Answers
The rules of the transformations using the translation notation are;
11) [tex]T_{(2, \,-1)}[/tex]
12) [tex]T_{(-5, \,2)}[/tex]
13) [tex]T_{(-1, \,3)}[/tex]
14) [tex]T_{(0, \,-1)}[/tex]
15) [tex]T_{(3, \,4)}[/tex]
16) [tex]T_{(-3, \,1)}[/tex]
17) [tex]T_{(1, \,0)}[/tex]
18) [tex]T_{(6, \,-5)}[/tex]
19) [tex]T_{(4, \,0)}[/tex]
20) [tex]T_{(2, \,4)}[/tex]
21) [tex]T_{(1, \,-5)}[/tex]
22) [tex]T_{(5, \,-1)}[/tex]
23) [tex]T_{(0, \,-1)}[/tex]
24) [tex]T_{(-2, \,-1)}[/tex]
25) [tex]T_{(-3, \,-2)}[/tex]
What is a translation transformation?A translation transformation is a rigid transformation in which the location of the image obtained from the pre-image is different, but the dimensions are the same.
11) The transformation is similar to a rigid transformation
The change in coordinate is from (2, 2), to (4, 1), which is a translation 2 units to the right and -1 unit down
12) The shape is preserved and the length of the sides are also preserved, therefore, the transformation is a rigid transformation, with a change from (5, 3) to (0, 5), which is a translation 5 units to the left and 2 units up.
13) The change in the coordinates from the pre-image to the image are from V(-3, 2) to V(-4, 5), which is a transformation of 1 unit to the left and 3 units up
14) The coordinates of a point on the pre-image is T(-5, 2), and the coordinates of the corresponding point on the image is T'(-5, 1), which is a translation of one unit downwards, [tex]T_{(0, \,-1)}[/tex]
15) A point on the pre-image is T(-3, -1), the corresponding point on the image is T'(0, 3), which indicates that the rule for the transformation is a translation of 3 units to the right and a vertical translation of 4 units upwards
16) The difference between the x and y values are;
Δx = 0 - 3 = -3
Δy = -3 - (-4) = 1
The transformation is therefore of the form [tex]T_{(-3, \,1)}[/tex], which is a translation of 3 units to the left and 1 unit upwards
17) The change in the x and y values are;
Δx = -2 - (-3) = 1
Δy = -3 - (-3) = 0
The rule of the transformation is therefore of the form [tex]T_{(1, \,0)}[/tex], which is a translation one unit to the right.
18) The change in the x and y values of the transformation are;
Δx = 1 - (-5) = 6
Δy = -4 - 1 = -5
The rule of the transformation is therefore, [tex]T_{(6, \,-5)}[/tex], which is a translation of 6 units to the right and 5 units down
19) The transformation of J(-5, 3), K(-3, 5), L(0, 1) to J'(-1, 3), K'(1, 5), L'($, 1) is a transformation of the form [tex]T_{(4, \,0)}[/tex] which is a horizontal translation 4 units to the right
20) H(-4, -3), I(-5, 0), J(-3, 0), K(-2, 1) to H'(-2, 1), 'I(-3, 4), J'(-1, 4), K'(0, 5) The transformation rule is [tex]T_{(2, \,4)}[/tex], which is a translation 2 units to the right and 3 units up
21) E(0, 1), F(-1, 5), G(0, 5), H(3, 2), to E'(1, -4), F'(0, 0), G'(1, 0), H'(4, -3), which is a transformation with the rule, [tex]T_{(1, \,-5)}[/tex], which is a translation one unit to the right and five units down
22) B(-4, -2), C(-3, 3), D(-2, 1) to B'(1, -3), C'(2, 2), D'(3, 0), which is a transformation of the form [tex]T_{(5, \,-1)}[/tex], which is a translation of 5 units to the right and 1 units down
23) I(2, 1), H(4, 4), G(5, 0) to I'(2, 0), H'(4, 3), G'(5, -1), which is a transformation with the rule [tex]T_{(0, \,-1)}[/tex], which is a translation of one unit down
24) X(1, -4) W(3, 0), V(3, -4) to X(3, -5) W(5, -1), V(5, -5), which is a transformation with the rule, [tex]T_{(-2, \,-1)}[/tex], which is a translation of 2 units to the left and 1 units down
25) G(1, -1), F(2, 3), E(4, 2), D(4, -3) to G'(-2, -3), F'(-1, 1), E'(1, 0), D'(1, -5) which is a transformation with the rule, [tex]T_{(-3, \,-2)}[/tex], which is a translation of 3 units to the left and 2 units down
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Related Questions
Solve the equation x^2-2zx+3xy-6zy=0 for x in terms of y and z
Answers
Answer:
x = 2z
x = -3y
Explanation:
Given the below quadratic equation;
[tex]x^2-2zx+3xy-6zy=0[/tex]Let's go ahead and factor the above completely as seen below;
[tex]\begin{gathered} x(x-2z)+3y(x-2z)=0 \\ (x-2z)(x+3y)=0 \end{gathered}[/tex]We'll now apply the Zero-product property which states that if the product of two numbers is equal to zero, it means that at least one of the numbers is equal to zero.
Applying the Zero-product rule, we'll have;
[tex]\begin{gathered} x-2z=0 \\ x=2z \\ Or \\ x+3y=0 \\ x=-3y \end{gathered}[/tex]In a card game, Bryce scores three times as many points as Jordan. Jordan scores four points fewer than Keturah, and Keturah scores two times as many points as Amelia. If Amelia scores 5 points, how many points did Bryce score?
Answers
Bryce made the basket equals 18 points.Amelia received a point total of 10 points.The point Jordan scored was 6 points.
How to find Bryce points ?
In a card game, Bryce scores three times as many points as Jordan. Jordan scores four points fewer than Keturah, and Keturah scores two times as many points as Amelia.
Amelia score the point :
2*5=10
Amelia received a point total of 10 points.
Jorden score the point :
10-4 =6 points
The point Jordan scored was 6 points.
Bryce score the points
3*6 = 18 points
Where
Bryce made the basket equals 18 points.
so,Bryce made the basket equals 18 points.Amelia received a point total of 10 points.The point Jordan scored was 6 points.
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Which of the following square roots is a rational number
Answers
First, we need to define rational numbers
Rational numbers are numbers that can be express as a quotient or fraction
From the question given, The square root of 16 is 4, this can be express as 4/1
Hence, it is a rational number
Therefore the correct option is A
What is the answer Im stressing
Answers
The value of corresponding angle x is 157°.
What are properties of parallel lines?Properties of Parallel Lines:
The pairs of corresponding angles are equal.
The pairs of vertically opposite angles are equal.
The pairs of alternate interior angles are equal.
The pairs of alternate exterior angles are equal.
Given: m║n
So, using the property of parallel lines we have the angles on the same side of transversal are supplementary. Let 23° is tranversal to α, then
23° +α = 180°
⇒α = 180°-23°
⇒α = 157°.
Now, using the property of vertically opposite angles we have
α = x = 157°
⇒ x = 157°
Therefore, the value of x is 157°.
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Find the value of x.
Answers
Answer:19
Step-by-step explanation:
Answer:
[tex]x=\sqrt{\frac{9}{2}}[/tex]
Step-by-step explanation:
[tex]a^2+b^2=c^2\\x^2+x^2=3^2\\2x^2=9\\x^2=\frac{9}{2} \\x=\sqrt{\frac{9}{2} }[/tex]
Rosita mom is 42 years old she is six times as old as Rosita. The equation 6a=42 can be used to find Rosita age .A. 36 B. 7C. 48D. 8
Answers
We have the next equation
42=6a
we need to clear a
a=42/6
a=7
the answer is 7
HELP PLEASE! Solve and show work.
4x + 6 < -6
Answers
Answer:
Step-by-step explanation:
1. 4x+6<-6
2. 4x<-6-6
3. 4x<-12
4. x<-12/4
5. x<-3
6. The answer is x < -3.
Sally picked five buckets of blueberry she put 500 berries in each basket how many blueberries did Sally pick in all
Answers
Since each bucket contained 500 berries and there are 5 buckets we can find the total amount of berries by multiplying the number of berries per bucket by the number of buckets. This is done below:
[tex]\begin{gathered} \text{total}=500\cdot5 \\ \text{total}=2500\text{ berries} \end{gathered}[/tex]Sally picked 2500 blueberries.
Put the following equation of a line into slope-intercept form, simplifying all fractions.
12x-20y=
12x−20y=
\,\,-100
−100
Answers
The slope intercept form of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept. The given equation can be written in terms of slope in y = 0.6x + 5.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
Given that,
The equation of the line is 12x - 20y = -100
In order to write the given equation in slope-intercept form, write the given equation in terms of y as,
12x - 20y = -100
=> 20y = 12x + 100
=> y = 12 / 20x + 100 / 20
=> y = 0.6x + 5
Where slope is 0.6 and y-intercepts is 5.
Hence, the slope-intercept form of the given equation is y = 0.6x + 5.
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Find the area and perimeter of the rectangle based on information given Length = 5 Width = x + 2
Answers
Given the length and the expression that represents the width of a rectangle, you need to remember that:
• The area of a rectangle can be calculated by multiplying its dimensions:
[tex]A=lw[/tex]Where "l" is the length and "w" is the width.
• The perimeter of a rectangle is:
[tex]P=2l+2w[/tex]Where "l" is the length and "w" is the width.
Then, knowing that:
[tex]\begin{gathered} l=5 \\ w=x+2 \end{gathered}[/tex]- You can set up that the area of this rectangle is:
[tex]A=5(x+2)[/tex]Simplifying, you get:
[tex]\begin{gathered} A=(5)(x)+(5)(2) \\ A=5x+10 \end{gathered}[/tex]- And the perimeter is:
[tex]\begin{gathered} P=(2)(5)+(2)(x+2) \\ P=10+2x+4 \\ P=2x+14 \end{gathered}[/tex]Hence, the answer is:
- The area is:
[tex]A=5x+10[/tex]- The perimeter is:
[tex]P=2x+14[/tex]a teacher writes a number set on the board as shown. 5,6,7,8
Which value of x in the number set makes 6(2x+12)=144
Answers
6 is the value of x in the number set makes 6(2x+12)=144
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The number set has numbers
Five comma, six comma, seven comma eight
5,6,7,8
We need to find which value of x in the number set makes 6(2x+12)=144
Now x=5
6(2x+12)=6(2(5)+12)
=6(10+12)
=6(22)
=132
So 5 is not value of x for 6(2x+12)=144
Now x=6
6(2x+12)=6(2(6)+12)
=6(12+12)
=6(24)
=144
5 is value of x for 6(2x+12)=144
Hence 6 is the value of x in the number set makes 6(2x+12)=144
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FOR BRAIBLIEST AND 50 POINTS! I NEED THIS ASAP!
Directions: Graph these in one cartesian plane(clue: it would form a triangle)
Answers
The solution is the area between the three lines, a triangle with vertices marked (see attached).
what is the distance between (-3,-8) and (6,-8)
Answers
Answer:
9
Step-by-step explanation:
√(6 - -3)2 + (-8 - -8)2
= √(9)2 + (0)2
= √81
= 9
Hope this helps you out :)
6x2 - 24x + 18 = 0
Answer please
Answers
Answer:
The answer is -1 or -3
Step-by-step explanation:
You woud use the quadritic formula
[tex]x=\frac{ -b+- \sqrt{b^{2} -4ac} \\}{2a}[/tex]
[tex]x=\frac{-24 +- \sqrt{576-432} }{12} \\[/tex]
[tex]x=\frac{-24+- \sqrt{144} }{12}[/tex]
[tex]x=\frac{-24+12}{12}\\\\x=\frac{-12}{12} \\x = -1[/tex]
or
[tex]x=\frac{-24-12}{12} \\\\x= \frac{-36}{12} \\\\x= -3[/tex]
To get the answer of -1 or -3
equation represents the distancetraveled against the wind?ProblemAt full speed, Hal travels 600 miles in 2 hourswith the wind. The same distance againstthe wind takes 3 hours.What's the maximum speed of Hal's airplanein still air? What's the speed of the wind?Click on the correct answer.3(x - y) = 6003(x + y) = 600x-speed of the airplane in still airy speed of the wind2(x - y) = 6002(x + y) = 60080888Ma
Answers
Take into account:
x = speed of the airplane
y = speed of the air
consider that the product in between time and speed is equal to the distance traveled in the time.
Then, if the airplane took 3 hours complete 600 miles, agaist the wind, you have that the distance traveled by the airplane is 3x without wind. The speed of the wind decelerates the airplane. The "distance traveled by the wind is 3y"
Then, when you subtract the previous terms you obtain:
3x - 3y = 600 factorize 3 left side
3(x - y) = 600
You have 80$ to spend on clothes jeans cost 34$ and t shirts cost 9$ without any added tax how many pairs of jeans can I purchase if I buy 1 t shirt
Answers
Answer:
2 pairs of jeans
Step-by-step explanation:
1) Subtract the cost of the t-shirt
As we are given the information that she will only be buying one t-shirt it
means that we can get rid of the price of it...
$80-$9 = $72
2) Find the number of jeans
Knowing that we have $72 left we have figure out how many jeans she
can buy by dividing 72 by 34...
$72 ÷ $34 = 2
Hope this helps, have a great day!
Can you help me I can’t understand this question
Answers
Answer:
the graph given has a greater unit rate
Step-by-step explanation:
basically, you have to compare the gradients of both the graphs
one graph's equation is given i.e y=47/2 where 47/2 is the gradient/slope now find the gradient/slope of the given graph:
slope = x2-x1/y2-y1
chose any two coordinates on the graph and input them in the equation
I chose (2,94) and (4,188)
inputting them in the equation:
188-94/4-2
=94/2
now see which one is greater 47/2 or 94/2
94/2 is greater than 47/2 so it has a greater unit rate
Please help I have a test on this and I’m not sure how to do this
Answers
ANSWER
[tex]y=-\frac{1}{4}x^2+\frac{3}{4}x+1[/tex]EXPLANATION
We want to find the equation for the function graphed.
We see that the function passes through -1 and 4 on the x-axis and 1 is the y-intercept.
These are called the roots of the function. The roots are the x values where the function equals 0.
We can find the function by applying the roots:
[tex]y=a\mleft(x-x_1\mright)\mleft(x-x_2\mright)[/tex]where x1 and x2 are the roots.
a = leading coefficient
Therefore, we have that:
[tex]\begin{gathered} y=a(x-(-1))(x-4) \\ y=a(x+1)(x-4)_{} \end{gathered}[/tex]Expand the brackets:
[tex]\begin{gathered} y=a(x^2-4x+x-4) \\ y=ax^2-4ax+ax-4a \\ y=ax^2-3ax-4a \end{gathered}[/tex]Now, we have to find a.
To do that, we use the y-intercept of the function (0, 1). The y-intercept is the value of the function when x is 0.
Therefore, when x = 0, y = 1:
[tex]\begin{gathered} 1=0-0-4a \\ \Rightarrow-4a=1 \\ a=-\frac{1}{4} \end{gathered}[/tex]Now, substitute the value of a into the function obtained earlier.
[tex]\begin{gathered} y=-\frac{1}{4}x^2-3(-\frac{1}{4})x-4(-\frac{1}{4}) \\ \Rightarrow y=-\frac{1}{4}x^2+\frac{3}{4}x+1 \end{gathered}[/tex]That is the equation of the function graphed.
9000÷20=N ????? pls answer
Answers
To get the value of N let's do the division.
The value of N is 450
A ____________________ is a protective barrier that surrounds only plant cells, providing structural support.
Mitochondria
Chloroplast
Cell wall
Nucleus
Answers
A Cell wall is a protective barrier that surrounds only plant cells, providing structural support.
A cell wall, a large central vacuole, and plastids like chloroplasts are all present in plant cells. The cell wall is a thick, stiff layer that surrounds and supports the cell structurally and physically. It is located outside the cell membrane.
What is cell wall?the dense, nonliving covering that protects and sustains the majority of plant, bacterial, fungal, and algal cells. cellular wall.
The cell membrane is a layer of defense that covers the surface of the cell and serves as a partition between the interior of a cell and its surroundings. The cell membrane also regulates the materials that enter and exit the cell.
A cell is protected by its cell membrane, also known as the plasma membrane. Additionally, it maintains a constant environment inside the cell, and that membrane serves a variety of purposes. One is to move compounds out of the cell that are harmful as well as nutrients into the cell.
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8. Lori bought a shirt and a hat at a half-off sale.
If she spent a total of $21 on the two items,
what was the original price of the hat?
Answers
Answer:
the hat cost 18
Step-by-step explanation:
if the shirt is 24 half the price of the shirt is 12 so 21-12= 9 which is the price of the hat discounted.
The original price of the hat is 18 because 9 x 2 = 18
Fill in the table and sketch the exponential function on a graph. y = 4^xxy-3-2-1023
Answers
We must plot the following exponential function:
[tex]y=f(x)=4^x.^{}[/tex]Replacing the values of x in the function above, we complete the table:
[tex]\begin{gathered} x=-3\rightarrow y=f(-3)=4^{-3}=\frac{1}{64}=0.015625, \\ x=-2\rightarrow y=f(-2)=4^{-2}=\frac{1}{16}=0.0625, \\ x=-1\rightarrow y=f(-1)=4^{-1}=\frac{1}{4}=0.25, \\ x=0\rightarrow y=f(0)=4^0=1, \\ x=1\rightarrow y=f(1)=4^1=4, \\ x=2\rightarrow y=f(2)=4^2=16, \\ x=3\rightarrow y=f(3)=4^3=64. \end{gathered}[/tex]So we have the following points:
• (-3, 1/64) = (-3, 0.015625),
,• (-2, 1/16) = (-2, 0.0625),
,• (-1, 1/4) = (-1, 0.25),
,• (0, 1),
,• (1, 4),
,• (1, 16),
,• (1, 64).
Now, plotting each point (x, y) and joining them, we get the following graph:
One clarification: the label of the points in the graph have been rounded.
Answer
The points of the table are:
• (-3, 1/64)
,• (-2, 1/16)
,• (-1, 1/4)
,• (0, 1),
,• (1, 4),
,• (1, 16),
,• (1, 64).
The graph of the points and the function is:
One clarification: the label of the points in the graph have been rounded.
Alexa went shopping for a new pair of pants. Sales tax where she lives is 8.75%. What
number should she multiply the price of the pair of pants by to find the total plus tax
in one step?
Answers
To find the total plus tax she must multiply the price of the pair of pants and 108.75% ≈ 1.0875.
Given:
Alexa went shopping for a new pair of pants.
Sales tax where she lives is 8.75%.
Let x be the price of pants.
Total plus tax = prices of pair of pants * 1.0875.
= x * 1.0875
= 1.0875x.
Therefore to find the total plus tax she must multiply the price of the pair of pants and 108.75% ≈ 1.0875.
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Find the center and radius of the circle: x² + y² - 2x + 4y = -1
Answers
We need to complete the perfect square in x and y, that is,
[tex]x^2-2x=(x-1)^2-1[/tex]and
[tex]y^2+4y=(y+2)^2-4[/tex]Then, our given equation can be rewritten as:
[tex](x-1)^2-1+(y+2)^2-4=-1[/tex]which is equal to
[tex]\begin{gathered} (x-1)^2+(y+2)^2-5=-1 \\ \end{gathered}[/tex]By moving -5 to the right hand side, we have
[tex]\begin{gathered} \mleft(x-1\mright)^2+\mleft(y+2\mright)^2=-1+5 \\ \mleft(x-1\mright)^2+\mleft(y+2\mright)^2=4 \\ \mleft(x-1\mright)^2+\mleft(y+2\mright)^2=2^2 \end{gathered}[/tex]Since the general circle equation is
[tex]\mleft(x-h\mright)^2+\mleft(y-k\mright)^2=r^2[/tex]then, the answer is:
[tex](x-1)^2+(y+2)^2=2^2[/tex]then, the center is (h,k)= (1, -2) and the radius is r=2
Candace order a $4 sandwich a $2 drink in the $3 smoothie for lunch she has $10 as symbols to the equation to represent this situation and solve it
Answers
Let's start by adding all the values for what Candace order:
Total for the order: $4 + $2 + $3 = $9
since she has a $10 bill,
she will be able to pay for it, and have the following change back:
$10 - $9 = $1
she will get back $1.
The math equations we created are then:
4 + 2 + 3 = 9
10 - 9 = 1
can you please help me
Answers
in this problem we have that
y+20=x+15 -------> by vertical angles
isolate variable y
y=x+15-20
y=x-5 ------> equation A
and
(3x+5)+(x+15)=180 ------> by form a linear pair (sipplementary angles)
solve for x
4x+20=180
4x=160
x=40
substitute the value of x in equation A
y=40-5
y=35
therefore
x=40 and y=35
how much is -5x+2=52
Answers
Find x
-5x+2=52
_______________
-5x + 2 = 52
subtracting 2
-5x + 2 -2 = 52 -2
-5x + 0 = 50
-5x = 50
Dividing by -5
-5/ -5 x = 50/ -5
1x= -10
x= -10
__________________
Answer
x= -10
Suppose that the amount in grams of a radioactive substance present at time t (in years) is given by A(t) = 800e -0.86t. Find the rate of change of the quantity present at the time when t = 5. O 9.3 grams per year 0 -72.7 grams per year 0-9.3 grams per year O 72.7 grams per year
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} A\mleft(t\mright)=800e^{-0.86t} \\ \Delta A(t)=-0.86\cdot800e^{-0.86t} \\ \Delta A(5)=-0.86\cdot800e^{-0.86\mleft(5\mright)} \\ A(5)=-9.34 \\ A(5)=-9.3g\text{ / year} \end{gathered}[/tex]Hence, the correct option is the third option -9.3 grams per year
Analysts at the Milk Company calculated the average price of a gallon of its milk over 10 years. The
following table shows the years since 2010 and the average price of a gallon of milk at those times.
Years (since 2010) 1 3 6 8 9
Price (in dollars) 3.57 3.49 3.20 2.90 3.04
Which data display would you use to represent this data?
Histogram
Line plot
Scatter plot
Line graph
Answers
The data display method that can be used to represent the data is a scatter plot. The correct option is therefore;
Scatter plot
What is a scatter plot?A scatter plot is a graph formed by plotting the ordered pairs of a set of data on the coordinate axis such that a pattern is formed that reveals the presence of any correlation or pattern between the variables.
The data in the table are presented as follows;
Year (since 2010) [tex]{}[/tex] Price (in Dollars)
1 [tex]{}[/tex] 3.57
3 [tex]{}[/tex] 3.49
6 [tex]{}[/tex] 3.2
8 [tex]{}[/tex] 2.9
9 [tex]{}[/tex] 3.04
The value calculated by the analysts at the Milk Company = The average price of a gallon of the company's milk over 10 years.
The information obtainable from the data includes the variation of the price of milk with the number of years.
The number of data points are 5, while the number of years in 10 years is 10. Therefore, 5 data points are left out and can be estimated using a trend line that matches the data.
The data display method that will suitable represent the data is therefore a scatter plot that can be further analyzed with a trend line.
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Answer:
it the second graph im taking the quiz right noww
Step-by-step explanation:
At Lakeville South High School, 60% of students have high-speed internet access, 30% have a mobile computing device, and 20% have both. The proportion of students that have neither high-speed internet access nor a mobile computing device is:
A. 0%
B. 10%
C. 30%
D. 80%
E. 90%
Note: the answer is 30% but I can't for the life of me figure out why
Answers
That have neither high-speed internet access nor a mobile computing device is 30%.
What is Venn diagram?Venn diagrams are utilized in various fields including business, measurements, semantics, and so forth. Venn charts can be utilized to outwardly coordinate data to see the connection between sets of things, like shared characteristics and contrasts, and to portray the relations for visual correspondence.
According to question:In school, 60% of students have high-speed internet access, 30% have a mobile computing device, and 20% have both.
Venn diagram for the situation
Thus remaining 30% students hat have neither high-speed internet access nor a mobile computing device.
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