arturo earns 1,800 per month. he pays 600 a month on rent. what is the ratio of his rent to his monthly income

The coefficient of x in the simplified form of the expression is -117.

The simplified form of an algebraic expression is the expression that has been reduced to its simplest possible form by combining like terms and performing any applicable operations, such as addition, subtraction, multiplication, and division.

Given that

= 3(x + 4)(x - 5)^2 - 6(x + 2)^3

Apply the distributive property.

= (3x + 3 × 4)(x−5)^2 − 6(x + 2)^3

Expand using the FOIL Method.

= (3x+12)((x−5)(x−5))−6(x+2)^3

= (3x+12)(x^2−10x+25)−6(x+2)^3

Expand ( 3 x + 12 ) ( x^2 − 10 x + 25) by multiplying each term in the first expression by each term in the second expression.

= (3x) × x^2 + 3x(−10x) + 3x × 25 + 12x^2 + 12(−10x) + 12×25 − 6(x+2)^3

= 3x^3 − 30x^2 + 75x + 12x^2 − 120x + 300 − 6(x+2)^3

= 3x^3 − 18x^2 − 45x + 300 − 6(x+2)^3

SImplify 6(x+2)^3 using Binomial expansion;

= −3x^3 − 54x^2 − 117x + 252

Therefore, we can conclude that the coefficient of x is - 117.

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10. Showing that ΔWVU ∼ ΔQRS, x = B. 5

11. Showing that ΔKML ∼ ΔEMD, x = A. 8.

A triangle is a geometric shape that is formed by connecting three straight lines to form a closed shape. It is a three-sided polygon and is one of the most basic shapes in geometry. The three lines that form a triangle are called sides, and the points where the sides meet are called vertices.

10. Showing that ΔWVU ∼ ΔQRS, we have:

WV/QR = VU/RS

⇒ (13x + 7)/45 = 88/55

Cross-multiplying, we have:

(13x + 7)55 = 45 x 88

= 715x + 385 = 3 960

= 715x = 3 960 - 385 = 3 575

∴ x = 3 575/715 = 5.

Thus, x = 5.

11. Showing that ΔKML ∼ ΔEMD, we have:

KM/EM = ML/MD = (3x - 2)/14 = 27/18

(3x - 2)18 = 14 x 27

= 54x - 54 = 378

= 54x = 378 + 54 = 432

⇒ x = 432/54 = 8.

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Step-by-step explanation:

I think this is the way it has to be done (I added a photo)

Answer:

(6,0 ) is located in 1st quardrant o is x axis and 6 is y axix upuards

After making the table using the given ratios we can conclude that Miguel will save $90 if he earns $120.00.

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio.

A proportion is an equation that equalizes two ratios.

For example, you might write the ratio as 1: 3 (there are 3 girls for every guy), which would suggest that there are 1 in 4 boys and 3 in 4 girls.

By typically dividing two figures, ratios contrast them. If you were comparing one data point (A) to another data point, your formula would be A/B. (B).

So, the solution in the form of a table would be:

Money Earned    Money saved                  Ratio

10                              7.5                                3/4

50                            37.5                                3/4

120                             ?                                   3/4

150                          112.5                                3/4

? /120 =  3/4  => ? =   90

Miguel will save $90 if he earns $120.00.

Therefore, after making the table using the given ratios we can conclude that Miguel will save $90 if he earns $120.00.

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Correct question:

Miguel created the ratio table below to show how he uses the money he earns at work. Miguel’s Money Money Earned Money Saved $10.00 $7.50 $50.00 $37.50 $120.00? $150.00 $112.50 How much money will he save if he earns $120.00? $30.00 $45.00 $90.00 $75.00

Answer: 2.6

Step-by-step explanation:

Finding the right trigonometric function to use

In this problem, we have to choose between three trigonometric functions:

sine, cosine, and tangent

Each function relates the angle of a right triangle to 2 of the three sides of the triangle:

the sine of an angle is equal to the ratio of the side opposite to the angle to the hypotenuse of the triangle: [tex]sin(x)=\frac{opposite}{hypotenuse}[/tex]

[tex]tan(x)=\frac{opposite}{adjacent}[/tex]

[tex]cos(x)=\frac{adjacent}{hypotenuse}[/tex]

In this case, we are given the hypotenuse and need to find the side adjacent to the angle, so we will use cosine.

Calculating the adjacent side

Plugging in the values for the hypotenuse and the angle to the cosine equation, we get

[tex]cos(58)=\frac{x}{5}\\x=5(cos(58))\\[/tex]

Entering into a calculator, we get x≈2.6

True. In an indirect proof, also known as proof by contradiction, you start by assuming the opposite of what you intend to prove is true.

You then use deductive reasoning and logical steps to show that the assumption leads to a contradiction or an impossibility. This means that the assumption must be false and therefore the original statement you intended to prove must be true.

What is contradiction?

A contradiction is a situation where two or more statements, beliefs, or ideas are in direct opposition to one another, making them logically inconsistent or incompatible with each other. In other words, a contradiction occurs when there is a conflict between two or more pieces of information that cannot both be true at the same time.

For example, if someone says "I am currently in New York City," and then in the same conversation says "I am currently in Los Angeles," this is a contradiction because it is impossible to be in two different locations at the same time.

What is deductive reasoning?

Deductive reasoning is a method of reasoning in which specific conclusions are drawn from general principles or premises. It is a logical process that involves starting with a general principle or hypothesis, and then using specific observations or evidence to reach a specific conclusion.

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Complete question is: In an indirect proof, also known as proof by contradiction, you start by assuming the opposite of what you intend to prove is true.

The required velocity and position of the object at time t for the given acceleration a(t) is given by v(t) = (t, 1/2t^2) and r(t) = (1/2t^2, 1/6t^3 - 1/2) respectively.

Velocity of the object at time t,

Integrate the acceleration function a(t) with respect to time.

This gives us the velocity function v(t),

v(t)

= ∫a(t)dt

= (∫1dt, ∫tdt)

= (t, 1/2t^2) + C

where C is a constant of integration.

The value of C using the information that v(0) is parallel to the x-axis,

v(0)

= (0, C)

=(k, 0)

where k is some constant.

This means that C must be equal to 0.

And k must also be equal to 0 in order for v(0) to be parallel to the x-axis.

Velocity function is,

v(t) = (t, 1/2t^2)

Position of the object at time t,

Integrate the velocity function v(t) with respect to time.

This gives us the position function r(t),

r(t)

= ∫v(t)dt

= (∫t dt, ∫1/2t^2dt) + C'

where C' is a constant of integration.

Value of C' using the information that the object is at the origin when t=1,

r(1)

= (0, 0)

= (C', 1/2 + C'')

where C'' is another constant.

This means that C' must be equal to 0.

And C'' must be equal to -1/2 in order for the object to be at the origin when t=1.

Position function is,

r(t) = (1/2t^2, 1/6t^3 - 1/2)

Therefore, the velocity of the object and the position of the object at time t is equal to v(t) = (t, 1/2t^2) and r(t) = (1/2t^2, 1/6t^3 - 1/2) respectively.

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Answer:

17/250

Step-by-step explanation:

6.8% = 0.068 =

factor pairs of 68 include 4 * 17

68/1000 = divide top & bottom by 4

17/250

The value of x is 1.0 for the given triangle.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are:

The given triangle is a right triangle because it presents one of your angles equal to 90º. The figure shows:

Therefore, you have the opposite side of the angle u, the angle u and the variable x. Thus, you can apply the equation for sin (u) for finding x.

[tex]sin (x) = \frac{opposite\ side}{hypotenuse} \\ \\ sin (37) = \frac{0.6}{x}[/tex], knowing that sin37°=0.602

[tex]0.602=\frac{0.6}{x} \\ \\[/tex]

x=0.997, round to the nearest tenth

x=1.0

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In conclusion the simplified expression is:

√3/√6 = 3√2/6 = √2/2

How to simplify?

a)

To rationalize the denominator of √15/√5, we need to eliminate the square root in the denominator. We can do this by multiplying both the numerator and denominator by √5.

√15/√5 × √5/√5 = √75/5

We can simplify √75 by breaking it down into its prime factors:

√75 = √(355) = 5√3

Therefore, the simplified expression is:

√15/√5 = 5√3/5 = √3

b)

To rationalize the denominator of √3/√6, we need to eliminate the square root in the denominator. We can do this by multiplying both the numerator and denominator by √6.

√3/√6 × √6/√6 = √18/6

We can simplify √18 by breaking it down into its prime factors:

√18 = √(233) = 3√2

Therefore, the simplified expression is:

√3/√6 = 3√2/6 = √2/2

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Triangle UTS and triangle VTS are congruent using ASA criteria. Hence, SU = SV using CPCT.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

Although having the same form, each might have different sizes.

There are no matching angles that are not equal.

Similar equivalent side ratios exist.

Given: ST bisects ZUTV.

angle UTS ≅ angle VTS (as ST bisects ZUTV)

angle TUS and angle TVS are right angles as shown in the figure.

Thus, triangle UTS and triangle VTS are congruent using ASA criteria.

Hence, SU = SV using CPCT.

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It transform rectangle in  8 units left and then 7 units down then  x-axis and subsequently the y-axis were reflected and after this translated 7 units down

A set of translations, rotations, reflections, and dilations on a figure constitute a series of transformations in geometry. A composition of transformations is what results when two or more transformations are joined to create a new transformation. In a composition, one transformation creates a picture that serves as the foundation for the subsequent other transformation.

The possible transformations that rectangle ABCD could have undergone to become rectangle A′′B′′C′′D′′ are as follows: -

It was translated 8 units left, then 7 units down, for rectangle ABCD.

- First, the x-axis and subsequently the y-axis were reflected by the rectangle ABCD.

- Rectangle ABCD was translated 7 units down after being rotated 180 degrees around its origin.

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The perimeter of the given quadrilateral EGFH is 33 inches as shown in below figure.

A quadrilateral is a geometric shape with four angles and four straight sides. Quadrilaterals come in a wide variety of shapes, including squares, rectangles, trapezoids, and kites. Each kind of quadrilateral has its own set of characteristics and properties, but they all have four sides and four angles in common.

Draw two tangents from an outside point to the circle always in equal lengths;

So, the perimeter of quadrilateral EGFH = length of each tangents

the perimeter of quadrilateral EGFH = EG + GF + FH + HE

the perimeter of quadrilateral EGFH = 12 + (5+4) + (4+0.5) + (0.5+7)

the perimeter of quadrilateral EGFH = 12+ 21

Therefore, the perimeter of quadrilateral EGFH = 33 inches

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Complete question in figure-

Using expression 3 x 14, The rate chart will be

Number of Scoops of Coffee Grounds 18 24 30 36 42.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and operations (such as addition, subtraction, multiplication, division, and exponentiation) that represents a mathematical phrase or idea. Expressions can be simple or complex and may involve functions, trigonometric functions, logarithms, and other mathematical operations.

Now,

To find the number of scoops of coffee grounds needed for 14 pots of coffee, we can use proportional reasoning and set up a proportion:

Number of scoops of coffee grounds / Number of pots of coffee = 18 / 6

Simplifying the fraction on the right side of the equation gives us:

Number of scoops of coffee grounds / Number of pots of coffee = 3

To solve for the number of scoops of coffee grounds needed for 14 pots of coffee, we can multiply both sides of the equation by 14:

Number of scoops of coffee grounds / Number of pots of coffee = 3

Number of scoops of coffee grounds / 14 = 3

Number of scoops of coffee grounds = 3 x 14

Number of scoops of coffee grounds = 42

So the completed rate chart is:

Number of Pots of Coffee 6 8 10 12 14

Number of Scoops of Coffee Grounds 18 24 30 36 42.

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To find the annual interest rate, we can use the formula:

simple interest = (principal x rate x time) / 100

where principal is the initial amount, rate is the annual interest rate, and time is the time period in years.

We know that the principal is $100, the simple interest is $3, and the time period is 6 months, which is half a year.

So, we can plug in these values and solve for the annual interest rate:

$3 = ($100 x rate x 0.5) / 100

$3 = $0.5 x rate

rate = $3 / $0.5

rate = 6

Therefore, the annual interest rate is 6%.

Answer:

To calculate the annual interest rate, we can use the simple interest formula:

I = P * r * t

Where:

- I is the interest earned

- P is the principal amount

- r is the annual interest rate

- t is the time period in years

In this case, we know that the principal amount is $100, the interest earned is $3, and the time period is 6 months, or 0.5 years. We can plug these values into the formula and solve for r:

3 = 100 * r * 0.5

r = 3 / (100 * 0.5)

r = 0.06, or 6%

Therefore, the annual interest rate is 6%.

I hope this helps!

1 - 5 = 5

6 - 10 = 6

11 - 15 = 7

16 - 20 = 2

c. 11 - 15.

By solving the ratio, we get the value of x is 3.

What is a ratio?

a ratio is a comparison of two quantities or values, often expressed as a fraction. Ratios can be used to express the relationship between two or more quantities.

Let the total number of tiles on the bathroom floor be represented by the variable "t".

Since 1/4 of the tiles are blue, we know that:

number of blue tiles = 1/4 * t

Similarly, we can find the number of green tiles:

number of green tiles = 3/4 * t

Now, we can use the given ratio of blue tiles to green tiles to create an equation:

(2x+1)/(4x+9) = (number of blue tiles) / (number of green tiles)

Substituting the values we found earlier, we get:

(2x+1)/(4x+9) = (1/4 * t) / (3/4 * t)

Simplifying this equation, we get:

(2x+1)/(4x+9) = 1/3

6x + 3 = 4x + 9

2x = 6

x = 3

Therefore, the value of x is 3.

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The solution to the system of equations 3x - y = 4 and -2x + 7y = 20 is obtained as x = 48/19 and y = 68/19.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The system of equations is -

3x - y = 4

-2x + 7y = 20

The matrix for the system of equations is -

[tex]\left[\begin{array}{c c | c}3 & -1 & 4 \\-2 & 7 & 20\end{array}\right][/tex]

To solve the matrix, we can use row operations to get it into row echelon form -

The first row operation is -

[tex]R_1=\frac{1}{3}R_1[/tex]

On applying the first row operation we get -

[tex]\left[\begin{array}{c c | c}1 & \frac{-1}{3} & \frac{4}{3} \\-2 & 7 & 20\end{array}\right][/tex]

The second row operation is -

[tex]R_2=R_2+2R_1[/tex]

On applying the second row operation we get -

[tex]\left[\begin{array}{c c | c}1 & \frac{-1}{3} & \frac{4}{3} \\0 & \frac{19}{3} & \frac{68}{3}\end{array}\right][/tex]

The third row operation is -

[tex]R_2=\frac{3}{19}R_2[/tex]

On applying the third row operation we get -

[tex]\left[\begin{array}{c c | c}1 & \frac{-1}{3} & \frac{4}{3} \\0 & 1 & \frac{68}{19}\end{array}\right][/tex]

The fourth row operation is -

[tex]R_1=R_1+{\frac{R_2}{3}}[/tex]

On applying the fourth row operation we get -

[tex]\left[\begin{array}{c c | c} 1 & 0 & \frac{48}{19} \\0 & 1 & \frac{68}{19}\end{array}\right][/tex]

Therefore, the solution is x = 48/19 and y = 68/19.

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Definitions: A definition is a statement that explains the meaning of a word or a concept. It clarifies what something is or what it means. For example, the definition of "circumference" is the distance around a circle.

examples of the question :-

Example: The definition of a polygon is a closed shape with straight lines.

Theorems: A theorem is a statement that has been proven to be true through a logical argument or a set of mathematical steps. Theorem is often used in mathematics, but it can also be used in other fields of study. For example, the Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Example: The theorem of the maximum value of a continuous function on a closed interval states that if f is a continuous function on the closed interval [a, b], then f attains a maximum value and a minimum value on that interval.

Formulas: A formula is a mathematical expression that shows the relationship between two or more variables. It can be used to solve problems or to make predictions. For example, the formula for the area of a rectangle is length times width.

Example: The formula for the circumference of a circle is C=2πr, where C is the circumference, r is the radius, and π is a mathematical constant.

Step-by-Steps: Step-by-step instructions are a series of directions or actions that need to be followed in order to complete a task or solve a problem. It is often used in math or science to explain a process or a procedure. For example, a step-by-step instruction on how to solve a quadratic equation might look like this:

Step 1: Write the equation in standard form.

Step 2: Identify the values of a, b, and c.

Step 3: Substitute these values into the quadratic formula.

Step 4: Simplify the equation and solve for x.

Example: A step-by-step instruction on how to find the derivative of a function might look like this:

Step 1: Identify the function.

Step 2: Use the power rule, product rule, or quotient rule to find the derivative.

Step 3: Simplify the derivative by combining like terms and simplifying fractions.

Step 4: Check your work by taking the derivative of the derivative to see if it matches the original function.

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Answer:

f(g(x))

f(x+9)

5(x+9)-6

5x + 45-6

5x+39

and,

g(f(x))

g(5x-6)

5x-6+9

5x +3

The addition of the red vector <-4, -1>, and the blue vector, <2, 3> indicates that green vector, which is the result of adding the red and blue vectors is; <-2, 2>

A vector is a physical quantity that has both magnitude and direction.

The graphical representation of the red vector can be obtained by making the origin the starting point and ending at the point (-4, -1). The vector points 4 units to the left of the x-direction and downwards 1 units in the y-direction.

Please find attached the drawing of the red vector created with MS Excel

The blue vector can be represented by an arrow that starts at the origin and has an ending point at (2, 3). The blue vector points 2 units to the right in the x-direction and 3 unit upwards in the y-direction.

Please find attached the drawing of the blue vector created with MS Excel

The two vectors can be added by translating the initial point of the red vector to the terminal point of the blue vector, then a new arrow can be drawn to the origin from the new terminal point of the red vector.

The new arrow represents the sum of the vectors

The coordinate of the tip of the new arrow is; (-4 + 2, -1 + 3) = (-2, 2)

The green (new) vector is; <-2, 2>

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Answer:

8

Step-by-step explanation:

7+1

Answer:

x = 100 , y = 6

Step-by-step explanation:

[tex]\frac{x}{5}[/tex] = 20 ( multiply both sides by 5 to clear the fraction )

x = 5 × 20 = 100

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

8y - 6 = 9y - 12 ( subtract 9y from both sides )

- y - 6 = - 12 ( add 6 to both sides )

- y = - 6 ( multiply both sides by - 1 )

y = 6

Answer: 12

Step-by-step explanation:

Answer:

x=√715

Step-by-step explanation:

Using Pythagorean Theorem,,

(34) ^2= (21)^2+x^2

⇒x^2= 1156-441

⇒x^2= 715

⇒x= √715

After answering the provided question, we can conclude that The quadratic equation completed perfect square trinomial is (2c - 11)².

A quadratic equation is x[tex]ax2+bx+c=0[/tex], which is a single variable quadratic polynomial. a 0. Because this polynomial is of second order, the Fundamental Theorem of Algebra ensures that it has at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic equation. This means it has at least one word that must be squared. The formula "[tex]ax2 + bx + c = 0[/tex]" is a common solution for quadratic equations. where a, b, and c are numerical coefficients or constants. where the variable "X" is unidentified.

To make the trinomial [tex]4c² - 22c[/tex] + ... a perfect square, we need to add a constant term that will make it a perfect square trinomial.

Here are the steps to follow:

Therefore, the missing monomial is 121.

The completed perfect square trinomial is (2c - 11)².

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Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that the diameter of a circle is 13ft . We are interested in finding out the circumference of the circle.

Firstly we know that radius is half of the diameter . So we can calculate the radius as ,

[tex]\longrightarrow r =\dfrac{d}{2} \\[/tex]

Substitute the respective value ,

[tex]\longrightarrow r =\dfrac{13}{2} \ ft\\[/tex]

[tex]\longrightarrow r = 6.5 \ ft \\[/tex]

Secondly we can find the circumference as ,

[tex]\longrightarrow \boxed{\rm Circumference= 2\pi r } \\[/tex]

where "r" is the radius of the circle.

On substituting the respective values, we have;

[tex]\longrightarrow C = 2 \pi\times 6.5 \ ft \\[/tex]

[tex]\longrightarrow \boxed{\boldsymbol{ C = 13\pi \ ft }} \\[/tex]

Hence the circumference of the circle is 13π ft .

To determine whether the relation represented in the given table is a function, we need to check whether each input (x-value) in the table is associated with a unique output (y-value).

We can see that the input value "12" has two different output values, "16" and "19". This means that the relation is not a function since the same input is associated with multiple outputs.

Therefore, the relation represented in the given table is not a function.