What is the perimeter of abcd ?

2. a. A fish is 12 meters below the surface of the ocean. What is its elevation?

Alex17521 [72]

Answer:

A. -12 meters

B. 28 meters

C. 40 meters

Step-by-step explanation:

The surface of the ocean would be 0.

Taking this into account, 12 meters below would be 0 - 12, which is -12. Therefore A's elevation would be -12.

For the sea bird, 28 meters above the surface, which is again 0, would be 0 + 28. B's elevation is 28.

Since the fish is 12 meters below the surface and the sea bird is 28 meters above the surface, simply add the two numbers up to get a total of 40 meters. C would be 40 meters.

5 0

3 years ago

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A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

Sveta_85 [38]

Answer:

$\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

$\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s$

where B stands for Base area

and P for Base Parimeter

so

$\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s$

now we need our algebraic skills to figure out s

simplify parentheses:

$\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144$

reduce fraction:

$\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144$

simplify multiplication:

$\displaystyle \: 16s + 64 = 144$

cancel 64 from both sides;

$\displaystyle \: 16s = 80$

divide both sides by 16:

$\displaystyle \: \therefore \: s = 5$

now we'll use Pythagoras theorem to figure out height

according to the theorem

$\displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2}$

substitute the value of l and s:

$\displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2}$

simplify parentheses:

$\displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2}$

simplify squares:

$\displaystyle \: {h}^{2} + 16 = 25$

cancel 16 from both sides:

$\displaystyle \: {h}^{2} = 9$

square root both sides:

$\displaystyle \: \therefore \: {h}^{} = 3$

recall the formula of a square pyramid

$\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h$

where A stands for Base area (l²)

substitute the value of h and l:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3$

simplify multiplication:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3$

reduce fraction:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}$

hence,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

8 0

3 years ago

Let P=x^2+6<br> PLEASE SHOW WORK!!<br> 15 POINTS

stellarik [79]

Answer:

Step-by-step explanation:

P = x^2 + 6

$(x^2+6)^2 - 21 = 4x^2 + 24\\(x^2+6)^2 - 4x^2 - 45 = 0$

Solving for 4x^2:

P = x^2 +6

P - 6 = x^2

4(P - 6) = 4x^2

Substitution:

$p^2 - 4p - 24 - 45 = 0\\p^2 -4p - 69 = 0$

4 0

3 years ago

How many faces does the solid made from the net below have? A. 7B. 8C. 12D. 18

Kruka [31]

Answer:

B. 8

Explanation:

The figure forms a septagon.

The hexagons form the base, and the rectangles attached to them form the sides.

Therefore, in total the solid has two hexagons as sides and 6 rectangles connecting the hexagon to the base hexagon. Hence, in total the solid has

2 + 6 = 8 faces.

7 0

2 years ago

Covert 15/7/8 to a decimal

serg [7]

Answer:

0.268

Step-by-step explanation:

In the attached file

4 0

3 years ago

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