Karina M. by Karina Martin _ Student - EastCaryMS

Absolute Value

kmmartin22 — 2017-07-12 18:06:11 UTC

Definition - How far away a number is from 0. To remove the negative sign from a number.

Exp. The absolute value of -6 is 6.
The absolute value of 9, is 9.

How it relates:

You can find the absolute value of an integer, for example, 8. You can solve on what the absolute value is using an expression, such as a number line.

Sample problem:

What is the absolute value of -12?

Answer:

Integer

kmmartin22 — 2017-07-12 18:06:42 UTC

Definition - A whole number, no fractions involved.

Exp. The numbers 4, 5, and 6 are all integers. Even as negatives, such as -7.

How it relates:

Integers can go in many expressions, such as 3 * 5, or -9 + 7. Integers can also appear in a variable, for example, 8x.

Sample problem:

-4+7

Answer:

Variable

kmmartin22 — 2017-07-12 18:08:41 UTC

Definition - A symbol to stand for an unknown number.

Exp. x + y, 10x * 2y

How it relates:

Variables can be combined with Integers, such as 5y, or 3x. They can also be used in equations, for example, x = y, or 3x = 6.

Sample problem:

Which number is the variable in this expression?

15x + xy

Answer:

Expression

kmmartin22 — 2017-07-12 18:09:06 UTC

Definition - A mathematical phrase containing variables, and operators.

Exp. 3x + 4y

How it relates:

Expressions can contain many numbers, such as integers and variables. One example could be 2y + 8, or 5x * -7x.

Sample problem:

What is the value in this expression?
(If x equals 4, and m equals 6)

6x + 5m

Answer:

Essential Question

kmmartin22 — 2017-08-03 00:03:00 UTC

When doing addition, and both the numbers are negative, the answer will be negative. For example, in the problem -6 + -8, you follow the normal addition rules, only that the answer will be a negative. If there is a positive and a negative number in the problem, there are a different set of rules to follow. You first have to subtract the smaller number from the bigger number. When you get the answer to that, you use the sign of the bigger number. In the problem 3 + -4, you would first subtract 4 - 3, which equals 1. You would then use the sign of the bigger number, in this case, 4 is the largest number, so the final answer would be -1. In a subtraction problem, if the numbers are both negative, the answer will be negative. For example, in the problem -9 - (-3), you would follow the normal subtraction rules, and get the answer of -6. You could also imagine it as a number line, as you are moving from left to right. (Example below)

You could also get a positive answer even if they are both negative. In the problem -3 - (-4), the first integer is smaller than the second. Using the number line, as you move four spaces to the right, you would get the answer of 1. If both the signs are different, such as -8 - 4, you would add the opposite. You would change the sign of the smaller number, and then add both numbers. In this problem, it would change to -8 + -4, which would equal -12.

Multiplication and Division are both the same thing. If both numbers are the same sign, the answer will be a positive. If both signs are different, the answer will be negative. For example, in the problem -4 * -3, both the signs are the same, so the answer will be positive 12. The same thing for the problem -15 / -3, both the signs are the same, the answer will be positive 5. In the problem 6 * -8, we can see that the signs are different, so the answer will be a negative, -48. The problem 60 / -12, the signs are also different, which means the answer will be a negative, -5.

Example of a number line (for subtracting negative from negative):

Integers Grade - 100%

2017-08-06 18:47:48 UTC

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kmmartin22 — 2017-08-10 00:04:18 UTC

Essential Questions:

kmmartin22 — 2017-08-23 18:06:08 UTC

How would you explain to someone how to convert a fraction to a decimal?

kmmartin22 — 2017-08-23 18:07:20 UTC

First, you need to divide the numerator by the denominator. In the example below, we would need to divide 3 by 4. 4 doesn't go into 3, so we would need to add a 0 next to the 3, as shown below. You would put the decimal point in between the 3 and 0, and always be very careful on where you put it, otherwise it could mess up the whole problem. Next, you would put on how much 4 can go into 30, which is 7, and subtract like normal, and then put the 7 after the decimal point. The remainder is 2 and we would put another 0, and it after the 2 to make it 20. 4 goes into 20 5 times, and we would put the 5 after the 7. We are left with no remainders, and left with the final answer of 0.75, which equals 3/4. Sometimes, some numbers seem to always go on forever, and no matter how many 0's you put, you always end up with the same number. In this scenario, we would put a small dash over the number that keeps of repeating, shown on example #2.

How would you explain to someone how to convert a decimal to a fraction?

kmmartin22 — 2017-08-23 18:08:20 UTC

To convert a decimal to a fraction, you need to say it according to it's place value. In this example, 0.35 is "thirty-five over one hundred", or 35/100. Simplify it if possible. In this problem, 35 and 100 can both be divided by five, which gives you 7/20 as the final answer.

How would you explain to someone how to convert a mixed number into a improper fraction?

kmmartin22 — 2017-08-23 18:09:14 UTC

You first need to make the whole number a fraction, and you do that by multiplying the whole number by the denominator. In the example below, we would multiply 2 by 7. You then add that answer to the numerator. Lastly, you add that number to the numerator fraction already there above the denominator.

How would you explain to someone how to complete a multiplication problem that includes decimals?

kmmartin22 — 2017-08-23 23:45:31 UTC

Multiplication with decimals is like doing it with no decimals at all. you pretend that the decimals aren't there. In the problem below, we would need to change 4.5 and 3.2 into whole numbers because you cannot multiply decimals. You also need to take note on how many decimal places you moved the two numbers. In this case, we moved both numbers by 1 place, and combined makes 2 places. Multiply the whole numbers like normal. Once you get your answer to that, you put the decimal point back by moving to the left the number of places you moved the decimals before making them whole.

Vocabulary Terms:

kmmartin22 — 2017-08-23 23:54:46 UTC

Common Denominator

kmmartin22 — 2017-08-23 23:55:11 UTC

Definition:

When two or more fractions have the same denominator.

E.g.

4/6 and 5/6

The "6" is the common denominator.

Sample problem:

Simplify both fractions to get the least common denominator.

Equivalent Fractions

kmmartin22 — 2017-08-23 23:56:04 UTC

Definition:

Fractions that have the same amount, even if they look different.

E.g.

2/ 3 = 4/6

These two fractions show the same amount. We can simplify 4/6 by dividing both the numerator and the denominator by 2, since both numbers can go into 2. This gives us the answer of 2/3.

Sample problem:

Are these fractions equivalent?

Improper Fraction

kmmartin22 — 2017-08-23 23:56:18 UTC

Definition:

When the numerator overpowers the denominator.

E.g.

8/7

In this case, 8 > 7. The numerator must be less than the denominator in order to it to be a proper fraction.

Sample problem:

Improper or proper?

Mixed Number

kmmartin22 — 2017-08-23 23:56:30 UTC

Definition:

A whole number combined with a fraction.

E.g.

2 1/2

In this example, the whole number is 2, and is combined with the fraction 1/2.

Sample problem:

Change the improper fraction into a mixed number.

E.g. #2

kmmartin22 — 2017-08-28 00:12:46 UTC

Image

kmmartin22 — 2017-08-28 03:37:06 UTC

A Common Denominator is when two or more fractions have the same denominator. The image below shows that 5/8 and 7/8 may have different numerators, but both fractions have the same denominators.

Image

kmmartin22 — 2017-08-28 03:37:18 UTC

An Improper Fraction is when the numerator is either greater or the same as the denominator.

Image

kmmartin22 — 2017-08-28 03:37:44 UTC

A Mixed Number is a whole number alongside with a fraction. The picture below shows the whole number (4), combined with the fraction 5/8.

Image

kmmartin22 — 2017-08-28 03:38:05 UTC

Equivalent Fractions are fractions that share the same amount. In the image below, 1/2 and 4/8 are both the same amount. 4/8 can be simplified to 1/2.

Rational Numbers Grade - 100%

2017-08-30 11:34:37 UTC

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kmmartin22 — 2017-10-02 23:20:35 UTC

Essential Questions:

kmmartin22 — 2017-10-04 23:30:25 UTC

Find the fraction of a repeating decimal.

kmmartin22 — 2017-10-04 23:31:38 UTC

First, you have "X" represent the repeating decimal. For example, in .1424242... "42" is the repeating decimal, so we would put X for 42. Next, you would need to move the decimal point BEFORE the repeating decimal, resulting in the number 1.424242... The decimal point moved 1 space, which equals 10x. Then, we would need to put the decimal point AFTER the repeating decimal, resulting in the number 142.424242... The decimal moved 3 spaces, which equals 1000x. Line up the equations, putting the larger equation first.

1000x= 142.424242...
- 10x=1.424242...

Solve for X, meaning subtracting the X's, resulting in 990. You ignore the repeating decimals, as they are cancelling each other out. You then subtract the remaining whole numbers, in this case, 142-1, which equals 141. You then "divide" both sides by 990, giving you your fraction 141/990, simplfied to 47/330.

How to estimate the square root of a number.

kmmartin22 — 2017-10-05 00:06:36 UTC

First, it's a good idea to have the perfect squares from 1 to 100 memorized. You should then find two perfect square roots that your number is between. For example, if you need the square root for 31, the square root of 25 is 5, and the square root of 36 is 6. Because 31 is 6 away from 25, and 5 away from 36, the square root is about 5.6.

Vocabulary:

kmmartin22 — 2017-10-05 00:21:44 UTC

Repeating decimal

kmmartin22 — 2017-10-05 00:22:01 UTC

Definition:
A decimal that consists of some numbers that repeat infinitely, there's no end.

E.g.
4.333333...

The "3" is the repeating decimal, it keeps repeating.

Sample problem:
Convert this repeating decimal into a fraction.
(.7777...)

ANSWER:

Irrational number

kmmartin22 — 2017-10-05 00:27:03 UTC

Definition:
A number that can't be expressed as a fraction.

E.g.
π (Pi)

"Pi" is infinite decimal with many different numbers, can't be expressed ad a fraction.

Example / Non example

E.g. - π (Pi)
"Pi" can't be converted into a fraction. Therefore it is a irrational number.

Non E.g. - Any rational number, such as repeating decimals (.5555...)

Cube root

kmmartin22 — 2017-10-05 00:27:12 UTC

Definition:
A number multiplied by itself 3 times to get a cubic value.

E.g.
The cube root of 64 is 4.
(4x4x4=64)

Sample problem:
What is the cube root of 27?

ANSWER:
(Using estimation at the start)

Square root

kmmartin22 — 2017-10-05 00:27:20 UTC

Definition:
A number multiplied by itself to produce a number / square root.

E.g.
The square root of 25 is 5.
(5x5-25)

Sample problem:
What is the square root of 49?

ANSWER:
(Also using a form of estimation)

Image

kmmartin22 — 2017-10-05 23:21:37 UTC

A repeating decimal is a decimal that goes on forever; keeps on repeating.

Image

kmmartin22 — 2017-10-05 23:21:44 UTC

As the definition above says, a cube root is a number timed by itself 3 times to get a cubic unit.

Image

kmmartin22 — 2017-10-05 23:21:53 UTC

A square root is a number timed by itself to create a number. In the image below, it shows that the square root of 25 is 5, as 5x5 is 25.

Image

kmmartin22 — 2017-10-05 23:21:57 UTC

And irrational number is a number that can't turn into a fraction. Pi is a popular example, as it keeps going on forever with different numbers, and it's not possible to convert it into a fraction.

Equations Grade - 100%

2017-10-09 14:34:42 UTC

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kmmartin22 — 2017-10-23 21:16:57 UTC

Essential Questions

kmmartin22 — 2017-10-23 21:18:16 UTC

Vocabulary

kmmartin22 — 2017-10-23 21:18:47 UTC

Inequality

kmmartin22 — 2017-10-24 00:17:29 UTC

Definition
Uses symbols for less than, greater than, less than or equal to, and greater than or equal to.

< (less than)
> (greater than)
≥ (greater than or equal to)
≤ (less than or equal to)

How it relates
An inequality can technically have more than one answer. This results in a solution set; a set of multiple solutions. Such as {3, 4, 5 , 6...}.

Sample problem
7x + 4 ≥ 25

ANSWER:

Solution set

kmmartin22 — 2017-10-24 00:17:40 UTC

Definition
A set of values that satisfy a set of an equation / inequality.

E.g.
{4, 3, 2, 1..}

How the word relates
The solution set is the result of an inequality. A solution set can be best expressed in a number line, to help get the idea of the solution.

Sample problem
Six less than the product of 3 and a number is greater than or equal to 15. What is the solution set?

When do you flip the inequality?

kmmartin22 — 2017-10-24 17:58:27 UTC

You flip the inequality when you multiply / divide with a negative number on both sides. You solve the problem like normal, but just flip the sign when you multiply / divide with a negative number. For example:

-6x - 9 ≥ 15

Graph

kmmartin22 — 2017-10-24 18:05:15 UTC

≥ (greater than or equal to)

kmmartin22 — 2017-10-24 23:31:51 UTC

≤ (less than or equal to)

kmmartin22 — 2017-10-24 23:34:25 UTC

> (greater than)

kmmartin22 — 2017-10-24 23:39:53 UTC

- descriptive words

kmmartin22 — 2017-10-24 23:44:20 UTC

• fewer than
• below
• under

- descriptive words

kmmartin22 — 2017-10-24 23:47:55 UTC

• above
• more than
• over

- descriptive words

kmmartin22 — 2017-10-24 23:49:45 UTC

• maximum
• at most
• up to

- descriptive words

kmmartin22 — 2017-10-24 23:50:57 UTC

• minimum
• at least
• profit

- word form

kmmartin22 — 2017-10-24 23:54:23 UTC

Angelina has more than 14 pencils in her pencil case.

- word form

kmmartin22 — 2017-10-24 23:54:42 UTC

The theater has a seat capacity of 50 people.

- word form

kmmartin22 — 2017-10-24 23:54:50 UTC

There are at least 7 birds on the tree.

- word form

kmmartin22 — 2017-10-24 23:55:02 UTC

Kelly has less than 8 coins in her jar.

< (less than)

kmmartin22 — 2017-10-25 02:46:19 UTC

kmmartin22 — 2017-10-25 02:49:11 UTC

kmmartin22 — 2017-10-25 02:55:52 UTC

kmmartin22 — 2017-10-25 02:56:53 UTC

kmmartin22 — 2017-10-25 02:58:07 UTC

kmmartin22 — 2017-10-25 03:00:05 UTC

Inequalities Grade - 100%

2017-10-27 00:33:32 UTC

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kmmartin22 — 2017-11-13 00:05:50 UTC

Essential Questions

kmmartin22 — 2017-11-13 00:07:19 UTC

Vocabulary

kmmartin22 — 2017-11-13 00:07:38 UTC

Unit Rate

kmmartin22 — 2017-11-13 00:12:58 UTC

Definition
When the second rate is 1 unit / quantity.

E.g. 14 apples in 2 baskets, unit rate is 7 apples in one basket.

Sample Problem
Find the unit rate of 65 students in 5 buses.

ANSWER:

Proportion

kmmartin22 — 2017-11-13 00:13:13 UTC

Definition
When two ratios / fractions are equal, or a comparison of two numbers.

E.g. 1/2 = 4/8

Sample Problem
What could make these fractions proportional?

6/8 =?/24

ANSWER:

Indirect Measurment

kmmartin22 — 2017-11-13 00:13:55 UTC

Definition
Using proportion to find the distance / length of similar figures.

E.g. Use shadows or mirrors to find length.

How it Relates
Indirect measurement is a method of using proportion to find unknown sides of similar figures. You can use shadow lengths to help find the lengths / height / distance. You can also use already known sides to help find the unknown sides.

Constant of Proportionality

kmmartin22 — 2017-11-13 00:14:15 UTC

Definition
The constant value of a ratio of two proportions.

E.g. Constant is × 6 (multiplying 6).

Sample Problem
What is the constant of proportionality?

ANSWER:

Explain what has to be true for two figures to be similar.

kmmartin22 — 2017-11-13 00:16:05 UTC

Both figures must be the same shape, but in different size. The shapes must also have the same angles and the corresponding sides must be proportional.

Example:

What are the 4 types of slope?

kmmartin22 — 2017-11-14 00:17:46 UTC

The 4 types are positive, negative, zero, and undefined slope. An example slope for a positive slope would be y = 3x + 2, or m = 3/1. For negative, an example would be y = -5x + 3, or m = -5/3. An example for a zero slope would be y = 0/7, 0/7, or y = 7. And finally, an example for a undefined slope would be x = 4

What are the different parts of a linear equation?

kmmartin22 — 2017-11-14 00:18:16 UTC

The formula for a linear equation is y = mx + b. You find the "y" as the first variable, and it stands for the y coordinate. Next is "m", which is the slope, or the rise/run. The "x" then stands for the x coordinate. Last is the "b", which determines the y-intersept.

Image

kmmartin22 — 2017-11-14 01:20:36 UTC

Unit rate is when you take the ratio and reduce it to its lowest term or singular unit. For example, you work 49 hours in a 7-day week, so the unit rate would be 7 hours a day (7/1). You reduce 49/7 by dividing 49 by 7, which is 7.

Image

kmmartin22 — 2017-11-14 01:20:43 UTC

Proportion is comparing two numbers, and the numbers can represent anything (people, objects, etc.). You write a proportion with a colon (3:6), or a equivalent fraction (3/6).

Image

kmmartin22 — 2017-11-14 01:20:48 UTC

Indirect measurement is when you use proportions to find the distance / length in similar figures. If sides are given, you could use the available sides to help you find the unknown sides.

Image

kmmartin22 — 2017-11-14 01:20:59 UTC

Constant of proportionality can also be written as y = kx, where "k" is the constant. Two quantities such as x and y are proportional if yx is constant.

Proportional Reasoning and Linear Equations Grade - 99%

2017-11-21 01:11:09 UTC

- x=4 is an example of an equation for undefined slope not the slope value. 22/0 or -4/0 would be examples.

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kmmartin22 — 2018-02-16 00:13:42 UTC

Triangle Inequality Theorem

kmmartin22 — 2018-02-20 00:36:21 UTC

Definition
The sum of any two sides of a triangle must be greater than the remaining side (third side).

Sample Problem
Determine if you can make a triangle based on the side measurements.

4 in, 7 in, 2 in

ANSWER:
Why? It's because 4+2=6, and it is less than 7.

Supplementary Angles

kmmartin22 — 2018-02-20 00:36:23 UTC

Definition
When there are two angles which add up to 180 degrees.

Sample Problem
Which of these angles are supplementary?

ANSWER:
Both A and B are supplementary angles, since both have two angles that equal 180 degrees. C is a complementary angle, meaning two angles make up only 90 degrees.

Triangle Sum Theorem

kmmartin22 — 2018-02-20 00:36:26 UTC

Definition
Three interior angles of any triangle add up to 180 degrees.

Sample Problem
Find the missing angle.

ANSWER:
Since a triangle must have angles that equal 180 degrees, using the two angles already given, that helps find the missing angle.

Complementary Angles

kmmartin22 — 2018-02-20 00:36:30 UTC

Definition
Two angles in which the sum is 90 degrees.

Sample Problem
Find the missing angle.

ANSWER:
Since a complementary angle is when there are two angles that make up 90 degrees, using the angle measurement already given helps solve for the missing angle.

Adjacent Angles

kmmartin22 — 2018-02-20 00:36:45 UTC

Definition
Two angles that share a vertex and one ray.

Sample Problem
Which of these examples of angles are adjacent?

ANSWER:
They are all adjacent, because they each share a vertex, and one ray.

Vertical Angles

kmmartin22 — 2018-02-20 00:37:27 UTC

Definition

Two angles that are opposite from each other when two lines cross. Share the same vertex.

Sample Problem
Find the missing angles.

ANSWER
Using the 120 degrees already given, thst helps solve for the rest of the angles. The angle below 120 must also equal 120 because it is corresponding. 120+120=240, and 360-240=120. 120÷2=60, which is the remaining missing angle for both the left and right.

Picture/Image

kmmartin22 — 2018-02-21 00:35:40 UTC

The Triangle Inequality Theorem states that of two sides of a triangle must be greater than the third side of the triangle. If the total measurement of the two sides is not greater than the third side, then the figure is not classified as a triangle.

Picture/Image

kmmartin22 — 2018-02-21 00:35:54 UTC

Supplementary angles are when two angles in a figure equal to 180 degrees.

Picture/Image

kmmartin22 — 2018-02-21 00:36:43 UTC

The Triangle Sum Theorem states that three interior angles for every triangle must equal to 180 degrees.

Picture/Image

kmmartin22 — 2018-02-21 00:37:02 UTC

Complementary angles are when there are two angles that add up to 90 degrees.

Picture/Image

kmmartin22 — 2018-02-21 00:37:15 UTC

Adjacent angles are when there are two angles that share a vertex and a ray.

Picture/Image

kmmartin22 — 2018-02-21 00:37:30 UTC

Vertical angles is when there are two lines cross and two angles are opposite from each other. Both angles share the same vertex.

Geometric Properties Grade - 100%

2018-02-26 01:31:14 UTC

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kmmartin22 — 2018-03-01 18:56:13 UTC

Area of a triangle

kmmartin22 — 2018-04-18 18:09:41 UTC

1/2bh

Problem:
A triangle has a base of 5 and a height of 3. What is the area?

Answer:
1/2 x 5 x 3
7.5 in²

Area of a rectangle

kmmartin22 — 2018-04-18 18:10:15 UTC

lw

Problem:
A rectangle has a length of 7 and a width of 5. What is the area?

Answer:
7 x 5
35 ft²

Area of a parallelogram

kmmartin22 — 2018-04-18 18:10:36 UTC

bh

Problem: A parallelogram has a base of 9 in and a height of 5 in. What is the area?

Answer:
5 x 9
45 in²

Area of a trapizoid

kmmartin22 — 2018-04-18 18:10:42 UTC

h(base 1 + base 2)/2

Problem: Find the area of this trapizoid with a base 1 of 5, base 2 of 8, and a height of 3.

Answer:
3(5+8)/2
39/2
19.5 ft²

Area of a circle

kmmartin22 — 2018-04-18 18:10:59 UTC

3.14 × r²

Problem: You have just bought a pizza, and want to find the area of it. It has a radius of 7. What is the area?

Answer:
3.14 x 7²
153.86 in²

Volume of a triangular prism

kmmartin22 — 2018-04-18 18:11:08 UTC

1/2 × b × h × H

Problem: Find the volume of this triangular prism.

Answer:
1/2 x 6 x 5 x 10
150 in³

Volume of a sphere

kmmartin22 — 2018-04-29 00:05:40 UTC

4/3 × 3.14 × r³

Problem: Find the volume of a sphere with a radius of 4 in.

Answer:
4/3 x 3.14 x 4³
267.94 in³

Volume of a cylinder

kmmartin22 — 2018-04-29 00:05:54 UTC

3.14 × r² × H

Problem: Find the volume of a cylinder with a radius of 3 and a height of 8.

Answer:
3.14 x 3² x 8
226.08 in³

Volume of a cone

kmmartin22 — 2018-04-29 00:06:04 UTC

3.14 × r² × H × 1/3

Problem: Find the volume of a cone with a radius of 2 in and a height of 6 in.

Answer:
3.14 x 2² x 6 x 1/3
25.12 in³

Cylinder surface area

kmmartin22 — 2018-04-29 00:06:19 UTC

2 × 3.14 × r² + 2 × 3.14 × d x H

Problem: Find the area of a cylinder with a radius of 2 and a height of 7.

Answer:
2 x 3.14 x 2² + 3.14 x 4 x 7
113.04 in²

Square pyramid surface area

kmmartin22 — 2018-04-29 00:06:34 UTC

s² + 2(bh)

Problem: Find the surface area of a square pyramid with sides of 3 in and a slant height of 5 in.

Answer:
3² + 2(3×5)
39 in²

Volume of a square pyramid

kmmartin22 — 2018-04-29 00:06:59 UTC

1/3 × l × w × h

Problem: Find the volume of a square pyramid with sides of 6 ft and a slant height of 7 ft.

Answer:
1/3 x 6 × 6 × 7
84 in³

Circumference of a circle

kmmartin22 — 2018-04-29 00:07:25 UTC

2 x 3.14 x radius

Triangular prism surface area

kmmartin22 — 2018-04-29 00:08:50 UTC

bh + H(side 1 + side 2 + side 3)

Problem: Find the surface area of this triangular prism.

Answer:
4 x 5 + 11(5+3+3)
141in²

Rectangular prism surface area

kmmartin22 — 2018-04-29 00:09:51 UTC

2(lw + wh +lh)

Problem: Sarah wants to wrap a present. The box is 3 in length, 4 in in width, and 6 in height. How much wrapping paper will she need?

Answer:
2(3 × 4 + 3 × 6 + 4 × 6)
108 in²

Essential ques. #1

kmmartin22 — 2018-04-29 00:52:44 UTC

To find the area of an inscribed shape, you need to find the area of the whole shape, the finding the area of the unshaded region. Then, you will subtract the area of the unshaded region from the whole shape, to find the area of the shaded region. To find the area of a composite shape, you need to break up the shape into a familiar shape (ex. rectangle), and combine the area's of each shape.

Problem: What is the area of the shaded region?

Answer:
Square=100 in²
Circle=78.5 in²
Final area=21.5 in²

Essential ques. #2

kmmartin22 — 2018-04-29 00:53:09 UTC

Rectangle
If the length doubles but the width stays the same, the area is doubled. Basically, if one dimension changes, the area will change by the same scale factor as the dimension. If you change both dimensions, you take the scale factor that the dimensions changed by from each dimension and multiply them. That is the scale factor for the area, what it will change by.

Circle
For the circle, if the radius doubles, the area quadruples. If the radius triples, the area is increased by 9, because you multiply by how much your increasing twice, and so on.

Problem: What would happen to the area if the radius is quadrupled?

Answer: The area would increase by 16.
ORIGINAL: 153.86 in
NEW: 2461.76 in

kmmartin22 — 2018-05-01 02:36:18 UTC

Problem: What would happen to the area if both dimensions increased by 5?

Answer: The area would increase by 10.
ORIGINAL: 48 in²
NEW: 480 in²

kmmartin22 — 2018-05-01 03:18:11 UTC

Problem: What is the area of this composite shape?

kmmartin22 — 2018-05-01 03:24:03 UTC

Answer:
Rectangle 1=48 in²
Rectangle 2=15 in²
Final area=63 in²

Circumference of a circle

kmmartin22 — 2018-05-01 05:21:55 UTC

3.14 × d
2 × 3.14 × r

Problem: What is the circumference of the circle if the diameter is 8 in?

Answer:
3.14 × 8
25.12 in

2d/3d Grade - 100%

2018-05-04 12:20:06 UTC