Solve equation for x
216=6^4x+5

Answer:

Step-by-step explanation:

You can’t solve this equation as none of the numbers have the same coefficient to solve. If you wanted to solve for x and y, you will need two equations as there are two unknown variables in the equation and the only way to solve for x and y is to use simultaneous method which includes two equations.

The vertices of the resulting image, quadrilateral H’ I’ J’ K’ include the following:

H' (4, -1).

I' (2, -3).

J' (-4, 1).

K' (-2, 3).

In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, rotating a point 270° about the origin would produce a point that has the coordinates (y, -x).

By applying a rotation of 270° about the origin to quadrilateral HIJK, the location of its vertices is given by:

(x, y)                                   →         (y, -x)

Ordered pair H (1, 4)        →    Ordered pair H' (4, -(1)) =  (4, -1).

Ordered pair I (3, 2)        →    Ordered pair I' (2, -(3)) =  (2, -3).

Ordered pair J (-1, -4)        →    Ordered pair J' (-4, -(-1)) =  (-4, 1).

Ordered pair K (-3, -2)        →    Ordered pair K' (-2, -(-3)) =  (-2, 3).

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Yes, every odd integer can be written as the difference of two squares.

To prove this, let k be a positive integer. Then the difference of the squares of k+1 and k is (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1, which is an odd integer. Thus, every odd integer can be written as the difference of two squares.

To prove this, we first chose a positive integer, k. We then found the difference of the squares of k+1 and k to be (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1. Since 2k + 1 is an odd integer, it follows that every odd integer is the difference of two squares.

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Answer:

(a - 1)(3p - 2)

Step-by-step explanation:

3p(a - 1) - 2(a - 1) ← factor out (a - 1) from each term

= (a - 1)(3p - 2)

The number we are looking for is N = 2 × 2^3 × 3^2 = 72.

Let's first recall some properties of the number of divisors of an integer. If we factorize an integer n as a product of prime powers, say

n = p_1^a_1 × p_2^a_2 × ... × p_k^a_k

then the number of divisors of n is given by

d(n) = (a_1 + 1) × (a_2 + 1) × ... × (a_k + 1).

Using this fact, we can deduce some information about the number we are looking for. Let's call it N. We know that N has 8 divisors, so it must be of the form

N = p_1^2 × p_2^2, or N = p_1^7,

where p_1 and p_2 are distinct prime numbers.

Now, we are told that each of N/2 and N/3 has four divisors. We can use the same fact about the number of divisors to conclude that

N/2 = q_1^3 × q_2, or N/2 = q_1^1 × q_2^3,

and

N/3 = r_1^3 × r_2, or N/3 = r_1^1 × r_2^3,

where q_1, q_2, r_1, and r_2 are distinct prime numbers.

To simplify the notation, let's introduce the variables a, b, c, d, e, and f, defined by

p_1 = q_1^a × q_2^b,

p_2 = r_1^c × r_2^d,

N/2 = q_1^e × q_2^f,

N/3 = r_1^g × r_2^h.

Using the information we have so far, we can write down equations for a, b, c, d, e, f, g, and h in terms of unknown exponents:

a + 1 × (b + 1) = e + 1 × (f + 1) = 4,

c + 1 × (d + 1) = g + 1 × (h + 1) = 4,

2a × 2b = ef,

2c × 2d = gh.

We can solve this system of equations by trial and error. For example, we can start by trying all possible values of a and b such that 2a × 2b = 4. This gives us two possibilities: a = 0, b = 2, or a = 1, b = 1. Using the first possibility, we get e = 3, f = 1, which leads to N/2 = q_1^3 × q_2, and hence N = 2 × q_1^3 × q_2^2. Substituting this into the equation for the sum of divisors, we get

(1 + q_1 + q_1^2 + q_1^3) × (1 + q_2 + q_2^2) = 216.

We can solve this equation by trial and error as well, or by observing that 216 = 2^3 × 3^3, and hence the two factors on the left-hand side must be equal to 2^3 and 3^3, respectively. This gives us the unique solution q_1 = 2 and q_2 = 3, and hence N = 2 × 2^3 × 3^2 = 72.

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The value of the unknown lengths in these similar triangles is FH is 6.67 units and EG is 27 units.

A triangle is a polygon with three sides and three angles. It is a two-dimensional shape that is commonly studied in mathematics, geometry, and other fields. The sum of the angles in a triangle is always 180 degrees, and the lengths of the sides can vary. Triangles can be classified based on the lengths of their sides and the measures of their angles. Common types of triangles include equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have many important properties and are used in various applications, including construction, engineering, and physics.

Here,

1. Let x be the length of FH. We have:

AB/EF = BD/FH

12/8 = 10/x

Cross-multiplying, we get:

12x = 80

x = 80/12

x ≈ 6.67

Therefore, FH ≈ 6.67.

2. Let y be the length of EG. We have:

AC/BD = FH/EG

15/9 = 5/y

Cross-multiplying, we get:

5y = 135

y = 135/5

y ≈ 27

Therefore, EG ≈ 27.

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Answer: Let x be the number of hamburgers sold.

Then, the number of cheeseburgers sold is 3x.

The total number of burgers sold is x + 3x = 4x.

Given that the total number of burgers sold is 416, we have:

4x = 416

x = 416/4

x = 104

Therefore, 104 hamburgers were sold.

Step-by-step explanation:

Total seats in plane: 186

108+64+14

5/7 of 14 is: 10

14÷7= 2

2x5= 10

5/16 of 64 is: 20

64÷16=4

5×4= 20

5/9 of 108 is: 60

108÷9= 12

12x5= 60

60+20+10=90

90/186 of seats are being used

simplified: 15/31

No

If an angle of measurement of 140° then; a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.0233 cm times as long as 1/360th of the circumference of the circle. Also if a circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long then length of the arc subtended by the angle's rays 8.4 cm. Another circle is centered at the vertex of the angle then arc subtended by the angle's rays is 70 cm long,Therefore the circumference of the circle is 180 cm.

a.) To find the fraction of the circle's circumference subtended by the angle's rays, we divide the angle measure by 360 degrees:

fraction of circle's circumference = 140/360

Simplifying this fraction, we get:

fraction of circle's circumference = 7/18

To find the length of the arc subtended by the angle's rays, we multiply the fraction of the circle's circumference by the circumference of the circle. Let's call the circumference of the circle "C":

length of arc = (7/18)*C

We're also told that the length of 1/360th of the circumference is equal to 0.06 cm. So, we can write:

(1/360)*C = 0.06

Multiplying both sides by 360, we get:

C = 360*0.06 = 21.6 cm

Now, we can substitute this value of C into the expression for the length of the arc:

length of arc = (7/18)*C

length of arc = (7/18)*(21.6)

length of arc = 8.4 cm (rounded to one decimal place)

Therefore, the length of the arc subtended by the angle's rays is 8.4 cm.

b.) We're given that 1/360th of the circumference of the circle is 0.06 cm long. To find the length of the arc subtended by the angle's rays, we need to multiply 140/360 by 0.06:

length of arc = (140/360)*0.06

length of arc = 0.0233 cm (rounded to four decimal places)

Therefore, the length of the arc subtended by the angle's rays is approximately 0.0233 cm.

c.) We're told that the length of the arc subtended by the angle's rays is 70 cm. To find the circumference of the circle, we need to find the length of 1/360th of the circumference first. We can do this by dividing 70 by 1/360:

(1/360)*C = 70

Multiplying both sides by 360, we get:

C = 70*360 = 25,200 cm

Therefore, the circumference of the circle is 25,200 cm. We can also verify this by dividing the length of the arc by the fraction of the circumference subtended by the angle's rays:

length of arc = (7/18)*C

C = (18/7)*length of arc

C = (18/7)*70

C = 180 cm (rounded to one decimal place)

This is a different value than we got earlier, so we need to check our calculations. It turns out that the previous calculation was incorrect - we made a mistake when multiplying 7/18 by 21.6. The correct calculation gives us:

length of arc = (7/18)*C

length of arc = (7/18)*(21.6)

length of arc = 8.4 cm (rounded to one decimal place)

Now, we can calculate the circumference of the circle:

length of arc = (7/18)C

C = (18/7) *length of arc

C = (18/7) *70

C = 180 cm (rounded to one decimal place)

Therefore, the circumference of the circle is 180 cm.

Also, If an angle of measurement of 140° then; a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.0233 cm times as long as 1/360th of the circumference of the circle.

b. A circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long.The length of the arc subtended by the angle's rays 8.4 cm

c. Another circle is centered at the vertex of the angle.

The arc subtended by the angle's rays is 70 cm long,Therefore the circumference of the circle is 180 cm.

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The 12 months of age) as percentiles of the CDC growth chart reference population.

The most likely description of Sarah's weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population is: 85th percentile at 3 months; 85th percentile at 6 months; 90th percentile at 9 months; 95th percentile at 12 months.What is percentile in statistics?In statistics, a percentile is a value below which a specific percentage of observations in a group falls. It is used to split up data into segments that represent an equal proportion of the entire group, resulting in a data set split into 100 equal portions, with each portion representing one percentage point. Sarah's weight is in the 85th percentile at 3 months, 85th percentile at 6 months, 90th percentile at 9 months, and 95th percentile at 12 months is a most likely description of her weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population.

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We can graph this solution on the number line by placing a point at 7.6.

Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.

80∠ 10x + 4 = 20

80 10x + 4 = 20

80 - 4 = 10x

76 = 10x

7.6 = x

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We can graph this solution on the number line by placing a point at 7.6.

Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.

80∠ 10x + 4 = 20
80 10x + 4 = 20
80 - 4 = 10x
76 = 10x
7.6 = x

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Yes, W_2 = {p_2 = a_2t_2 + a_1t + a_0 ∈ ℙ_2 | a_0 = 2} is a subspace of the vector space ℙ_2.

Yes, W_1 = {[a b c; d 0 0] ∈ M_{2x3} | b = a + c} is a subspace of the vector space M_{2x3}.

Vector spaces are closed under vector addition and scalar multiplication, and in this case, ℙ_2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.

Vector spaces are closed under vector addition and scalar multiplication, and in this case, M_{2x3} is the set of all 2x3 matrices with the standard matrix addition and scalar multiplication with reals.

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Answer:

[tex]x = 4\sqrt{3}[/tex]

Step-by-step explanation:

The triangle is right-angled

In a right-angled triangle, the following equality holds

[tex]\tan x = \dfrac{\text{Side Opposite x}}{\text{Side adjacent to x}}\\\\\tan 30 = \dfrac{4}{x}\\\\[/tex]

[tex]\tan 30 = \dfrac{1}{\sqrt{3}}\\\\\dfrac{1}{\sqrt{3}} = \dfrac{4}{x}\\\\[/tex]

Cross multiply:
[tex]1 \times x = 4 \times \sqrt{3}\\\\x = 4\sqrt{3}[/tex]

Probability of D2 being sunny = 0.78.

On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.

Therefore, we need to find the chances that D2 is sunny.

There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.

Now, Let us find the probability of D2 being sunny.

We have the following possible cases for D2.

D1 = Sunny; D2 = Sunny

D1 = Sunny; D2 = Rainy

D1 = Rainy; D2 = Sunny

D1 = Rainy; D2 = Rainy

The probability of D1 being sunny is 0.9.

When a sunny day follows a sunny day, the probability is 0.8.

When a sunny day follows a rainy day, the probability is 0.6.

Therefore, the probability of D2 being sunny is given by the formula:

Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.

Therefore, the probability that D2 is sunny are 0.78 or 78%.

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As per the equations, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.

Factoring is the process of breaking down a mathematical expression or number into its component parts, which can then be multiplied together to give the original expression or number. In algebra, factoring is often used to simplify or solve equations.

An equation is a statement that shows the equality of two expressions, typically separated by an equals sign (=). The expressions on both sides of the equals sign are called the "left-hand side" and "right-hand side" of the equation.

In the given question,

Let's call the age of the first dog "x" and the age of the second dog "y". We know that their ages add up to 15, so we can write:

x + y = 15

We also know that their ages multiply to 44, so we can write:

x * y = 44

Now we have two equations with two unknowns, which we can solve simultaneously to find the values of x and y.

One way to do this is to use substitution. From the first equation, we can solve for one variable in terms of the other:

y = 15 - x

We can substitute this expression for y into the second equation:

x × (15 - x) = 44

Expanding the left side, we get:

15x - x^2 = 44

Rearranging and simplifying, we get a quadratic equation:

x^2 - 15x + 44 = 0

We can factor this equation as:

(x - 11)(x - 4) = 0

Using the zero product property, we know that this equation is true when either (x - 11) = 0 or (x - 4) = 0.

Therefore, the possible values of x are x = 11 and x = 4.If x = 11, then y = 15 - x = 4, which means that the ages of the two dogs are 11 and 4.

If x = 4, then y = 15 - x = 11, which means that the ages of the two dogs are 4 and 11.

Therefore, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.

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The speed (in knots) at which the distance between the ships A and B is changing at 6 PM is given as 36 knots or 36 nautical miles per hour.

Consider that the ship A is in the west direction and the ship B is in the north direction and both the ships are in regular motion of speed which is 16 knots and 15 knots and the distance between them is 50 nautical miles.

Using the Pythagoras theorem, the relation of the distance x which represents the distance between ships at 6PM to the distances that each ship has travelled can be given as follows:

x^2 = (50 + 16t)^2 + (15t)^2

where, t is the number of hours that has passed since noon.

Differentiating both sides of the above equation with respect to time, we get:

2x*(dx/dt) = 2(50 + 16t)*(16) + 2*(15t)*(15)

t = 6, at 6 PM, therefore substituting the value and solving, we get:

2x(dx/dt) = 2[(50 + 16(6)]*(16) + 2*[15(6)]*(15)

2x(dx/dt) = 4194

dx/dt = 2097/x

Now substituting the value of x that corresponds to 6 PM:

x^2 = (50 + 16(6))^2 + (15(6))^2

x^2 = 3385

x = √3385 ≅ 58.19

Putting this value in dx/dt, we get:

dx/dt = 2097/58.19 ≅ 36.00 knots

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the sale price of the cell phone after the 35% discount is $315.25.

How to solve and what is sale?

To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:

Sale price = Regular price - Discount amount

Sale price = $485 - (0.35 x $485)

Sale price = $485 - $169.75

Sale price = $315.25

Therefore, the sale price of the cell phone after the 35% discount is $315.25.

A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.

In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.

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The contrapositive of the given statement is "If it is not a cat, then it is a lion."

The contrapositive of the statement "If it is not a lion, then it is a cat" can be obtained by negating the original statement and switching the positions of the antecedent (the "if" part) and the consequent (the "then" part).

The contrapositive takes the form:

"If it is not a cat, then it is a lion."

So, the contrapositive of the given statement is "If it is not a cat, then it is a lion."

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Answer:

x = 45.

Step-by-step explanation:

Given a straight line with the equation.

First collect like terms:

2x + x = 180 - 45

Then calculate:

3x = 135

Finally after dividing both sides by 3:

x = 45

Answer:

[tex]{ \sf{a = { \blue{ \boxed{{53 \: \: \: \: \: \: \: \: }}}}} \: cm}[/tex]

Step-by-step explanation:

[tex] { \mathfrak{formular}}\dashrightarrow{ \rm{4 \times side \: length}}[/tex]

Each side has length of a?

[tex]{ \tt{perimeter = a + a + a + a}} \\ \dashrightarrow{ \tt{ \: 212 = 4a}} \\ \\ \dashrightarrow{ \tt{4a = 212}} \: \\ \\ \dashrightarrow{ \tt{a = \frac{212}{4} }} \: \: \\ \\ { \tt{a = 53 \: cm}}[/tex]

Answer:

Below

Step-by-step explanation:

Mass of bouncies + box = 17342     subtract mass of box from both sides

   mass of bouncies  =  17342 - 429 = 16913 g

Unit mass per bouncy = 505 g / 45 bouncy  

Number of Bouncies =  16913 gm / ( 505 g / 45 bouncy )  = 1507.1 bouncies

  With the given info, I am afraid it IS 1507 bouncies in the box

      maybe since the question asks for APPROXIMATE number, the answer is     1510 bouncies    ( rounded answer) ....or 1500

Answer:

-1/3

Step-by-step explanation:

Answer:

-1/3

Step-by-step explanation:

The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.

The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.

The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.

A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.

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Answer:

Y=x^2+7x-3

complete the square to re-write the quadratic function in vertex form.

pls help

Step-by-step explanation:

To complete the square, we need to add and subtract a constant term inside the parentheses, which when combined with the quadratic term will give us a perfect square trinomial.

y = x^2 + 7x - 3

y = (x^2 + 7x + ?) - ? - 3 (adding and subtracting the same constant)

y = (x^2 + 7x + (7/2)^2) - (7/2)^2 - 3 (the constant we need to add is half of the coefficient of the x-term squared)

y = (x + 7/2)^2 - 49/4 - 3

y = (x + 7/2)^2 - 61/4

So the quadratic function in vertex form is y = (x + 7/2)^2 - 61/4, which has a vertex at (-7/2, -61/4).

In Rosettenville, a suburb of Johannesburg, South Africa, Robert Brozin and Fernando Duarte acquired the Chicken Land restaurant in 1987, launching Nando's.

The eatery was renamed Nando's in honor of Fernando. The restaurant incorporated influences from former Mozambican Portuguese colonists, many of whom had relocated to Johannesburg's southeast after their country gained independence in 1975. Expansion was an essential component of their vision from the beginning. Nando's had already grown from one restaurant in 1987 to four by 1990. It became increasingly difficult to implement a common strategy and decision-making became inefficient as new outlets were maintained as separate businesses.

In 1995, Nando's International Holdings (NIH) was established as a new international holding because managing this growingly complex global structure had become extremely challenging. The South African branch of Nando's Group Holdings (NGH) was successfully listed on the Johannesburg Stock Exchange on April 27, 1997. NGH was 54% owned by NIH, with the remaining 26% available to the general public and former joint venture partners. The main goals of the share offer and listing were to broaden the group's capital base and enable group restructuring.

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The solutions to the equation are x = -4 and x = 1.

The quadratic formula, which is often employed in the disciplines of mathematics, physics, engineering, and other sciences, is a potent tool for resolving quadratic problems. We must first get the values of a, b, and c from the quadratic equation in order to apply the quadratic formula. To get the answers for x, we then enter these values as substitutes in the formula and simplify.

The given equation is 4x² + 6x - 13 = 3x².

Rearranging the equation we have:

x² + 6x - 13 = 0

The quadratic formula is given as:

x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a = 1, b = 6, and c = -13.

x = (-6 ± √(6² - 4(1)(-13))) / 2(1)

x = (-6 ± √(100)) / 2

x = (-6 ± 10) / 2

x = -8/2 or x = 2/2

x = -4 or x = 1

Hence, the solutions to the equation are x = -4 and x = 1

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The expressions that are equivalent to (x-2)² is x² - 4x + 4. (option B)

Now, let's look at the expression (x-2)². This is a binomial expression that can be simplified by applying the rules of exponents. Specifically, we can expand this expression as follows:

(x-2)² = (x-2) * (x-2)

= x * x - 2 * x - 2 * x + 2 * 2

= x² - 4x + 4

So, the expression (x-2)² is equivalent to x² - 4x + 4.

However, the problem asks us to identify other expressions that are equivalent to (x-2)². To do this, we can use the process of factoring. We know that (x-2)² can be factored as (x-2) * (x-2). Using this factorization, we can rewrite (x-2)² as:

(x-2)² = (x-2) * (x-2)

= (x-2)²

So, (x-2)² is equivalent to itself.

Hence the correct option is (B).

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Complete Question:

Which expressions are equivalent to (x−2)²?

Select the correct choice.

A. (x + 2) (x - 2)

B. x² - 4x + 4

C. x² - 2x + 5

D. x² + x - 2x

Answer:

-12 is the y intercept while your slope is -4

Step-by-step explanation:

If a triangle with all sides of equal length has a perimeter of 15x + 27, the expression for the length of one of the sides is (5x + 9).

The perimeter of a triangle is the sum of the lengths of all three sides. If all the sides of the triangle are equal, you can find the length of one side by dividing the perimeter by 3. Here, the perimeter is given as 15x + 27. Therefore, the length of one side will be (15x + 27) / 3 = 5x + 9. Hence, an expression for the length of one of the sides is (5x + 9).

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