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3 years ago

What is the area of the triangle? 10,6,8

Mathematics

1 answer:

Ivenika [448]3 years ago

4 0

Answer:

multiply then divide then multiply again

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A photocopy machine can print 735 copies in 7 minutes. What is the rate at which the machine prints the copies per minutes

qaws [65]

Answer:

105

Step-by-step explanation:

Divide 735 by 7

5 0

3 years ago

Read 2 more answers

When I double my number, subtract three, subtract my number, and add four, I get my number plus two. What is my number?

marishachu [46]

Answer:

Any real number

Step-by-step explanation:

Let your no.= x

double the number=2x

add 4 = 2x+4

subtract same number=2x+4-x

subtract 3=2x+4-x-3

get number plus 1=x+1

so equation we get

2x+4-x-3=x+1

x+1=x+1

x=x

it means x is equal to all real number

So your number can be any real number

7 0

3 years ago

WHAT IS THE REMAINDER WHEN <img src="https://tex.z-dn.net/?f=32%5E%7B37%5E%7B32%7D%20%7D" id="TexFormula1" title="32^{37^{32} }"

Feliz [49]

Recall Euler's theorem: if $\gcd(a,n) = 1$ , then

$a^{\phi(n)} \equiv 1 \pmod n$

where $\phi$ is Euler's totient function.

We have $\gcd(9,32) = 1$ - in fact, $\gcd(9,32^k)=1$ for any $k\in\Bbb N$ since $9=3^2$ and $32=2^5$ share no common divisors - as well as $\phi(9) = 6$ .

Now,

$37^{32} = (1 + 36)^{32} \\\\ ~~~~~~~~ = 1 + 36c_1 + 36^2c_2 + 36^3c_3+\cdots+36^{32}c_{32} \\\\ ~~~~~~~~ = 1 + 6 \left(6c_1 + 6^3c_2 + 6^5c_3 + \cdots + 6^{63}c_{32}\right) \\\\ \implies 32^{37^{32}} = 32^{1 + 6(\cdots)} = 32\cdot\left(32^{(\cdots)}\right)^6$

where the $c_i$ are positive integer coefficients from the binomial expansion. By Euler's theorem,

$\left(32^{(\cdots)\right)^6 \equiv 1 \pmod9$

so that

$32^{37^{32}} \equiv 32\cdot1 \equiv \boxed{5} \pmod9$

7 0

2 years ago

I know the answer but plz explain it. 5:3 × 6:2

stira [4]

5:3 x 6:2 can also be written as a fraction
5/3 x 6/2
Multiply across
30/6
Simplify
5/1
Rewrite
5:1 is your answer, or if your teacher does not want it simplified, 30:6

Hope I helped! :)

3 0

3 years ago

An airplane travels 6903 kilometers against the wind in 9 hours and 8613 kilometers with the wind in the same amount of time. Wh

Rzqust [24]

Answer:

The rate of the plane is 862 miles per hour

Step-by-step explanation:

An airplane travels 6903 kilometers against the wind in 9 hours.

Speed = distance / time

Speed of the airplane while travelling against the wind is

6903/9 = 767 miles per hour

The airplane travelled 8613 kilometers with the wind in the same amount of time. This means that the speed while travelling with the wind will be

8613/9 = 957 miles per hour

Let x = speed of the airplane

Let y = speed of the wind

While travelling against the wind,

x - y = 767 - - - - - -- 1

While travelling with the wind,

x + y = 957 - - - - - - -2

Subtracting equation 2 from equation 1,

-y - y = 767 - 957

-2y = -190

y = -190/-2

y = 95 miles per hour

x = 957 - y

x = 957 - 95

x = 862 miles per hour

4 0

3 years ago