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3 years ago

What is the volume of this prism ?

Mathematics

1 answer:

Cloud [144]3 years ago

8 0

Answer:160 B.

Step-by-step explanation: first you seperate the two rectangles. then find volume of both by multipling lenngh times with times height then add both of your volumes.

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Margo can purchase tile at a store for $0.69 per tile and rent a tile saw for $36. At another store she can borrow the tile saw

TEA [102]

Answer:

<h3>30 tiles need to buy for same cost in both store.</h3>

Step-by-step explanation:

Let x be the number of tiles to buy for same cost in both store.

18+0.69 · n = 1.29 · n,

1.29n -0.69n =18 or

0.6n =18

n =18/0.6=30

Therefore, 30 tiles need to buy for same cost in both store.[Ans]

7 0

2 years ago

Read 2 more answers

A metallurgist needs to make 12.4 lb. of an 10) alloy containing 50% gold. He is going to melt and combine one metal that is 60%

sergeinik [125]

Now, let's say, we add "x" lbs of the 60% gold alloy, so.. how much gold is in it? well, is just 60%, so (60/100) * x, or 0.6x.

likewise, if we use "y" lbs of the 40% alloy, how much gold is in it? well, 40% of y, or (40/100) * y, or 0.4y.

now, whatever "x" and "y" are, their sum must be 12.4 lbs.

we also know that the gold amount in each added up, must equal that of the 50% resulting alloy.

$\bf \begin{array}{lccclll}
&\stackrel{lbs}{amount}&\stackrel{gold~\%}{quantity}&\stackrel{gold}{quantity}\\
&------&------&------\\
\textit{60\% alloy}&x&0.6&0.6x\\
\textit{40\% alloy}&y&0.4&0.4y\\
------&------&------&------\\
\textit{50\% alloy}&12.4&0.50&6.2
\end{array}$

$\bf \begin{cases}
x+y=12.4\implies \boxed{y}=12.4-x\\
0.6x+0.4y=6.2\\
-------------\\
0.6x+0.4\left( \boxed{12.4-x} \right)=6.2
\end{cases}
\\\\\\
0.6x-0.4x+4.96=6.2\implies 0.2x=1.24\implies x=\cfrac{1.24}{0.2}
\\\\\\
x=\stackrel{lbs}{6.2}$

how much of the 40% alloy? well, y = 12.4 - x.

5 0

3 years ago

A cyclist travels 4 miles in 15 minutes and then a further 6 miles in 25 minutes without stopping.

Tcecarenko [31]

Total distance traveled = 4 + 6 = 10 miles

Total time = 15 + 25 = 40 minutes

Speed = 10 miles ÷ 40 minutes = 0.25 mph

7 0

2 years ago

Read 2 more answers

2x - 5y = - 15

UkoKoshka [18]

Answer:

2x+15=5y

y=(2x+15)/5

hope this helps

7 0

2 years ago

Read 2 more answers

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