One of the legs of a right triangle measures 2 cm and its hypotenuse measures 5 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth."

Answers

Answer 1

When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm,  [tex]\sqrt{21}[/tex]     is the measurement of the other leg.

what is Pythagoras theorem ?

Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The Pythagorean Theorem demonstrates how to calculate the side lengths of a right triangle by adding the areas of three intersecting squares. As the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite, this theorem is a very helpful tool. Given a triangle ABC with sides measuring a, b, and c, and the equation a2 + b2 = c2, Make another triangle with sides of lengths a and b and a right angle.

given

by Pythagoras theorem

[tex]c^{2} = a^{2} + b^{2} \\5^{2} = 2^{2} + b^{2} \\5^{2} - 2^{2} = b^{2} \\25 - 4 = b^{2} \\21 = b^{2} \\b =\sqrt{21}[/tex]

When the hypotenuse of a right triangle measures 5 cm and one of its legs measures 2 cm,  [tex]\sqrt{21}[/tex]     is the measurement of the other leg.

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Related Questions

What is the answer to 2/3x=-36

Answers

the answer to your question is 36

The sixth-grade class is holding a week long fund-raiser. The class set a goal of raising $700. 0. So far they have raised $176. 95. Write an equation that can be used to solve for x, the amount of money the class still must raise to meet their goal

Answers

An equation that can be used to find the value of,x=$700.0 - $176.95.

What is an equation ?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

The statement is not an equation if there is no "equal to" sign in it.

According to our question-

x= $700.0 - $176.95

523.05

Hence, An equation that can be used to find the value of,x=$700.0 - $176.95.

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What is the hardest math in high school?

Answers

Geometry, most people find geometry the hardest because it builds upon algebra 1 with shapes and angles

Sport

Soccer

Jogging

Walking

Skiing

Football

Total

Hrs

5

20

10

5

10

50

Calculate the

portion for jogging

in degrees

[?]

20 hrs.

Total Sport Hours

Answers

The portion for walking in degrees when Soccer take 5 hours, Jogging take 20 hours, Walking take 10 hours, Skiing take 5 hours and Football take 10 hours of the total 50 hours of sport hours is 72 degrees.

Therefore the answer is 72°.

To calculate the portion of walking in degrees, we first need to find the total amount of time spent walking. In this case, it is 10 hours.

Next, we need to find the total amount of time spent on all sports, which is 50 hours.

Now we can calculate the portion of walking by taking the amount of time spent walking (10 hours) and dividing it by the total amount of time spent on sports (50 hours).

This gives us the fraction of time spent walking which is

10/50

= 1/5

Finally, we can convert this fraction to degrees by multiplying it by 360 (the number of degrees in a full circle).

So the portion of walking in degrees is

(1/5) × 360

= 72 degrees

--The question is incomplete, complete question is given below--

"Calculate the portion for walking in degrees when Soccer take 5 hours, Jogging take 20 hours, Walking take 10 hours, Skiing take 5 hours and Football take 10 hours of the total 50 hours of sport hours."

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PLEASE HELP ME I REALLY NEED IT!!!!!!!!

Answers

Answer: for A it is: 3 and 4 represent the number values for X and Y.

Step-by-step explanation:

Sorry, but you B and C you did not give enough information

Find the volume of the cylinder to the nearest tenth. Use 3.14 for
4 in.
I
7 in.
in³

Answers

On solving the provided question we can say that - Height(h) = h; Radius(r) = r; Length(l) = l Volume of cylinder A(V)=Volume of cylinder B(v) => [tex]4\pi R^2H = \pi r^2h[/tex]

what is cylinder?

One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.

Cylinder A

Height(h) = H; Radius(r) = 2R; Length(l) = L

Cylinder A

Height(h) = h; Radius(r) = r; Length(l) = l

Volume of cylinder A(V)=Volume of cylinder B(v)

[tex]4\pi R^2H = \pi r^2h[/tex]

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What is the solution to the system of linear equations 3x 2y equals 14 5x y equals 32?

Answers

The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (6, 10).

3x + 2y = 14

5x + y = 32

Subtracting 3x from both sides of the first equation:

2y = 14 - 3x

Substituting this into the second equation:

5x + (14 - 3x) = 32

Simplifying:

8x = 18

x = 18/8

x = 2.25

This x value is substituted into the first equation.:

2y = 14 - 3(2.25)

2y = 14 - 6.75y

= 7.25

The solution is (x, y) = (2.25, 7.25)

The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (2.25, 7.25). To solve the system, we first subtracted 3x from both sides of the first equation and then substituted this into the second equation. After simplifying, we obtained a value of x, which we then substituted into the first equation to obtain a value of y. This gave us the solution (x, y) = (2.25, 7.25).

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Analyze the function graph.
Select the best option to describe the function graph.
Linear Increasing
Linear Decreasing
Linear Constant
Nonlinear Increasing
Nonlinear Decreasing

Answers

The function graph is Linear Constant. Option C

What is the graph?

We know that when we plot a graph, there would be the vertical and the horizontal axis. We can be able to deduce the nature of the graph when we look at how the graph is going.

In this case, we can see that the graph is flat. The flatness of the graph would show us that there is neither an increase nor a decrease in the function that we have in view. The increase or the decrease can be seen from the direction of the line that is drawn across the graph.

Hence, the fact that the line is flat on the graph shows that it is linear constant.

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How do you find the terminal point of a line segment?

Answers

To find the terminal point of a line segment, identify the starting point, measure the length and direction, and use these parameters to calculate the coordinates of the terminal point.

To find the terminal point of a line segment, first identify the starting point of the line. Then, measure the length of the line segment and the direction in which it is going. Finally, use a combination of the starting point coordinates, the length, and the direction to calculate the coordinates for the terminal point of the line.

1. Identify the starting point of the line.

2. Measure the length of the line segment and the direction in which it is going.

3. Use the starting point coordinates, the length, and the direction to calculate the coordinates of the terminal point.

4. The coordinates of the terminal point are the location of the line segment’s endpoint.

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Does 12 20 and 16 form a Pythagorean triple?

Answers

No, 12, 20, and 16 do not form a Pythagorean triple. A Pythagorean triple is a set of three whole numbers, a, b, and c, such that a^2 + b^2 = c^2.

To determine if 12, 20, and 16 form a Pythagorean triple, we can substitute each number into the equation and solve for c.

Start by substituting 12 for a, 20 for b, and 16 for c:

12^2 + 20^2 = 16^2

144 + 400 = 256

544 ≠ 256

Since 544 does not equal 256, the numbers do not form a Pythagorean triple. We can also verify this by calculating the square of c to see if it is equal to the sum of the squares of a and b.

Start by substituting 12 for a, 20 for b, and 16 for c:

a^2 + b^2 = c^2

12^2 + 20^2 = c^2

144 + 400 = c^2

544 = c^2

Taking the square root of both sides:

√544 = √c^2

23.2 ≠ c

Since 23.2 does not equal c, the numbers do not form a Pythagorean triple.

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(i) Six donkeys are each given 5 ml spoons of medicine three times each day.
Calculate the number of whole days a 2 L bottle of medicine will last.
pls I really need the answer

Answers

Hello there!

Answer:

33 days

Step-by-step explanation:

Every day you give 5 ml of medicine to 6 donkeys. So you spent 5 ml * 6 = 30 ml per day

1 L = 1000 ml

To find the answer you should volume of bottle divide by 30 ml per day:

1000 ml / 30  = 33.333...

It means that if will be possible to use the bottle 33 days but then it will be left

A manufacturer tests 1200 computers and finds that 9 of them have defects. Find the probability that a computer chosen at random has a defect. Round your answer to the nearest hundredth.

Answers

Probability that computer chosen at random has defect is 0.0075.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes.

What is probability?

It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 12.

Total number of computers=1200

Total number of damage computers=9

Probability that question chosen at random has defect = 9/1200=0.0075

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having trouble with this, can anyone help?

(equation needs to be put in y=mx+b form)

Answers

Check the picture below.

A company i expanding it building area from 18,000 quare feet to 25,380 quare feet. What i the percentage increae of the area of the building pace?

Answers

41% is the percentage increase of the area of the building pace.

What is percentage?

When the denominator is 100, percentages are really just fractions. We place the percent sign (%) next to the number to indicate that the number is a percentage.

Comparing two amounts while rebasing the second amount to 100 is the simplest way to use percentages. The word percentage comes from the Latin term per centum, which means "by the hundred." In the 16th century, the Latin term made its way into English. It was later abbreviated to %.

A company is expanding it building area from 18,000 square feet to 25,380 square feet.

= (25,380 - 18,000)

= 7,380

Now,

= 7,380 / 18,000

= 0.41

the percentage increase of the area of the building pace: 0.41 / 100 = 41%

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expand the polynomial (x+1)(x+2)(y-3)

Answers

Answer: X^2y + 3xy + 2y -3x^2 -9x -6
explanation

1. Foil (x+2)(x+1)

X^2 +2x + x + 2

2. Simplify

X^2 + 3x + 2

3. Distribute x^2 + 3x +2 (y-3)

X^2y + 3xy + 2y -3x^2 -9x -6


A card is drawn from a standard deck of 52 cards. What is the theoretical probability, as a decimal, of drawing a number 8? Round the decimal to the nearest hundredth.

Answers

The probability of picking a card at random from a standard deck of 52 cards is 0.019 or 0.02(approx)

What is probability?

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: A card is drawn from a standard deck of 52 cards. Let the probability be P then P= 1/52

                                     =0.02

Hence, The probability of picking a card at random from a standard deck of 52 cards is 0.019 or 0.02(approx)

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In AABC, AB = AC and AP 1 BC. If AB= (2x + 3) cm, AC = (3y-1) cm, BP = (y + 1) cm and PC = (x + 2) cm find the values of x and y.

Answers

Answer:

x = 1y = 2

Step-by-step explanation:

Given isosceles triangle ABC with AB≅AC, altitude AP, and AB=(2x+3), AC=(3y-1), BP=(y+1), and PC=(x+2), you want the values of x and y.

Isosceles triangle

Corresponding parts of ∆ABP and ∆ACP are congruent, so we have ...

  2x +3 = 3y -1

  x +2 = y +1

Solution

Subtracting twice the second equation from the first gives ...

  (2x +3) -2(x +2) = (3y -1) -2(y +1)

  -1 = y -3 . . . . simplify

  2 = y . . . . . . add 3

Substituting into the second equation, we have ...

  x +2 = 2 +1

  x = 1 . . . . . . . .subtract 2

The values of x and y are 1 and 2, respectively.

How many real solutions of 2x 3y 5 are possible?

Answers

The equation 2x + 3y = 5 has one real solution.

To find it, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable.

For example, you can solve for y to get y = (5 - 2x)/3, and then substitute this into the equation to get 2x + 3((5 - 2x)/3) = 5, which you can then solve for x. Doing this will give you x = 5/4, which means that the solution is (5/4, 5/3).

Linear equations are equations that involve two variables and can be expressed in the form ax + by = c, where a and b are constants and x and y are the variables. These equations have one real solution, which can be found by solving for one of the variables and then substituting the result into the equation to find the other variable. Once both variables are known, the solution to the equation is the point (x,y) that satisfies both equations.

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I need help with this question. :Probability and Statistics thanks

Answers

The number of possible combinations of 4 digit codes would be 72.

What are permutation and combination?

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

Given, I am creating a 4 digit code with the numbers 1 to 10.

Now, From 1 to 10 there are (10 - 1 + 1 ) = 10 and we are taking 4 numbers at a time.

Therefore the number of combinations of 4 digit codes would be,

[tex]^9C_4\times2![/tex]. As the number consists of two digits.

= [9!/(9 -2)!×2!]×2!.

= 9!/7!.

= 72 possible ways.

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When a space shuttle returns from a mission, the last part of its descent to the ground
must be between 17 degrees and 19 degrees with the horizontal (ZZ). If the pilot of
space shuttle Pioneer plans to descend from 11,700 feet (UH) at an angle of 18
degrees (ZZ) from the runway, determine the horizontal distance from the landing site
(ZU) at which the pilot must begin the descent.
Use the diagram to determine the measure of the sought side.

Answers

Answer:

please see the followings,

11700 ÷ tan 18 = ZU

Find the equation of the line. Write the answer in standard form.

Answers

Answer:

1.Given points are:-

(1,2)=(x1/,y1)

(3,4)=(x2,y2)

Now,from two point formula,

y-y1=(y2-y1)/(X2-X1)×(X-X1)

or,y-2=(4-2)/(3-1)×(X-1)

or,y-2=2/2×(X-1)

or,y-2=1(X-1)

or,y-2=X-1

or, X -1-y+2=0

or,X-y+1=0 is the req. eqn in standard form

2.Given points are:-

(2,5)=(x1, y1)

(3,7)=(x2,y2)

Now, from two point formula,

y-5=(7-5)/(3-2)×(X-2)

or,y-5=2/1×(X-2)

or,y-5=2(X-2)

or,y-5=2X-4

or,2X-y-4+5=0

or,2x-y+1=0 is the req. eqn in standard form.

c.do similarly

and*mark me brainliest

Answer:

see explanation

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

First obtain the equations in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

(1)

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 2 ) and (x₂, y₂ ) = (3, 4 )

m = [tex]\frac{4-2}{3-1}[/tex] = [tex]\frac{2}{2}[/tex] = 1 , then

y = x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 4 ) , then

4 = 3 + c ⇒ c = 4 - 3 = 1

y = x + 1 ( subtract y from both sides )

0 = x - y + 1 ( subtract 1 from both sides

- 1 = x - y , that is

x - y = - 1 ← in standard form

Use the same procedure for the next 2 questions

(2)

(x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (3, 7 )

m = [tex]\frac{7-5}{3-2}[/tex] = [tex]\frac{2}{1}[/tex] = 2 , then

y = 2x + c ← is the partial equation

using the point (2, 5 ) to find c

5 = 2(2) + c = 4 + c ( subtract 4 from both sides )

1 = c

y = 2x + 1 ( subtract y from both sides )

0 = 2x - y + 1 ( subtract 1 from both sides )

- 1 = 2x - y , that is

2x - y = - 1 ← in standard form

(3)

(x₁, y₁ ) = (5, 2 ) and (x₂, y₂ ) = (3, 12 )

m = [tex]\frac{12-2}{3-5}[/tex] = [tex]\frac{10}{-2}[/tex] = - 5 , then

y = - 5x + c

using the point (5, 2 ) to find c

2 = - 5(5) + c = - 25 + c ( add 25 to both sides )

27 = c

y = - 5x + 27 ( add 5x to both sides )

5x + y = 27 ← in standard form

Eight rooks are placed at positions sampled randomly without replacement on an chessboard. Two rooks attack each other if they are in the same row or in the same column. What is the probability that none of them attacks any of the others

Answers

There is a 60% chance that none of them will assault any of the others.

Explain about the Probability?

Only the likelihood that something will happen is included in probability. When we don't know how something will turn out, we could talk about the possibility of one or the likelihood of different outcomes. The scientific study of events that fit into a probability distribution is known as statistics.

It is based on the probability that something will happen. The fundamental principle of theoretical probability is the explanation of probability. For instance, when a coin is flipped, there is a 12% chance that it will land on its head.

Probability is a statistic that is used to show the possibility or likelihood that an event will happen. Probabilities can be expressed as fractions from 0 to 1 or as percentages from 0% to 100%.

  = 64/8 = 8

   =  8 - 2

    =  4

    =  64- 4

     = 60

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Let u = PQ be the directed line segment from P(0,0) to Q(9,12), and let c be a scalar such that c < 0. Which statement best describes cu?
A) the terminal point of vector cu lies in quadrant II
B) the terminal point of vector cu lies in quadrant III
C) the terminal point of vector cu lies in quadrant I
D) the terminal point of vector cu lies in quadrant IV

Answers

The terminal point of vector cu lies in quadrant III.

Option B is the correct answer.

What are coordinates in a graph?

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

p = (0, 0) and Q = (9, 12)

u = PQ = (9 - 0, 12 - 0) = (9 , 12)

Now,

cu = (9c, 12c)

where c < 0

If c = -1

cu = (-9, -12)

The coordinates (-x, -y) lie in quadrant III.

(-9, -12) is in quadrant III.

Thus,

Vector cu lies in quadrant III.

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Find the length of the third side. If necessary, round to the nearest tenth

Answers

Answer:

Step-by-step explanation:

Let AB = 3 units , BC = 1 unit and AC = ? (TO BE CALCULATED)

By Pythagoras theorem:

(AC)²=(AB)²+(BC)²

therefore, (AC)²= 3²+1²

(AC)²=9+1

(AC)²=10

(AC) = √10 = 3.03 cm

You bought the meat for Saturday’s cookout a package of hotdogs cost 160 and a package of hamburgers cost five dollars you brought a total of eight packages of me and you spent $23. How many packages of hamburger meat did you buy?

Answers

The total number of hamburger meat he bought is 3.

Find the number of hamburger meat bought?

Package of hot dogs cost $1.60 and  package of hamburgers cost $5.

You bought  total of 8 packages of a meat and you spent $23.

Therefore we have,

let

x = total number of package of hot dogs.

y = total  number of package of hamburger.

Hence,

x + y = 8

1.60x + 5y = 23

multiply equation(i) by 5

5x + 5y = 40

1.60x + 5y = 23

Subtract equation(ii) from equation(i) we get

3.4x = 17

x = 17 / 3.4

x = 5

y  = 8  - 5

y = 3

Therefore, total   number of hamburger meat he bought is 3.

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Using a number line, find both the intersection and the union of the following
intervals:
(-∞,2) and [0,∞)

Answers

The union of the intervals is (-∞,∞)
The intersection of the intervals is [0,2)

Hope this helped!

What is the answer of 2x^2 4x 6 0?

Answers

The answer of the equation "2x^2 -  4x - 6 =  0" is -1 and 3.

The equation is solved using factorization:

2x^2 -  4x - 6 =  0        , given equation

2x^2 -  6x + 2x - 6 =  0     , factorizing

2x(x - 3) + 2 ( x - 3 ) = 0    , taking 2x common from the first two terms and 2 common from the last two terms

(2x + 2) (x - 3) = 0

now solving further

( 2x + 2 ) = 0   &   ( x - 3 ) =0

2x = (0 - 2)    ,          x  = (0 +  3)

2x = (-2)        ,         x = 3

x = (-2/2)

x = -1

Thus, the equation gives the solution as x = -1 and x = 3.

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I really need help on this one too

Answers

The solution is Option C and Option D.

The exponential function is given by f ( x ) = 2 ( 3 )ˣ

The exponential function is given by f ( x ) = 800 / 4ˣ

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 7 , 19 , 31 , 43 }

The equation of line is y = 12x + 7

This is a linear equation

b)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 5 , 10 , 15 , 30 }

The equation is a quadratic equation

c)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 2 , 6 , 18 , 54 }

The equation is y = 2 ( 3 )ˣ

This is an exponential function

d)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 800 , 200 , 50 , 12.5 }

The equation is f ( x ) = ( 800 / 4ˣ )

This is an exponential function

Hence , the exponential equations are solved

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After 2+3/2-x+1/3x have been combined using the least common denominator of 6x, what is the numerator?

Answers

On solving the provided question, we can say that In light of this, the lowest common denominator of the equation is (x - 4)(x + 1)(x - 2) (x - 2)

What is equation?

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

equation is given as:

x2 — 3x — 4 = x2 — Ox + 8

x2 — 4x + x — 4 =

x(x — 4) + I(x — 4)

Factor out x - 4

(x + I)(x — 4) = x-2(x-4)

The common factor between the two sides of the equation is x – 4.

In light of this, the lowest common denominator is (x - 4)

(x + 1)(x - 2) (x - 2)

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A utility pole is 5 ft high. A 8 ft cable is stretched from the top of the pole to a stake in the ground. How far is the stake from the pole?

Answers

The distance between the stake from the pole is 6.25 ft.

What is the Pythagorean theorem?

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that a utility pole is 5 ft high. An 8 ft cable is stretched from the top of the pole to a stake in the ground.

The distance will be calculated as,

B² =  H² - P²

B = √(8² - 6²)

B = √ ( 64 - 36 )

B = √39

B = 6.25 ft

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