Given m||n, find the value of x.<br> +<br> m<br> (2x+6)º(x+9)<br> Someone please help?

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

2 years ago

You and three friends go to the town carnival. You have a coupon for $20 off that will save your group money! If the total bill

Lunna [17]

Answer:

30 that singular tickets for each friend and if your asking for total it would be 120. :)

Step-by-step explanation:

They paid 100 but they had a 20$ off coupon, this means the orignial total would be $120 so 120 divided by 4 (there's four people) = $30 each :)

hope this helped

5 0

2 years ago

What is the quadratic function that is created with roots at 2 and 4 and a vertex at (3, 1)?

Arada [10]

Hello,

y=k*(x-2)(x-4)
and is passing throught (3,1)
==>1=k*(3-2)(3-4)==>k=-1

y=-(x-2)(x-4) is an answer

4 0

2 years ago

Please answer this correctly

katen-ka-za [31]

Answer:

8

Step-by-step explanation:

Okay so there is 32 cups in 8 quarts and he sold 6 cups Saturday and 18 cups Sunday.

Add 8+18

Subtract 24-32 to get 8

6 0

3 years ago

Read 2 more answers

3/5 List the first five multiples of the denominator of the fraction in order.

inessss [21]

5: 5, 10,15,20,25 ( Not sure if 5 counts as one, if it does not, then 30 is another multiple.)

5 0

3 years ago

Given m||n, find the value of x. + m (2x+6)º(x+9) Someone please help?