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3 years ago

#5: Solve the following equation 60=5r-4r+14 (Show Work Here)

Mathematics

1 answer:

BigorU [14]3 years ago

6 0

Answer:

r = 46

Step-by-step explanation:

To solve the equation, solve for r by isolating the variable. Whatever you do to one side, do to the other.

1) First, simplify the right side by combining like terms. Subtract the coefficients of the terms with the same variables. Subtract 5r by 4r.

$60 = 5r-4r + 14\\60 = r + 14$

2) Now, finally isolate r by subtracting both sides by 14.

$60 = r + 14\\46 = r$

So, r = 46.

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What is the transformation of f(x)= x^3:

mariarad [96]

Answer:

7. Down 5

8. Horizontal reflection

9. Vertical stretch by a factor of 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 7

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

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

Comparing the parent function with the given function, we can see that 5 has been subtracted from the parent function.

Therefore, the transformation is:

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

Question 8

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

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

Comparing the parent function with the given function, we can see that the parent function has been multiplied by -1.

Therefore, the transformation is:

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

Question 9

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

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

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

Therefore, the transformation is:

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

Learn more about graph transformations here:

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2 years ago

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3 years ago

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kirill115 [55]

Answer:

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Step-by-step explanation:

Given that,

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