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3 years ago

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Please HELP I NEED HELPPPPPPPPPPPPP Natasha is constructing the bisector of PQ¯¯¯¯¯. She has already constructed an arc as shown

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What should Natasha do for her next step?

A. Place the point of the compass on point X and draw an arc, using QX as the width for the opening of the compass.

B. Place the point of the compass on point X and draw an arc, using the same width for the opening of the compass as the first arc.

C. Place the point of the compass on point Q and draw an arc, using the same width for the opening of the compass as the first arc.

D. Place the point of the compass on point Q and draw an arc, using QX as the width for the opening of the compass.

1 answer:

Korvikt [17]3 years ago

6 0

C is your correct answer

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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

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,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

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2 years ago

Do not pass go. proposition or not?

kolbaska11 [484]

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8 0

3 years ago

Dominic had $500 in his wallet. He went to the nursery and purchased 8 rose bushes at $22 each, 12 evergreen shrubs at $18 each,

timurjin [86]

Answer:

176+216+75=467

500-467=33

so 33 is the answer

Step-by-step explanation:

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3 years ago

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What is the quotient of -3/8 and -1/3?

Sedaia [141]

Answer:

D

Step-by-step explanation:

-3/8 ÷ (-1/3)

-3/8 × (-3/1)

9/8

1 1/8

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3 years ago

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A collection of nickels and quarters are worth $2.85. There are 3 more nickels than quarters. How many nickels and quarters are

Alex777 [14]

Answer:

nickels = 12

quarters = 9

Step-by-step explanation:

Let number of quarters be "q", and

number of nickels be "n"

Nickels are worth $0.05 and Quarters are worth $0.25

Since all of them are worth 2.85, we can write:

0.25q + 0.05n = 2.85

Also, we know, there are 3 more nickels than quarters, so we can write:

n = 3 + q

Now, we can substitute equation 2 into equation 1 to get:

$0.25q + 0.05n = 2.85\\0.25q + 0.05(3+q) = 2.85\\0.25q+0.15+0.05q=2.85$

Now, we solve for q:

$0.25q+0.15+0.05q=2.85\\0.3q=2.70\\q=9$

There are 9 quarters.

We know n = 3 + q

So,

n = 3 + 9

n = 12

There are 12 nickels

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3 years ago