How do you solve a 3 by 3 system of equations using matrices?

[tex]x^2[/tex] - (b+c)x +bc=0  is the quadratic equation whose roots are b,c.

If the roots of a quadratic equation are given, the equation can be written by factoring the equation using the roots.

Given the roots, let's say r1 and r2, the quadratic equation can be written as (x - r1)(x - r2) = 0.

Expanding the above equation x^2 - (r1 + r2)x + r1r2 = 0

Therefore, if the roots of a quadratic equation are given as r1 and r2, the quadratic equation can be written as:

x^2 - (r1 + r2)x + r1r2 = 0

since we are given that the root of the equation are b,c;

so r1=b,r2=c;

putting the value in the above equation we get the equation with b and c as root:

[tex]x^2[/tex] - (b+c)x +bc=0

To know more about quadratic equation click on below link:

https://brainly.com/question/30098550#

#SPJ4

Complete question :

The coefficient b and c in the equation [tex]x^2+bx+c[/tex] is also root of another equation where c≠0 .

please write the equation

In algebra, a symbol is used to denote an unknown numerical value in an equation or algebraic expression.

A variable in mathematics is a letter that is substituted for an unknown integer in equations, expressions, and formulas.

An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed.

The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.

A.) (x) ≈ 0.572[tex]$$x^4[/tex] − 15.63x³ + 146.273x² − 523.325x + 687.334

Approximately 203 automobiles were produced in 2007, according to estimates.

B.) f(x) ≈ 0.423x³ − 12.463x2 + 123.485x − 223.309

Approximately 178 automobiles were produced in 2007, according to estimates.

C.) f(x) ≈ 0.572[tex]$$x^4[/tex] + 15.63x³ − 146.273x² − 523.325x + 687.334

Approximately 203 automobiles were produced in 2007, according to estimates.

D.) f(x) ≈ 0.423x³ + 12.463x² − 123.485x + 223.309

Approximately 178 automobiles were produced in 2007, according to estimates.

To learn more about variables refer to;

https://brainly.com/question/112703

#SPJ4

Number of cars manufactured in 2007 will be equal to 178 or 203 based on quartic model.

A variable in mathematics is a letter that is substituted for an unknown integer in equations, expressions, and formulas.

An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed.

The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.

A.) (x) ≈ 0.572 − 15.63x³ + 146.273x² − 523.325x + 687.334

Approximately 203 automobiles were produced in 2007, according to estimates.

B.) f(x) ≈ 0.423x³ − 12.463x2 + 123.485x − 223.309

Approximately 178 automobiles were produced in 2007, according to estimates.

C.) f(x) ≈ 0.572 + 15.63x³ − 146.273x² − 523.325x + 687.334

Approximately 203 automobiles were produced in 2007, according to estimates.

D.) f(x) ≈ 0.423x³ + 12.463x² − 123.485x + 223.309

Approximately 178 automobiles were produced in 2007, according to estimates.

To learn more about variables refer to;

brainly.com/question/112703

#SPJ4

The value of y in the equation is y = x / 100.

Subject of the formula is a variable which is expressed in terms of other variables involved in the formula.

Therefore, let's make y the subject of the formula in the equation x = 100y.

Hence, we will find y in terms of x.

Therefore,

x = 100y

divide both sides of the equation by 100

100y  / 100 = x / 100

y = x / 100

Therefore,

y = x / 100

learn more on variable here: brainly.com/question/9144253

#SPJ1

Answer:

Acc.to question,

A+B=90° (since,they are complementary angles)

or,A+ A/2=90°(since,A is. twice the measure of B)

or,3A/2=90°

or,A=(90°×2)/3

:.A=60°

Also,

B=A/2=60/2=30°

Answer:

Mary bought the most flour

Step-by-step explanation:

Ana bought 12 3/6 kg of flour

12 3/6 = 75/6 = 12.5 kg of flour

Mary has brought 14 2/8 kg of flour

14 2/8 = 114/8 = 14.25 kg of flour

Kristina bought 11 8/12 kg of flour.

11 8/12 = 140/12 = 11.66 kg of flour

So, Mary bought the most flour.

the value of x would be 22/3 after simplification.

The acts or process of simplifying something such that it is simpler to accomplish or understand, or the item that is the consequence of such simplifying: The group offers suggestions on how to make trade procedures simpler. In mathematics, we generally use the PEMDAS method to simplify the values.

Given, the equation in the form of x is  3/4(x−8)= −1/2

For the value of x

3/4(x−8)= −1/2

multiply by 4 on both sides

3(x - 8) = -2

divide by 3 into both the sides

x - 8 = -2/3

add 8 on both sides

x = -2/3 + 8

x =  22/3

therefore, the value of x for the given equation 3/4(x−8)= −1/2 is 22/3.

Learn more about simplification here:

https://brainly.com/question/16879174

#SPJ2

Yes, isosceles triangles have three congruent angles.

An isosceles triangle is a triangle with at least two congruent sides and two congruent angles. The two congruent sides and two congruent angles form an isosceles triangle. The two congruent angles are known as the base angles, and they are opposite to the two congruent sides. The third angle in an isosceles triangle must also be congruent to the two base angles in order for the triangle to be true. This is because the angles of a triangle must always sum up to 180 degrees. Therefore, isosceles triangles have three congruent angles. These angles are all equal in measure and have the same shape. The angles of each isosceles triangle can be different from other isosceles triangles, but the angles are still congruent to each other. Therefore, isosceles triangles have three congruent angles.

Learn more about triangle here

https://brainly.com/question/2773823

#SPJ4

The length and width of the rectangle will be 16 centimeters and 13 centimeters, respectively.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

The length of a rectangle is 3cm longer than its width. If the perimeter of the rectangle is 58 cm. Then the equations are given below.

L = 3 + W                ...1

2(L + W) = 58

L + W = 29                ...2

From equations 1 and 2, then we have

3 + W + W = 29

2W = 26

W = 13 cm

Then the length of the rectangle will be given as,

L = 3 + 13

L = 16 cm

The length and width of the rectangle will be 16 centimeters and 13 centimeters, respectively.

More about the perimeter of the rectangle link is given below.

https://brainly.com/question/15287805

#SPJ1

50-3x<20

the answer is C. 11

In response to the question, we may say that As a result, the orangutan's expression mass in kilogrammes is roughly 64.55 kg.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

To convert pounds to kilogrammes, divide the pound weight by the conversion ratio of 2.2.

Hence, to calculate the orangutan's mass in kilos, do the following:

Divide the orangutan's weight in pounds by the conversion ratio of 2.2:

142 pounds divided by 2.2 is 64.54545... kilos (rounded to the nearest hundredth)

As a result, the orangutan's mass in kilogrammes is roughly 64.55 kg.

To know more about expression visit :-

https://brainly.com/question/14083225

#SPJ1

Answer:

girl I have the same question

The formula for finding the height of an isosceles triangle is h = (2*A)/b, where h is the height, A is the area of the triangle, and b is the base of the triangle.

The formula for finding the height of an isosceles triangle is h = (2*A)/b, where h is the height, A is the area of the triangle, and b is the base of the triangle. To use this formula, the area of the triangle must first be calculated. To do this, multiply the base of the triangle by its altitude, or the perpendicular distance from the base to the vertex opposite it. Once the area is known, the height of the triangle can be calculated by multiplying the area by two and dividing it by the base. This will give the height of the triangle. For example, if a triangle has a base of 5 and an area of 10, then the height of the triangle is (2*10)/5, or 4.

Learn more about isosceles triangle here

https://brainly.com/question/2456591

#SPJ4

The missing information, considering the volume of the cone and the cylinder, is given as follows:

The volume of a cylinder of radius r and height h is given as follows:

Vcy = πr²h.

The volume of a cone is one third that of the cylinder, hence:

Vco = πr²h/3.

At the second row, the volume of the cylinder is three times that of the cone, hence:

40π x 3 = 120π.

Considering the volume of the cylinder and the radius, the height is obtained as follows:

πr²h = 120π

9h = 120

h = 120/9

h = 13.3.

For the third row, we have that the base area is of 36π squared units, hence the radius is obtained as follows:

πr² = 36π

r = 6. (as the base is circular).

Hence the diameter is of 12 units, as the length of the diameter is twice that of the radius.

The volume of the cylinder is three times that of the radius, hence:

3 x 48π = 144π

Meaning that the height is then calculated as follows:

πr²h = 144π

36h = 144

h = 144/36

h = 4.

More can be learned about the volume of a cylinder at https://brainly.com/question/9554871

#SPJ1

Answer: ummm B

Step-by-step explanation:

Answer: B

Step-by-step explanation: To make his special energy drink Jerome uses 8 cups of water and 3 cups of drink mix. So the ratio of drink mix to water is 3:8.

Spiders are arachnids with eight legs, as do all arachnids. Spiders differ from insects in that they have only six legs.

Crabs and prawns are also members of the phylum Arthropoda, which includes spiders. Spiders walk on eight legs, but they also have two additional legs that they utilise as hands. The front legs are called pedipalps, or palps for short.

Proteins are secreted by glands on spiders, which aid in the formation of the web. For a number of objectives, including prey capture, prey detection, tunnel lining, egg sacs, and prey wrapping, spiders can create a variety of webs or silks.

Spiders are venomous carnivores who hunt their prey with poison.In Everglades National Park, arachnids such as spiders, scorpions, mites, ticks, whip scorpions, and pseudoscorpions are all common.

To learn more about spider refer to:

https://brainly.com/question/885563

#SPJ1

Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.

While the denominator of a percentage is always 100, a proportion is the relationship or equivalence between two ratios or fractions. Both proportion and percentage can be expressed as fractions.

A percentage is an equation in which two ratios are made equal to one another.

Out of a possible 100, the percentage is given.

Because 32 ounces is the difference between 128 and 96, making it 1/3 of 96, we can divide $4.80 by 3 to get $1.60, then add $1.60 to $4.80 to get $6.40.

Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.

The complete question is,

It cost $4.80 for a 96-ounce bottle of orange juice. How much should be charged for a 128-ounce container in order to equalize the unit rates of the two sizes? Describe your thought process.

To learn more about proportion refer to:

https://brainly.com/question/19994681

#SPJ4

The number of subscriber is increasing by factor 1,12 every month. The number of subscribers m months since the beginning of the year can expressed by the growth model equation S(m) = 150 . e^(0.12m)

The problem can be solved using exponential growth model.

1) The relation between growth rate and doubling time is given by:

doubling time = 70 / growth rate

In this case, doubling time = 6 months.

Hence,

growth rate = 70/6 = 11.67% = 0.1167 ≈ 0.12

Growth factor is defined as:

Growth factor = 1 + growth rate

                       = 1 + 0.12 = 1,12

2) The growth model of the number of subscribers is given by:

S(m) = So . e^(r.m)

Where:

S(m) = number of subscriber after m months

So= initial number of subscriber

r = growth rate

t = time period

Substitute So = 150 and r = 0.12

S(m) = 150 . e^(0.12m)

Learn more about growth model here:

https://brainly.com/question/16407547

#SPJ4

The triangle in the figure can be proved by ASA, SAS, and AAS

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

Side -  Side - Side = SSS

Side - Angle - Side = SAS

Angle - Side - Angle = ASA

Angle - Angle - Side = AAS

Hypotenuse and one leg = HL

The problem requires the prove by ASA, SAS, and AAS to ensure that the the triangles are congruent.

Alternate angles in the figure are also equal

According to the ASA rule, two triangles are said to be congruent if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.

The Angle-Angle-Side (AAS) Congruence Theorem states that two angles and a non-included side in one triangle must be congruent with two angles and the equivalent non-included side in another triangle for the triangles to be congruent.

Learn more about angles here:

https://brainly.com/question/29393764

#SPJ1

Answer: 0.8333

Step-by-step explanation:

Mai uses 10 ounces of cheese to make 4 pizzas, so she uses 10/4 = <<10/4=2.5>>2.5 ounces of cheese per pizza.

To make 15 pizzas, she will need 152.5 = <<152.5=37.5>>37.5 ounces of cheese.

The solution to the equation is g = 4π² ( L / T² )

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.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The formula to determine the time period of a simple pendulum is given by

T = 2π √ ( L / g )   be equation (1)

where L = length of string

g = acceleration due to gravity

On simplifying the equation , we get

Divide by 2π on both sides of the equation , we get

√ ( L / g ) = T / 2π

Squaring both sides of the equation , we get

( L / g ) = T² / ( 2π )²

( L / g ) = T² / 4π²

Now , taking reciprocals on both sides of the equation , we get

g / L = 4π² / T²

Multiply by L on both sides of the equation , we get

g = 4π² ( L ) / T²

On simplifying the equation , we get

g = 4π² ( L / T² )

Therefore , the value of A is 4π² ( L / T² )

Hence , the equation is g = 4π² ( L / T² )

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

The cost of filling the cone to its full capacity would be = 189.4 cents

A cone is a three-dimensional figure in geometry that tapers from a flat base (usually a circular base) to a point called a vertex or longitude (which forms an axis through the center of the base).

The formula for the volume of a cone = πr²h/3

Height (h) = 5 inches

Radius (r) = 3 inches

π = 3.14

volume = 3.14 × 3² × 5/3

= 3.15 × 9 × 1.67

= 47.35 in³

But 1 in³ = 4 cents

47.35 in³ = X

Make X the subject of formula;

X = 47.35 × 4 = 189.4 cents.

Learn more about cone here:

https://brainly.com/question/28008266

#SPJ1

Therefore, the players are 6.84 meters apart from each other.

An item that is propelled by the application of an external force and then travels freely while being affected by gravity and air resistance is referred to as a projectile. Projectiles are generally used in sports and combat, despite the fact that every item traveling through space is a projectile.

The straight line that traverses a point with a slope equal to the derivative of the curve at that location is said to be the tangent line to a plane curve at that point in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

If we let x be the distance between the players, then we can use the tangent function to relate the angle of elevation to the distance between the player and the basket:

tan(40°) = 3.5/x

tan(50°) = 3.5/(x+1)

We can solve for x in both equations, and set them equal to each other, we get x= 6.84m

Therefore, the players are 6.84 meters apart from each other.

To learn more about Pythagoras' Theorem visit:

https://brainly.com/question/343682

#SPJ1

x+5 is the way we can write 5 more than a number.

In a formula or equation involving mathematical operations, the representation of numbers by alphabet is referred to as algebra.

Using the knowledge provided above, we must translate the mathematical statement provided in the question into an algebraic expression. Let's say that number is "x". The result of adding 5 to the provided number is a number that is 5 greater than this number. Thus, a number that is 5 more than x is equal to x+5. As a result, "5 more than a number" is represented by the algebraic expression "x+5".

To learn more about number here:

https://brainly.com/question/17429689

#SPJ4

The equation for the linear model in the scatter plot is Y = -2x + 56.

To calculate this equation, we need to find the slope (m) and the y-intercept (b). The slope is calculated with the formula m = (y2 - y1) / (x2 - x1), where x and y represent the coordinates of two points on the graph.

The two points closest to the line in the scatter plot are (2, 48) and (4, 52). Substituting these values into the formula gives us m = (52 - 48) / (4 - 2) = 4/2 = 2.

The y-intercept is the point where the line crosses the y-axis. To find it, we need to substitute the slope and one point's coordinates into the equation y = mx + b. For our equation, we will use the coordinates (2, 48). Substituting these values into the equation gives us 48 = 2x + b, and solving for b gives us b = 48 - 2(2) = 44.

Therefore, the equation for the linear model in the scatter plot is Y = -2x + 56.

Learn more about scatter plot here:

https://brainly.com/question/29231735

#SPJ4

Answer:

A translation is a type of transformation that moves each point in a figure the same distance in the same direction.

Step-by-step explanation:

Translations are often referred to as slides. You can describe a translation using words like "moved up 3 and over 5 to the left" or with notation.

The  polynomial Y⁴+ 4y²+ 5 does not have zeroes.

Polynomials are an essential component of the "language" of mathematics and algebra. They are used to express numbers as a result of mathematical operations in nearly every field of mathematics. Polynomials can also be used as "building blocks" in other kinds of mathematical expressions, such as rational expressions.

Polynomials can be used to represent a wide range of everyday mathematical processes. A polynomial can be formed by adding the costs of items on a grocery bill. A polynomial can be used to calculate the distance travelled by a vehicle or object. Polynomials can be used to calculate the perimeter, area, and volume of geometric figures. These are just a few of the many uses for polynomials.

We know that,   (a +b)² = a² + b² + 2ab

Here given that,

⇒ y⁴ + 4y² + 5 = 0

⇒ y⁴ + 4y² + 4 + 1 = 0

⇒ (y² + 2)² + 1 = 0

Because the first term is a square, the expression (y² + 2)² + 1  will never be zero for any value of y.

Learn more about polynomial

https://brainly.com/question/11536910

#SPJ4

Assuming the bags are filled at a constant rate, the average time it takes to fill one bag of leaves is 5 minutes.

To calculate the average time it takes to fill one bag of leaves, we need to know the total amount of time spent filling bags and divide that by the number of bags filled.

First, we know that the staff works an average of six hours per day. Since mowing and raking typically take four hours, we can assume that the remaining two hours are spent filling bags.

To find out how long it takes to fill one bag, we divide the total time spent filling bags by the number of bags filled. In this case, it would be:

(2 hours) / (24 bags) = 0.083 hours (or 5 minutes)

So the average time it takes to fill one bag of leaves is 5 minutes.

It's important to note that this is an average time and may not reflect the exact time it takes for each bag to be filled. Factors such as the size of the bag, the type of leaves being filled, and the skill level of the staff could all affect the time it takes to fill a bag.

To learn more about the average, visit:

brainly.com/question/14402983

#SPJ4

Answer:

Each child will have 3/16 pound of Halloween candy.

Step-by-step explanation:

To find out how much candy each sibling gets, we need to divide 3/4 by 4

3/4 divided by 1/4 = 3/16

Therefore, our answer is 3/16.

So the solution to the system of equations is:

c = 4, d = 1

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, separated by the 'equal' sign.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given equation I is [tex]3c+6d=18[/tex] and equation II is [tex]6c-2d=22[/tex]

We can start by multiplying the first equation by -2 and adding it to the second equation. This will eliminate the d variable:

[tex]-6c - 12d = -36[/tex]

[tex]6c - 2d = 22[/tex]

[tex]0c - 14d = -14[/tex]

solving this we know value of [tex]d=1[/tex]

So we know that d = 1, and we can substitute that into the first equation to find the value of c:

[tex]3c + 6d = 18[/tex]

[tex]3c + 6(1) = 18[/tex]

[tex]3c = 12[/tex]

[tex]c = 4[/tex]

So the solution to the system of equations is:

[tex]c = 4, d = 1[/tex]

To know more about algebra visit:

https://brainly.com/question/24875240

#SPJ4