Using pythagoras theorem formula, c² = a² +b² We can see that the two shorter sides have the same length which is 5cm
Since all the sides of the triangle are the same, hence the two triangles are congruent.
What is Pythagoras' theorem ?
Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
The two shorter sides have the same length which is 5cm
Since all the sides of the triangle are the same, hence the two triangles are congruent.
Let the sides of the triangles be a, b and c. According to Pythagoras theorem;
c² = a² +b²
where:
a is the hypotenuse (longest side)
For triangle A:
c = 13
b = 12
Get "a"
13² = 12² +b²
b² = 25
=> b = 5 cm
Similarly for triangle B:
c² = 5² +12² = 169
=> c=13 cm
We can see that the two shorter sides have the same length which is 5cm
Since all the sides of the triangle are the same, hence the two triangles are congruent.
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Mr. and Mrs. DiNapoli have two sons and three daughters, When the whole family is together for dinner, they have to bring one extra chair to the table. How many chairs do they usually have around the table?
Answer:
6
Step-by-step explanation:
You want to know how many chairs are usually around the table if 1 chair must be added to accommodate Mr. and Mrs. DiNapoli and their two sons and three daughters.
TotalThe number present for a family dinner is ...
1 (Mr. DiNapoli) +1 (Mrs. DiNapoli) +2 (sons) +3 (daughters) = 7
ChairsIf one chair is added to make 7, then there are usually ...
7 - 1 = 6 . . . . chairs at the table
EXTRA 30 POINTS IF U GET THEM RIGHT!!!!!!!!!!!!!1
1. What is the surface area of a rectangular prism with dimensions 15.5 inches by 6 inches by 4 inches?
2. The list represents the ages of students in a gymnastics class.
10, 10, 11, 12, 12, 13, 13, 14, 14, 15
If another student of age 15 joins the class, how is the mean affected?
3.What is the distance from (−5, −19) to (−5, 32)?
4.What is the perimeter, in centimeters, of a rectangle with vertices located at (−20, 14), (4, 14), (−20, −5), and (4, −5)?
5.What is the area of a right triangle with a base of 7 feet and a height of 16 feet?
6.A swimming pool in the shape of a rectangular prism has dimensions of 17.5 feet by 13 feet by 6 feet. What is the maximum amount of water that the pool can hold?
Answer:
what is this i do not know sorry so no 30 points right
The equation y = 4x + 3 models the data below.
x 12 3 4 5 6 78
y 8 13 16 21 26 29 33. 37
a. Calculate the residuals and use the points (x, residual) to make a scatter
plot.
b. Complete the statement below to explain why the model is or is not a good
fit.
The points
So, the equation y = 4x +3
a good fit.
5
2
4-
-2
44
-5-
Point
1
Undo
2
3
Redo
7
x Reset
8
9 10
the plot is attached below and the slope is 4.
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
We know that formula two find the slope of the line joining two points which is
The equation y = 4x + 3 models the data below.
x 1 2 3 4 5 6 7 8
y 8 13 16 21 26 29 33 37
The plot will be using this data.
Hence the plot is attached below and the slope is 4.
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pls help me in this questions pleeeaasee
parm=parallelogram
The diagram of AOCG is given in the attached image.
AOCG is a rectangle.
What is rectangular shape?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.
Given:
AOCG is a parallelogram.
And GC = GA = 5 centimeters.
The opposite sides of the parallelogram are equal and parallel.
So,
AO = OC = 5 centimeters.
And ∠CGA = 90°.
The diagram of AOCG is given in the attached image.
All the parallel sides are equal to one another.
And ∠CGA = 90°.
So, AOCG is a rectangle.
Therefore, AOCG is a rectangle and the image is given
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Tom makes $ in 281.10 days. How much does he make in 5 days?
Tom earns $100 in 5 days if he makes $5622 in 281.10 day, in the given arithmetic problem.
What is arithmetic?A branch of mathematics that deals with the properties of numbers is known as arithmetic, which uses the four operations. A branch of mathematics that deals with the properties of numbers is known as arithmetic, which uses the four operations.
The four operations are addition, subtraction, multiplication, and division. The guidelines for each procedure are very specific.
One of the fundamental principles of addition and subtraction is that while addition increases a number's overall value, subtraction decreases it.
Given that he earn $5622 in 281.10 day
In 1 day he earns = 5622/281.10
= $20
So in 5 days he earns = 5 × $20
= $100
Thus, Tom earn $100 in 5 days if he makes $5622 in 281.10 day, in the given arithmetic problem.
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Full question:
Tom makes $5622 in 281.10 days. How much does he make in 5 days?
Kanta read 2/3 of her chemistry book containing 420 pages Krishna read 3/49f the same who read more pages and by how many pages
Answer:255
Step-by-step explanation:
2) In 2000, the population of a town in 20,000 and decreased by 2% each year.
a) Write an equation to model this scenario.
b) What will the population be in 2025?
The equation which states that the population of a town is 20,000 and decreased by 2% each year is y=20000(1-0.2x)
What is an equation example?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
What are the types of equations?Different Types of Equations
Linear Equation.
Radical Equation.
Exponential Equation.
Rational Equation.
Let the population be y and the of years be x
According to the question, the equation should be
y=20000(1-0.02x)
In 2025 the population will be
y=20000(1-0.02*25)
y=100000
The population will become 10000
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7.86x4.564 report the following answer into significant figures
Answer:
35.87
Step-by-step explanation:
First, what is 7.86 by 4.564?
It is 35.87304.
But the answer needs to be in significant figures, so how do we do that?
Well, significant figures are the numbers that comes after the decimal place. For example, 0.52, which has 2 significant figures.
So with 7.86, there are 2 significant figures and with 4.565, there are 3.
We want to use the one with the least amount of significant figures, so we would round our answer to the hundredth:
35.87
Hope this helps!
The required answer is 35.8730
The number of significant figures in a measurement represents the level of precision in that measurement. In general, the last digit in a number is considered uncertain and is rounded based on the number of significant figures.
When performing arithmetic calculations, the result should be rounded to the same number of significant figures as the least precise measurement used in the calculation.
In this case, the least precise measurement is 4.564, with four significant figures. Therefore, the final result of the calculation 7.86 x 4.564 should be reported with four significant figures.
The answer is 35.87304 and should be reported as 35.8730
(Please mark my answer Brainliest if this helped.)
What is the value of y that makes T Parallel to U
Answer: y = 18
Sentence: The value of y that makes T Parallel to U is 18.
Step-by-step explanation:
We are given 3 expressions:
(7x)(6y + 9)(3x + 36)We know that since the angle (7x) is on the same line as the angle (3x + 36), we can therefore determine that they correspond to each other. I referred an image to help demonstrate this concept. So since they correspond to each other, that means they have the same value (meaning they are equal to each other).
We can set both expressions equal to each other.
7x = 3x + 36
And solve:
7x = 3x + 36
-3x -3x
4x = 36
/4 /4
x = 9
now we know the value of x, we can plug it into one of the equations. We can plug it in to 3x + 36 to help with the process in solving y.
3(9) + 36 = 63 degrees
Since 6y + 9 and 3x + 36 (63 degrees) are supplementary angles, we can subtract 180 from 63.
180 - 63 = 117
now we know that 117 degrees = 6y + 9 BUT!, we need to solve for y, because that's what the question is asking for.
So lets solve for y:
117 = 6y + 9
-9 -9
108 = 6y
/6 /6
y = 18
do you know the ansawer ?
Answer:
1/70
Step-by-step explanation:
(63-40) (21-10) 23 11 23-22 1
(---------)-(--------)=------ - ------ = -------- = --
( 70 ) ( 35 ) 70 35 70 70
4. Solve the triangle using either Law of Cosines or Law of Sines. In △DEF, f=25, e=8
and m∠F=131°.
Round your final answer to the nearest tenth. **
Angle D= Angle E= Angle d=
Answer:
Step-by-step explanation:
Using the Law of Cosines, we can find the remaining angle measures of the triangle.
Angle D = cos-1[(25^2 - 8^2 - (25^2 * cos(131°)))/(-2*8*25)] = 20.5°
Angle E = cos-1[(8^2 - 25^2 - (8^2 * cos(131°)))/(-2*25*8)] = 61.4°
Angle F = 180° - (20.5° + 61.4°) = 98.1°
Round to the nearest tenth:
Angle D = 20.5°
Angle E = 61.4°
Angle F = 98.1°
find answers to 13, 15, and 16 (will mark brainliest)
A bank has launched a three-year structured deposit that offers an effective annual interest of 8% for the first 18 months, quarterly interest of 1.5% for the next 6 months and semi-annual interest of 2% for the last 12 months. If I wish to receive $100, 000 on the maturity date (that is, on the last day of the third year), how much, to the nearest dollar, should I invest? (Assume that interest rates and principal are guaranteed)
Answer:
To determine how much you should invest to receive $100,000 on the maturity date, you will need to calculate the present value of the cash flows at the beginning of the investment. The present value is the amount of money you would need to invest today to receive a certain amount at a future date, taking into account the time value of money and the interest rate.
You can calculate the present value by using the formula:
PV = CF / (1 + r)^t
Where:
PV = present value
CF = cash flow (the amount you will receive at the maturity date)
r = interest rate
t = time (in years)
The first 18 months, the interest rate is 8% per year, which is equivalent to 8/12 = 0.67% per month.
The next 6 months, the interest rate is 1.5% per quarter, which is equivalent to 1.5/4 = 0.375% per month.
The last 12 months, the interest rate is 2% per semi-annual, which is equivalent to 2/2 = 1% per month.
For the first 18 months, the present value of the cash flow is:
PV = 100,000 / (1 + 0.0067)^(18/12) = 95,167
For the next 6 months, the present value of the cash flow is:
PV = 95,167 / (1 + 0.00375)^(6/12) = 94,853
For the last 12 months, the present value of the cash flow is:
PV = 94,853 / (1 + 0.01)^(12/12) = 94,853
So, to receive $100,000 on the maturity date, you should invest 94,853 dollars to the nearest dollar.
The perimeter of an isosceles triangle is 32.7 inches. The length of its base is 9.5 inches. Find the length of each of the other two identical sides.
Answer:
1.72 inches
Step-by-step explanation:
= P=2s×b
= 32.7=2s×9.5
= 32.7=19s
= 32.7/19=19s/19
= s=1.72
If the exchange rate is 1 U.S. dollar to 81 Japanese yen, how many yen would you spend to purchase something that costs 50 dollars?
If the exchange rate is 1 U.S. dollar to 81 Japanese yen, to purchase something that costs 50 dollars, you would have to spend 50 x 81 = 4050 Japanese yen.
Answer: You would have to spend 4050 yen to buy something that costs 50 dollars.
Step-by-step explanation: Since we already know the amount of yen that's equal to a dollar, all we have to do is multiply that number by the amount of dollars being spent.
This gives us: 81 * 50 = 4050. You would have to spend 4050 yen to buy something that costs 50 dollars.
James has a $7,500 unsubsidized 10-loan with an interest rate 4.29%. He wants to pay only the interest while attending school. His payments is due on the 10th of each month. He made his last payment on February 10th, and this is a leap year. Calculate the amount that he will pay on March 10th. (Keep in mind that they are 366 days in a leap year.)
The amount that he will pay on March 10th is $1287 with interest rate.
What does the arithmetic behind interest rates mean?The annual rate that is charged for borrowing (or made by investing), given as a single percentage number, represents the real yearly cost of money throughout the course of a loan.
Given that he is aware that he can begin loan repayment on a $7,500 loan in 4.5 years at the present interest rate of 4.29%, the following will be applicable:
4.29% of 7500 after the first year
4.29 × 7500/100
321.75
After the 4.5-year term, multiply the interest by 4.5 to determine the overall interest:
321.75 × 4
$1287.
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Dalton has $3.05 in dimes and quarters. He has 13 more dimes than quarters. How many quarters does he have?
The number of quarters Dalton has is 5.
How to find the number of quarters?Dalton has $3.05 in dimes and quarters. He has 13 more dimes than quarters. Therefore, the number of quarters he has can be calculated as follows:
Hence, using system of equation,
Therefore,
let
x = number of quarters
y = number of dimes
y = x + 13
0.25x + 0.1y = 3.05
using substitution method,
0.25x + 0.1(x + 13) = 3.05
0.25x + 0.1x + 1.3 = 3.05
0.35x = 3.05 - 1.3
0.35x = 1.75
x = 1.75 / 0.35
x = 5
Therefore,
number of quarters = 5
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Consider parallelogram JKLM below.
Use the information given in the figure to find x, mZM, and mZMJ
M
J
51°
3.
3x
L
70°
K
Date:
1.Ayacka and Erica sells newspapers on weekends to earn extra money for every 9 newspapers,how many did Erica sells
The cost of the 20 papers will be $200.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Ayacka and Erica sells newspapers on weekends to earn extra money for every 9 newspapers the cost is $90, Erica sells 20 newspapers.
The cost of 20 news papers will be calculated as,
Cost = ( 90 x 20 ) / 9
Cost = $200
The complete question is given below.
Ayacka and Erica sells newspapers on weekends to earn extra money for every 9 newspapers the cost is $90, Erica sells 20 newspapers. What is the cost?
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converting within measurement sytems
Converting within measurement systems means that we are changing the unit of measurement from one to another.
What is Converting within measurement systems?It is referred to as converting units within measuring systems if we do it using the metric or conventional systems. The conventional system and the metric system are the two most widely used measurement systems. In other words, we are not converting units from customary to metric or vice versa.
Simple unit conversions can be performed mentally or with one-step multiplication or division. There are, however, more difficult conversions that call for many conversions between a wide range of units.
The Unit Factor Method, another name for the Dimensional Analysis process, is a mathematical technique that takes advantage of the fact that any number or statement may be multiplied by "one" without changing its value. By multiplying the previous measurement by one (or more) different representations of the number 1, you can convert units. Although the measurement's value is unaffected by the factor of 1, the measurement's units are.
A ratio of one is referred to as a conversion ratio or unit factor. The names of the units that will be used in the conversion are listed in this ratio. It can be used to convert values both within the English and Metric Systems and between the two. The idea of equivalent values serves as the foundation for the conversion ratio.
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Complete question:
What do you mean by converting within measurement systems?
I.
Encircle the number(s) that is (are) not in the domain of the given
rational algebraic expression.
-1/4x
-3
-1
0
4
Answer:
see explanation
Step-by-step explanation:
the denominator of a rational expression cannot be zero as this would make the expression undefined.
equating the denominator to zero and solving gives the value/s that x cannot be.
1
4x = 0 ⇒ x = 0
x = 0 ← is an excluded value in the domain
2
8x + 3 = 0
8x = - 3
x = - [tex]\frac{3}{8}[/tex]
x = - [tex]\frac{3}{8}[/tex] ← is an excluded value in the domain
3
2 - 10x = 0
- 10x = - 2
x = [tex]\frac{-2}{-10}[/tex] = [tex]\frac{1}{5}[/tex]
x = [tex]\frac{1}{5}[/tex] ← is an excluded value in the domain
4
x + 12 = 0
x = - 12
x = - 12 ← is an excluded value in the domain
5
(2x - 1)(x + 6) = 0
equate each factor to zero and solve for x
2x - 1 = 0
2x = 1
x = [tex]\frac{1}{2}[/tex]
x + 6 = 0
x = - 6
x = - 6 and x = [tex]\frac{1}{2}[/tex] ← are excluded values in the domain
If BD=7x-10, BC=4x-29, and CD=5x-9, find each value
Answer: We know that in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Using the triangle inequality theorem, we can set up the following inequality:
BD + BC > CD
7x - 10 + 4x - 29 > 5x - 9
Simplifying, we get:
11x - 39 > 5x - 9
Subtracting 5x from both sides, we get:
6x - 39 > -9
Adding 39 to both sides, we get:
6x > 30
Dividing by 6 from both sides, we get:
x > 5
So x must be greater than 5.
To find the value of BD, we can substitute the value of x in the equation:
BD = 7x - 10
BD = 7(5) - 10 = 25 - 10 = 15
To find the value of BC, we can substitute the value of x in the equation:
BC = 4x - 29
BC = 4(5) - 29 = 20 - 29 = -9
To find the value of CD, we can substitute the value of x in the equation:
CD = 5x - 9
CD = 5(5) - 9 = 25 - 9 = 16
So, BD = 15, BC = -9, CD = 16
Step-by-step explanation:
How do you subtract fl oz from liters?
Answer:
Step-by-step explanation:
Convert a liter or liters what how ever many the question says to fl oz. 1 liter= 33.814, so if you need to minus 2 cups then just minus 16 fl oz, from 33.814, or the given amount in the question.
Answer:
Step-by-step explanation:
1. convert fl oz to liters using a conversion factor
2. 1 liter = 33.814 fl oz approx
3. you must divide the # of fl oz by 33.814
4. For example, if you wanted to subtract 20 fl oz from 3 liters, you would first convert the 20 fl oz to liters: 20 fl oz/33.814 = 2.406
5. Then you would subtract the converted fl oz from the liters: 3 liters-0.594 liters= 2.406 liters
20 fl oz = 0.594 liters, and 3 liters minus 0.594 liters equals 2.406 liters
Hope this helps!
The floor of a round hut has a diameter of 4 yards. What is the floor's area?
Answer:
A = 12.5663706 yd2
Step-by-step explanation:
The equations x + 5 y = 10, 3 x minus y = 1, x minus 5 y = 10, and 3 x + y = 1 are shown on the graph below.
On a coordinate plane, there are 4 lines. Green line goes through (0, negative 1) and (1, 2). Blue line goes through (0, 1) and (1, negative 2). Pink line goes through (0, 2), and (2, 1.5). Orange line goes through (negative 2, negative 2.5) and (2, negative 1.5).
Which is the approximate solution for the system of equations x + 5 y = 10 and 3 x + y = 1?
(–0.3, 2.1)
(–0.3, –2.1)
(0.9, –1.8)
(0.9, 1.8)
They intersect in the 2nd quadrant. Only one answer choice (–0.3, 2.1)
What is y-intercepts?
Horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.
The graph shows you the lines all differ in their y-intercepts. This means you can identify the y-intercepts of the equations of interest, and you will know which lines to look at.
The y-intercept is found by setting x=0 and solving for y:
x +5y = 10
0 + 5y = 10
y = 10/5 = 2
3x +y = 1
3·0 +y = 1
y = 1
The two lines of interest are the ones that have y-intercepts of 2 (pink) and 1 (blue). They intersect in the 2nd quadrant. Only one answer choice can apply: (–0.3, 2.1)
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What is the difference when -2 is subtracted from 2?
Answer:
Step-by-step explanation:
2-(-2)
=2+2
=4
Answer: the difference when -2 is subtracted from 2 will be 4
Step-by-step explanation: according to question
2 -(-2)
=2+2 ( - + - = +)
= 4
(2x^2+5)-(4x-1) why isnt it complete
Answer:
Step-by-step explanation:
Do you mean "isn't complete or not in final form?"
If it does, it is because the equation is not yet simplified. You can still change its structure by distributing the negative sign to the right parenthsis to make it a whole polynomial.
[tex](2x^{2} + 5) - (4x-1)\\2x^{2} + 5 - 4x + 1\\2x^{2} - 4x + 6\\[/tex]or
[tex]2 (x^{2} - 2x + 3)[/tex]
A person takes up 20 inches of space on a stadium bleacher. If one row of bleachers is 100 feet long and
there are 25 rows of bleachers, how many people can fit into the stands?
Answer:
Generally, figure the average person takes up 18 inches of space on a bleacher seat. That is the industry standard. Therefore, for 4-row bleachers, consider these lengths and seating capacity. 7.5 feet – 20 seats (90 inches divided by 18 inches equals 5 seats, times 4 rows equals 20 seats).
Step-by-step explanation:
A checkout clerk at a department store is expected to complete 16 transactions every hour. In the past 20 minutes, he completed 6 transactions. Choose True or False for each statement. If the clerk continues at the same rate, he will meet his goal of 16 transactions in 1 hour. Choose... At his current rate, the clerk will complete 12 transactions in 1 hour. Choose... At his current rate, the clerk will complete 9 transactions every half hour. Choose... If the clerk continues at this rate for a 6-hour shift, he will complete 96 transactions. Choose...
Step-by-step explanation:
16 transactions per hour (60 minutes).
in short :
16/1
or 16/60 (for minutes instead of 1 hour)
in 20 minutes 6 transactions.
so,
6/20
hour many transactions then in 1 hour (60 minutes) ?
60 = 20×3
so, to bring the ratio to 1 hour (60 minutes) we need to multiply the denominator by 3. and to keep the ratio value, we need to to do the same thing also to the numerator.
therefore,
6/20 × 3/3 = 18/60
so, the clerk will do 18 transactions per hour.
he will meet his goal of 16 : true
he will even exceed but definitely meet his goal.
12 transactions in 1 hour : false
9 transactions every half hour : true
as he will do 18 transactions in 1 hour, he will do half of these transactions (9) in half an hour.
96 transactions in 6 hours : false
18/1
6 = 1×6
so, with the same trick as above we get
18/1 × 6/6 = 108/6
and we see, he would complete 108 transactions in a 6- hour shift.
96 would be right, if the actual ratio would be 16/1 :
16/1 × 6/6 = 96/6
You will be writing a short essay on how you can apply the processes you have learned in this unit to solve one of those questions.
Option 1: Solving by Factoring
Please explain in detail the strategy, Solving by Factoring, discussed in the lesson Quadratic in Form Polynomials. Include an example with this explanation to clearly explain the process.
Answer:
Step-by-step explanation:
Solving by factoring is a strategy used to solve quadratic in form polynomials, which are equations that can be written in the form of ax^2 + bx + c = 0. The goal of this strategy is to factor the equation into two binomials that are equal to zero. Once the equation is factored, we can use the zero product property to set each binomial equal to zero and solve for the roots or solutions of the equation.
The process of factoring begins by finding the greatest common factor of all the terms in the equation. Once the GCF is identified, it can be factored out of the equation. Next, we look for two binomials that multiply to give the remaining terms in the equation and add to give the remaining constant term.
For example, consider the equation: 3x^2 + 6x - 9 = 0.
To factor this equation, we first find the GCF of all the terms, which is 3. We can factor out 3 from all the terms, giving us: 3(x^2 + 2x - 3) = 0.
Now, we look for two binomials that multiply to give x^2 + 2x - 3 and add to give -2. We can see that (x-3)(x+1) satisfies this condition.
By factoring the equation, we have now factored the polynomial into (x-3)(x+1) = 0. We can use the zero product property to set each binomial equal to zero and solve for the roots: x-3 = 0 and x+1 = 0. The solutions are x=3 and x=-1.
By using the factoring strategy, we were able to solve the quadratic in form polynomial 3x^2 + 6x - 9 = 0 and find the roots x=3 and x=-1. This strategy can be applied to any quadratic in form polynomial and is a useful tool in solving equations.
