The table in the figure at the right is 34 in. across. The shaded regions are made of mahogany. What is the area of thee mahogany? Round your answer to the nearest tenth.
Answer:
408.7 in^2
Step-by-step explanation:
If you want to know how to find the area of a regular octagon by hand, the easiest procedure is to apply the standard formula for the area of a regular polygon. The formula is the following:
area of regular polygon = perimeter * apothem / 2,
where the apothem is the distance for the center of the polygon to the mid-point of a side. The perimeter can be calculated a few ways: by summing up the length of each side, multiplying the length of one side by the number of sides.
6
AXYZ will be translated so that the coordinates of X' are (5,11).
y
Y
14
13
12
X
11
10
9
8
N
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
What will be the coordinates of Z' ?
(5,8)
B (6,7)
© (7,6)
D (8,5)
Answer:
Isometry: An isometry is a transformation that maintains congruency. This means that the transformation does not change the figure's size or shape.
Make sure your child is familiar with the Cartesian coordinate system including the horizontal x-axis, the vertical y-axis, and the (x,y) convention used for locating points.
If you have not already done so, you may wish to review this congruency lesson with your child.
Translations
This section will help your child to translate congruent figures on a Cartesian plane. It will also introduce translation vectors which show the distance and direction of the translation.
Translations
Figure J is the pre-image. Figure S is translated.
A figure is a translation if it is moved without rotation.
Translation Vector
A Translation Vector is a vector that gives the length and direction of a particular translation. Vectors in the Cartesian plane can be written (x,y) which means a translation of x units horizontally and y units vertically.
figure being translated
Vectors translations can be written as shown in either of these two ways:
format example for writing vectors
This vector can be said to be ray AB or vector D.
You translate a figure according to the numbers indicated by the vector. So if one point on a figure has coordinates of (-3,3) and the translation vector is (-1,3), the new coordinate is (-4,6). You add or subtract according to the signs in the numbers in the vector.
Work through the two examples below with your child to see how to apply translation vectors.
square translated on cartesian grid
The red square's coordinates are:
(-4,3); (-4,8); (-9,3); (-9,8).
What are the coordinate pairs under a translation vector of (1,-1) as shown by the blue square?
The new coordinates are:
(-3,2); (-3,7); (-8,2); (-8,7).
You can see that the translation did not move the figure far because the vector translation is small.
square translated on cartesian grid
We will try a different vector translation of (3,-9) on the same red square
The new coordinates are:
(-1,-6); (-1,-1); (-6,-6); (-6,-1).
Get you child to try the next example. Do not look at the answer until he or she has tried to work it through the task.
single triangle on cartesian grid
Task: Translate ΔABC with a vector translation of (6,-2)
Steps:
Find the coordinates of Δ ABC.
Add 6 to the X coordinates and subtract 2 (or add -2) from the Y coordinates.
Plot the new coordinates on the grid.
Answer and Explanation
Coordinates of ΔABC are:
(-5,1); (-2.5,7); (0,1)
Add 6 and subtract 2
A1 = (-5 + 6, 1 - 2) = (1,-1)
B1 = (-2.5 + 6, 7 - 2) = (3.5,5)
C1 = (0 + 6, 1 - 2) = (6,-1)
Plot ΔA1B1C1
Rotations
This section will show your child how to rotate a figure about the origin on a Cartesian plane. Work through the two examples below:
Note: Make sure your child knows that the origin is the intersection of the X and Y axes; (0,0) on the Cartesian plane.
Rotation Transformation: Example 1
Look at the four triangles on the Cartesian plane below. Each one is rotated about the origin as shown in the table.
Triangle B Triangle C Triangle D
90° rotation of Triangle A about the origin 90° rotation of Triangle B about the origin 90° rotation of Triangle C about the origin
180° rotation of Triangle A about the origin 180° rotation of Triangle B about the origin
270° rotation of Triangle A about the origin
The coordinates are:
Triangle A (-2,2) (-10,2) (-6,8)
Triangle B (2,2) (2,10) (8,6)
Triangle C (2,-2) (10,-2) (6,-8)
Triangle D (-2,-2) (-2,-10) (-8,-6)
Note the pattern in the coordinates for corresponding vertices on the triangles.
Rotation Transformation: Example 2
The coordinates of Pentagon ABCDE are:
(0,4); (7,4); (9,2); (7,0); (0,0)
Pentagon ABCDE is rotated 180° about
the origin making the coordinates of
Pentagon A1B1C1D1E1:
(0,-4); (-7,-4); (-9,-2); (-7,0); (0,0)
Note how the coordinates of
corresponding vertices are opposite
integers (just the +/- sign is different).
This is always the case with 180°
rotations about the origin.
Reflections
This section will help your child to reflect a figure over an axis on a Cartesian plane
Work through the two reflection examples below.
Reflection Transformation: Example 1
The coordinates of LMNO are:
(-7,5); (0,5); (-2,1); (-5,1)
LMNO is reflected over the X-axis
making the coordinates of
L1M1N1O1:
(-7,-5); (0,-5); (-2,-1); (-5,-1)
Note how the x-coordinates remain the
same but the y-coordinates change to
their opposite integer (i.e. the sign changes).
This is always the case with reflections over the X-axis.
Step-by-step explanation:
The solution is, the coordinates of Z' will be z' = (6,7),
i.e. option B is correct.
What is transformation?A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.
here, we have,
Given that,
X' are (5,11).
now, See attachment
Required that,
The image of Z i.e. z'
From the attachment:
X =(7,11)
This implies that:
X' = ( x- 2, y)
Using the same rule for z;
z=(8,7)
z' = (8-2, 7)
z' = (6,7)
Hence, The solution is, the coordinates of Z' will be z' = (6,7),
i.e. option B is correct.
To learn more on transformation click:
brainly.com/question/20211457
#SPJ7
(6,2)-(4,5)-(9,4) dilated by a scale factor of 3
Answer:
1 . 6 , 2 is 18 ,6
2.4,5 is 12 ,15
3. 9,4 is 27,12
but is ans is wrong
F(t) = 212 - 6t
What is the value of t when F(t) = 140
Answer: -628
Step-by-step explanation:
F(140) = 212 - 6(140)
F(140) = 212 - 840
F(140) = -628
What is the answer.. to this !
Answer:
A = 3.14
Step-by-step explanation:
A = π[tex]r^{2}[/tex]
A = 3.14 x [tex]1^{2}[/tex]
(diameter = 2)
(remember, radius is half of the diameter)
(radius = 1)
A = 3.14
LAST QUESTION PLS HELP ME
Are of triangle
PLSS HELP!!
Write an algebraic expression for 4 more than 3 times a number
Answer:
3x+4
Step-by-step explanation:
The algebraic expression will be : 3x + 4
What is an algebraic expression ?
An expression built up from integer constants , variables and algebraic operations .
Let the number be : x
now , in the algebraic expression for 4 more then 3 times a number
First we need to make the number 3 time = 3x
then in that expression we need to add 4 , we get = 3x+ 4
The algebraic expression will be : 3x + 4
Learn more about algebraic expression:
https://brainly.com/question/953809?referrer=searchResults
#SPJ2
Find the measure
of the angle indicated.
Your answer
Answer:
44°
Step-by-step explanation:
This is an inscribed angle and its measure is equal to the measure of arc it sees (minor arc BC in this case)
88 ÷ 2 = 44°
I need help me this somebody help!
Answer:
M1=136
m4=180-136
=44////
Can you help me with this question please
Answer:
the answer is 9^8
Step-by-step explanation:
9^3 * 9^5 = 9^ 3 + 5 = 9^8
Find the equation of the line
perpendicular to y = 6x - 2 that
also intersects the point (6, -2).
y=mx+
Answer:
your answer will be y= -1/6x+(-1)
Step-by-step explanation:
I hope this helps ^_^
how many one-digit integers are there
Write the coordinates of the vertices after a translation 12 units down.
Answer:
I don't know.
Step-by-step explanation:
I don't know.
Find the output when the input is -2: y = -3x -5
Pls help will mark brainliest
Answer:
750
Step-by-step explanation:
Andre is running in an 80-meter hurdle race. There are 8 equally-spaced hurdles on the race track. The first hurdle is 12 meters from the start line and the last hurdle is 15.5 meters from the finish line. Calculate how far apart the hurdles are from one another in decimal form?
Answer: 32 meters
Step-by-step explanation:
Which of the following expressions represents "subtract 17 from x
Answer:
x-17
Step-by-step explanation:
Answer:
x-17
I might be incappable
Find the area of a circle with a radius of 2.
Either enter an exact answer in terms of it or use 3.14 for IT and enter your answer as a decimal.
units2
What does x equal when y=5
PLEASE HELP ME! 50 POINTS! I WILL GIVE BRAINLIEST! Decide whether the table could represent a proportional relationship. If the relationship could be proportional, what would be the constant of proportionality?
Bettie's Boutique is having a 20% off sale.
|original price| sale price|
—————————————
|$15. | $12. |
—————————————
|$25. |$20. |
—————————————
|$35. |$28. |
————————————-
Answer:
15 and 12 makes a pattern of -3
25 and 20 makes a pattern of -5
35 and 28 makes a pattern of -7
Step-by-step explanation:
5 x 3=15
5 x 5=25
5 x 7=35
Answer:14
Step-by-step explanation:
Savannah has $92,637 in a savings account that earns 9% annually. The interest is not compounded. How much interest will she earn in 5 years
Answer:
$41686.65
Step-by-step explanation:
Given data
Principal = $92,637
Rate= 9%
Time= 5 years
The simple interest expression is given as
SI= PRT/100
Substitute
SI= 92637*9*5/100
SI= 4168665/100
SI=$41686.65
Hence the interest is $41686.65
Please help
Write an equation for the situation: Karen wrote a check for $72. She subtractded the amount from her checkings account and found that the balance was $383 after writing this check. What was her balance before writing the check?
10 points
Answer:
She had $455 before
How many years will it take for $3,000 to double at a simple interest rate of 2%?
A. 2 years
B. 5 years
C. 10 years
D. 50 years
Answer:
3000=3000*0.02t
3000/60=t
t=50 yrs
Step-by-step explanation:
Can someone help me?
Help Plz
Will mark brainliest
Answer:
False, true, false, true
Step-by-step explanation:
Sin T = 7/25
Cos T = 24/25
Sin C = 24/25
Cos C = 7/25
who else is on the verg of a MENTAL BREAKDOWN because they want highschool to end
just me ok
Answer: I guess High School is as bad as my big sister says it is.
Step-by-step explanation:
I'm in 8th grade, I'm going to highschool this yearrrr! Poor me...
how many solutions does 2x+6=7x5 have
Answer:
14.5
Step-by-step explanation:
2x=7*5-6 will be 14.5
Answer:
One solution.
Step-by-step explanation:
Since the right side of the equation is a constant, there can only be one solution:
[tex]2x+6=7*5[/tex]
[tex]2x+6=35[/tex]
[tex]2x=35-6[/tex]
[tex]2x=29[/tex]
[tex]x=14.5[/tex]
14.5 is the only answer.
please answer correctly and quickly all question please please please
The bus fare for 8 passesngers is Rs. 384, how many more passengers can travel in the bus if the bus fare amounts to Rs. 576?
Answer:
12 passengers so four more can travel in the bus.
Step-by-step explanation:
384/8= rs 48 per person.
amount= 576
576/48 = 12 passengers.
Step-by-step explanation:
here
8 passengers=Rs. 384
1 passenger= Rs. 384/8
=Rs. 48
Rs. 576= ? passengers
now,
Rs. 576/ 48
= 12passengers
12 passengers - 8 passengers
= 4 passengers
therefore, 4 more passengers can travel in the bus fare amount to Rs. 576.