Answer:
2x + 2.9 = 30.6
Step-by-step explanation:
We are to represent the unknown number that Mark thinks of with x
If Mark doubles this unknown number, he multiplies it by 2 and the unknown number becomes - 2x
He then adds 2.9
The equation becomes 2x + 2.9
The answer of the above equation is 30.6
This gives : 2x + 2.9 = 30.6
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
The total number of students in the seventh grade is 9 more than 4 times as many students as are in the art class. there are 101 students in the seventh grade. how many students are in the art class.
Answer:
There are 23 students in art class
8. Jill bought a soda for $3 and eight candy bars. She spent a total of $43.
Answer:$5.00
Step-by-step explanation:
Let c = the cost of each candy bar
3 + 8c = 43
8c = 40
c = $5.00
Answer:
each candy bar costs 5 dollars
Step-by-step explanation:
43-3=50 and 40÷8=5
what is the volume of this cylinder?
Answer:
volume of a cylinder is πr²h
ie
3.14 × 7× 7 × 11
you get
1692.46
Miguel has a ball of modeling clay that has a diameter of 3.5 centimeters. The cylindrical container it is placed in has a base area of 7.1 square centimeters and a height of 5 centimeters. What is the volume of empty space in the container?
Answer:
48.1 cubic meters or 48100000 cubic centimeters
Step-by-step explanation:
Firstly we need to find the radius.To find that we divide the diameter by two.3.5÷2=1.75
Volume of Cylinder=Pi×radius squared×height
Lastly 3.14×1.75×1.75×5=48.1
I hope this helps you in any way:)
Need help quick Picture provided
Jocelyn said that the triangle below is not a right triangle. Her work is shown below. Explain what she did wrong and show Jocelyn the correct solution.
Jocelyn said that the triangle below is not a right triangle. Her work is shown below. Explain what she did wrong, and show Jocelyn the correct solution.
one class of 28 students has a ratio of 3 girls to 4 boys. if this ratio holds true for the entire 6th grade of 140 students, how many girls are there
Answer: 105 girls because the ratio from girls to boys is 3:4 and that means that 3/4 are girls so 3/4 times 140 is 105
Step-by-step explanation:
through: (-3,-4) and (0,4)
Answer:
The slope = 8/3
Step-by-step explanation:
Let's find the slope between your two points.
(−3,−4);(0,4)
(x1,y1) = (−3,−4)
(x2,y2) = (0,4)
Use the slope formula:
m= y2−y1 / x2−x1
= 4 − −4 / 0 − −3
= 8/3
Answer:
m = 8/3
Graph:
hope this helps and is right :)
SOS PLEASE HELP
Write the equation for this line
PLZ HELP!This is my only question left!!! plzzzzz
Answer:
12.84 degrees
Step-by-step explanation:
sin(x)=2/9
if two points pass through each other it will be function or if it doesn't pass
Answer:
If two points pass through each other it means that it is not a function. The vertical line test shown proves that fact.
Step-by-step explanation:
Which graph has a slope of 4/5?
Answer: The second one
Step-by-step explanation:
HELP , I WILL MARK U BRAINLIEST FLR CORRECT ANSWER
Answer:
I'm pretty sure you would need a battery...
HELPPP PLS !!!!!!!!!!!!!!!!!!!
2. What type of association does this
graph show?
Positive
negative
none
all of the above
An ice cream factory makes 300 quarts of ice cream in 2 hours. How many quarts could be made in 12 hours? What was that rate per day?
Answer:
1800 in 12 hours
3600 in 24 hours
Step-by-step explanation:
300 in 2 hours
12/2 = 6 times as much in 12 hours
6(300) = 1800 in 12 hours
3600 in 24 hours
1. x-y=1
x+y=-5
2. x-4y=10
2x+y=2
3. -5x+y=0
x+y=6
4. y=6-2x
y=4
5. 2y=16
4x-y= 4
6. x=y -4
3x+y=12
7. y- 2x=-6
5x-y= 9
8. 3y+x= 2
y-x=-6
Answer:
what is the question write it in thecomments and ill answer
Answer:
1.) (y+1)+y=-5
2y=-6
y=-3
x+(-3)=-5
x=-2
plug in to check if it works
2.) 2(4y+10)+y=2
9y+20=2
9y=-18
y=-2
x-4(-2)=10
x+8=10
x=2
3.) -5(-y+6)+y=0
5y-30=0
5y=30
y=6
x+(6)=6
x=0
4.) 4=6-2x
-2=2x
x=-1
y=6-2(-1)
y=8
5.) 4x-(8)=4
4x=12
x=3
4(3)-y=4
12-y=4
-y=-8
y=8
6.) 3(y-4)+y=12
4y-12=12
4y=24
y=6
x=6-4
x=2
7.) 5x-2x-6=9
3x=15
x=5
5(5)-y=9
25-y=9
-y=-16
y=16
8.)3(x-6)+x=2
4x-18=2
4x=20
x=5
y-5=-6
y=-1
hope this helped :)) also make sure to plug the x and y back into both equations :))
Bearings Problem Solving Question:
From a lighthouse two boats can be sighted. Boat 1 on a bearing of 60° at a distance of 2km and Boat 2 on a bearing of 340° at a distance of 3km.
a) If Boat 1 is in need of assistance, what bearing would Boat 2 need to travel on to reach it?
b) Assuming Boat 1 does not move, how far would Boat 2 have to travel?
9514 1404 393
Answer:
a) 123.4°
b) 3.3 km
Step-by-step explanation:
In (N, E) coordinates, Boat 1 is located relative to the lighthouse at ...
2(cos(60°), sin(60°)) = (1.0, 1.732) . . . . . km
Boat 2 is located at ...
3(cost(340°), sin(340°)) = (2.819, -1.026) . . . . . km
So, relative to Boat 2, Boat 1 is located at ...
(1, 1.732) -(2.819, -1.026) = (-1.819, 2.758) . . . . . km
This is at a bearing of ...
arctan(2.758/-1.819) = 123.4°
and a distance of ...
√(1.819² +2.758²) ≈ 3.304 . . . . . km
a) Boat 2 would need to travel on a bearing of 123.4°.
b) Boat 2 would need to travel 3.3 km.
_____
Additional comment
We use (North, East) coordinates so we don't have to do the mental gyrations necessary to translate to and from (E, N) coordinates. The latter would correctly orient a map relative to the X-Y Cartesian plane. The former are equivalent to flipping the map over and looking at it from the back side. This is a "rigid transformation", so angles and distances remain unchanged.
312.6÷100=
need the ansss
Answer:3.126
Step-by-step explanation: move the decimal however many zeros there are to the left
How do the temperatures on Neptune compare to Earth's temperatures?
Find the area........
Answer:
6) 121.2 sq meters
7) 40 sq ft
8) 70 sq meters
Step-by-step explanation:
#6 and 7: base x height
#8: base x height / 2
At a middle school, 46 students have blonde hair. There are 230 students in the school. What percent of the students have blonde hair?
Answer:
20% of the students have blonde hair
Answer:
20%
Step-by-step explanation:
HELP
Observe the graph below.
The graph shows a ___ function that is asymptotic to ____
Answer:
The graph shows a LOGARITHMIC function that is asymptotic to X=1
Step-by-step explanation:
2) solve for s please
Answer:
75
Step-by-step explanation:
A line's y-intercept is -9, and its slope is 1. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y=x-9
Step-by-step explanation:
Seventh grade > L.8 Solve percent equations: word problems JS6
Harold's Diner offers its clients a choice of regular and diet soda. Last night, the diner served
40 sodas in all, 10 of which were regular. What percentage of the sodas were regular?
find the value of x plz
i’ll give brainliest, just help me please : )
Determine the number of liters of a 30% saline solution and the number of liters of a 60% saline solution that are required to make 10 liters of a 50% saline solution.
Answer:
Number of liters of 30% solution = x = 3.3 liters
Number of liters of 60% solution = y
= 6.67 liters
Step-by-step explanation:
Let us represent:
Number of liters of 30% solution = x
Number of liters of 60% solution = y
Determine the number of liters of a 30% saline solution and the number of liters of a 60% saline solution that are required to make 10 liters of a 50% saline solution.
30% × x + 60% × y = 10 × 50%
0.3x + 0.6y = 5...... Equation 1
x + y = 10...... Equation 2
x = 10 - y
We substitute 10 - y for x in Equation 1
Hence
0.3(10 - y) + 0.6y = 5
3 - 0.3y + 0.6y = 5
- 0.3y + 0.6y = 5 - 3
0.3y = 2
y = 2/0.3
y = 6.67 liters
Solving for x
x = 10 - y
x = 10 - 6.67
x = 3.33 liters
Hence:
Number of liters of 30% solution = x = 3.3 liters
Number of liters of 60% solution = y
= 6.67 liters