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3 years ago

Give the greatest common divisor of $6^3$ and $3^6$.

Mathematics

2 answers:

zysi [14]3 years ago

8 0

Answer:

Step-by-step explanation:

Greatest common divisor is the largest positive integer that divides each integer in the given problem

6³ = (2* 3)³ = 2³ * 3³

3⁶ = 3³ * 3³

Greatest common divisor = 3³ = 3* 3* 3 = 27

Lady bird [3.3K]3 years ago

3 0

Answer:

Step-by-step explanation:

Since 3^6 is only divisible by 3 and powers of 3(including 1) the gcd of 3^6 and 6^3 mus be a power of 3 hence we need to find the highest powers of 3 that divide 6^3 and that divide 3^6, which are respectively 3^3 and 3^6, hence, taking the smaller one (since we want it to divide both), our answer is 3^3=27.

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1: Is 5 / 3(1-x) Equivalent to 8-8x<br><br> 2: Is 2(6 - 3x) equivalent to 2(3x) +x?

iris [78.8K]

Answer:

1. no. 2.no

Step-by-step explanation:

1. $\frac{5}{3 - 3x}$

= (5\3) × (1/1-x)

but 8-8x = 8(1-x)

2. 2(6-3x) = 12-6x =6(2-x)

2(3x) + x= 6x +x = 7x

4 0

3 years ago

24% is 7kg.What is 40%?

Bas_tet [7]

Answer:

18.1437

Step-by-step explanation:

divide the mass value by 2.205

3 0

3 years ago

7 more than 6 times a number is negative forty seven what us the number

romanna [79]

Answer:

The number is -9.

Step-by-step explanation:

If we let the number be x we have the equation 6x + 7 = -47.

6x + 7 - 7 = -47 - 7

6x = -54

x = 054/6

x = -9.

3 0

4 years ago

given the vector with a manitude of 9m at an angle a of -80 degrees, decompose this vector into two vector components oarallel t

lana [24]

Answer:

We have the magnitude, M, and the angle A.

(The angle is always measured from the +x-axis)

Then we have that:

x = M*cos(A)

y = M*sin(A)

in this case:

M = 9m

A = -80°

x = 9m*cos(-80°) = 1.562

y = 9m*sin(-80) = -8.86m

Now, the component parallel to the x axis is:

x = 9m*cos(-80°) = 1.562 m

And the slope of something parallel to the x-axis is always zero, as this is a constant line.

3 0

3 years ago

Which systems of equations intersect at point A in this graph?

abruzzese [7]

Answer:

The point of intersection of the system of equations is:

(x, y) = (-2, 1)

The correct system of equations intersect at point A in this graph will be:

$\begin{bmatrix}y=4x+9\\ y=-3x-5\end{bmatrix}$

Thus, the second option is correct.

Step-by-step explanation:

Given the point

A (-2, 1)

Let us check the system of equations to determine whether it intersect at point A in this graph.

Given the system of equations

$\begin{bmatrix}y=4x+9\\ y=-3x-5\end{bmatrix}$

Arrange equation variable for elimination

$\begin{bmatrix}y-4x=9\\ y+3x=-5\end{bmatrix}$

$y+3x=-5$

$-$

$\underline{y-4x=9}$

$7x=-14$

so the system of equations becomes

$\begin{bmatrix}y-4x=9\\ 7x=-14\end{bmatrix}$

Solve 7x = -14 for x

$7x=-14$

Divide both sides by 7

$\frac{7x}{7}=\frac{-14}{7}$

Simplify

$x = -2$

For y - 4x = 9 plug in x = 2

$y-4\left(-2\right)=9$

$y+4\cdot \:2=9$

$y+8=9$

Subtract 8 from both sides

$y+8-8=9-8$

Simplify

y = 1

Thus, the solution to the system of equations is:

(x, y) = (-2, 1)

From the attached graph, it is also clear that the system of equations intersects at point x = -2, and y = 1.

In other words, the point of intersection of the system of equations is:

(x, y) = (-2, 1)

Therefore, the correct system of equations intersect at point A in this graph will be:

$\begin{bmatrix}y=4x+9\\ y=-3x-5\end{bmatrix}$

Thus, the second option is correct.

3 0

3 years ago