which condenses to the interval notation (-2.5, 0); be sure not to mix this up with ordered pair notation which unfortunately looks identical.
----------
The graph is decreasing when the curve goes downhill when moving to the right.
This happens on two separate intervals of -∞ < x < -2.5 and 0 < x < ∞ which condense to the interval notation (-∞, -2.5) and (0, ∞) respectively.
Joining those two intervals up with the union symbol gets us
(-∞, -2.5) U (0, ∞)
a membership at the Y is $20 a month plus a down payment of $80 You have $500 to spend. How many MONTHS can you go to the gym for
Answer:
you can go to the gym for 21 months.
Step-by-step explanation:
1.) Organize: membership per month= $20, down payment= $80, to spend= $500.
2.) Make an equation: 20m+80<500.
3.) Solve: (subtract the down payment first) 500-80= 420 (divide 420 ($ left after the downpayment) by the monthly fee) 420/20= 21.
4.) Convert: (make sure not to mix up with numbers and subtract and or divide by the wrong numbers!) 21m.
5.) Finalize: you can go to the gym for 21 months.
Hope this helps! Comment below this if you have any questions :)
k+4=5
k=?
Please I need help
Answer:
1 its an obvious answer cause 1+4=5
>
EXAMPLE 3
Marcus is putting new tiles on his kitchen floor. Each file is 1 square
foot. The kitchen floor is 6.1 feet wide and 9 feet long. Exactly how
many tiles will he use?
Someone please help its slope
Answer:
got u hommie -x-5
Step-by-step explanation:
graphed it on desmos
Answer: I hope this helps.
Step-by-step explanation:
Given −29.032 ÷ −0.76, find the quotient.
Answer:
38.2
Step-by-step explanation:
[tex]\boxed{+38.2}\\\\\sf 29 - 0\\= 29(0)\\29(0) - 228(76 \times 3)\\= 62(3)\\62(3) - 608(76 \times 8)\\= 15(2)\\15(2) - 152(76 \times 2)\\= 0[/tex]
Notice every time a number ended up in the hundreds place, it was because a number for example, 2, was dropped into the next digit of the number. Let's say I get 18 from subtracting, and there is a 4 in the hundreds place, then 18 becomes 184 subtracted by any number below it that the divisor can multiply to.Note: Anytime 2 negative numbers are divided by each other, they will have a positive quotient.3. If Kristen spent 200 dollars then
was given 350 dollars, how much
does she have altogether?
Answer:
Step-by-step explanation:
Doesn't she have 350 dollars now? She already spent the 200 and she was THEN given 350.
What form of correspondence does the function f(x) = 2x + 5 have?
A function is defined as a relation between a set of inputs having one output each. The function f(x)=2x+5 is a one-one
What is Function?A function is defined as a relation between a set of inputs having one output each.
we need to check correspondence of the function f(x) = 2x + 5.
f(x)=2x+5
f'(x)=2
i.e increasing function (one-one).
But it is not onto because f(x) does not take all values in N.
Range of f(x)=Codomain.
It is a one one function.
Therefore the given function f(x)=2x+5 is a one one function.
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The value of 6 in the digit 43. 967 is
A. Unit
B. Tenths
C. Hundredths
D. Hundred
Answer:
C
Step-by-step explanation:
What are the exact values of a and b?
By using trigonometric relations, we will see that:
a = 7/2, b = (7*√3)/2
So the correct option is the second option, counting from the top.
What are the exact values of a and b?
Here we have a right triangle where we only know the value of the hypotenuse and one of the angles, and we want to find the measures of both of the legs (also known as cathetus).
Then we will use the two relations:
cos(θ) = (adjacent cathetus to the angle)/(hypotenuse)
With that relation we can find the value of b:
cos(30°) = b/7
cos(30°)*7 = b = (7*√3)/2
The other relation we will use is:
sin(θ) = (opposite angle to the given angle)/(hypotenuse)
With that we can get the value of a:
sin(30°) = a/7
sin(30°)*7 = a = 7/2
Then the correct option is:
a = 7/2, b = (7*√3)/2
Which is the second option, counting from the top.
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Write the expression that represents this phrase: the quotient of 10 and x
The given statement "the quotient of 10 and x" can be written in the form of an expression as 10/x
What is an Expression?An expression in mathematics is a group of numbers, variables, and mathematical operations created in accordance with context-dependent principles.
Expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's sequence of operations and other features.
The given statement "the quotient of 10 and x" can be written in the form of an expression as shown below.
The quotient of 10 and x → 10/x
Hence, The given statement "the quotient of 10 and x can be written in the form of an expression as10/x
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17 added to 4 times a number is 57.
(4n)17 = 57
(17 + 4)n = 57
17 + 4n = 57
17 + 4 + n = 57
order the fractions from least to greatest 3/5 1/5 1/6
Answer:
1/5, 1/6, 3/5.
Step-by-step explanation:
Answer:
1/6, 1/5, 3/5
Does this help?
Question 9 (1 point)
What was Sonia Sotomayor's strategy when she got a bad grade on a paper in college?
Sotomayor became the youngest judge in the Southern District and the first Hispanic federal judge in New York State. She became the first Puerto Rican woman to serve as a judge in a U.S. federal court.
1961: Sonia Sotomayor and her younger brother, Juan Jr., with their parents, Juan and Celina, within the family’s Bronxdale Homes apartment, a housing project project.
Sonia Maria Sotomayor was born in City in the borough of the Bronx, where she spent her youth . Her parents, Juan and Celina, were both born in Puerto Rico. Juan was a mill-hand , Celina a nurse. When Sonia was three, shortly after the birth of her brother, Juan, the family moved from a little apartment in the South Bronx to the Bronxdale Homes, a housing project project. From kindergarten through eighth grade, Sonia Sotomayor attended the Blessed Sacrament Parish School. Life reception was difficult, as strained finances and friction between her parents were aggravated by her father’s worsening alcoholism. Little Sonia Maria Sotomayor found refuge in books and within the home of a loving grandmother who lived nearby. At age seven, Sonia Maria Sotomayor was diagnosed with diabetes. Living with this disease taught her self-reliance; she soon learned to sterilize her own needles and inject herself with insulin.
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an air conditioning system can circulate cubic feet of air per minute. how many cubic yards of air can it circulate per minute?
We know that ,
1 feet= 0.33 Yard
Given that .
An air conditioning circulate 1 cubic foot per minutes
So it circulates 0.33 Yards per minute .
an air conditioning system can circulate 360 cubic feet of air per minute. how many cubic yards of air can it circulate per minute13.32 yards per minute
Given that an air conditioning system can circulate 360 cubic feet of air per minute. This is the rate of cubic feet per minute. That is,
Rate = volume/time. Which is
360 = volume/ 1
Volume = 360 cubic feet
Convert cubic feet to cubic yard
1 cubic foot = 0.037 cubic yards
Multiply this by 360
Cubic yards = 360 × 0.037
Cubic yards = 13.32
Therefore, if 360 cubic feet can circulate air per minute, this is equal 360 cubic feet of air per minute. how many cubic yards of air can it circulate per minute to 13.32 cubic yards of air which can circulate air per minute
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tolerance is an allowance made for imperfections in a manufactured object. the manufacturer of an oven specifies a temperature tolerance of ±15ºf. this means that the temperature inside the oven will be within 15ºf of the temperature to which it is set. write an absolute value equation to find the maximum and minimum temperatures inside the oven when the thermostat is set to 400ºf. let t represent the temperature inside the oven.
The highest temperature recorded was 415°F(maximum).
At its lowest, the temperature is 385°F(minimum).
How to to find the maximum and minimum temperatures ?The function of absolute value calculates the separation between a point and an origin.
A less-than-compound inequality is represented by:
[tex] |x| \leq a[/tex]
then the solution is
[tex] - a \leq \: x \: \leq \: a[/tex]
according to the question
Temperature T is set to 400°F with a tolerance of 15°F, meaning that the absolute difference between T and 400°F may not be greater than 15°F; in other words:
[tex] |T - 400| \leq \: 15[/tex]
now apply the solution
[tex] - 15 \leq \: T - 400 \leq \:15[/tex]
then simplify this
[tex]T - 400 \ge \: - 15 \\ T \geq \: - 15 + 400 \\ T \geq \: 385[/tex]
[tex]T - 400 \leq \: 15 \\ T \leq \: 15 + 400 \\ T \leq \: 415[/tex]
Hence, The highest temperature recorded was 415°F(maximum).
At its lowest, the temperature is 385°F(minimum).
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Given y = x² + 3x - 2, find y when x = -2
Answer:
y = -4
Step-by-step explanation:
y = x² + 3x -2
y = (-2)² + 3(-2) - 2
y = 4 - 6 - 2
y = -4
I hope this helps!
Line AB contains points A(4, 5) and B(9, 7). What is the slope of AB?
O
U/N N/UT
아름
25 52
이름
돌
The slope of the line AB which passes through the points (4, 5) and B(9, 7) is 2/5.
According to the given question.
We have a line AB containing the points A(4, 5) and B(9, 7).
Here, we have to find the slope of line AB.
As we know that, as we know that, the slope of a line is the ratio of the amount that y increases as x increases some amount.And the slope formula is m=(y2-y1)/(x2-x1) if a lines passes through the point (x2, y2) and (x1, y1).
Therefore, the slope of the line AB which passes through the points (4, 5) and B(9, 7)
= (7 - 5)/(9 - 4)
= 2/5
Hence, the slope of the line AB which passes through the points (4, 5) and B(9, 7) is 2/5.
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Solve system of equations.
-3 x-y=4
4 x+2 y=-8
The solution of the given system of equations is (0, -4)
We will use the substitution method.
Given the system of equations:
-3x - y = 4 ............ (1)
4x + 2y = -8 ..........(2)
Add 3x to both sides of (1):
-3x - y +3x = 4 + 3x
-y = 4+3x
Multiply by (-1)
y = -(4+3x)
Substitute y = -(4+3x) into equation (2)
4x + 2y = -8
4x + 2. (-(4+3x)) = -8
4x - 8 - 6x = -8
-2x -8 = -8 (Add 8 to both sides)
-2x -8 + 8 = -8 + 8
-2x = 0
x = 0
Substitute x = 0 into:
y = -(4+3x)
y = -(4+3 . 0) = -4
The solution is (0, -4)
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Expand:
y^4
i fell asleep in math class.. what is this smh
The expansion of the expression given as y^4 is y^4 = y * y * y * 4
How to expand the expression?The expression is given as:
y^4
According to the exponent law of indices, we have
x^n = x * x * x * ..... *xn
This means that, the expansion of the expression given as y^4 is
y^4 = y * y * y * 4
Hence, the expansion of the expression given as y^4 is y^4 = y * y * y * 4
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Answer: y * y * y * y
Step-by-step explanation:
y is being multiplied by itself four times
The temperature has been dropping 3 degrees Celsius per hour since midnight. If the temperature is
11 degrees at midnight, what is the temperature at 3:00AM?
Answer:
2 degrees Celsius
Step-by-step explanation:
I did this by just counting it out:
if the temperature drops 3 degrees every hour, that means we just subtract 3 for every hour after midnight
12:00-11
1:00-8
2:00-5
3:00-2
hope this helps :D