45 mi/h = how many ft/s

Which set of side lengths form a right triangle?

sergiy2304 [10]

It is the last numbers I'm positive

6 0

3 years ago

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

Two-step equations. Solve X 7x - 32 = 3

tester [92]

7x-32=3
7x=3+32
7x=35
x=35/7
x=5
HOPE IT HELPS U!!
have a great day ahead ! :)

4 0

3 years ago

I was absent when we learned this, please help

Lapatulllka [165]

Part a
For horizontal 8*50% = 4 and for vertical 12*75%= 9.
So these values are less than the originals so the new frame is a reduction.
Part b
For horizontal 8*125% = 8*1.25 = 10 and for vertical 12*140% = 12*1.4 =16.8
So these values are greater than the originals sothe new frame is a enlargement.

5 0

3 years ago

The equation p=100-10t represents the percent p of battery power remaining in a cell phone after t hours

Fantom [35]

Answer:

We have the equation:

P(t) = 100 - 10*t

where t is the number of hours.

at t = 0, we have:

P(0) = 100 - 0 = 100

so at the initial time, we have 100% of the battery power.

Now with this equation we can find the numbers of hours that we have left in our phone, this is finding the time t at which the power left is equal to zero:

P(t) = 0 = 100 - 10*t

10*t = 100

t = 100/10 = 10

So the battery power will last for 10 hours.

7 0

3 years ago