Complete the function for this graph.

Can you please help me find the area? Thank you. :)))

Phoenix [80]

The figure shown in the picture is a rectangular shape that is missing a triangular piece. To determine the area of the figure you have to determine the area of the rectangle and the area of the triangular piece, then you have to subtract the area of the triangle from the area of the rectangle.

The rectangular shape has a width of 12 inches and a length of 20 inches. The area of the rectangle is equal to the multiplication of the width (w) and the length (l), following the formula:

$A=w\cdot l$

For our rectangle w=12 in and l=20 in, the area is:

$\begin{gathered} A_{\text{rectangle}}=12\cdot20 \\ A_{\text{rectangle}}=240in^2 \end{gathered}$

The triangular piece has a height of 6in and its base has a length unknown. Before calculating the area of the triangle, you have to determine the length of the base, which I marked with an "x" in the sketch above.

The length of the rectangle is 20 inches, the triangular piece divides this length into three segments, two of which measure 8 inches and the third one is of unknown length.

You can determine the value of x as follows:

$\begin{gathered} 20=8+8+x \\ 20=16+x \\ 20-16=x \\ 4=x \end{gathered}$

x=4 in → this means that the base of the triangle is 4in long.

The area of the triangle is equal to half the product of the base by the height, following the formula:

$A=\frac{b\cdot h}{2}$

For our triangle, the base is b=4in and the height is h=6in, then the area is:

$\begin{gathered} A_{\text{triangle}}=\frac{4\cdot6}{2} \\ A_{\text{triangle}}=\frac{24}{2} \\ A_{\text{triangle}}=12in^2 \end{gathered}$

Finally, to determine the area of the shape you have to subtract the area of the triangle from the area of the rectangle:

$\begin{gathered} A_{\text{total}}=A_{\text{rectangle}}-A_{\text{triangle}} \\ A_{\text{total}}=240-12 \\ A_{\text{total}}=228in^2 \end{gathered}$

The area of the figure is 228in²

8 0

1 year ago

Is the following relation a function? (4,2), (1,1), (0,0), (1, -1), (4, -2). Give the domain and range.

Vlada [557]

(x,y)
to be a function
for every x, ther must be only 1 y to corespond to it
basically, x must NEVER repeat with a different y
list them

ah, we see (1,1) an d(1,-1)
also (4,2) and (4,-2)
double offense
1 repeats with 1 and -1
4 repeats with 2 and -2

not a function

domain is all x values
range is all y values
if they repeat, don't list them

domain=(0,1,4)
range=(-2,-1,0,1,2)

8 0

4 years ago

If you have 80 employees and you grew 116%, what was the amount of original employees?

Nezavi [6.7K]

Answer: 69

Step-by-step explanation:

Let the original employee be x , this means that

116% of x = 80

$\frac{116x}{100}$ = 80

116x = 8000

divide through by 116

x = 8000/116

x = 68.96551724

Since we are dealing with employees , therefore x ≈ 69

This means that there were 69 employees originally

7 0

3 years ago

Every 3 Days Marco fills up his car with gas. Every 3 Days he washes his car. On what day will Marco fill his car and wash it.

GenaCL600 [577]

The answer is Thursday and Sunday hope this helps :D

8 0

3 years ago

Determine the standard deviation of the data below. (1, 2, 3, 4, 5)

Burka [1]

Answer:

$\sqrt{2}$ or 1.414

Step-by-step explanation:

1) Find the mean. 1+2+3+4+5 = 15. 15/5= 3

2) For each data point, find the square of its distance to the mean. (4, 1, 0, 1, 4)

3) Sum the values from Step 2. 10

4) Divide by the number of data points. 10/5= 2

5) Take the square root. $\sqrt{2}$

4 0

3 years ago