# data[].attributes.body
- Question 2 is only correct if two dimensions are changed.  If one dimension is changed the area will only change by that same scale factor.
- Make sure you are adding the two bases for a trapezoid, not multiplying them.

# data[].attributes.body
The old area is multiplied by the squared scale factor to get the new area.
A rectangle has the dimensions of 2 by 3, the area would be 6. You multiply by a scale factor of 2 then the rectangle becomes 4 by 6, and the new area results in being 24.
A triangle has a base of 2 and a height of 4 so an area of 4. The dimensions are multiplied by a scale factor of 4 so the new base is 8 and the new height is 16. The new area would be 64.

# data[].attributes.body
Formula: 2(lw+lh+wh)
Find the surface area of a building in new york with a length of 7 yards and width of 8yards and height of 15yards. 2(56+105+120). This will leave you with an answer of 562 yards.

# data[].attributes.body
Formula: 4/3piRadiusCubed
Find the volume of a globe in items classroom with a radius of 9 ft. You would do 4/3 times 3.14 times 9 cubed. You would get 3052.08 feet.
4/3*3.14*9cubed.

# data[].attributes.body
1/2bhl
Example problem: Find the volume of a glass prism used in science with a base of 12cm, a height of 9 and a length of 18. ( 1/2x12x9x18) You would get 972 cm cubed.

# data[].attributes.body
composite figures: Find the area of each figure separately and add the areas together
Inscribed figures: Find the area of each figure separately and  subtract the areas.
Composite figure: Find the area of the figure to the left. The half circles together would make a full circle, and it has a 4 yd radius. So you would do 3.14 times 4 squared. This gives you 50.24 yd squared. Then you'll have to find the rectangle which is 8 by 9. You multiply these together and get 72 yd squared. Finally, you add the two areas together and get a total of 122.24 yd squared.
Inscribed Figure: Find the area of the shaded region on the picture to the left. You would find the area of the square first, which has sides of 5. You'd multiply 5 by 5 and get 25. Then to find the area of the circle inside the square, you would do 3.14 times 2.5 squared. 2.5 is the radius. You will get 19.625 yd squared for the area of the circle. To find the area of the shaded region, you would subtract the area of the circle from the area of the total square because that will tell you the leftover space. You get an answer of 5.375 yd squared.

# data[].attributes.body
bh•H(side one, side two, side three)
Example problem: Find the surface area of a triangular glass prism timmy is using in science with a base of 3 and a height of 4. The length of each side is 6 and the height of the prism is 8.(connecting side).
3•4+8(3+6+6)
12+15(8)
12+120
132u²

# data[].attributes.body
b²+2(bh)
Timmy is looking at more pyramids in Egypt. Find the surface area of a smaller pyramid with a base of 3mi and a height of 5mi. 3²+2(3*5)
9+30
39 miles

# data[].attributes.body
Formula: 3.14*r²h/3.
Find the volume of a spiders ice-cream cone with the radius of 4cm and a height of 4cm. You would do 3.14*4²*4/3
You would get 67.02 cm.

# data[].attributes.body
2*3.14R
Find the circumference of a circular pizza with a diameter of 12.
Radius is half diameter (6) You would do 2*3.14*6.
This would give you an answer of 37.7.

# data[].attributes.body
3.14*R²
Timmy wants to find the area of a circle with a diameter of 6. To do this, we know that the radius is half the diameter so the radius is 3. This makes the formula 3.14*3². This gives you an answer of 28.27 units squared

# data[].attributes.body
Formula: 1/3b²h
Example:Timmy wants to find the volume of a square pyramid in egypt with a base of 3 miles and a height of 6miles.  You would get 18 miles.

# data[].attributes.body
Formula: 2πrh+2πr²
Example: Find the total surface area of soda can timmy is drinking from with a base radius of 5 inches and a height of 7 inches.
2π(5)(7)+2π(5)²
This equals 376.99 inches squared.

# data[].attributes.body
Formula: Pi radius squared • height
Example: Find the volume of a cylinder soda can timmy is drinking from with a height of 10 and a diameter of 12.
Radius is hald diameter, so radius is 6.
To do this you would first do 3.14 times 6 squared. This equals 113.04. Then you take that and multiply it by 10, which gives you 1130.97 units cubed.

# data[].attributes.body
1/2h(base one, base 2.)
Timmy wants to find the area of a trapezoid painted on the wall because he has weird hobbies. The trapezoid has a height of 5, one base is 14 and the other is 5 less than the first base. 1/2*5(14*9) 57.5 units squared is what you would get.

# data[].attributes.body
BxH
Example problem: Timmy wants to find the area of a eraser drawn on the bathroom stall with the base of 5 and the height of 10. You would multiply these numbers by eachother and get an area of 50 units squared.
5x10

# data[].attributes.body
LxW
Example problem: Find the area of square office with the length of 4yd and the width of 3yd. You would multiply these numbers together because theyre the length and the width and you would get 12 yard.

# data[].attributes.body
1/2 bxh
Example problem: Timmy needs help to find the area of a triangle with a base of 6 and a height half of that. You would do 1/2 times 6x3. You would get 9 units squared/

# data[].attributes.body
- Items for prime coordinates are all about coordinates, not prime coordinates.
- x,y rules for rotating 90 cw and ccw are incorrect and you are missing x,y rules for reflections. 90 cw is y,-x and 90ccw is -y,x

# data[].attributes.body
If the triangle is rotated 90 degrees clockwise, it would become y, -x
If the triangle is rotated 90 degrees counterclockwise, it would become -y, x.
If the triangle is rotated 180 degrees counterclockwise, it becomes -x,-y.

# data[].attributes.body
Definition: A set of values that show an exact location or position on a graph.
https://www.mathsisfun.com/definitions/coordinates.html
This website will bring you to a page that shows the definition of coordinates and an explanation and examples.
The dots on the image below are examples of the location of the prime coordinates.

# data[].attributes.body
Def: A transformation preformed by "spinning" the figure around a fixed point (known as the center of rotation.)
http://www.mathsisfun.com/geometry/rotation.html
This leads you to a mathisfun website where it has a definition and examples.
The image below shows a triangle being rotated 180 degrees counter clockwise.

# data[].attributes.body
Def: A transformation that moves each point along a ray which starts from a fixed center, and multiplied distances from this center as a common factor. This is a non rigid transformation.
http://www.mathwarehouse.com/transformations/dilations/dilations-in-math.php
This website will bring you to a definition of what dilation is and interactives to help you understand better.
Picture: The image below shows an example of a triangle being dilated by a scale factor of two.

# data[].attributes.body
Def: A "flipping" of an object over a line (known as the line of reflection)
https://www.mathsisfun.com/geometry/reflection.html
This link will bring you to a math is fun website that shows you a definition and examples of what a reflection is.
Picture: The image below shows an example of a triangle being reflected over the line of reflection

# data[].attributes.body
Def:"Sliding": moving a shape without rotating or flipping it.
The shape still looks exactly the same, just in a different place.
Related website: https://www.mathsisfun.com/definitions/translation.html
This link includes the definition, and an example with different shapes of what it is.
This image shows an example of a triangle being translated.

# data[].attributes.body
Definition: each of the pairs of opposite angles made by two intersecting lines.
What would x be?

It would be 37 because its equal to 74 because they're vertical, and 37 times 2 equals 74.
This picture shows an example of vertical angles.

# data[].attributes.body
Def: The sum of the interior angles of a triangle that add up to 180 degrees.
Ex problem: Jim is having trouble once more because he never pays attention in class. He can't find out if it would make a triangle if the angles were 85, 65, and 30. Explain why or why not.
Yes it would be a triangle because all the interior angles add up to 180 which follows the TST.
This image shows an example problem in where you'd have to din the missing angle using the triangle sum theorem.

# data[].attributes.body
def:

either of two angles whose sum is 180°.

Sample problem: Jim is having trouble once again. He can't find out if this is 180 degrees. Help him find out and explain why or why not.

Yes, it is because if you add both angles together (140 and 40) it will equal 180.
This picture shows an example of supplementary angles.

# data[].attributes.body
def: either of two angles whose sum is 90°
Sample problem:
Jim has an issue. He can't figure out if his angles are complementary or not. Help him find out and explain why you chose your answer.

-------------------------------------->

Yes, it is 90 degrees because 43 and 47 add up to 90 degrees.

This image shows an example of complementary angles.

# data[].attributes.body
Definition:

he angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
This word relates to transversal because corresponding angles can be part of a transversal.
This image shows a few examples of corresponding angles on a transversal.

# data[].attributes.body
Def: (of a line) intersecting a system of lines.
An example of this would be two lines going in the same direction and another line cutting through it.
A non example would be a ray.
This image shows an example of transversal lines

# data[].attributes.headline
Proportional Reasoning and Linear Equations Grade - 98%

# data[].attributes.subject
Proportional Reasoning and Linear Equations Grade - 98%

# data[].attributes.body
- Slope values should be given, not an equation for the different types of slope.

# data[].attributes.body
Y=MX+B.
y is the Y corrdiante
x is the X coordinate
m is the slope
b is the y intercept

# data[].attributes.body
They must be
1. The same shape, but different sizes
2. Have congruent corresponding angles
3. Have proportional corresponding sides.

# data[].attributes.body
Positive slope, negative slope, zero slope, and undefined slope.
Positive slope: 2x + 3
Negative slope: -2x + 8
Undefined slope: X=6
Zero Slope: Y=2

# data[].attributes.body
Defintion: The ratio of the length in a drawing (or model) to the length of the real thing
Example of the word:  In the drawing anything with the size of "1" would have a size of "10" in the real world
Non- Example: The building on the road is 12 feet.
This image shows an example of scale factor. It shows that for every 2cm on the floor plans it is 1 meter in real life.

# data[].attributes.body
Definition: means that you're measuring something by measuring something else.
Example of the word: Using other side lengths or proportions too find the length of what you are trying too find.
Non-Example: Direct measurement, like measurement of current by  ammeter.
Image: This shows an example of indirect measurement.

# data[].attributes.body
Definition: a part, share, or number considered in comparative relation to a whole.
Example problem: Find something proportionate too 2/3. The answer would be 6/9. 6 divided by 3 is 2 and 9 divided by 3 is 3.
This image shows an example of proportional triangles. They are different sizes, but they are proportional.

# data[].attributes.body
Definition: a comparison of two measurements in which one of the terms has a value of 1.
Sample problem, work, and answer: 8 ducks for 23.60
too find the unit rate of this  you would have too divide 23.60 by 8. You would get an answer of 2.95 a duck.
This image shows you an example of unit rate.

# data[].attributes.body
- Number lines should match the statements for each inequality.
- missing the question.

# data[].attributes.body
Definition: the set of all the solutions of an equation or condition.
Example:
3x+5=11 | (2)
Steps:
3x= 11-5
3x = 6
x= 6/3
x=2
so 2 would be your solution set
This picture shows an example and definition of what a solution set is.

# data[].attributes.body
Defintion: The relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”
This link takes you to a mathisfun explanation of introduction to inequalities. It goes over the different signs and how too graph it on a number line.
inequality.html
This picture shows the inequality signs that are greater or less than, and greater than or less than and equal too.

# data[].attributes.body
At most
Maximum
Below to equal too
Lower or equaltoo
Example:
The maximum points you can score on the test is 100.

# data[].attributes.body
- At least
- No less than
- Minimum
- Above or equal too
Example:
You must be at least 5feet to ride this rollercoaster

# data[].attributes.body
more than
Exceeds
Over
Higher than
Example:
Sarah exceeds 823 donuts

# data[].attributes.body
- fewer than
- below
- under
-lower
Example:
Rapley has fewer than 100 donuts left

# data[].attributes.body
Steps~
1: Box the variable and draw a line down through the = sign
2:Follow order of operations in reverse
3:Get rid of the number that isn't with the variable beading or subtracting
4:Get the variable by itself by multiplying or dividing
Example~
3y + 2 = 11
Subtract 2 because it is not with the variable
That would leave you with
3y    =   9
To get rid of the 3, divide by 3 because it is the opposite of multiplication. That would leave you with
y = 3
( Your answer )

# data[].attributes.body
( The variable x is going to equal the number you are converting to a fraction )
1: Find out what the repeating number is
2: Place the digits that are repeating to the right of the decimal point.
3: Place the repeating digit left of the decimal point, and you would have to move it over 1 space to the right which is basically multiplying the decimal number by 10. Place the repeating numbers to the right of the decimal
4: Subtract the left sides of the two equations, then subtract the right.
( Difference should be positive )
Example: .55555
The two equations would be
10x= 5.5555555
and
x= 0.5555555
So,
10x-x=5.55555-0.555555
You would get 9x = 5.
Once you divide both sides by 9, you get x=5/9

# data[].attributes.body
Definiton: the number in the set of real numbers that when added to a given number will yield zero: The additive inverse of 2 is −2.
Example: The additive inverse of 214 is -214, because it results in 0.
Non-example: 56 and -55 would not be additive inverses because it does not result in 0.
This shows an example of additive inverse

# data[].attributes.body
Definition:
a decimal fraction in which a figure or group of figures is repeated indefinitely.

This image shows examples of repeating decimals
An example of repeating decimal is 20/9, which equals 2.222222...
A non example would be 20/8, which is 2.5

# data[].attributes.body
Definition: a number that produces a specified quantity when multiplied by itself.
Sample problem: Find the square root of 81. Well 9x9 equals 81, so the square root would be 9.
This picture shows square roots of various numbers

# data[].attributes.body
Definition:  the number that produces a given number when cubed.
Sample problem: To first find the cube root, you have to understand what a cubed number is. A cubed number is when you use a number 3 times in a multiplication. To find the cube root you do the opposite. Lets find the cube root of 125.  well 5x5 is 25, then 25x5 is 123. The cube root is 5.

cube-root.html Link takes you to mathisfun explanation.

# data[].attributes.body
- Missing an example problem for all essential questions.

# data[].attributes.body
To convert a mixed number to improper fraction,  multiply the denominator by the whole number. Then, add the numerator to the product.

# data[].attributes.body
To divide fractions,  follow these rules (KCF). Keep the first fraction, change to multiplication, and flip the 2nd fraction. Then, just multiply across like normal. To multiply, if needed, change to an improper fraction. Then just multiply across. At the end of both, simplify!

# data[].attributes.body
To convert a decimal to fraction, first write the decimal divided by one or the decimal over one. Multiply the bottom and top numbers for every one after the decimal point. So if there is 3 numbers after the decimal point, then you would use 1000). Then, reduce the fraction.

# data[].attributes.body
To convert a fraction to a decimal
Step one: Find a number that you can multiply the denominator by to get a number that is 1 followed by zeros.
Then multiply both the top and bottom by that number is
How ever many zeros you multiplied by, move the decimal down that many spaces in your answer.

Another way to do it would be to devide the numerator by the denominator

# data[].attributes.body
Definition: a fraction in which the numerator is greater than the denominator
Example problems:
Which is an improper fraction?
4 1/2, 3 3/8, 6/2, 9 1/100
It would be 6/2 because the numerator is greater than the denominator.
Turn 1 2/3 into a improper fraction
To do this you would multiply the denominator times the while number, and add the numerator. This would give you 5/3
This image below shows how the numerator is the larger number.

This shows you what an improper fraction is, where the numerator is greater than the denominator.

# data[].attributes.body
Definition: Fractions which have the same value, even though they may look different
Example problem: Which one of these pairs are equivalent fractions?
3/7, 8/9
2/4, 5/10
1/12,1/6
You would have to make them have common denominators, so you would change it to 40. two times ten is 20 and five times 4 is 20. These turn out to be the exact same fraction, making them equivalent.
An example of this would be 8/8 and 39/39
A non example would be 1/2 and 9/16

# data[].attributes.body
Definition: A shared multiple of the denominators of several fractions.
Example: Find the common denominator of 3/4 and 1/2
To do this list out all your multiples
2,4,6,8
4,8,12,16
Then see if they have any numbers in common
The first one that shows up is 4, Which would be your LCM
Then, multiply the numerator and denominator by the factor that it would take to get to your common denominator.
https://www.mathsisfun.com/least-common-denominator.html
This link takes your to a Math is fun explanation.

# data[].attributes.body
Definition:  number consisting of an integer and a proper fraction.
Example problem: Turn 48/7 too a mixed number. 7 Goes into 48 6 times, and there is 6 in between 42 and 48, so it would be 6/7. This explains what that would be as a mixed number

# data[].attributes.body
To solve multiplication and devision problems, if it has an even number of negatives its positive and an uneven number it is negative. For multiplying, if it has the same sign, it is always positive. If it has 2 different signs, it will always be negative. An example of this would be -6(-8) which would equal 48, which is positive because they have the same symbol. For devision, if it has the same sign it is always positive. if it has different signs it will always be negative. An example would be -48/-6= 8

# data[].attributes.body
To subtract two negatives, you would change the negative integer to a positive integer and add instead of subtract. If you subtract a positive number from a negative number, count backwards from the amount you're subtracting. To subtract a negative from a positive, add the opposite and follow the rules of addition. An example would be  14-(-5)= 19 because you would change the negative sign to positive and subtraction to addition.
To add negatives and positives, if they do not have the same sign, you subtract the smaller number from the bigger one. Take the sign of the larger number in your answer. An example would be -27 + 72 which equals 45 because you would subtract 27 from 72 and take the sign of the bigger number.

# data[].attributes.body
Definition: A number that can be made by dividing two integers. (An integer is a number with no fractional part.)

Example: 0.75 is a rational number to 3/4

# data[].attributes.body
Definition: a collection of symbols that jointly express a quantity.

An example of an expression would be 4x + (6-7)

# data[].attributes.body
Definition: a quantity that during a calculation is assumed to vary or be capable of varying in value.

Sample problem:
5+ x = 14
To figure out what x represents, you would subtract 5 from 14, giving
you the answer of 9.
https://www.mathsisfun.com/definitions/variable.html

This link takes you too a mathisfun explanation

# data[].attributes.body
Definition: A whole number; a number that is not a fraction
https://www.mathsisfun.com/whole-numbers.html
The link takes you to a mathisfun explanation