y = − 1/3 x + 2
y = x + 2
What is the solution to the system of equations?
A) (0, 2)
B) (2, 0)
C) (-1, 3)
D) (0, -2)

Answer:

y=2/3x+2

Step-by-step explanation:

2x-3y=12

3y=2x-12

y=2/3x-12/3

y=2/3x-4

----------------

y-y1=m(x-x1)

y-(-2)=2/3(x-(-6))

y+2=2/3(x+6)

y=2/3x+12/3-2

y=2/3x+4-2

y=2/3x+2

Answer:

Correct Pairs:

E(4, 4), F(8, 3), G(10, 6), and H(8, 6) ⇒ a translation 7 units right

E(3,4), F(-1,3), G(-3, 6), and H(-1,6) ⇒ a reflection across the y-axis

E(-3,-4), F(1,-3), G(3,-6), and H(1,-6) ⇒ a reflection across the x-axis

E(-3,-1), F(1,-2), G(3, 1), and H(1,1) ⇒ a translation 5 units down

Step-by-step explanation:

In Mathematics Geometry, translation just means 'moving'. A move without altering the size, rotation or anything else. When you perform a translation on a shape, the coordinates of that shape will change.

Translation right means you would add the translated unit to the x-coordinates of the of the point, let say P(x, y), in the original object.

Translation down means you would subtract the translated unit from the y-coordinates of the of the point, let say P(x, y), in the original object.

In Mathematics, a reflection just means a 'flip' over a line.

A reflection across x axis means, if a point P(x, y) is reflected across the x-axis, the x coordinate remains the same, while y coordinate changes its sign. i.e. the point (x, y) is changed to (x, -y).

A reflection across y axis means, if a point P(x, y) is reflected across the y-axis, the y coordinate remains the same, while x coordinate changes its sign. i.e. the point (x, y) is changed to (-x, y).

Now, lets head towards the solution:

Analyzing "a translation 7 units right"

As the given ABCD Quadrilateral has vertices as A (-3, 4),  B (1, 3), C (3, 6) and D (1, 6).

As EFGH is congruent to ABCD.

And

A translation of ABCD 7 units right would bring the following transformation:

A (-3, 4),  B (1, 3), C (3, 6) and D(1, 6) ⇒ A'(4, 4), B'(8, 3), C'(10, 6), and D'(8, 6)

As EFGH ≅ ABCD

So,

Here are the matching vertices when a translation 7 units right is made:

E(4, 4), F(8, 3), G(10, 6), and H(8, 6) ⇒ a translation 7 units right

Analyzing "a reflection across the y-axis"

As the given ABCD Quadrilateral has vertices as A (-3, 4),  B (1, 3), C (3, 6) and D (1, 6).

As EFGH is congruent to ABCD.

And

A reflection of ABCD across the y-axis would bring the following transformation:

A(-3, 4), B (1, 3), C(3, 6) and D(1, 6) ⇒ A' (3, 4), B'(-1, 3), C'(-3, 6) and D'(-1, 6)

As EFGH ≅ ABCD

So,

Here are the matching vertices when a reflection across the y-axis is made:

E(3,4), F(-1,3), G(-3, 6), and H(-1,6) ⇒ a reflection across the y-axis

Analyzing "a reflection across the x-axis"

As the given ABCD Quadrilateral has vertices as A (-3, 4),  B (1, 3), C (3, 6) and D (1, 6).

As EFGH is congruent to ABCD.

And

A reflection of ABCD across the x-axis would bring the following transformation:

A(-3, 4), B (1, 3), C(3, 6) and D(1, 6) ⇒ A' (-3, -4), B'(1, -3), C'(3, -6) and D'(1, -6)

As EFGH ≅ ABCD

So,

Here are the matching vertices when a reflection across the x-axis is made:

E(-3,-4), F(1,-3), G(3,-6), and H(1,-6) ⇒ a reflection across the x-axis

Analyzing "a translation 5 units down"

As the given ABCD Quadrilateral has vertices as A (-3, 4),  B (1, 3), C (3, 6) and D (1, 6).

As EFGH is congruent to ABCD.

And

A translation of ABCD 5 units down brings the following transformation:

A (-3, 4),  B (1, 3), C (3, 6) and D(1, 6) ⇒  A' (-3, -1),  B'(1, -2), C'(3, 1) and D'(1, 1)

As EFGH ≅ ABCD

So,

Here are the matching vertices when a translation 5 units down is made:

E(-3,-1), F(1,-2), G(3, 1), and H(1,1) ⇒ a translation 5 units down

Here is summary of matched Pairs:

E(4, 4), F(8, 3), G(10, 6), and H(8, 6) ⇒ a translation 7 units right

E(3,4), F(-1,3), G(-3, 6), and H(-1,6) ⇒ a reflection across the y-axis

E(-3,-4), F(1,-3), G(3,-6), and H(1,-6) ⇒ a reflection across the x-axis

E(-3,-1), F(1,-2), G(3, 1), and H(1,1) ⇒ a translation 5 units down

Keywords: reflection, translation, transformation

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Answer:

$6770.65

Step-by-step explanation:

The purchase price is $20,300

The depreciation rate is 9.5% per year, in decimal, that is:

9.5/100 = 0.095

We want to find the value of car after 11 years. We will use the compound decay formula:

[tex]F=P(1-r)^t[/tex]

Where

F is the future value (what we want to find after 11 years)

P is the present value, purchase price (20,300 given)

r is the rate of depreciation (r = 0.095)

t is the time in years ( t = 11)

Substituting, we solve for F:

[tex]F=P(1-r)^t\\F = 20,300(1-0.095)^{11}\\F=20,300(0.905)^{11}\\F=6770.65[/tex]

Thus,

The value of the car would be around $6770.65, after 11 years

The missing question is find x , y and the measure of each angle

The values of x and y are x = 28 and y = 30

The measures of ∠ABC is 26°, ∠CBD is 64° and ∠DBE is 116°

Step-by-step explanation:

Let us revise the meaning of complementary angles and supplementary angles

∵ ∠ABC = x

∵ ∠CBD = 2y + 4

∵ ∠ABC and ∠CBD are complementary

- That means their sum is 90°, add their values and equate

   the sum by 90

∴ x + (2y + 4) = 90

∴ x + 2y + 4 = 90

- Subtract 4 from both sides

∴ x + 2y = 86 ⇒ (1)

∵ ∠DBE = (3y + x)

∵ ∠CBD and ∠DBE are supplementary

- That means their sum is 180°, add their values and equate

   the sum by 180

∵ ∠CBD = (2y + 4)

∴ (2y + 4) + (3y + x) = 180

- Add like terms

∴ x + 5y + 4 = 180

- Subtract 4 from both sides

∴ x + 5y = 176 ⇒ (2)

Now we have a system of equations to solve them

Subtract equation (1) from equation (2) to eliminate x

∵ 3y = 90

- Divide both sides by 3

∴ y = 30

- Substitute the value of y in equation (1) to find x

∵ x + 2(30) = 86

∴ x + 60 = 86

- Subtract 60 from both sides

∴ x = 26

∵ ∠ABC = x

∴ The measure of angle ABC is 26°

∵ ∠CBD = 2y + 4

∴ ∠CBD = 2(30) + 4 = 60 + 4 = 64°

∴ The measure of angle CBD is 64°

∵ ∠DBE = 3y + x

∴ ∠DBE = 3(30) + 26 = 90 + 26 = 116°

∴ The measure of angle DBE is 116°

The values of x and y are x = 28 and y = 30

The measures of ∠ABC is 26°, ∠CBD is 64° and ∠DBE is 116°

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The question involves using the properties of complementary and supplementary angles to form equations and solve for the variables x and y.

This question is about solving for variables using information about complementary and supplementary angles. A pair of angles are complementary if the sum of their measures is 90 degrees, and supplementary if the sum of their measures is 180 degrees.

In this case, ∠ABC= x and ∠CBD=(2y+4) are complementary, so their sum is 90 degrees. This gives us the equation: x + 2y + 4 = 90.

Similarly, ∠CBD and ∠DBE=(3y+x) are supplementary, meaning their sum is 180 degrees. This gives us the second equation: 2y + 4 + 3y + x = 180.

By solving these two equations, we can determine the values of x and y.

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Answer:

-7 feet above the ground

Step-by-step explanation:

Answer:

The slope will be 2/2 which is equal to 1.

Answer:

Step-by-step explanation:

The slope is 2/2 which equals to 1.

Final answer:

The question involves an algebraic expression defining Y in terms of x in Mathematics.

Explanation:

The subject of this question is Mathematics.

To define the expression given, Y is equal to 2 plus the product of 3 and x, it can be represented as: Y = 2 + 3x.

This is a basic algebraic expression where Y depends on the value of x.

Answer:

Hence Cos X = 40/41 .

Step-by-step explanation:

Given-   X Y = 41 units, Y Z = 9 units, X Z = 40 units, ∠ Z= 90°,

∵ ∠ Z = 90°, so Δ XYZ is a right triangle.

∴ By Pythagorean Theorem-

Cos X = [tex]\frac{Base}{Hypotenuse}[/tex]

Cos X = [tex]\frac{X Z}{X Y}[/tex]

Cos X = [tex]\frac{40}{41}[/tex]

Answer:

B.

Step-by-step explanation:

Try solving:

13x - 5 = - 5 + 13x

13x - 13x = -5 + 5

0 = 0.

Therefore it is an identity.

We could make x any real value and the identity would hold.

The given equation 13x - 5 = -5 + 13x is an identity with infinite solutions. The option B is correct.

The given equation is 13x - 5 = -5 + 13x. To determine what kind of solution this equation has, we should simplify and solve for x. Starting by adding 5 to both sides of the equation to cancel out the -5, we get 13x = 13x. This results in the terms involving x on both sides of the equation being identical. Hence, no matter what value of x we substitute, the equation will always hold true.

Therefore, the equation represents an identity, meaning that it is true for all real numbers and there are infinite solutions. This is because subtracting or adding equal amounts on both sides of an equation does not change its solutions, leading to an expression of an identity.

Answer:

Karoun bought 12n + 15 numbers of pencils.

40 pencils

Step-by-step explanation:

If there are n numbers of pencils in each box of the pencil then there are 4n numbers of pencils in each package of pencils.

Now, Karoun bought 3 packages of pencils and get (5 × 3) = 15 pencils free of cost.

Therefore, Karoun bought (4n × 3) + 15 = 12n + 15 numbers of pencils. (Answer)

Now, if n = 10 pencils then in each package of pencils there will be 4n i.e. (4 × 10) = 40 pencils. (Answer)

Answer:

1.35

Step-by-step explanation:

$9=100%

15%        x

-----  =   ----

100%     9

Cross multiply:

100x=135

Solve:

x=1.35

15% of $9 is $1.35

:)

Answer: $1.35

Step-by-step explanation: To find 15% of $9, first write 15% as a decimal by moving the decimal point 2 places to the left to get .15.

Next, "of $9" means times 9 so we multiply .15 times 9 or (.15)(9) which gives us 1.35. So 15% of $9 is $1.35.

Answer:

[tex]\sqrt{85}[/tex]

Step-by-step explanation:

Given

x - [tex]\frac{1}{x}[/tex] = 9 ← square both sides

(x - [tex]\frac{1}{x}[/tex])² = 9²

x² - 2 + [tex]\frac{1}{x^2}[/tex] = 81 ( add 2 to both sides )

x² + [tex]\frac{1}{x^2}[/tex] = 83

Now

(x + [tex]\frac{1}{x}[/tex])² = x² + [tex]\frac{1}{x^2}[/tex] + 2, thus

x² + [tex]\frac{1}{x^2}[/tex] = 83 + 2 = 85

(x + [tex]\frac{1}{x}[/tex] )²= 85 ( take the square root of both sides)

x + [tex]\frac{1}{x}[/tex] = [tex]\sqrt{85}[/tex]

Answer:

data collection error

Answer:

B. Data Collection Error.

Step-by-step explanation:

Answer:

508.8 seconds (8.48 minutes)

Step-by-step explanation:

Answer:

all work is shown and pictured

Answer:

-(x^2+4)

Step-by-step explanation:

Answer:

(-x-2i)(x-2i)

Step-by-step explanation:

D. x = –2, x = 2, and x = 3

Please correct me If I'm wrong, I did the math myself and this is what I got.

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling for this one.  It involves natural logs and being able to solve equations that require natural logs.  The formula is as follows:

[tex]T(t)=T_{1}+(T_{0}-T_{1})e^{kt}[/tex] where

T(t) is the temp at time t

T₁ is the enviornmental temp

T₀ is the initial temp

k is the cooling constant which is different for everything, and

t is the time (here, it's in minutes)

If we are looking first for the temp after 20 minutes, we have to solve for the k value.  That's what we will do first, given the info that we have:

T(t) = 80

T₁ = 30

T₀ = 100

t = 5

k = ?

Filling in to solve for k:

[tex]80=30+(100-30)e^{5k}[/tex] which simplifies to

[tex]50=70e^{5k}[/tex] Divide both sides by 70 to get

[tex]\frac{50}{70}=e^{5k}[/tex] and take the natural log of both sides:

[tex]ln(\frac{5}{7})=ln(e^{5k})[/tex]

Since you're learning logs, I'm assuming that you know that a natural log and Euler's number, e, "undo" each other (just like taking the square root of something squared).  That gives us:

[tex]-.3364722366=5k[/tex]

Divide both sides by 5 to get that

k = -.0672944473

Now that we have a value for k, we can sub that in to solve for T(20):

[tex]T(20)=30+(100-30)e^{-.0672944473(20)}[/tex] which simplifies to

[tex]T(20)=30+70e^{-1.345888946}[/tex]

On your calculator, raise e to that power and multiply that number by 70:

T(20)= 30 + 70(.260308205) and

T(20) = 30 + 18.22157435 so

T(20) = 48.2°

Now we can use that k value to find out when (time) the temp of the object cools to 35°:

T(t) = 35

T₁ = 30

T₀ = 100

k = -.0672944473

t = ?

[tex]35=30+100-30)e^{-.0672944473t}[/tex] which simplifies to

[tex]5=70e^{-.0672944473t}[/tex]

Now divide both sides by 70 and take the natural log of both sides:

[tex]ln(\frac{5}{70})=ln(e^{-.0672944473t})[/tex] which simplifies to

-2.63905733 = -.0672944473t

Divide to get

t = 39.2 minutes

The temperature of the object after 20 minutes is 48.2° and temperature of body will be 35° after 39.2 minutes.

The formula can be expressed as:

[tex]\[ \frac{dT}{dt} = -k(T - T_a) \][/tex]

where:

[tex]\( T \)[/tex] is the temperature of the object at time [tex]\( t \)[/tex],

[tex]\( T_a \)[/tex] is the ambient temperature,

[tex]\( k \)[/tex] is a positive constant that depends on the characteristics of the object and the environment.

First, we need to find the constant [tex]\( k \)[/tex]. We have the following data:

Initial temperature of the object, [tex]\( T_0 = 100^\circ \)[/tex],

Temperature of the object after 5 minutes, [tex]\( T_1 = 80^\circ \)[/tex],

Ambient temperature, [tex]\( T_a = 30^\circ \)[/tex],

Time [tex]\( t_1 = 5 \)[/tex] minutes.

Using the integrated form of Newton's law of cooling, we have:

[tex]\[ T = T_a + (T_0 - T_a)e^{-kt} \][/tex]

Plugging in the values for [tex]\( T_1 \)[/tex] and [tex]\( t_1 \)[/tex], we get:

[tex]\[ 80 = 30 + (100 - 30)e^{-k \cdot 5} \][/tex]

Solving for [tex]\( k \)[/tex], we find:

[tex]\[ 50 = 70e^{-5k} \][/tex]

[tex]\[ e^{-5k} = \frac{50}{70} \][/tex]

[tex]\[ -5k = \ln\left(\frac{50}{70}\right) \][/tex]

[tex]\[ k = -\frac{1}{5}\ln\left(\frac{50}{70}\right) \][/tex]

Now that we have [tex]\( k \)[/tex], we can find the temperature after 20 minutes [tex]\( t_2 = 20 \)[/tex] minutes:

[tex]\[ T_2 = 30 + (100 - 30)e^{-k \times 20} \][/tex]

Substituting [tex]\( k \)[/tex] into the equation, we get:

[tex]\[ T_2 = 30 + (100 - 30)e^{\frac{1}{5}\ln\left(\frac{50}{70}\right) \times 20} \][/tex]

[tex]\[ T_2 = 30 + 70e^{\frac{20}{5}\ln\left(\frac{50}{70}\right)} \][/tex]

[tex]\[ T_2 = 30 + 70e^{4\ln\left(\frac{50}{70}\right)} \][/tex]

[tex]\[ T_2 = 30 + 70\left(\frac{50}{70}\right)^4 \][/tex]

[tex]\[ T_2 = 48.2^\circ[/tex]

Now, we need to solve for the time [tex]\( t_3 \)[/tex] when the temperature of the object is [tex]\( 35^\circ \)[/tex]:

[tex]\[ 35 = 30 + (100 - 30)e^{-kt_3} \][/tex]

[tex]\[ 5 = 70e^{-kt_3} \][/tex]

[tex]\[ e^{-kt_3} = \frac{5}{70} \][/tex]

[tex]\[ -kt_3 = \ln\left(\frac{5}{70}\right) \][/tex]

[tex]\[ t_3 = -\frac{1}{k}\ln\left(\frac{5}{70}\right) \][/tex]

Substituting [tex]\( k \)[/tex] into the equation, we get:

[tex]\[ t_3 = -\frac{5}{\ln\left(\frac{50}{70}\right)}\ln\left(\frac{5}{70}\right) \][/tex]

[tex]\ln\left(\frac{50}{70}\right)} = -0.336[/tex]

[tex]\ln\left(\frac{5}{70}\right) = -2.639[/tex]

[tex]|\[ t_3 = -\frac{5}{(-0.336)\right)} \times\ -2.639}|[/tex]

[tex]\ t_3 = 39.2 \text{minutes}[/tex]

The person has to travel 40 feet from the bottom to  the top of the escalator

Solution:

Given that escalator lifts people to the second floor of a building, 20 ft

above the first floor

The escalator rises at a 30° angle

To find: Distance person travel from the bottom to  the top of the escalator

The above scenario forms a right angled triangle where the escalator follows the path of the hypotenuse.

The diagram is attached below

In the right angled triangle ABC,

AC represents Distance person travel from the bottom to  the top of the escalator

AB = 20 feet

angle ACB = 30 degree

We know that,

[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]

[tex]sin 30 = \frac{20}{AC}[/tex]

[tex]\frac{1}{2} = \frac{20}{AC}\\\\AC = 20 \times 2 = 40[/tex]

So the person has to travel 40 feet from the bottom to  the top of the escalator

Write an algebraic expression that is the quotient of a variable term and a constant

The algebraic expression that is the quotient of a variable term and a constant is [tex]quotient = \frac{x}{5}[/tex]

In arithmetic, a quotient is the quantity produced by the division of two numbers

Here given in question that quotient of a variable term and a constant

So the quotient produced by division of variable term and constant

A variable is a special type of amount or quantity with an unknown value. Though it can be anything, you often see letters like x or y as variables in algebraic equations

Let the variable term be "x"

Constants are the terms in the algebraic expression that contain only numbers

Let the constant be "5" (Note that it can be any number, here we choose 5)

So the quotient of a variable term and a constant is:

An algebraic expression is a mathematical expression that consists of variables, numbers and operations.

[tex]quotient = \frac{\text{ variable term}}{constant}[/tex]

[tex]quotient = \frac{x}{5}[/tex]

[tex]quotient = x \div 5[/tex]

Each side of a square has a length of 5x. Use your area expression to find the area of the square when x = 2.2 centimeters. Show your work.

The area of square is 121 square centimeter

Solution:

Given that each side of square has length of 5x

The area of square is given as:

[tex]\text{ area of square }= (side)^2[/tex]

[tex]\text{ area of square} = (5x)^2\\\\\text{ area of square} = 25x^2[/tex]

Given x = 2.2 centimeter

[tex]\text{ area of square} = 25(2.2)^2 = 25 \times 4.84 = 121[/tex]

Thus area of square is 121 square centimeter

Final answer:

An algebraic expression x/3 is provided as an example, and the area of a square with side length 5x is calculated when x = 2.2 cm.

Explanation:

Algebraic expression: An example of an algebraic expression that is the quotient of a variable term and a constant is x/3, where x is the variable term and 3 is the constant.

Finding the area of a square: Given that each side of a square is 5x, the area is found by squaring the side length. So, Area = (5x)^2 = 25x^2.

Calculating the area when x = 2.2 cm: Substituting x = 2.2 into the area expression gives 25*(2.2)^2 = 25*4.84 = 121 cm².

Answer:

The second choice

Step-by-step explanation:

Answer:

|4x-2| = -6

Step-by-step explanation:

recall that the absolute value of anything must be greater or equal to zero (i.e 0 or positive).

in the first option, we can see that the absolute value of the expression (4x-2) gives a negative number. This violates our definition above hence it cannot be true.

Answer: c  

Step-by-step explanation:

Answer:

f(x)=3/2(8/7)^-x

Step-by-step explanation:

If you turn the fractions into decimals ([tex]\frac{3}{2}(\frac{8}{7} )[/tex]^-x = 1.5(1.14)^-x), put that number into y= in your graphing calculator and press graph you will be able to see, verses the other functions, that the line decreases.

Answer:

The length of the ladder is 9.2 meters

Step-by-step explanation:

Given as :

The angels of elevation of a ladder against a wall = 60°

The Distance of the foot of the ladder fro the wall = d = 4.6 meters

Let The length of the ladder = h meters

Now, According to question

cos angle = [tex]\dfrac{\textrm base}{\textrm hypotenuse}[/tex]

Or, cos 60° = [tex]\dfrac{\textrm d}{\textrm h}[/tex]

Or, 0.5 = [tex]\dfrac{\textrm 4.6}{\textrm h}[/tex]

∴  h = [tex]\dfrac{\textrm 4.6}{\textrm 0.5}[/tex]

i.e h = 9.2

So,The length of the ladder = h = 9.2 meters

Hence The length of the ladder is 9.2 meters Answer

Answer:

One (1) significant figure.

Step-by-step explanation:

All non zero digits are always significant zeros. Since there is no decimal point, the 0 is a trailing zero, and does not count as a significant figure.

Answer:

[tex]\frac{(\frac{3}{5}*1000) }{6}[/tex]

Step-by-step explanation:

First, let's find out how many words Maria has left to write. If she has already finished 2/5 of her essay, she has 3/5ths left to write. We can do 3/5 times 1000 to find out how many words are left.

[tex]\frac{3 }{5} * \frac{1000}{1}[/tex]

[tex]\frac{3000}{5}[/tex]

[tex]600[/tex]

Thus, there are 600 words left to write.

Now to find the amount of time, we can find how take to write 600 words at a pace of 6 words per minute by dividing 600 by 6.

[tex]\frac{600}{6}[/tex]

[tex]100[/tex]

It will take 100 minutes for Maria to write the rest of her essay. Now let's think about an expression that tells us this information. It sounds like your questions is supposed to have options, but I doesn't seem like you've posted them, no worries however.

So first, the amount she has left to write.

[tex](\frac{3}{5} * 1000)[/tex]

We know this is 600, but we don't have to simplify it for the expression.

Now thinking back to how we found the time, we can divide this '600' by 6.

[tex]\frac{(\frac{3}{5}*1000) }{6}[/tex]

This is the expression that shows the amount of time it will take to write the rest of the essay.

[tex]\frac{((1-(\frac{2}{5})*1000) }{6}[/tex] is also a valid solution.

Final answer:

Maria has 600 words left to write in her essay, and at 6 words per minute, it will take her 100 minutes to finish writing the remaining part.

Explanation:

Maria has written 2/5 of her essay, which means she has written 400 words (2/5 of 1,000 words). To find out how long it will take her to write the remaining 3/5 of her essay, we need to calculate 3/5 of 1,000 words, which is 600 words. If she writes at a pace of 6 words per minute, we can find the time by dividing the remaining number of words by her writing pace.

The expression that shows the amount of time it will take her to finish the essay is:
 (Total remaining words) / (Words per minute)
 = (3/5  of 1,000) / 6
 = 600 / 6
 = 100 minutes

Answer:

f(x) = (x - 2)²

Step-by-step explanation:

f(x) = x² - 4x + 4 is a perfect trinomial.

You know a trinomial is perfect when double the square root of the first term multiplied by the square root of the last term equals the middle term.

As an equation, a trinomial in the form ax² + bx + c = 0:

2√a√c = b is a perfect trinomial.

Perfect trinomial are factored in this form:

(√a ± √c )(√a ± √c ) = (√a ± √c )²

Whether the sign is + or - depends on if the middle term is positive or negative.

In f(x) = x²-4x+4, the middle term is a negative.

The square root of the first term is 1.

The square root of the second term is 2.

The factored form is (x - 2)²

Final answer:

To find the inverse of a matrix, follow these steps: 1. Check if the matrix is square and has a non-zero determinant. 2. Use the formula for finding the inverse of a 2x2 matrix. 3. For larger matrices, use row reduction or the adjugate matrix.

Explanation:

To find the inverse of a matrix, follow these steps:

Check if the matrix is square (the number of rows equals the number of columns). If it is not, then the matrix does not have an inverse.

Calculate the determinant of the matrix. If the determinant is 0, then the matrix does not have an inverse.

If the matrix is square and has a non-zero determinant, use the formula for finding the inverse of a matrix. For a 2x2 matrix:

A-1 = 1/det(A) * [d -b;
-c a]

where A is the original matrix, A-1 is the inverse matrix, det(A) is the determinant of A, and a, b, c, and d are the entries of A.

If the matrix is larger than 2x2, you can use methods such as row reduction or the adjugate matrix to find the inverse.

Answer:

8 inches

Step-by-step explanation:

90 miles -------------> represented by 3 inches

1 mile -------------> represented by 3/90 inches

240 miles ----------> represented by 3/90 x 240 = 8 inches

To determine the length of a line segment that represents 240 miles on a scale drawing, set up a proportion using the information given. The line segment would be 8 inches long.

To determine the length of a line segment that represents 240 miles on a scale drawing, we can set up a proportion using the information given. The scale in the drawing states that 3 inches represent 90 miles. We can cross-multiply and solve for the unknown length as follows:

3 inches / 90 miles = x inches / 240 miles

To solve for x, we can multiply both sides of the equation by 240 and then divide by 90:

x inches = (3 inches / 90 miles) * 240 miles

x inches = 8 inches

Therefore, a line segment that represents 240 miles on the scale drawing would be 8 inches long.

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