All Answers

#1

+37091

+1

To be odd, the number must end in 1 3 5 or 7 4 choices for the last position

8 choices for each of the other four positions

8 x 8 x 8 x 8 x 4 = .......

ElectricPavlovJan 10, 2022

#2

+37091

+1

Sum of interior anges = ( n-2) * 180

now divide by n to find the measure of each interior angle (n-2)* 180/n

the exterior angles are supplementary ( and exterior is 10 times bigger)

10* ( 180 - (n-2)*180/n) = (n-2)*180/n

1800 - 10(n-2)*180/n = (n-2)*180/n

1800 = 11 (n-2)*180/n

1800n = (11n-22) * 180

-180n = -3960

n = 22 sides

ElectricPavlovJan 10, 2022

#1

+26

0

Note that $512 = \boxed{2^9} = 2^{3 \cdot 3} = (2^3)^3 = \boxed{8^3}$.

pogyouJan 10, 2022

#1

+26

0

Squaring both sides, we get that $\left(m + \frac 1m \right)^2 = 8^2$. Expanding gives $m^2 + \frac{1}{m^2} + 2 = 8^2$, so hence $m^2 + \frac{1}{m^2} = 8^2 - 2 = 62$. Squaring both sides again, we get that $\left(m^2 + \frac{1}{m^2}\right)^2 = 62^2$. Expanding gives $m^4 + \frac{1}{m^4} + 2 = 62^2$, so hence $m^4 + \frac{1}{m^4} = 62^2 - 2 = \boxed{3842}$.

pogyouJan 10, 2022

#1

+26

0

Let the measure of an exterior angle of the polygon be $x$. Then $x + 10x = 180^\circ$, so $x = \left(\frac{180}{11}\right)^\circ$. The measure of an exterior angle of a regular polygon with $\ell$ sides is equal to $\left(\frac{360}{\ell}\right)^\circ$. Thus, $\left(\frac{360}{\ell}\right)^\circ = \left(\frac{180}{11}\right)^\circ$, so the polygon has $\boxed{22}$ sides.

pogyouJan 10, 2022

#1

+26

0

We can express all of the terms with exponent base $3$, giving $2y = 5 + 12 + 16 - 9 = 24 \implies y = \boxed{12}$.

pogyouJan 10, 2022

#4

+4

0

Mathematics is the science and study of quality, structure, space, and change. ... Through abstraction and logical reasoning mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects

EtheredgeJan 10, 2022

#1

+14985

+1

What is this value of k?

Hello Guest!

x + y + 3z = 10 | *5

-4x + 8y + 5z = 7 | *3

kx + 2z = 3

5x +5y +15z = 50

-12x+24y+15z = 21

-------------------------

17x -19y = 29 | *2

x + y + 3z = 10 | *2

kx + 2z = 3 | *3

2x + 2y +6z = 20

3kx +6z = 9

--------------------------

(2 - 3k)x + 2y = 11 | *19

(38 - 57k)x + 38y = 209

34x - 38y = 58

-------------------------------

(38 - 23k)x = 267 | :23

(1.652 - k)x =11.609

$x=\dfrac{11.609}{1.652-k}$

$y=\frac{34x-58}{38}=\frac{\frac{34\cdot 11.609}{1.652-k}-58}{38} $

$y=\dfrac{10.387}{1.652-k}-1.526$

$z=\frac{3-kx}{2}=\frac{ 3-\frac{11.609k}{1.652-k} }{2}$

$z=1.5-\dfrac{5.8045k}{1.652-k}$

$\large k\in \mathbb R$ | -$\infty$ < k < $\infty$

!

asinusJan 10, 2022

#1

+14985

+1

If f(x) = -2, find the sum of all possible values of x.

Hello Guest!

The sum of all possible values of x is: x = -2 and x = 4.75

!

asinusJan 10, 2022

#1

+14985

+1

Find sin B.

Hello Guest!

$sin\ B=\frac{\sqrt{9^2-8^2}}{9}=\frac{\sqrt{17 }}{9}=\color{blue}0.45812$

!

asinusJan 10, 2022

#1

+26

0

Note that $\triangle ACE$ and $ABDE$ have the same base and height, and since the area of a rectangle is equal to $bh$ and the area of a triangle is equal to $ \frac{bh}{2} $, we get that $ \frac{[\triangle ACE]}{[ABDE]} = \boxed{\frac{1}{2}} $.

pogyouJan 10, 2022

#1

0

By Chinese Remainder Theorem, there exists exactly one unique residue$\pmod{12}$ that satisfies the given conditions. In this case, it is not difficult to notice that a residue of $\boxed{2}$ works.

GuestJan 10, 2022

#2

+26

0

This is equivalent to the question "How many numbers can be expressed with 8 or less digits in binary?"

Hence, every number from $1_2$ to $11{,}111{,}111_2$ works, for an answer of $\boxed{255}$

.

pogyouJan 10, 2022

#1

0

Sum of exterior angles = 360

360 / 15 = 24