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hjlf
3 years ago
12

An 8-sided die is formed when two square pyramids are attached by their bases. The perimeter of the base shape is 6 centimeters.

The distance between the tallest points of the two pyramids is 2 centimeters.
Mathematics
1 answer:
lawyer [7]3 years ago
3 0

Answer:

7.5cm²

Complete question:What is the surface area of the 8-sided figure?

Step-by-step explanation:

Consider the half of the 8-sided die i.e the pyramid ABCDE:

As the base is 6 of the perimeter, so each side of the base is 6/4=3/2

Now, the distance between the tallest points is 2 cm, so the height of Pyramid ABCDE is 1 cm.

Considering the right triangle EOM:

EO=1, OM= 3/4 (it is half of AB=3/2) and EM is the hypothenuse, so by the pythagorean theorem length of EM is 

\sqrt{1+ ( \frac{3}{4} )^{2} }=  \sqrt{1+ \frac{9}{16} }= \sqrt{ \frac{25}{16} }= \frac{5}{4}   (cm)

5. So side EBC has area  

\frac{1}{2}BC*EM=  \frac{1}{2}* \frac{3}{2}* \frac{5}{4}= \frac{15}{16}

6. The total area is 8*Area(EBC)=8* \frac{15}{16}= \frac{15}{2}=7.5 ( cm^{2} )

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8.4.9 On or off the line & Practice Problems
Andrews [41]

Answer:

Number of quarters → 15

Number of dimes → 2

Step-by-step explanation:

Let the number of dimes I have = y

And number of quarters = x

Since, I have amount in my pocket = $2

Therefore, 0.10y + 0.25x = 2

100(0.10y + 0.25x) = 100×2

25x + 10y = 200

5x + 2y = 40

2y = -5x + 40

y = -2.5x + 20 ---------(1)

Total number of coins in my pocket = 17

x + y = 17

y = -x + 17 ---------(2)  

By using a graphing calculator we can graph these two lines (As attached)

Solution of the given system of equations will be the point of intersection of these lines.

Solution → (2, 15)

Number of quarters → 15

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4 0
3 years ago
PLEASE ANSWER- Which sequence is graphed below?
boyakko [2]

Answer:

pretty sure its C, good luck

6 0
2 years ago
Point A has the coordinates (2,2). What are the coordinates of its image point if it is translated 2 units up and 5 units to the
Marysya12 [62]
A translation of 2 units up will increase the y coordinate by 2 units and a translation by 5 units to the left will decrease the x coordinate by 5. Hence after these translations point (2,2) becomes 

<span>(2 - 5 , 2 + 2) = (-3,4) </span>

When point (-3,4) is reflected in the x axis, its y coordinate changes sign and point (-3 ,4) becomes 

<span>(-3,-4)</span>
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3 years ago
The graph shows a function f(x). Determine the following values.
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2

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Step-by-step explanation:

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6 0
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Read 2 more answers
The height of a parallelogram is 5 feet more than it's base. If the area of the parallelogram is 204 square feet, what is its ba
siniylev [52]
The base is x.
The height is 5 feet more than the base, so it's x+5.
The area of a parallelogram is the product of its base and its height. The area is 204 square feet.

x(x+5)=204 \\&#10;x^2+5x=204 \\&#10;x^2+5x-204=0 \\&#10;x^2+17x-12x-204=0 \\&#10;x(x+17)-12(x+17)=0 \\&#10;(x-12)(x+17)=0 \\&#10;x-12=0 \ \lor \ x+17=0 \\&#10;x=12 \ \lor \ x=-17

The length of the base of a parallelogram must be a positive number, so x=12.

\hbox{the base:} \\ x=12 \\ \\&#10;\hbox{the height:} \\ x+5=12+5=17

The base is 12 feet long, the height is 17 feet long.
8 0
3 years ago
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