The equation below describes a function of x . y=−4x+12

Answers

Answer 1

The solution for x in the function when the equation  y=−4x+12 equals -12 is -6

How to determine the solution for x in the function?

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

y=−4x+12

To make the equation legible, we need to rewrite it

So, we have the following representation

y = −4x + 12

Also from the question, we have

y = -12

This means that we calculate x when y = -12

Substitute the known values in the above equation, so, we have the following representation

-12 = -4x + 12

So, we have the following equation

-4x + 12 = -12

Add -12 to both sides of the equation

So, we have the following representation

-4x + 12 - 12 = -12 - 12

Evaluate the like terms in the equation

-4x = -24

Divide both sides of the equation by -4

x = 6

Hence, the solution is 6

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Possible question

The equation below describes a function of x . y=−4x+12

Solve for x when y = -12


Related Questions

The table below shows the energy of a 10 kg ball as a function of velocity. How much energy will the ball have at 10 m/s? velocity 0,2,3,6,10 energy 0,20,45,180,?

Answers

The amount of energy that the ball will have at 10 m/s is; 600 J

How to find the energy from velocity?

From the given table, we see that when the velocity is 2 m/s, then the energy is 20 J.

If we take the square of the velocity, we get 2² = 4.

Thus, we need to multiply 4 by 6 to get the energy that is equal to 24 as 4 * 6 = 24.

Similarly;

For velocity equal to 3 m/s, the energy is given as:

E = 6 * 3²

E = 54 J

Thus, the general formula to find the energy is given as:

E = 6 * v²

where;

E is the energy

v is the velocity

Now, for velocity equal to 10 m/s, energy is given as;

E = 6 * 10

E = 60 J

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Express each improper fraction as a mixed or whole number

Answers

All the improper fractions in mixed or whole numbers are as follows:

(A) 8/8 = 8(B) 15/3 = 5(C) 16/5 = 3⅕(D) 9/2 = 4½(E) 25/6 = 4⅙(F) 43/4 = 10¾(G) 24/2 = 12(H) 28/5 = 5⅗

What are whole numbers?A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. n amalgam of a whole number and a legal fraction is a mixed fraction.

So, the given improper fractions in the mixed or whole numbers are:

(A) 8/8 = 8(B) 15/3 = 5(C) 16/5 = 3⅕(D) 9/2 = 4½(E) 25/6 = 4⅙(F) 43/4 = 10¾(G) 24/2 = 12(H) 28/5 = 5⅗

Therefore, all the improper fractions in mixed or whole numbers are as follows:

(A) 8/8 = 8(B) 15/3 = 5(C) 16/5 = 3⅕(D) 9/2 = 4½(E) 25/6 = 4⅙(F) 43/4 = 10¾(G) 24/2 = 12(H) 28/5 = 5⅗

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- Lyra was trying to determine the slope ratio for the triangle at right, and she
says the answer is 2.675. Isiah claims that cannot be correct. Who is
right? How do you know?

Answers

Answer:

  Isiah is correct. The slope is about 0.344.

Step-by-step explanation:

Lyra and Isiah want the slope of the hypotenuse in a triangle with an angle of elevation of 19°.

Slope

The slope is the ratio of "rise" to "run". In a right triangle, that is the ratio "opposite"/"adjacent". This ratio is the tangent of the angle of elevation.

  tan(19°) ≈ 0.344

The slope is about 0.344. Isiah is correct.

Isiah knows Lyra is not correct because the slope in a triangle with a 45° angle is 1. Lyra' value of 2.675 is about right for an angle of 69.5°, much greater than either 45° or the given angle of 19°.

__

Additional comment

Unfortunately, the diagram is not drawn to scale. This is often the case with diagrams in geometry problems. The diagram here is misleading in that it seems to show a slope greater than 1 for a 19° angle.

2x-84=108
x=?

please help ​

Answers

Answer:

X=

Step-by-step explanation:

Let's solve your equation step-by-step.

2x−84=108x

Step 1: Subtract 108x from both sides.

2x−84−108x=108x−108x

−106x−84=0

Step 2: Add 84 to both sides.

−106x−84+84=0+84

−106x=84

Step 3: Divide both sides by -106.

−106x

−106

=

84/−106x=−42/53

What’s the answer plss someone help

Answers

The value of x in the given figure is x = 22.56 m .

In the question ,

a figure is given where the measure of angle(C) = 70° and angle(A) = 30°

In the triangle ABC ,

By Angle Sum Property Of Triangle  

angleA + angleB + angleC = 180°

30° + angleB + 70° = 180°

angleB = 180° - 100°

angle(B) = 80°

By using Sine Law ,

a/Sin(A) = x/Sin(C)

From the figure ,

a = 12 m

we get ,

12/Sin(30°) = x/Sin(70°)

x = (Sin70° × 12)/Sin(30°)

x = 11.2763/0.5

x = 22.5526

x ≈ 22.56 m

Therefore , The value of x in the given figure is x = 22.56 m .

The given question is incomplete , the complete question is

Find the value of x in the given figure ?

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tickets for a community theater cost $11 for each main floor seat and $6 for each balcony seat. there are 400 seats on the main floor, and these seats were sold out for the evening performance. the total revenue from ticket sales was $5060. how many balcony seats were sold?

Answers

The number of balcony seats sold is 110

Finding Unknown quantity using Linear equation:

The linear equation is an equation that is used to find an unknown quantity or an unknown number. In this, we will represent the Uknown value with a variable like x, y, z, etc.  

Here we have

Tickets for a community theater cost $11 for each main-floor seat
and $6 for each balcony seat.

There are 400 seats on the main floor, which are sold out for the evening performance  

The total revenue from ticket sales was $5060.

Here we don't know the number of balcony seats.

Let us assume that number of balcony seats = x

Then total revenue = 400(11) + 6x = 5060

=> 4400 + 6x = 5060

=> 6x = 5060 - 4400

=> 6x = 660

=> x = 110  

Therefore,

The number of balcony seats sold = 110

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Find the total surface area of the cone in the figure. (Use π = 3. 14. )

Question 12 options:


A)


266. 9 cm2


B)


219. 8 cm2


C)


314. 0 cm2


D)


282. 6 cm2

Answers

The correct option A, 266. 9 cm²;  total surface area of the cone given in figure is found as 266.9 sq cm.

Define the term surface area of cone?A cone's surface area is the total area that its surface takes up in a 3D plane. That curved surface area plus its circular base area will add up to the object's total surface area.A cone's surface area is calculated as the sum of its curved surface area and base area, or πr² + πrL, where r is the radius of the cone's base and L is its slant height.

For the given question.

Height of cone  - 12 cm Radius of cone - 5 cm π = 3. 14

Put values -

Total surface area = πr (h + r)

Total surface area = 3.14 x 5 (12 + 5)

Total surface area = 3.14 x 5 x 17

Total surface area = 266.9 sq cm.

Thus, total surface area of the cone given in figure is found as 266.9 sq cm.

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PLEASE HELP FAST!!!! ILL GIVE BRAINLIEST!!!!

A linear function contains the following points.

What are the slope and y-intercept of this function?

A. The slope is 11/2
The y-intercept is (0, -5).

B. The slope is 2/11
The y-intercept is (0, -5).

C. The slope is 11/2
The y-intercept is (-5, 0).

D. The slope is 11.
The y-intercept is (0, -5).

Answers

A? seems like the only right answer here ?

Carlos’s is a receptionist at a law firm, he spend 2 minutes routing each phone call as it come in. Write an equation that shows how the total number of minutes Carlos spend routing call y depend on the number of call x

Answers

Answer: 2y   or   2 x y

Step-by-step explanation:

2 times the minutes

therefor if carlos answers 4 calls, you would say 2 x 4 and you ranswer would be 8 minutes.

If $3000 is invested at tan interest rate if 4.8%, compounded hourly for two years what is the ending balance?

Answers

The final balance is $97,920.

Compound interest is calculated on the principal as well as the interest accumulated over the previous period. It differs from simple interest in that interest is not added to the principal when calculating interest for the following period.

Given this, The principal is $3000.

Interest rate = 4.8%

Time = 2 years We must find the final balance.

The end balance formula is

C = P[ 〖(1+r)〗^n – 1]

C = 3000[ 〖(1+4.8)〗^2 – 1]

C = 3000 [ 〖(5.8)〗^2 – 1]

C = 3000 [ 33.64 – 1]

C = 3000 ( 32.64)

C = 97,920

Therefore the ending balance is $97,920

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-5/8 + 1/4. Add.

Simplest form.

Answers

Answer: -3/8 or -0.375

Step-by-step explanation:

you have to get similar denominators to simplify

so times 1/4 by 2 to get 2/8

and then just do 2/8 - 5/8 and you get the answer

Brandon invested $7,900 in an account paying an interest rate of 6\tfrac{1}{8}6 8 1 ​ % compounded daily. Jacob invested $7,900 in an account paying an interest rate of 6\tfrac{5}{8}6 8 5 ​ % compounded monthly. After 15 years, how much more money would Jacob have in his account than Brandon, to the nearest dollar?

Answers

Using the properties of compound interest we can calculate that Jacob will have $1485 more than Brandon in his account.

Brandon invested $7,900 at the rate of 6 1/8% compounded daily.

Principal = $7900

Time = 15 years

Rate = 6 1/8% = 49/8 %

Amount earned after n years:

[tex]A=P (1+\frac{r}{n})^{nt}[/tex]  

Now we will use these values to find the amount at the end of 15 years.

P = 7900

r = 0.06625

n = 365

t = 15

[tex]A=P (1+\frac{.06125}{365})^{15\times 365}[/tex]

or, A = 19797.104...

or, A ≈ 19797.1

Again, Jacob invested the same sum at compound interest monthly at

6 5/8% .

Amount earned after 15 years:

P = 7900

r = 6.125

n = 12

t = 15

[tex]A=P (1+\frac{.06625}{12})^{15\times 12}[/tex]

or, A = 21282.383..

or, A ≈ 21282.38

Amount earned by Jacob more than Brandon

= $21282.38 - $19797.1

= $148785.283..

≈ $1485

Hence Jacob will have $1485 more than Brandon in his account.

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how many one-to-one functions are there from a set with five elements to sets with the following number of elements? a) 4 b) 5 c) 6 d) 7

Answers

a)4

so it's seven factorial divided by 7-5 factorial

Plot the image of point P under a translation by 7 units to the left.

Answers

Answer:

-1,4

Step-by-step explanation:

move the point to the left 7 times

Solve the double-ended inequality:
2x-5<4x+2<2x-3

Answer: _ _ x _ _

Answer with a number in the first box, inequality in the second box, than after the x an inequality in the 3rd box and a number in the last box.

EG 5 > x > 18

Answers

The solution of the double-ended inequality is -7/2 < x < -5/2

Solving Linear Inequalities

From the question, we are to solve the doubled ended inequality.

The given inequality is

2x - 5 < 4x + 2 < 2x -3

From the inequality, we can write that

2x - 5 < 4x + 2 and 4x + 2 < 2x - 3

Now, we will solve each of the inequalities separately

Solving 2x - 5 < 4x + 2

Add 5 to both sides

2x - 5 + 5 < 4x + 2 + 5

2x < 4x + 7

Subtract 4x from both sides

2x - 4x < 4x - 4x + 7

-2x < 7

Divide both sides by -2 and reverse the sign

x > -7/2

-7/2 < x

Solving 4x + 2 < 2x - 3

Subtract 2x from both sides of the equation

4x - 2x + 2 < 2x - 2x -3

2x + 2 < -3

Subtract 2 from both sides

2x + 2 -2 < -3 - 2

2x < -5

Divide both sides by 2

x < -5/2

Putting the two solutions together, we get

-7/2 < x and x < -5/2

-7/2 < x < -5/2

Hence, the solution is -7/2 < x < -5/2

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Shaq is climbing on the side of a mountain. From a spot on the
4
1/2 of
mountain, he climbs up of a kilometer. He then climbs down
5
a kilometer. How many kilometers is Shaq from his original starting
point?

Answers

In linear equation, 22.5 kilometer  is Shaq from his original starting point.

What is linear equation?

The algebraic equation y=mx+b is known as a linear equation. m being the slope and b being the y-intercept, and just a constant and a first-order (linear) term are used. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

Shaq is he climbs up on the side of a mountain = 4 1/2 = 9/2

  then he climbs down = 5 kilometer

Shaq from his original starting point = 9/2 * 5

                                                          = 45/2 = 22.5 kilometer

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1
Writing the function f(x) = 4x + 2, what does f(x) represent?

Answers

The phrase [tex]f (x)[/tex] denotes a formula with [tex]x[/tex] serving as its input variable. Not multiply f and x, though!

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable .

The x in [tex]f(x)[/tex] is referred to the argument of the function or simply the argument in function notation. Therefore, the response is just 2 if they ask for a argument and give you the equation [tex]f(2)[/tex].

Hence,  the phrase [tex]f (x)[/tex] represents a formula with [tex]x[/tex] serving as its input variable.

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Write the coordinates of the verticals after a rotation 90 degrees counterclockwise around the origin

Answers

After a counterclockwise 90° rotation, the coordinates of A'B'C' are:

A' = (3, 3)B' = (6, 5)C' = (3, 6)

What are Coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.The origin is the point at which all lines in a coordinate system intersect. When x and y are both equal to zero, the axes intersect. The origin's coordinates are (0, 0). The coordinates of one point in the coordinate system are included in an ordered pair.

So, the coordinates after the counterclockwise rotation of 90°:

The coordinates of ABC are:A = (3, -3)B = (6, -3)C = (5, -6)

After counterclockwise 90° rotation, coordinates of A'B'C' are:

A' = (3, 3)B' = (6, 5)C' = (3, 6)

(Refer to the graph attached below)

Therefore, after a counterclockwise 90° rotation, the coordinates of A'B'C' are:

A' = (3, 3)B' = (6, 5)C' = (3, 6)

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PLEASE HELP!!!
The two lines graphed below are parallel. How many solutions are there to the system of equations?
A. Zero
B. Two
C. One
D. Infinitely many

Answers

Answer:

Step-by-step explanation:

It would be D.

Arianna is going to use a computer at an internet cafe. The cafe charges an initial fee to use the computer and then an additional price per minute of usage. Let
C
C represent the total cost of using a computer for
t
t minutes at the internet cafe. The table below has select values showing the linear relationship between
t
t and
C
.
C. Determine the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

Answers

Using the linear function, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.

In the given question,

Arianna is going to use a computer at an internet cafe.

The cafe charges an initial fee to use the computer and then an additional price per minute of usage.

Let C represent the total cost of using a computer for t minutes at the internet cafe.

We have to determine the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

The additional change per unit = Slope of the linear function

The linear function C(t) given as;

C(t)=mt+b...............(1)

where m=slope and b=vertical intercept

Then, Slope = change in C(t)/change in t

Slope = ∆C(t)/∆t

We taking he given two point to find the slope

C(t) = 9.90 for t=1

C(t) = 15.30 for t=7

∆C(t)=15.30-9.90

∆C(t)=5.40

∆t=7-1

∆t=6

So, The required slope=5.40/6

The required slope=0.9=m

Now finding the value of b.

As we know that,

C(t) = 9.90 for t=1

The equation using this should be

9.90=m×1+b

Now putting the value of m in this equation

9.90=0.9×1+b

9.90=0.9+b

Subtract 0.9 on both side, we get

b=9

Now finding the number of minutes Arianna can use a computer if she only has $15.75 available to pay.

Putting the value in equation (1)

15.75=0.9t+9

Subtract 9 on both side

15.75-9=0.9t+9-9

0.9t=6.75

Divide by 0.9 on both side

0.9/0.9 t=6.75/0.9

t=7.5

Hence, the number of minutes Arianna can use a computer if she only has $15.75 available to pay is 7.5 minutes.

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Two families go to a zoo. The Smith family of two adults and three children pay £61. The Jones family of three adults and five children pay £96. Work out the cost of an adult ticket and the cost of a child ticket. In your working, let 'a' stand for an adult ticket and 'c' stand for a child ticket.​

Answers

The cost of an adult ticket is £17 and a child ticket is £9.

Let's assume 'a'  for an adult ticket and 'c' for a child ticket

The cost of tickets for the Smith family of 2 adults and 3 children is £61

Equating, [tex]2a+3c=61[/tex]

[tex]2a=61-3c[/tex]

Dividing by 2, [tex]a=30.5-1.5c[/tex]        (equation 1)

Now, the cost of tickets for the Jones family of three adults and five children is £96

Equating, [tex]3a+5c=96[/tex]                 (equation 2)

Using equation 1, [tex]3(30.5-1.5c)+5c=96[/tex]

[tex]91.5-4.5c+5c=96[/tex]

[tex]91.5+0.5c=96[/tex]

[tex]0.5c=96-91.5[/tex]

[tex]0.5c=4.5[/tex]

[tex]c = \frac{4.5}{0.5}[/tex]

[tex]c=9[/tex]

Similarly, putting the answer of equation 2 in equation 1

we get, [tex]a=30.5-1.5c[/tex]

[tex]a=30.5-1.5(9)[/tex]

[tex]a=17[/tex]

Therefore, adult tickets cost £17 and child tickets cost £9

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Elena had 24 base hits in 110 at bats. She has done a lot of practice and now thinks that for all of her future at bats in this season, she will have a batting average of 0.350. If she does, then how many more at bats will Elena need so that with this average, she reaches a 0.300 batting average overall for the whole season?

Answers

Elena will need 180 more bats

Let she bats  b more needs

Total bats =  110 + b

Base hits = 24 + 0.35 b

From the question, we have

( 24 + 0.35b) / (110 + b) = 0.300

24 + 0.35b = 33 + 0.3 b

0.05 b = 9

b = 9 / 0.05 = 180

Subtraction:

The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.

The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference. As the first integer to be subtracted from in a subtraction phrase, a minuend is the first number in the subtraction process.

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help meeeeeeeeeeeeeee pleaseee

Answers

The table of solutions should be completed based on the given equation (y = 2x²) as follows:

x                    y_

-2                  8

-1                   2

0                   0

1                    2

2                   8

Also, a graph of the solution to the given equation is shown in the image attached below.

What is a graph?

In Mathematics, a graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would complete the table based on the given equation as follows:

When x = -2, the value of point y is given by:

y = 2x²

y = 2(-2)²

y = 2 × 4

y = 8

When x = -1, the value of point y is given by:

y = 2x²

y = 2(-1)²

y = 2 × 1

y = 2

When x = 0, the value of point y is given by:

y = 2x²

y = 2(0)²

y = 2 × 0

y = 0

When x = 1, the value of point y is given by:

y = 2x²

y = 2(1)²

y = 2 × 1

y = 2

When x = 2, the value of point y is given by:

y = 2x²

y = 2(2)²

y = 2 × 4

y = 8

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express (3) - (2tan^2 x) in terms of cos x

Answers

The expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. Similarly, any tirigonometric equation can be convereted into other forms of trigonometric functions.

What is trigonometric functions?

Denoting the relation between a right-angled triangle's angle and sides are trigonometric functions, which are periodic functions.

Consider the given expression.

[tex]3-2tan^2x\\[/tex]

Now, substitute [tex]\frac{sinx}{cosx}[/tex] for [tex]tanx[/tex] as follows:

[tex]3-2tan^2x=3-2(\frac{sinx}{cosx})^2\\=3-2(\frac{sin^2x}{cos^2x})[/tex]

Now, all the terms are converted into cos x except the sin x terms in the numerator. Hence, using the relation between sin x and cos x. Substitute [tex]1-cos^2x[/tex] for [tex]sin^2x[/tex].

[tex]3-2tan^2x=3-2(\frac{1-cos^2x}{cos^2x})[/tex]

Now, all the terms are in cos x. Hence, the expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. In the similar way any function can be conveted into other trigonometric functions.

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What value of b will complete the square in the expression below and make the
expression a perfect square trinomial?
x²+bx+144
Enter the perfect square trinomial as a squared binomial.

Answers

At b= 24 will complete the square in the expression x^2 + bx + 144.

What is perfect square trinomial?

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b^2 = 4ac has the form ax^2 + bx + c, it is said to be a perfect square. The formula for the perfect square trinomial is (ax)^2 + 2abx + b^2 = (ax + b)^2.

Consider the given expression

x^2 + bx + 144

For this type of expression [tex]b = 2\sqrt{c}[/tex] will complete the square.

Here, c = 144

√144 = 12

So, b√c = 2(12) = 24

The expression becomes,

x^2 + 24x + 144 = (x + 12)^2

This is the perfect square.

Hence, b = 24  will complete the square in the expression x^2 + bx + 144.

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Compute and expressed the result as a mixed fraction?

1) 2+ 3/4

Answers

Answer:

2 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

2 + [tex]\frac{3}{4}[/tex]

= 2 [tex]\frac{3}{4}[/tex] ← as a mixed number

The manager of a large ocean front hotel would like to survey their guests to determine their satisfaction with the view from their room. The hotel has 10 floors. Half of the rooms overlook the ocean and the other half overlook the street. There are 50 rooms on each floor, for a total of 500 rooms. The hotel manager would like to select a sample of 50 rooms.

Answers

A stratified sample in this case can be selected as follows:

The rooms are divided by whether they overlook the ocean or the street, and 25 of each are selected.

How are samples classified?

The five most common classifications for sampling are listed as follows:

A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.

In this problem, the groups are given as follows:

Floors overlooking the ocean.Floors overlooking the street.

50 rooms will be sampled, hence the number that is sampled from each group is given as follows:

50/2 = 25 rooms from each group.

Missing Information

The problem asks to describe a stratified sample for this situation.

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what is the sum between 6/9 and 3/6

Answers

Answer:

21/18 or 1 and 3/18

Step-by-step explanation:

6/9 = 12/18

3/6 = 9/18

12/18 + 9/18 = 21/18 or 1 3/18

Answer:

[tex] \frac{6}{9} + \frac{3}{6} \\ \\ = \frac{2 \times 6 + 3 \times 3}{18} = \frac{12 + 9}{18} = \frac{21}{18} = \frac{7}{6} = 1 \frac{1}{6} [/tex]

the measure of each side of an equilateral triangle whose are is [tex]\sqrt{3}[/tex] cm² is

Brainlist

Answers

The measure of each side of an equilateral triangle is 2 cm whose area is √3 cm square.

What is a Triangle?

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.

We have been given the measure of each side of an equilateral triangle whose area is √3 cm².

Let the measure of each side would be "a"

We know that,

Area of an equilateral triangle = √3a² / 4

As per the question,

⇒ √3 cm²= √3a² / 4

⇒ √3a² = 4√3 / √3

⇒ a² = 4 = √4

⇒ a = 2 cm

Thus, the measure of each side of an equilateral triangle is 2 cm whose area is √3 cm square.

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A right triangle's hypotenuse is 1 cm longer than twice the length of the shortest side.
The third side is 1 cm less than twice the shortest side.
Find the length (in cm) of the hypotenuse.

Answers

Answer:

  17 cm

Step-by-step explanation:

You want the hypotenuse (c) in a right triangle that has c=2a+1, b=2a-1.

Pythagorean theorem

The relation between the side lengths in the right triangle is ...

  a² +b² = c²

Application

Substituting the given relations, we have ...

  a² +(2a-1)² = (2a+1)²

  a² +4a² -4a +1 = 4a² +4a +1

  a² -8a = 0 . . . . . . write in standard form

  a(a -8) = 0 . . . . . . factor

  a = 0 or a = 8

We are almost never concerned with triangles that have 0 area, so the solution of interest is a=8. Then the hypotenuse is ...

  c = 2(8) +1 = 17

The hypotenuse is 17 cm.

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Additional comment

You may recognize these side lengths as the (8, 15, 17) Pythagorean triple.

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