Mathematics High School

## Answers

**Answer 1**

The next time all three lights will flash at the same time will be in 210 seconds, or **3 minutes and 30 seconds.**

How to find the next time all three lights will flash at the same time

To find the time at which all three lights will flash at the same time, we need to find the LCM** (Least Common Multiple)** of the given times.

Prime** factorizing** each time, we get:

6 = 2 x 3

15 = 3 x 5

21 = 3 x 7

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers:

2 x 3 x 5 x 7 = 210

Therefore, the next time all three lights will flash at the same time will be in** 210 seconds**, or 3 minutes and 30 seconds.

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## Related Questions

i need help 7th grade quesiton will give brainlist thingy

### Answers

The terms and expressions are **matched **as follows:

The number of words made: w.The number of tiles not used: t.Points earned from words made: 10w.Points taken away from the tiles not used: 3t.

How to build the expressions?

We have that **letter w** represents the number of words made, while **letter t** represents the number of tiles not used.

Then the **multipliers **from the points are given to build the expressions, as follows:

Points earned from words made: 10w.Points taken away from the tiles not used: 3t.

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CAN SOMEONE Please help me?

### Answers

**Answer:**

Hope this works

**Step-by-step explanation:**

a^2+b^2=c^2.

Question A

Each square has a distance of 1, so the bottom is a length of 6, for the sides, they rise 4, and over 3, so 16+9=25, or 5. So the triangle has a perimeter of 16.

Question B

The top has a length of 8 and a bottom length of 5, side BA, (2^2)4+(4^2)16=20, or sqr20, which is 2sqr5 and sqr17 for side DC. So, 5+8+2sqr5+sqr17= 19.5952

The line through which of the following pair of points is perpendicular to l

?

PLEASE HELP!!!!!!!!!!!!!!

### Answers

Due to the negative **reciprocal** of -1/2, the straight line will have a slope of 2.

what is slope ?

The slope of a line in mathematics serves as a gauge for how steep it is. It represents the **rate** of rise or fall of the line as you move along it from left to right. The character "m" is frequently used to indicate slope. The coordinates of two locations on a line can be used to determine the slope of the line. Let the **coordinates** of two locations on the line be (x1, y1) and (x2, y2). The line's inclination is then determined by:

(y2 - y1) / (x2 - x1) (x2 - x1) = m

Depending on how the line is oriented, the inclination can be either positive, negative, zero, or undefinable.

given

On each set of points, the slope formula would be applied.

(y2 -y1)/(x2 - x1) (x2 - x1) = m

Due to the fact that -1/2's negative reciprocal is equal to 2, the slope of the vertical line will be 2.

Due to the negative reciprocal of -1/2, the straight line will have a slope of 2.

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construct a 3 × 3 matrix, not in echelon form, whose columns do not span r 3 . show that the matrix you constructed has the desired property.

### Answers

The **matrix **A = [1 0 0; 0 1 0; 1 1 0] does not span R3. We show that there exists a vector in R3 that cannot be expressed as a **linear **combination of the columns of A.

To show that the **columns **of A do not span R3, we need to show that there exists a vector in R3 that cannot be expressed as a linear combination of the columns of A. Let b = [0 0 1]T. We need to show that there do not exist **scalars **x, y, and z such that Ax = [0 0 1]T.

Ax = [1 0 0; 0 1 0; 1 1 0][x; y; z] = [x; y; x+y]

Setting this equal to b, we get x+y = 1, which is impossible to **satisfy **for any values of x and y. Therefore, the columns of A do not span R3.

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at 13:00 a water tank contained 200 litres of water. water flowed from the tank at a constant rate until at 15:30 the tank was completely empty. calculate the length of flow of water from the tank in litres per hour. if your answer id a decimal give your answer to 1dp

### Answers

The **flow** of **water** from the **tank** was 80 liters per hour.

**What is rate ?**

Rate refers to the amount of change in one quantity with respect to another quantity. It is often expressed as a ratio, and it is used to describe how quickly or slowly something is happening. For example, the rate of speed of a car is the distance traveled per unit of time. Similarly, the rate of interest on a loan is the amount of money charged per unit of time as a percentage of the loan amount.

The tank contained 200 liters of water at 13:00 and was completely empty by 15:30. The time between 13:00 and 15:30 is 2.5 hours.

The water flowed out of the tank at a constant rate for 2.5 hours, so we can calculate the rate by dividing the amount of water in the tank by the time:

rate = (amount of water) / (time)

The amount of water that flowed out of the tank is the difference between the initial amount (200 liters) and the final amount (0 liters):

amount of water = 200 - 0 = 200 liters

Substituting these values into the formula gives:

rate = (amount of water) / (time) = 200 / 2.5 = 80 liters per hour

Therefore, the **flow** of **water** from the **tank** was 80 liters per hour.

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helppp quick pls !! i need thiss

### Answers

The **surface area** of the **cylinder** is about **62.8** square centimeters.

Find the** radius** and **height** of the cylinder.

radius = 2

height = 3

Find the **area** of the **circle **on the **top** of the **cylinder**. Use **3.14** for** **.

[tex]A_{top}=\pi r^2[/tex]

≈ [tex]3.14 * 2 * 2[/tex]

≈ [tex]12.56[/tex]

The **circle** on the** bottom **of the **cylinder** is the **same**, so:

[tex]A_{bottom} =A_{top}[/tex] ≈ [tex]12.56[/tex]

Find the** circumference** of the **top** **circle**.

[tex]C = 2\pi r[/tex]

≈ [tex]2 * 3.14 * 2[/tex]

≈ [tex]12.56[/tex]

Now find the **area** of the **curved surface**. The **curved surface** is a **rectangle**. One** side length** is the **height**, and the other **side length **is the **circumference** of the **circle**.

[tex]A_{side} = C * h[/tex]

≈ [tex]12.56*3[/tex]

≈ [tex]37.68[/tex]

Now **add** the** areas** to find the** surface area** of the** cylinder**.

[tex]Surface[/tex] [tex]area=A_{top} +A_{bottom}+A_{side}[/tex]

≈ [tex]12.56 + 12.56 + 37.68[/tex]

≈ [tex]62.8[/tex]

Therefore, The **surface area** of the **cylinder** is about **62.8** square centimeters.

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An equivalent form of $f$ is given as $f\left(x\right)=x\left(x-2\right)\left(x-a\right)$ , where $a$ is a constant. What is the value of $a$ $?$

### Answers

The** value of a** is given by the third root of the function.

How to obtain the value of a?

The **function **for this problem is defined as follows:

f(x) = x(x - 2)(x - a).

According to the Factor Theorem, the function is defined as a product of it's linear factors, hence the **roots **of the function are given as follows:

x = 0.x - 2 = 0 -> x = 2.x - a = 0 -> x = a.

Hence the** value of a** is the third root of the function, which is the value on the graph at which the function crosses the x-axis along with x = 0 and x = 2.

Missing Information

The problem is incomplete, hence the general procedure to obtain the value of a is presented.

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Divide p(x) by g(x), where p(x) = x + 3x^2 - 1 and g(x) = 1 + x

### Answers

**Answer:**

3x - 2 remainder 2

**Step-by-step explanation:**

p(x) = 3x² + x / g(x) = x + 1 → 3x - 2 remainder 2

evaluation

complete the table.

(question on pic.)

### Answers

We have **shown** that PR = QS, as the two **diagonals** of the rectangle are **congruent**.

**What is rectangle ?**

A rectangle is a two-dimensional geometric shape that has four sides and four angles. It is a special case of a parallelogram where all angles are right angles, which means that opposite sides are parallel and congruent.

**According to given information :**

Statements:

PQRS is a rectangle with diagonals PR and QS.Opposite sides of a rectangle are congruent.LP and 2S are right angles (given).2P = LS (given).RS = RS (reflexive property).Triangle PSR is congruent to triangle QRP by SAS congruence (SSA congruence is not valid, but since we know that PS = QR and PR = QS, the included angles P and Q are right angles, so we can use SAS).PRQS (given).

Reasons:

Given.Property of a rectangle.Given.Given.Reflexive property of congruence.Triangle congruence by SAS.CPCTC (corresponding parts of congruent triangles are congruent).

Therefore, we have **shown** that PR = QS, as the two **diagonals** of the rectangle are **congruent**.

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If 1 meter = 3.28 feet, converting 612 feet to meters and rounding to the nearest hundredth gives _____.

### Answers

In **unit conversion ** the 612 **feet **is 186.53 m.

**What is unit conversion?**

The same **attribute **is expressed using a **unit conversion**, but in a different **unit **of **measurement**. **Time**, for example, can be expressed in minutes rather than hours, and **distance **can be translated from miles to **kilometres**, feet, or any other **unit **of **length**.

Here the given** unit conversion** from **meter **to **feet **then,

1 m = 3.28 feet.

Now the given unit is 612 feet. Now converting into **feet **then,

=> [tex]\frac{612}{3.28}[/tex]

=> 186.53 m.

Hence the **converting meters** into **feet **, the answer is 186.53 m.

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The price of petrol is increased from 12,58 per litre to 13,28 pee litre. Determine the percentage increase in the price of petrol

### Answers

The **percentage increase **in the price of petrol when increased from 12,58 per litre to 13,28 per litre is 5.56%

How to determine the percentage increase in the price of petrol

The change in the price of the petrol is given as

Increased from 12,58 per litre to 13,28 **per litre.**

This means that the **change **in the price is

Change = 13.28 - 12.58

Evaluate the difference

Change = 0.7

The percentage increase in the price of **petrol **is then calculated as

Percentage = 0.7/12.58 * 100%

Evaluate the prodcuts

Percentage = 5.56%

Hence, the change is 5.56%

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3. The little-known country Overtaxia has a sales tax of 333% on all items. If you buy a comic book priced at $1.99 in Overtaxia, how much would you pay in all?

### Answers

**Answer:**

**Step-by-step explanation:**

Let X represent the total amount of money you need to pay.

X= $1.99 x 3.33

= $6.6267

= $6.60 (rounded)

You need to pay $6.60 for the book in Overtaxia.

Tess plants flowers every year, and she noticed that her flowers tend to bloom earlier when the spring weather is warmer. She collected data for the past 666 years on the average March temperature where she lives, and the date in April her first flowers bloomed that year. A line was fit to the data to model the relationship.

Based on this equation, estimate the date in April her flowers will bloom if the average temperature in March is 5. 5°

Round your answer to the nearest whole number

### Answers

Plugging in 5.5 for the March **temperature** yields April 16th as the estimated bloom date.

What is equation?

An **equation** is a mathematical statement that two expressions are equal. It is written in the form of an expression, with an equal sign (=) between two expressions that have the same value. Equations are used to solve for unknown values, to determine relationships between different variables, or to describe a **mathematical process**.

Using the equation that was fit to the data, the date in April when Tess' flowers will bloom if the average temperature in March is 5.5° is April 16th. This is based on the equation: April bloom date = -24.47 + 0.75 (March temperature). Plugging in 5.5 for the March temperature yields April 16th as the estimated bloom date.

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A polynomial function is represented by the data in the table. x = -6, -2, 2, 6, 10 f(x) = 73, 17, -7, 1, 41

### Answers

Therefore, the **polynomial **function represented by the data in the table is:

f(x) = -0.008x⁴ + 0.15x³ - 0.52x² - 1.33x + 19.1.

What do polynomials in mathematics mean?

The only operations that can be used in a **polynomial** are addition, subtraction, multiplication, and non-negative integer exponentiation. In mathematics,** variables** are occasionally referred to as indeterminates. An example of a** polynomial** with a single variable, x, is x2 4x + 7.

To find the **polynomial** function represented by the data in the table, we can use polynomial interpolation.

We can start by writing down a general polynomial function of degree 4:

f(x) = ax^4 + bx^3 + cx^2 + dx + e

We can then substitute each of the five x values and their corresponding f(x) values from the table into this equation, resulting in five equations:

73 = 1296a - 216b + 36c - 6d + e

17 = 16a - 8b + 4c - 2d + e

-7 = 4a + 2b + c + d + e

1 = 1296a + 216b + 36c + 6d + e

41 = 10000a + 1000b + 100c + 10d + e

We can now solve this system of** linear equations** to find the values of a, b, c, d, and e. This can be done using a matrix equation or by using a calculator or computer program. The resulting polynomial function is:

f(x) = -0.008x⁴ + 0.15x³ - 0.52x² - 1.33x + 19.1

Therefore, the polynomial function represented by the data in the table is:

f(x) = -0.008x⁴ + 0.15x³ - 0.52x² - 1.33x + 19.1.

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i need help, please.

### Answers

**Answer:**

sqrt(29)

**Step-by-step explanation:**

We know that 5^2 = 25

and 6^2 = 36

so the number must be between 25 and 36

The only square root with a number between 25 and 36 is 29

sqrt(29)

**Answer:**

**b**

Step-by-Step explanation

You are told that you will have to wait for 5 hours in a line with a group of other people. If you answer no give an example of 2 outputs that are possible for the same inpu

### Answers

If you are told that you will have to wait for 5** hours** in a line with a group of other people, then the **number of minutes** that you have to wait 300.

When we want to convert a** measurement **from one unit to another, we need to use a conversion factor that relates the two units. In this case, we want to convert hours to minutes.

The** conversion factor** between hours and minutes is that there are 60 minutes in one hour. So, to convert hours to minutes, we need to multiply the number of hours by 60.

In this particular scenario, we are told that we will have to wait for 5 hours in a line. To find out how many **minutes** that is, we simply multiply 5 by 60:

5 hours x 60 minutes/hour = 300 minutes

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The given question is incomplete, the complete question is:

You are told that you will have to wait for 5 hours in a line with a group of other people. What is the number of minutes you have to wait ?

researchers must be cautious when designing web-based surveys because they are particularly sensitive to: undercoverage.

All of the answer choices are correct.

nonresponse.

voluntary response bias.

### Answers

**Researchers **must be cautious when designing web-based **surveys **because they are particularly sensitive to undercoverage, nonresponse and voluntary response bias. So, option B is correct.

Web-based surveys have become increasingly popular in recent years due to their **convenience **and cost-effectiveness. However, researchers must be cautious when designing web-based surveys because they are particularly sensitive to various types of biases that can affect the validity and reliability of the survey results.

One of the biases that can affect web-based surveys is **undercoverage**, which occurs when some members of the target population are not able to access or complete the survey due to lack of internet access, technical difficulties, or other reasons. This can lead to a biased sample that does not accurately represent the entire population of interest.

Another bias that can affect web-based surveys is **nonresponse**, which occurs when some individuals who are invited to participate in the survey choose not to do so. This can lead to a biased sample if those who choose not to participate have different characteristics or opinions from those who do participate.

Finally, web-based surveys are also susceptible to **voluntary **response bias, which occurs when individuals choose to participate in the survey because they have strong feelings or opinions on the topic, while others choose not to participate. This can lead to a biased sample that overrepresents certain groups or opinions.

Therefore, Option B is the correct answer.

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**Complete question** is:

Researchers must be cautious when designing web-based surveys because they are particularly sensitive to:

a. undercoverage.

b. All of the answer choices are correct.

c. nonresponse.

d. voluntary response bias.

Solving Square Root and Other Radical Equations.√3x+4=4A. 0B. 4C. 8D. 16

### Answers

The solution to the **equation **√3x+4=4 is x=4, which corresponds to option B.

To solve the equation √(3x+4)=4, we can begin by isolating the radical expression on one side of the equation. We can do this by squaring both sides of the equation, which will eliminate the **radical **sign:

(√(3x+4))^2 = 4^2

**Simplifying **the left side of the equation, we get:

3x+4 = 16

Subtracting 4 from both sides, we get:

3x = 12

**Dividing **both sides by 3, we get:

x = 4

To check whether the solution we obtained is valid, we can substitute it back into the **original equation **and verify that it satisfies the equation. In this case, we can substitute x=4 into the original equation and verify that √(3x+4)=4 is indeed true, confirming that x=4 is the valid solution.

Therefore, Correct option is B.

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Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection. y=2x+3 y−1/2x−2

### Answers

**Answer:**

(2, 2)

**Step-by-step explanation:**

The point of intersection is at (2, 2)

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

Given the line with equations:

y = 3 x − 4 and y = 1/ 2x + 1

Plotting the graphs using geogebra online tool, the point of intersection is at (2, 2)

if f(2x+3)=7x-10, g(x)=x+1/2 and ff(x)=g-1(x) find x

### Answers

**Answer: x=2.6**

**Step-by-step explanation:**

You only need to solve the first equation to find x

2x + 3 = 7x - 10

Subtract 2x from both sides

3 = 5x - 10

Add 10 to both sides

13 = 5x

Divide 13 and 5x by 5 (13/5=2.6 5x/5=x)

2.6 = x

Please help me on this math problem

### Answers

**Answer:**

here you go man , the final answer of question 1 is 14 and the final answer of question 2 is 6

A central angle of a circle measures 64°. The arc intercepted by this central angle measures 15 inches.

Which value best approximates the radius of the circle?

11.65 in.

13.43 in.

23.30 in.

26.86 in.

### Answers

**Answer:**

**Step-by-step explanation:**

13.43 because it is closest fr

PLEASE HELPPP!!!!! I DONT UDERSTAND

### Answers

**Answer:**

71/17

**Step-by-step explanation:**

So there's 17 students total unless I misscounted those tiny ahh dots

the miles walked by each are as follows;

2+2+3+3+4+4+5+5+5+6+6+6+6+7+7

=71

since you're looking for the average (AKA the 'mean') if the group, you gotta divide the total of all their collective miles (71) by the number of students (17)

so 71÷17

that can be written at 71/17

hope this helps & lmk if what I wrote's unclear fr

How is -24x + 72 equivalent to -24(x-3)? I don't understand it

### Answers

**Answer:**

Below

**Step-by-step explanation:**

-24(x-3)

-24x + 72 We used to distribute to get this

Compare the two equation

-24x + 72 = -24x + 72

We see they are the same that y they are equivalent.

What is the volume of the following cylinder (with a hole)? Use 3.14 for л.

Round to the nearest 10th.

Enter the numerical answer only. Do not enter units.

### Answers

**Answer:**

**Step-by-step explanation:**

To start, let's review the volume of a cylinder:

V = pi(r^2) * h

Since this cylinder has a hole (it looks like a roll of paper towels XD), we can basically get the volume of the large cylinder - the volume of the space inside:

V(cylinder with hole) = (3.14*8^2*30) - (3.14*2^2*30)

Just for reference, the 8 and the 2 came from the radius, which is half the diameter (the 'width' of the cylinder)

(3.14*64*30) - (3.14*4*30)

6028.8 - 376.8

5652 cm^3

Hope this helps!

Pls show your work thank you will mark the Brainliest

### Answers

**Answer: 20x^2 - 4x - 16**

**Step-by-step explanation: We can solve this with the distributive property. (5x+4)(4x-4). We start by multiplying the 5x * 4x, we get 20x ^2. Then we multiply the 5x * -4, and we get -20x, because of the -4. Then, we multiply the 4 * 4x, and you get 16x. Lastly, we need to multiply the 4 * -4, and we get -16. Now we have the equation, 20x^2 - 20x + 16x - 16. We need to combine our like terms, -20x + 16x, -4x. Now, we have our final answer, 20x^2 - 4x - 16.**

Which operator is evaluated first: x y < y - z * 2 ? group of answer choices - *

### Answers

The **operator **that is **evaluated **first is *

How to determine the first operator

From the question, we have the following parameters that can be used in our computation:

x y < y - z * 2

An expression is a **combination **of numbers, variables, and mathematical operations that can be evaluated or simplified.

An **expression **may contain constants, variables, and **operations **

By **BODMAS**, we evaluate the **product **first

Using the above as a guide, we have the following:]

x y < y - 2z

Hence, the first operator is the **product **operator

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Question 1

Write an inequality and a word sentence that represent the graph. Let x represent the unknown number.

Inequality:

### Answers

X is greater than zero

The open circle stands for just greater than and the arrow to the right stands for greater than

X > 0

Three organizations are collecting donations for a cause. Organization A begins with one donation, and the number of donations quadruples each hour. The table shows the numbers of donations collected by Organization B. The graph shows the numbers of donations collected by Organization C. a. What type of function represents the numbers of donations collected by Organization A? B? C? b. Find the average rates of change of each function for each 1-hour interval from t = 0 to 1 = 6. c. For which function does the average rate of change increase most quickly? What does this tell you about the numbers of donations collected by the three organizations?

### Answers

a) The number of **donations **collected by Organization A and B representslinear function and C has **exponential growth function **

b) Average rate of change of A and B is 4

Average rate of change of C is 121.3333

c) The rate of change of a **linear function **is constant, while the rate of change of an exponential function is always increasing .

d) The numbers of donations collected by the three organizations increasing as the time increases

What is exponential growth function?

A process called **exponential growth **sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is **proportionate **to the quantity itself, this phenomenon takes place.

a) The number of donations collected by Organization A and B represents linear function and C has exponential growth function

b) Average rate of change = ( f(x2) -f(x1) ) /( x2 - x1) ------(1)

x1 = 0, x2= 6

Organization A and B:

f(6)= 24 , f(0) = 0

(1) => Average rate of change = (24-0)/(6-0) = 24/6 = 4

Organization C:

f(6)= 729, ( y-coordinate 3 times the previous y-coordinate ), f(0) = 1

(1) => Average rate of change = ( 729 -1)/(6-0) = 728/ 6 = 121.333

c) The rate of change of a linear function is constant, while the rate of change of an exponential function is always increasing .

d) The numbers of donations collected by the three organizations increasing as the time increases

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please show work and explain in detail so i can understand it

### Answers

The **hypotenuse **measures **5 units **in length.

[tex]c^2 = a^2 + b^2[/tex]

[tex]c^2 = 3^2 + 4^2[/tex]

[tex]c^2 = 9 + 16[/tex]

[tex]c^2 = 25[/tex]

taking √ both **sides**:

c = √25

**c = 5**

**What is a hypotenuse?**

The name "Hypotenuse" in **mathematics** derives from the **Greek** word hypoteinousa, which means "extending under." This phrase is used in **geometry**, particularly with reference to right triangles. The hypotenuse is a right-angle triangle's longest side (the side which is opposite to the right angle). The term "hypotenuse" refers to a **right-angled triangle's** longest side as compared to the base and **perpendicular **lengths. The right angle, the largest angle of the three angles in a right triangle, is opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other **triangles**. Now, when we study the right-angled theorem or **Pythagoras Theorem**, this is better explained.

from the question:

The **Pythagorean **theorem, which states that in a right triangle, the square of the length of the **hypotenuse** is equal to the sum of the **squares **of the lengths of the other two sides, must be applied in order to answer this puzzle. The Pythagorean theorem can be used to determine the length of the hypotenuse in this situation since the right triangle has legs that are **3 and 4 lengths.**

[tex]c^2 = a^2 + b^2[/tex]

[tex]c^2 = 3^2 + 4^2[/tex]

[tex]c^2 = 9 + 16[/tex]

[tex]c^2 = 25[/tex]

taking √ both **sides**:

**c = √25**

**c = 5**

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