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2 years ago

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A number $x$ is equal to $7\cdot24\cdot48$. What is the smallest positive integer $y$ such that the product $xy$ is a perfect cu

be?

1 answer:

Wewaii [24]2 years ago

8 0

Take the prime factorization of $x$ .

$x = 7\times24\times48 = 7\times(2^3\times3)\times(3\times2^4) = 2^7\times3^2\times7$

If $xy$ is a perfect cube, then the smallest $y$ that makes this happen is $y=2^2\times3\times7^2 = \boxed{588}$ . We "complete" the cube by introducing just enough factors to get each prime power to be a multiple of 3.

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Dilate the the triangle, scale factor = 3 (positive 3, ignore the

HACTEHA [7]

Answer:

The rule of dilation is $P'(x,y) = 3\cdot P(x,y)$ .

The vertices of the dilated triangle are $A'(x,y) = (-21, -18)$ , $B'(x,y) = (-15,-10)$ and $C'(x,y) = (-3,-15)$ , respectively.

Step-by-step explanation:

From Linear Algebra, we define the dilation by the following definition:

$P'(x,y) = O(x,y) + k\cdot[P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation, dimensionless.

$k$ - Scale factor, dimensionless.

$P(x,y)$ - Original point, dimensionless.

$P'(x,y)$ - Dilated point, dimensionless.

If we know that $O(x,y) = (0,0)$ , $k = 3$ , $A(x,y) = (-7,-6)$ , $B(x,y) = (-5,-2)$ and $C(x,y) =(-1,-5)$ , then dilated points of triangle ABC are, respectively:

$A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)]$ (2)

$A'(x,y) = (0,0) + 3\cdot [(-7,-6)-(0,0)]$

$A'(x,y) = (-21, -18)$

$B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)]$ (3)

$B'(x,y) = (0,0) + 3\cdot [(-5,-2)-(0,0)]$

$B'(x,y) = (-15,-10)$

$C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)]$ (4)

$C'(x,y) = (0,0) +3\cdot [(-1,-5)-(0,0)]$

$C'(x,y) = (-3,-15)$

The rule of dilation is:

$P'(x,y) = 3\cdot P(x,y)$ (5)

The vertices of the dilated triangle are $A'(x,y) = (-21, -18)$ , $B'(x,y) = (-15,-10)$ and $C'(x,y) = (-3,-15)$ , respectively.

7 0

3 years ago

How to make a negative 1/4 time line

Vanyuwa [196]

It would be 1,4 if you turn it into a decimal ejfnf

6 0

4 years ago

Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1? f(x) = 3(x 4)(x – i)(x

Pepsi [2]

The polynomial function with leading coefficient of 3 and root -4, i, and 2 all with multiplicity of 1 is f(x) = 3(x+4)(x-i)(x+2)

<h3>Polynomial function</h3>

The Leading coefficients are the numbers written in front of the variable with the largest exponent.

Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero.

The multiplicity is the number of times a given factor appears in the factored form of the equation of a polynomial.

Therefore, the polynomial f(x) = 3(x+4)(x-i)(x+2) has a root -4 , 1 and -2.

The leading coefficient is 3. The multiplicity is all one.

learn more on polynomial here: brainly.com/question/13309002

#SPJ4

5 0

3 years ago

Find how many piranhas you can put in a cylindrical tank

mr Goodwill [35]

Answer: The correct answer is 10 piranhas.

Step-by-step explanation:

To calculate the total Volume of a cylinder we have to use the following formula:

Volume = Area * Height

Area = π * r² , where r= radius

The diameter is always the twice the radius so the diameter is 4 feet in this case and the radius is 2 feet so the area is

Area= 3.1416 * (2*2)

Area = 3.1416 * 4

Area = 12.5664 square feet

Volume = 12.5664 (area) * 1.25 (height).

Volume = 15.708 cubic feet

Each piranha needs 1.5 cubic feet so we have to divide the total Volume by the volume that each piranha needs

15.708/ 1.5 = 10.472 or ten pirahnas because we can't put a fraction of a piranha in the tank.

7 0

4 years ago

I don't understand this class and my teacher is stupid and won't go over it again to help me better understand

allochka39001 [22]

Answer:

Well i believe the answer is obtuse

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers