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3 years ago

Twelve decreased by twice a number is the same as 8 times the sum of the number and 4. What is the number.

Mathematics

1 answer:

oksano4ka [1.4K]3 years ago

7 0

Answer: -2

Step-by-step explanation:

Let the number be x , then twice the number is 2x.

Twelve decreased by twice the number = 12 - ( 2x )

8 times the sum of the number and 4 = 8 ( x + 4 )

combining the two , we have

12 - 2x = 8 ( x + 4 )

12 - 2x = 8x + 32

12 - 32 = 8x + 2x

-20 = 10x

x = -20/10

x = -2

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Answer:

y=2x-2

Step-by-step explanation:

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4 years ago

NO LINKS!!! What is the transformation f(x)= x^3:

Mama L [17]

Answer:

4. Horizontal shrink by a factor of ¹/₅

5. Left 5, Up 5

6. Right 5, Down 5

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

For a > 0

$f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}$

$f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}$

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

$f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}$

$y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a$

$y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}$

$y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}$

$y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}$

Identify the transformations that take the parent function to the given function.

Question 4

$\textsf{Parent function}: \quad f(x)=x^3$

$\textsf{Given function}: \quad f(x)=(5x)^3$

Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by 5.

Therefore, the transformation is:

$y=f(5x) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{5}$

As a > 1, the transformation visually is a compression in the x-direction, so we can also say: Horizontal shrink by a factor of ¹/₅

Question 5

$\textsf{Parent function}: \quad f(x)=x^3$

$\textsf{Given function}: \quad f(x)=(x+5)^3+5$

Comparing the parent function with the given function, we can see that there are a series of transformations:

Step 1

5 has been added to the x-value of the parent function.

$f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}$

Step 2

5 has then been added to function.

$f(x+5)+5 \implies f(x+5) \: \textsf{translated}\:5\:\textsf{units up}$

Transformation: Left 5, Up 5

Question 6

$\textsf{Parent function}: \quad f(x)=x^3$

$\textsf{Given function}: \quad f(x)=(x-5)^3-5$

Comparing the parent function with the given function, we can see that there are a series of transformations:

Step 1

5 has been subtracted from the x-value of the parent function.

$f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}$

Step 2

5 has then been subtracted from function.

$f(x-5)-5 \implies f(x-5) \: \textsf{translated}\:5\:\textsf{units down}$

Transformation: Right 5, Down 5

Learn more about graph transformations here:

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2 years ago

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Plz plz plz help me out!!

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3 years ago

Which statement is true regarding the graphed functions?

Vladimir79 [104]

let's analyze each case to determine the solution

case 1) f(0) = 2 and g(–2) = 0

For x=0-----> find the value of f(0) in the graph-----> f(0)=4

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 1) is false

case 2) f(0) = 4 and g(–2) = 4

For x=0-----> find the value of f(0) in the graph-----> f(0)=4

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 2) is false

case 3) f(2) = 0 and g(–2) = 0

For x=2-----> find the value of f(2) in the graph-----> f(2)=0

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 3) is true

case 4) f(–2) = 0 and g(–2) = 0

For x=-2-----> find the value of f(-2) in the graph-----> f(-2) is greater than 12

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 4) is false

therefore

the answer is

f(2) = 0 and g(–2) = 0-------> this statement is true

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4 years ago

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A home has a room with length 22 feet and width 25 ft.

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Answer:

O length = 11 inches width = 12.5 inches

Step-by-step explanation:

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