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kogti [31]

3 years ago

iv 3(12 + x) = - 8(6 - x)" alt="1 \div 3(12 + x) = - 8(6 - x)" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Darya [45]3 years ago

8 0

Buckle up, this one was a long one.

I set up 1 / 3(12 + x) as a fraction and set it equal to - 8(6 - x).

Get rid of the parentheses by distributing the integers on the outside. You get 1 / 36 + 3x = - 48 + 8x.

To get rid of the fraction, you multiply both sides by the (36 + 3x) polynomial to get 1 = (- 48 + 8x)(36 + 3x).

Now we do the FOIL method to get 1 = 24x^2 + 288x - 144x - 1728. Combine like terms to get 24x^2 + 144x - 1728 = 1.

Simply again by dividing each term the GCF of 24 to get 24(x^2 + 6x - 72) = 1.

Factor the inside of the parentheses to get 24(x + 12)(x - 6) = 1. Now divide both sides by 24 to isolate the x variables to get (x + 12)(x - 6) = 1/24.

Set each polynomial equal to 1/24 to get you possible answers for what x can be.

x + 12 = 1/24. Subtract 12 from both sides; you get x = - 12 + 1/24 to get x = - 11 23/24.

x - 6 = 1/24. Add 6 to both sides; you get x = 6 + 1/24 to get x = 6 1/24

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A triangle is shown. The table names different transformations that can be applied to the triangle.

Citrus2011 [14]

The given transformations are rigid transformation in which the image

can be located by a formula.

Response:

First reflect across the x-axis then reflect across the y-axis

Figure: Second graph

First, rotate 180° counterclockwise around the origin. Then reflect across the x-axis.

Figure: Third graph

First translate 9 units to the left. Then reflect across the x-axis

Figure: First graph

<h3>Which method is used to determine the transformation of an image?</h3>

The coordinates of (x, y) following a reflection across the x-axis is (x, -y)

The coordinates following a reflection across the y-axis is (-x, y)

The points of the triangle following the first transformation is therefore;

(4, 4) → (4, -4) → (-4, -4)

(8, 4) → (8, -4) → (-8, -4)

(6, 6) → (6, -6) → (-6, -6)

The image from the first transformation is (-4, -4), (-8, -4), (-6, -6), which

corresponds to the <u>second graph</u>.

The coordinates following a rotation of (x, y) by 180° about the origin is (-x, -y)

A reflection of the point (-x, -y) about the x-axis is (-x, y).

Therefore;

(4, 4) → (-4, -4) → (-4, 4)

(8, 4) → (-8, -4) → (-8, 4)

(6, 6) → (-6, -6) → (-6, 6)

The image from the second transformation is (-4, 4), (-8, 4), (-6, 6), which corresponds to the <u>third graph</u>.

The coordinates following a translation of 9 units to the left is (x - 9, y)

A reflection of the point (x - 9, y) about the x-axis is (x - 9, -y)

Therefore;

(4, 4) → (4 - 9, -4) = (-5, -4)

(8, 4) → (8 - 9, -4) = (-1, -4)

(6, 6) → (6 - 9, -6) → (-3, -6)

The image from the third transformation is (-13, -9), (-1, -4), (-7, -6), which corresponds to the<u> first graph</u>.

Learn more about rigid transformations here:

brainly.com/question/11408409

6 0

2 years ago

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Describe the transformations necessary to transform f(x) into g(x)

Aleks [24]

Using translation concepts, the transformations are given as follows:

a) The function is horizontally compressed by a factor of 3 and shifted down one unit.

b) The function is shifted right 3 units and vertically stretched by a factor of 2.

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Item a:

The transformations are:

x -> 3x, hence the function is horizontally compressed by a factor of 3.

y -> y - 1, hence the function is shifted down one unit.

Item b:

The transformations are:

x -> x - 3, hence the function is shifted right 3 units.

y -> 2y, hence the function is vertically stretched by a factor of 2.

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2 years ago

F(x)= x-2/ x-4

hodyreva [135]

Answer:

The discontinuity is x = 4

There no holes

The equation of the vertical asymptote is x = 4

The x intercept is 2

The equation of the horizontal asymptote is y = 1

Step-by-step explanation:

* Lets explain the problem

∵ $f(x)=\frac{x-2}{x-4}$

- To find the point of discontinuity put the denominator = 0 and find

the value of x

∵ The denominator is x - 4

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

* The discontinuity is x = 4

- A hole occurs when a number is both a zero of the numerator

and denominator

∵ The numerator is x - 2

∵ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

∵ The denominator is x - 4

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∵ There is no common number makes the numerator and denominator

equal to 0

∴ There no holes

- Vertical asymptotes are vertical lines which correspond to the zeroes

of the denominator of the function

∵ The zero of the denominator is x = 4

∴ The equation of the vertical asymptote is x = 4

- x- intercept is the values of x which make f(x) = 0, means the

intersection points between the graph and the x-axis

∵ f(x) = 0

∴ $\frac{x-2}{x-4}=0$ ⇒ by using cross multiplication

∴ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

* The x intercept is 2

- If the highest power of the numerator = the highest power of the

denominator, then the equation of the horizontal asymptote is

y = The leading coeff. of numerator/leading coeff. of denominator

∵ The numerator is x - 2

∵ The denominator is x - 4

∵ The leading coefficient of the numerator is 1

∵ The leading coefficient of the denominator is 1

∴ y = 1/1 = 1

* The equation of the horizontal asymptote is y = 1

6 0

3 years ago

Factor: k^2 + 7x + 10<br> A:(k+10)(k+4)<br> B:(k+2)(k+5)<br> C:(k+2)(k-5)<br> D:(k-2)(k-5)

Nata [24]

Answer:

the answer is B. (k+2)(k+5)

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