Answers
Given:
The figure QRST.
The rule of translation is [tex]T_{(3,-2)}(QRST)[/tex].
To find:
The coordinate of vertices after translation.
Solution:
According to the given rule of translation is [tex]T_{(3,-2)}(QRST)[/tex], we get
[tex](x,y)\to (x+3,y-2)[/tex]
From the given figure it is clear that the vertices of QRST are Q(1,3), R(3,-3), S(0,-2) and T(-2,1).
Using the above rule, we get
[tex]Q(1,3)\to Q'(1+3,3-2)=Q'(4,1)[/tex]
[tex]R(3,-3)\to R'(3+3,-3-2)=R'(6,-5)[/tex]
[tex]S(0,-2)\to S'(0+3,-2-2)=S'(3,-4)[/tex]
[tex]T(-2,1)\to T'(-2+3,1-2)=T'(1,-1)[/tex]
Therefore, the coordinates of the vertices after translation are Q'(4,1), R'(6,-5), S'(3,-4) and T'(1,-1).
The ordered pairs for the vertices of T(3, –2)(QRST) are
[tex]\mathbf{Q' = (4,1)}[/tex] [tex]\mathbf{R' = (6,-5)}[/tex] [tex]\mathbf{S' = (3,-4)}[/tex] and [tex]\mathbf{T' = (1, -1)}[/tex]
The coordinates of QRST are:
[tex]\mathbf{Q = (1,3)}[/tex]
[tex]\mathbf{R = (3,-3)}[/tex]
[tex]\mathbf{S = (0,-2)}[/tex]
[tex]\mathbf{T = (-2,1)}[/tex]
The transformation rule of [tex]\mathbf{T(3,-2)}[/tex] is:
[tex]\mathbf{(x,y) \to (x + 3,y -2)}[/tex]
So, we have:
[tex]\mathbf{Q' = (1 + 3,3 -2)}[/tex]
[tex]\mathbf{Q' = (4,1)}[/tex]
[tex]\mathbf{R' = (3 + 3,-3 -2)}[/tex]
[tex]\mathbf{R' = (6,-5)}[/tex]
[tex]\mathbf{S' = (0 + 3,-2 -2)}[/tex]
[tex]\mathbf{S' = (3,-4)}[/tex]
[tex]\mathbf{T' = (-2 + 3,1 -2)}[/tex]
[tex]\mathbf{T' = (1, -1)}[/tex]
Hence, the ordered pairs for the vertices of T(3, –2)(QRST) are
[tex]\mathbf{Q' = (4,1)}[/tex] [tex]\mathbf{R' = (6,-5)}[/tex] [tex]\mathbf{S' = (3,-4)}[/tex] and [tex]\mathbf{T' = (1, -1)}[/tex]
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Related Questions
What is f(3) if f(x) = 2x + 1?
Answers
f(3) = 2(3) + 1
f(3) = 6 + 1
Solution is 7
Answer:
f(3) = 7
Step-by-step explanation:
To evaluate f(3), substitute x = 3 into f(x), that is
f(3) = 2(3) + 1 = 6 + 1 = 7
5(x+3)-5
simplify this.
Answers
Answer:
5x+10
Step-by-step explanation:
Distribute:
=(5)(x)+(5)(3)+−5
=5x+15+−5
Combine Like Terms:
=5x+15+−5
=(5x)+(15+−5)
=5x+10
Pllzzzz help it’s an exam !!!! A side of the triangle below has been extended to form an exterior angle of 125 . Find the value of x
Answers
Answer:35
Step-by-step explanation:
take 180 and subtract those numbers and u get ur answer
I NEED HELP PLS!! i am so confused on what to do if you can explain that would be awesome!
Answers
Answer:I am pretty sure that it is that you add 26 and 71 and then subtract it by 180 and then the other one is across so it would be the same answer so it would be 83
Step-by-step explanation: I hope this helped
Factor the following expression: x^2+3x
Answers
I haven’t done this but hope this works
which of the following equations represents the graph?
A. y = 3/4x - 3
B. y = 3/4x + 4
C. y = 4/3x - 3
D. y = 4/3x + 4
Answers
Answer:
D) 4/3 x + 4
Step-by-step explanation:
The y-intercept is at point (0, 4) and the x--intercept is at point (-3, 0).
The equation for every straight line is y = mx + b. y is y, m is the slope, x is x, and b is the y value in the y-intercept
Now we will use the formula for slope, which is rise/run or more understandable , the change in y/change in x.
y2 - y1/x2 -x1
0 - 4/-3 - 0
-4/-3 = 4/3
Remember when I said the y-intercept was (0, 4) and b was the value of the y in the y-intercept? 4 is the value of y in the y-intercept.
The answer is 4/3x + 4.
Triangle ABC has coordinates A(1, 1); B(2, 5); C(5, 1). What would be the coordinates of A'B'C' if you translated ABC left 2 and up 5 units? (Hint: x-values go left and right; y-values go up and down) *
A'(-1, 6) B'(0, 10) C'(3, 6)
A'(3, -4) B'(4, 0) C'(7, -4)
Answers
Answer:
A'(-1, 6) B'(0, 10) C'(3, 6)
Answer:
I would say it's the first one
PLEASE SOMEONE HELP MEEE
Answers
Answer:
Alternate interior angle
Step-by-step explanation:
Hope this helps.
Answer:
your answer is A ....
an equation for a line with a slope of zero.
Answers
Answer:
M=0
Step-by-step explanation:
Youre welcome
Answer:
y=3
Step-by-step explanation:
Which equation represents the function graphed on the coordinate plane?
g(x)=|x+4|-2
g(x)=|x-4|-2
g(x)=|x-2|-4
g(x)=|x-2|+4
please help me this is due in a couple of minutes!!!!!! please help me.
Answers
Answer: A g (x)= [x+4]-2
Step-by-step explanation:
calculate the perimeter of this figure to the nearest tenth
Answers
Answer:
40.9
Step-by-step explanation:
Perimeter = 8 + 10 + 10 + 4 + 8.9
=> 20 + 4 + 8.9 + 8
=> 32 + 8.9
=> 40.9
This is already in the nearest tenth, so the answer = 40.9
If my answer helped, kindly mark me as the brainliest!!
Thank You!!
On the first day after the new moon, 2% of the Moon's surface is illuminated. On the second day, 6% is illuminated. Based on this information, predict the day on which the Moon's surface is 50% illuminated and 100% illuminated.
illuminated.
PLEASE HELPPPPPPP!!!!!!!!!!!
Answers
Answer:
Day 13= 50%
Day 26=100%
Step-by-step explanation:
Answers vary. Sample response: A simple approach is to attempt a linear model starting at Day 1. If the illumination is increased by 4% every day, then after 11 more days (after Day 2) it reaches 50%. In 13 more days, illumination reaches 100%. This gives a prediction of Day 13 for 50% and Day 26 for 100%.
The days where it is illuminated is Day 13= 50% and Day 26=100%
Linear model:Here A simple approach should be considered for linear model that begins at Day 1. In the case when the illumination is increased by 4% every day, so after 11 more days (after Day 2) it reaches 50%. In 13 more days, illumination reaches 100%.
Therefore, we can conclude that The days where it is illuminated is Day 13= 50% and Day 26=100%
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Expand the function f(x)=(3x+2)^4 with the binomial theorem, not factored
Answers
Step-by-step explanation:
Enter a problem...
Algebra Examples
Popular Problems
Algebra
Expand using the Binomial Theorem (3x+2)^4
(3x+2)4(3x+2)4
Use the binomial expansion theorem to find each term. The binomial theorem states (a+b)n=n∑k=0nCk⋅(an−kbk)(a+b)n=∑k=0nnCk⋅(an-kbk).
4∑k=04!(4−k)!k!⋅(3x)4−k⋅(2)k∑k=044!(4-k)!k!⋅(3x)4-k⋅(2)k
Expand the summation.
4!(4−0)!0!⋅(3x)4−0⋅(2)0+4!(4−1)!1!⋅(3x)4−1⋅(2)+4!(4−2)!2!⋅(3x)4−2⋅(2)2+4!(4−3)!3!⋅(3x)4−3⋅(2)3+4!(4−4)!4!⋅(3x)4−4⋅(2)44!(4-0)!0!⋅(3x)4-0⋅(2)0+4!(4-1)!1!⋅(3x)4-1⋅(2)+4!(4-2)!2!⋅(3x)4-2⋅(2)2+4!(4-3)!3!⋅(3x)4-3⋅(2)3+4!(4-4)!4!⋅(3x)4-4⋅(2)4
Simplify the exponents for each term of the expansion.
1⋅(3x)4⋅(2)0+4
Hope this helps!
Answer:81x^4+216x^3+216x^2+96x+16
Step-by-step explanation:cause yussss
Suppose you have 7 dimes and 6 nickels in your pocket. How many ways can you reach
into your pocket and select one of each type?
Answers
in triangle ABC, angle A is 25 degree, and Angle B is 105 degrees. what is the measure of angle c
Answers
This is because 105+25+x=180°
Hope this helps and good luck!! :)
What does it mean for a line to have an undefined slope?
Answers
Answer:
it means it is a vertices line and the x coordinates never change
Step-by-step explanation:
pls help i'll give branliest
Answers
Answer:
50
Step-by-step explanation:
good luck!!
Answer:
50
Step-by-step explanation:
hope its correct..............
Answer this please, will give 100 points.
Answers
Answer:
y=x doesent that mean 2=3 so what you do is the line that goes up thats y and the one that goes sideways thats x so at the to go to 2 then at the side go to 3
Answer:
Step-by-step explanation:
y=x doesent that mean 2=3
What is a fraction form of $1.80?
Answers
Answer:Okay, so the first thing to do here is show you that any number can be a fraction if you use a 1 as the denominator. Take a look:
1.80
1
What we really want to do though, is get rid of the decimal places completely so that the numerator in our fraction is a whole number. To do this, we have to count the numbers after the decimal point, which in this case is 80.
To get a whole fraction we need to multiply both the numerator and the denominator by 10 if there is one number after the decimal point, 100 if there are two numbers, 1,000 if it's three numbers and 10,000 if it's...well, you get the idea!
In our case 80 is 2 digits long so we need to multiply the numerator and denominator by 100.
Now we just need to do that multiplication to get our whole fraction:
1.80 x 100
1 x 100
=
180
100
The next step is to simplify this fraction and, to do that, we need to find the greatest common factor (GCF). This is sometimes also known as:
Greatest Common Divisor (GCD)
Highest Common Factor (HCF)
Greatest Common Denominator (GCD)
The GCF can be a bit complicated to work out by hand but you can use our handy GCF calculator to figure it out.
In the case of 180 and 100, the greatest common divisor is 20. This means that to simplify the fraction we can divide by the numerator and the denominator by 20 and we get:
180/20
100/20
=
9
5
And there you have it! In just a few short steps we have figured out what 1.80 is as a fraction. The complete answer for your enjoyment is below:
1 4/5
Note: because 180 is greater than 100 we have simplified this fraction even further to a mixed fraction.
Step-by-step explanation:
ANSWER ASAP FOR 35 POINTS!!
A pool has a diameter of 12 feet and a height of 2 feet. If each cubic foot holds 7.48 gallons of water, about how many gallons of water can the pool hold? Use 3.14 for pi.
A) 6764 gallons
B) 2255 gallons
C) 1691 gallons
D) 564 gallons
Answers
Answer:
cc
Step-by-step explanation:
A sequence of numbers can be thought of as a function, where fin) represents the n term of the sequence. Which of the following could be the domain of this function?
positive real numbers
O positive integers
Inational numbers
Orational numbers
Answers
Answer:
Rational numbers
Step-by-step explanation I put D on a test and I got it right
4
Erin says. "There are 30 boys in my sports club (to the nearest 10) and 20 girls (to the
nearest 10), so there must be 50 pupils to the nearest 10"
Is she right or wrong?
You must show working to explain your answer.
Answers
30+20=50. they’re estimating so it will not be far off.
A sixth-grade student bought three cans of tennis balls for $4 each. The sales tax for each can was $.95. Which expression(s) can be used to find the total amount the student spent. Select all that apply.
Answers
Given :
A sixth-grade student bought three cans of tennis balls for $4 each.
The sales tax for each can was $0.95.
To Find :
The total amount the student spent.
Solution :
Price of each can including taxes :
p = $( 4 + 0.95 )
p = $4.95
So, price of 3 such cans including tax is :
P = p×3
P = $( 4.95×3 )
P = $14.85
Therefore, total amount spend by the student is $14.85 .
write 268 in scientific notation
Answers
Answer:
2.68 x 10 to the second power
which equation represents the line that passes through points (5, 4) and (-5, 0)
Answers
(0-4)/(-5-5) = -4/-10 = 2/5
Y = 2/5x + b
Plug in one point
4 = 2/5(5) + b, b = 2
Solution: y = 2/5x + 2
The equation should be [tex]y = 2\div 5x + 2[/tex]
Given that,
The points are (5, 4) and (-5, 0)Based on the above information, the calculation is as follows:
here we need to find the slope.
[tex]= (y_2-y_1)\div (x_2-x_1)\\\\= (0-4)\div (-5-5) \\\\= -4\div -10 \\\\= 2\div 5\\\\Y = 2\div 5x + b[/tex]
Now
Put in one point
[tex]4 = 2\div 5(5) + b, b = 2[/tex]
So,
[tex]y = 2\div 5x + 2[/tex]
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pweese helppppppp meeeeeee
Answers
Answer:
No solution
Step-by-step explanation:
Graph these two equations and find a point where they intersect.
If they intersect, record the x values it intercepts. If it doesn't intersect, then it is no solution.
There are 20 children in a class 45% are girls, How many girls and boys are there?
Answers
Answer:
Step-by-step explanation:
each person represents 5%. so 45% are girls. 45/5 is 9, so 9 are girls. 20 minus 9 is 11 so 9 girls and 11 boys
The number of girls is 9 and the number of boys is 11.
Important information:
Total number of students = 2045% of total students are girls.Percentage:Using the given information, the number of girls is:
[tex]20\times \frac{45}{100}=9[/tex]
Now, subtract the number of girls from the total number of students.
[tex]20-9=11[/tex]
Therefore, the number of girls is 9 and the number of boys is 11.
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The relationship between two numbers is described below, where x represents the first number and y represents the second number.
The square of the first number is equal to the sum of the second number and 16. The difference of 4 times the second number and 1 is equal to
the first number multiplied by 7.
Select the equations that form the system that models this situation. Then, select the solution(s) of the system.
Answers
X=y+16
4y-1=7
Solve on both sides
4y=8
Y=8/2
Y=4
X= (4)+16
X=20
y=3x+5 6x - 2y = -10
Answers
Answer:
Parallel?
Step-by-step explanation:
6x = 2y + 10
3x = y + 5 divide both sides by 2
y = 3x + 5/3
Sam slopes, different intercepts.
#4 Where is 44 on the number line?
A) At 22.
C) Between 6 and 7, but closer to 6.
B) Between 6 and 7, but closer to 7
D) Between 7 and 8, but closer to 7.
Answers
Answer:
B), Between 6 and 7, but closer to 7
Step-by-step explanation:
The square root of 44 is around 6.6, so closer to 7
You can prove this by multiplying 6.6 by itself
6.6 x 6.6 = 43.56
