you said you will give use 20 points but it is marked as 5 Points.
3+5=8
8^2 is 8×8 which equals 64.
The square of the sum of 3 and 5 equals 64.
All of the angles combined =360 degrees
Vertical angles are congruent, so if angle 1 = 60, so does angle 3
Logically we have to find the measure of angle 4 and angle 2 combined and divide by 2
60 + 60 = 120
360 - 120 = 240
240 / 2 = 120
angle 4 = 120
angle 2= 120
angle 3 = 60
An equation is formed of two equal expressions. The number of rows in the original pattern will be 4.
<h3>What is an equation?</h3>
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of rows be represented by x. Now, the pattern has rows that are 5 tiles wide and an unknown number of rows. if you take these tiles and add one additional tile, you can create a pattern that has rows that are 3 tiles wide, with 3 more total rows than the original pattern. Therefore, we can write,
(Number of Tiles before) + 1 tile = (Number of Tiles afterward)
5x + 1 = 3(x+3)
5x + 1 = 3x + 9
5x - 3x = 9 - 1
2x = 8
x = 4
Hence, the number of rows in the original pattern will be 4.
Learn more about Equation:
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<span>
<span>first off your answer is 21.90 and the step by step i wrote it for you:) Finding the
square root of a number is the inverse
operation of squaring that number. Remember, the square of a number
is that number times itself. </span>
The perfect
squares are the squares of the whole numbers.
The square root
of a number, n, written below is the number that gives n when multiplied by
itself.
</span> <span>Many mathematical
operations have an inverse, or opposite, operation. Subtraction is the opposite
of addition, division is the inverse of multiplication, and so on. Squaring,
which we learned about in a previous lesson (exponents),
has an inverse too, called "finding the square root." Remember, the
square of a number is that number times itself. The perfect squares are the
squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 … </span>
The square root
of a number, n, written
<span>
is the number that gives n when multiplied by itself. For example,</span>
<span>because
10 x 10 = 100</span>
Examples
Here are the
square roots of all the perfect squares from 1 to 100.
Finding square
roots of of numbers that aren't perfect squares without a calculator
1. Estimate
- first, get as close as you can by finding two perfect square roots your
number is between.
2. Divide -
divide your number by one of those square roots.
3. Average -
take the average of the result of step 2 and the root.
<span>4. Use the result
of step 3 to repeat steps 2 and 3 until you have a number that is accurate
enough for you.
</span>
Example:
Calculate the square root of 10 ()
to 2 decimal places.
<span>1. Find
the two perfect square numbers it lies between.
</span>
<span><span>Solution:
</span><span>32
= 9 and 42 = 16, so
lies between 3 and 4.</span></span>
<span>2. Divide
10 by 3. 10/3 = 3.33 (you can round off your answer)</span>
<span>3. Average
3.33 and 3. (3.33 + 3)/2 = 3.1667</span>
<span>Repeat step
2: 10/3.1667 = 3.1579</span><span>Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623</span>
Try the answer
--> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001
If this is accurate
enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.
<span>Note:
There are a number of ways to calculate square roots without a calculator.
This is only one of them.</span>
<span><span>
</span>
</span>
<span>
<span />Example:
Calculate the square root of 10 ()
to 2 decimal places.
<span>1.
Find the two perfect square numbers it lies between.
</span>
<span><span>Solution:
</span><span>32
= 9 and 42 = 16, so
lies between 3 and 4.</span></span>
<span>2.
Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)</span>
<span>3.
Average 3.33 and 3. (3.33 + 3)/2 = 3.1667</span>
<span>Repeat
step 2: 10/3.1667 = 3.1579
Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623</span>
<span>Try
the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 =
10.0001</span>
If
this is accurate enough for you, you can stop! Otherwise, you can repeat steps
2 and 3.
</span>
<span>
<span><span>
<span> </span></span></span></span>
