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3 years ago

Find the area of the missing piece of the polygon and explain your process for finding it:

Mathematics

1 answer:

Otrada [13]3 years ago

8 0

Answer:

Step-by-step explanation:

In short, the sum of the opposite areas are equal.

x + 30 = 24 + 48

x = 42

To prove this, draw a line from each corner to the "center" where the four lines meet. Along each side of the square are two triangles. These triangles have the same base and the same height, and therefore have the same area.

If we say the triangles at the bottom have area a, the triangles on the left have area b, the triangles on top have area c, and the triangles on the right have area d, then we can write 4 equations:

a + b = x

b + c = 24

c + d = 30

a + d = 48

Adding the first and third equations:

a + b + c + d = x + 30

Adding the second and fourth equations:

a + b + c + d = 24 + 48

Therefore:

x + 30 = 24 + 48

x = 42

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0.3% of 460 plz is for tomorrow

DochEvi [55]

Answer:

1.38

Step-by-step explanation:

7 0

3 years ago

store announced that their $500 appliances were on sale for $475 what is the percent discount on the appliances

Aleks04 [339]

Answer:

We are given that a store announced that their $500 appliances were on sale.

The price of the appliances after discount is $475.

We are required to find the percent discount on the appliances.

To find the percent discount, we have to use the below formula:

$\frac{(Actual-discounted)}{Actual} \times 100\%$

$\frac{500-475}{500}\times 100\%$

$\frac{25}{500} \times 100\%$

$0.05 \times 100\%$

$5\%$

Therefore, the percent discount on the appliances is 5%

6 0

3 years ago

How many centimeters long is a leg of an isosceles right triangle if its hypotenuse has a length of 8√2 centimeters?

andrew-mc [135]

Answer:

The leg is 8 cm long

Step-by-step explanation:

An isosceles right triangle has the length of its hypotenuse and opposite equal

Let us call the length x

From Pythagoras’ , the square of the hypotenuse equals the sum of the squares of the two other sides

Thus, we have ;

x^2 + x^2 = (8 √2)^2

2x^2 = 128

x^2 = 128/2

x^2 = 64

x= √64

x = 8 cm

7 0

3 years ago

Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

The answer is none of the choices

7 0

1 year ago

You want to make a rectangular banner that is 18ft. Long with a trim around the entire border of the banner . You have no more t

lys-0071 [83]

Answer:

6 ft

Step-by-step explanation:

Given that:

Length of rectangular banner = 18 ft

Total trim of banner available = 48 ft

To find:

Possible widths of the banner = ?

Solution:

Maximum trim available of the banner around the entire border of the banner = 48 ft

i.e. we are given the total perimeter of the rectangular banner.

Formula for perimeter of a rectangle is given as:

$Perimeter = 2 \times (Length + Width)$

Putting the values of perimeter and length to find the value of width.

$48 = 2 \times (18 + Width)\\\Rightarrow 48 =36+2 \times Width\\\Rightarrow 2 \times Width = 48-36\\\Rightarrow 2 \times Width = 12\\\Rightarrow \bold{Width = 6\ ft}$

So, width possible is <em>6ft.</em>

3 0

3 years ago