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3 years ago

Write an equation of the line and interpret the slope:

Mathematics

1 answer:

Alexus [3.1K]3 years ago

3 0

Answer:

Equation = y=3x+12

Slope is 3

Step-by-step explanation:

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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

3 years ago

Make r the subject of the formula in I=E/R+r

allochka39001 [22]

Step-by-step explanation:

$I = \frac{E }{ R} + r$

$I - \frac{ E }{ R} = r$

$\frac{I R -E }{ R} = r$

HOPE IT HELPS Y

8 0

2 years ago

Hot Shot Electronics is designing a packing box for its new line of Acoustical Odyssey speakers. The box is a rectangular prism

Whitepunk [10]

V= W × H × L
81000 = 30 × H × 45
81000 = 1350× H
81000/1350 = 1350/1350× H
H = 60 cm

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3 years ago

Three runners competed in a race. Data were collected at each mile mark for each runner. If the runner ran at a constant pace, t

Pachacha [2.7K]

Answer: Runner C ;)

Step-by-step explanation:

4 0

3 years ago

2.268 nearest whole gram

MissTica

Answer:

It will be 2.27

Since the 8 in 2.268 is larger than 5, the 6 will turn to the next number. So, the answer will be 2.27.

8 0

4 years ago

Read 2 more answers

Write an equation of the line and interpret the slope:​

Write an equation of the line and interpret the slope: