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1 year ago

The graph of F(x) shown below resembles the graph of G(x) = x4, but it has

Mathematics

1 answer:

DerKrebs [107]1 year ago

3 0

Using translation concepts, the equation of F(x) is:

A. $F(x) = \frac{1}{3}x^4 - 2$

<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.

The parent function is:

$G(x) = x^4$

For function F(x), we have that:

It was shifted down 2 units, hence F(x) = G(x) - 2.

It was vertically compressed by a factor of 3, hence $F(x) = \frac{1}{3}G(x) - 2$

Then the equation is:

A. $F(x) = \frac{1}{3}x^4 - 2$

More can be learned about translation concepts at brainly.com/question/28098112

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3 years ago

A rectangle has a length that is three feet more than twice it’s width. If the area of the rectangle is 90 square feet, then alg

Mkey [24]

Answer:

$Length=27feet\\Width=12 feet$

Step-by-step explanation:

Let, the length of the rectangle be 'L'

and, width of the rectangle be 'W'

length=2*Width+3

$L=(2W+3) feet\\\\$

Area of the rectangle= 90 square feet

Area of a rectangle = Length*Width

$90=(2W+3)*W\\\\2W^2+3W=90\\\\2W^2+3W-90=0\\\\$

Using Factorization Method to solve quadratic equation:

$2W^2-12W+15W-90=0$

Taking common from the equation:

$2W(W-12)+15(W-12)=90\\\\(W-12)(2W+15)=0\\\\W-12=0\\\\W=12 feet$

$2W+15=0\\\\2W=-15\\\\W=-7.5 feet$

The Width cannot be negative, therefore Width(W)=12 feet

$Length=2*Width+3\\\\=(12*2)+3\\\\=24+3\\\\=27 feet$

$Length=27feet\\Width=12 feet$

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3 years ago

Lorena is trying to choose between two different savings accounts at H-Town Bank. She will deposit $3,500 dollars and will leave

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3 years ago

What is the equation in point slope form of the line that is parallel to the given line and passes through the point (4,1)?

vovikov84 [41]

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

$y-1=\stackrel{\stackrel{m}{\downarrow }}{2}(x-4)\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}$

so we're really looking for the equation of a line with a slope of 2 and that it passes through (4 , 1)

$(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{2}(x-\stackrel{x_1}{4})$

kinda twins.

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1 year ago

What are the x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2? x = (

Crank

The x =0 and y = 1 are coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2.

<h2>We have to determine</h2>

What are the x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2?

<h3>According to the question</h3>

A line segment at points A(2, -3) and B (-4, 9).

The x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2 is given by;

$\rm x=\dfrac{m}{(m+n)} [x_2- x_1]+ x_1 \\
\\
 y=\dfrac{m}{(m+n)} [y_2- y_1]+ y_1 \\
\\$

Where $\rm x_1 = 2 , \ x_2 =-4, \ y_1 =-3, \ y_2 = 9$

Substitute all the values in the formula;

$\rm x=\dfrac{m}{(m+n)} [x_2- x_1]+ x_1 \\\\$

$\rm x=\dfrac{1}{(1+2)} [-4-(2)]+ (2)\\\\ x = \dfrac{1}{3} \times (-6) +2 \\
\\
x = -2+2\\
\\
x=0$

$\rm y=\dfrac{m}{(m+n)} [y_2- y_1]+ y_1 \\\\ y=\dfrac{1}{(1+2)} [9-(-3)]+ (-3)\\\\
y = \dfrac{1}{3} \times (12) -3\\
\\
y = 4-3\\
\\
y =1$

Hence, the x =0 and y = 1 are coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2.

To know more about Coordinates click the link given below.

brainly.com/question/13847533

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3 years ago