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3 years ago

5

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

ct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the total area for the regular pyramid.

T. A. =

1 answer:

Vanyuwa [196]3 years ago

8 0

The total is 172,800 or 120

You might be interested in

Mrs . Porcelli’s classroom bulletin board is 2/1/4 feet long. Ms .Smith bulletin board is 3 times as long Mrs . Porcelli’s.How l

snow_lady [41]

Answer:

$6\frac{3}{4}\ ft$

Step-by-step explanation:

we know that

To find out how long is Ms.Smith’s bulletin board, multiply Mrs . Porcelli’s bulletin board by 3

so

$2\frac{1}{4}(3)$

but first convert mixed number to an improper fraction

so

$2\frac{1}{4}\ ft=2+\frac{1}{4}=\frac{9}{4}\ ft$

substitute

$\frac{9}{4}(3)=\frac{27}{4}\ ft$

convert to mixed number

$\frac{27}{4}\ ft=\frac{24}{4}+\frac{3}{4}=6\frac{3}{4}\ ft$

3 0

3 years ago

Solve the following equations: (a) x^11=13 mod 35 (b) x^5=3 mod 64

tino4ka555 [31]

a.

$x^{11}=13\pmod{35}\implies\begin{cases}x^{11}\equiv13\equiv3\pmod5\\x^{11}\equiv13\equiv6\pmod7\end{cases}$

By Fermat's little theorem, we have

$x^{11}\equiv (x^5)^2x\equiv x^3\equiv3\pmod5$

$x^{11}\equiv x^7x^4\equiv x^5\equiv6\pmod 7$

5 and 7 are both prime, so $\varphi(5)=4$ and $\varphi(7)=6$ . By Euler's theorem, we get

$x^4\equiv1\pmod5\implies x\equiv3^{-1}\equiv2\pmod5$

$x^6\equiv1\pmod7\impleis x\equiv6^{-1}\equiv6\pmod7$

Now we can use the Chinese remainder theorem to solve for $x$ . Start with

$x=2\cdot7+5\cdot6$

Taken mod 5, the second term vanishes and $14\equiv4\pmod5$ . Multiply by the inverse of 4 mod 5 (4), then by 2.

$x=2\cdot7\cdot4\cdot2+5\cdot6$

Taken mod 7, the first term vanishes and $30\equiv2\pmod7$ . Multiply by the inverse of 2 mod 7 (4), then by 6.

$x=2\cdot7\cdot4\cdot2+5\cdot6\cdot4\cdot6$

$\implies x\equiv832\pmod{5\cdot7}\implies\boxed{x\equiv27\pmod{35}}$

b.

$x^5\equiv3\pmod{64}$

We have $\varphi(64)=32$ , so by Euler's theorem,

$x^{32}\equiv1\pmod{64}$

Now, raising both sides of the original congruence to the power of 6 gives

$x^{30}\equiv3^6\equiv729\equiv25\pmod{64}$

Then multiplying both sides by $x^2$ gives

$x^{32}\equiv25x^2\equiv1\pmod{64}$

so that $x^2$ is the inverse of 25 mod 64. To find this inverse, solve for $y$ in $25y\equiv1\pmod{64}$ . Using the Euclidean algorithm, we have

64 = 2*25 + 14

25 = 1*14 + 11

14 = 1*11 + 3

11 = 3*3 + 2

3 = 1*2 + 1

=> 1 = 9*64 - 23*25

so that $(-23)\cdot25\equiv1\pmod{64}\implies y=25^{-1}\equiv-23\equiv41\pmod{64}$ .

So we know

$25x^2\equiv1\pmod{64}\implies x^2\equiv41\pmod{64}$

Squaring both sides of this gives

$x^4\equiv1681\equiv17\pmod{64}$

and multiplying both sides by $x$ tells us

$x^5\equiv17x\equiv3\pmod{64}$

Use the Euclidean algorithm to solve for $x$ .

64 = 3*17 + 13

17 = 1*13 + 4

13 = 3*4 + 1

=> 1 = 4*64 - 15*17

so that $(-15)\cdot17\equiv1\pmod{64}\implies17^{-1}\equiv-15\equiv49\pmod{64}$ , and so $x\equiv147\pmod{64}\implies\boxed{x\equiv19\pmod{64}}$

5 0

3 years ago

What is the measure of B (2n + 15) and D (3n - 5)? If ABCD is a parrallelogram

katovenus [111]

Answer : The value of angle B and angle D is 25⁰ and 35⁰ respectively.

Step-by-step explanation :

As we know that the opposite angles are equal in parallelogram.

According to the given figure,

∠A = ∠C

and

∠B = ∠D

Given:

∠B = (3n - 5)⁰

∠D = (2n + 15)⁰

From this we conclude that:

∠B = ∠D

(3n - 5)⁰ = (2n + 15)⁰

3n - 5⁰ = 2n + 15⁰

3n - 2n = 15⁰ - 5⁰

1n = 10⁰

n = 10⁰

∠B = (3n - 5)⁰ = (3×10 - 5)⁰ = 25⁰

∠D = (2n + 15)⁰ = (2×10 + 15)⁰ = 35⁰

Therefore, the value of angle B and angle D is 25⁰ and 35⁰ respectively.

5 0

3 years ago

Hiroshi has 4 engines and 18 box cars. Find the ratio of engines to box cars. Write the ratio as a fraction in simplest form.

lyudmila [28]

To write a ratio as a fraction, we simply take the first number in the ratio and make it the numerator while taking the second number in the ratio and making it the denominator.

Because we want the ratio of engines to box cars, our ratio should be:

number of engines/number of box cars

When we substitute in our respective values, we get:

4/18

To simplify this ratio, we have to find the GCF, or greatest common factor of the numerator and the denominator, which in this case is 2. To simplify, we divide both the numerator and the denominator by the GCF, as follows:

4/2 / 18/2

When we simplify, we get:

2/9

Therefore, your answer is 2/9.

Hope this helps!

4 0

3 years ago

Plzz help I have I noooo clue :(

iogann1982 [59]

The correct answer is C. Hope that helps!

7 0

3 years ago

Read 2 more answers