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1 year ago

Which function is a translation of the parent absolute value function?f(x) = 2X1 f(x) = (x+61f(x) = |x|F(x) = -4X1

Mathematics

1 answer:

artcher [175]1 year ago

8 0

Answer

Explanation

Translations move the parent function toward the left, right, downwards or upwards.

f(x) = 2 |x|

This stretches the function by a factor of 2, hence, it is not a translation.

f(x) = |x + 6|

This translates the parent absolut value functio

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The figure shows the layout of a symmetrical pool in a water park. What is the area of this pool rounded to the tens place? Use

k0ka [10]

Answer:

$2489ft^{2}$

Step-by-step explanation:

The pool are is divided into 4 separated shapes: 2 circular sections and 2 isosceles triangles. Basically, to calculate the whole area, we need to find the area of each section. Due to its symmetry, both triangles are equal, and both circular sections are also the same, so it would be enough to calculate 1 circular section and 1 triangle, then multiply it by 2.

<h3>Area of each triangle:</h3>

From the figure, we know that <em>b = 20ft </em>and <em>h = 25ft. </em>So, the area would be:

$A_{t}=\frac{b.h}{2}=\frac{(20ft)(25ft)}{2}=250ft^{2}$

<h3>Area of each circular section:</h3>

From the figure, we know that $\alpha =2.21 radians$ and the radius is $R=30ft$ . So, the are would be calculated with this formula:

$A_{cs}=\frac{\pi R^{2}\alpha}{360\°}$

Replacing all values:

$A_{cs}=\frac{(3.14)(30ft)^{2}(2.21radians)}{6.28radians}$

Remember that $360\°=6.28radians$

Therefore, $A_{cs}=994.5ft^{2}$

Now, the total are of the figure is:

$A_{total}=2A_{t}+2A{cs}=2(250ft^{2} )+2(994.5ft^{2})\\A_{total}=500ft^{2} + 1989ft^{2}=2489ft^{2}$

Therefore the area of the symmetrical pool is $2489ft^{2}$

3 0

3 years ago

What is the slope of a line that is perpendicular to the line x = –3? –3 0 1/3 undefined

Elena L [17]

Answer:

slope = 0

Step-by-step explanation:

The line with equation x = - 3 is a vertical line parallel to the y- axis

A perpendicular line is therefore a horizontal line parallel to the x- axis

The slope of the x- axis is zero, hence the slope of the horizontal line is

slope = 0

8 0

3 years ago

Davis Construction is building a new housing development. They begin by mapping the development out on a coordinate grid. They p

Mandarinka [93]

$\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -4}}\quad ,&{{ -1}})\quad 
% (c,d)
&({{ 6}}\quad ,&{{ 3}})
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left(\cfrac{{{ 6}} -4}{2}\quad ,\quad \cfrac{3-1}{2} \right)$