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2 years ago

What is 6x - 9 = 15?

1 answer:

6 0

Add 9 to both sides and you get 6x=24 then you divide 6 from both sides to get x by its self and the final answer will be 4

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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

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

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

Write an expression for 621 less d

MaRussiya [10]

D - 621 is the answer

3 0

3 years ago

Invasive species often experience exponential population growth when introduced into a new environment. Zebra mussels are an inv

Oliga [24]

Answer:

If ‘a’ is the initial population of the Zebra mussels, then every six months, the population of Zebra mussels quadruples, i.e. it becomes 4a. In t years, i.e. in 2t intervals of 6 months each, the population of Zebra mussels can be computed with the help of a geometric series a, ar, ar2, ar3, …. arn-1 ( the series being finite with n terms) where a is the 1st term , r is the common ratio and n is the number of terms in the series..

Here, in 2t years, there will be 2t + 1 terms in the geometric series including the initial term. Thus in the above series, a = 10, r = 4 and n = 2t + 1. Then the population of the Zebra mussels after 2t years is the (2t +1)st term of the geometric series I.e. 10* ( 42t)

In 15 months, t = 15/12 = 1.25. Then the population of Zebra mussels after 15 months will be 10*(42.5 ) = 10 * 25 = 320

If after t years, the population of the Zebra mussels become 1 million , then we have

1000000 = 10 * (42t) or, 100000= 42t or,105 = 42t Taking logarithms of both sides, we have 5 log 10 = 2t log 4 or, t = (5log10)/(2log4) = 5/1.20 years or (5/1.20) * 12 months = 50 months, i.e. 4 years and 2 months.

Step-by-step explanation:

8 0

3 years ago

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Need help PlsSSSSSSSSSSSSSSSSSSSSSSS

Makovka662 [10]

Answer:

min = 24 LQ = 27 median = 32 UQ = 37 Max=44

3 0

3 years ago

Read 2 more answers

39% of 50 is what number