Determine the value of x.

Which number in the monomial 215x18y3z21 needs to be changed to make it a perfect cube?

hoa [83]

We need to remember that:
xyz = (x)(y)(z)
if x, y and z are perfect cubes, then xyz would also be a perfect cube

Also,
(x^n)^m = x^(mn)
if it is a perfect cube, then it can be factored into the expression (x^n)^3, wherein n is a whole number.

All should be a perfect cube, given

215x^18(y^3)(z^21)

By writing the terms separately, we would see which one is to be changed.

215 = 5*43, we see this is not a perfect cube, we could changed it to 6^3 or 216

x^18=(x^6)^3

y^3=y^3
z^21=(z^7)^3

The other terms are perfect cubes except for the first one. So the correct answer would be the last option, 215 should be changed.

4 0

2 years ago

Read 2 more answers

A fish tank is in the shape of a cuboid.

zalisa [80]

Answer:

Length = 0.8m

Breadth = 0.3m

Volume = 108litres = 108÷1000 = 0.108m³

Volume = l x b x h

0.108 = 0.8 x 0.3 x h

0.108 ÷ ( 0.8 x 0.3 ) = h

0.45 = h

6 0

2 years ago

A soft drink machine outputs a mean of 27 ounces per cup. The machine's output is normally distributed with a standard deviation

postnew [5]

Answer: P(22 ≤ x ≤ 29) = 0.703

Step-by-step explanation:

Since the machine's output is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = output of the machine in ounces per cup.

µ = mean output

σ = standard deviation

From the information given,

µ = 27

σ = 3

The probability of filling a cup between 22 and 29 ounces is expressed as

P(22 ≤ x ≤ 29)

For x = 22,

z = (22 - 27)/3 = - 1.67

Looking at the normal distribution table, the probability corresponding to the z score is 0.047

For x = 29,

z = (29 - 27)/3 = 0.67

Looking at the normal distribution table, the probability corresponding to the z score is 0.75

Therefore,

P(22 ≤ x ≤ 29) = 0.75 - 0.047 = 0.703

6 0

2 years ago

I need help on 4 and 5 thanks for your help and time

DanielleElmas [232]

The answer for 4. | She rode her bike 5 and a half miles and 6 miles yesterday so the longer ride is yesterday
6 > 5'1/2
(I do not know 5. sorry.)
I hope this helps
Have a great day!

4 0

2 years ago

Find all points on the x-axis that are 14 units from the point (6,-7) All points on the x-axis that are 14 units from the point

Maksim231197 [3]

Answer: $(6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0)$ are the required points.

or (18.124,0) and ( -6.124,0) are the required points.

Step-by-step explanation:

Let (x,0) be the point on x -axis that are 14 units from the point (6,-7) .

Then by distance formula , we have

$\sqrt{(x-6)^2+(0-(-7))^2}=14\ \ \ [\ \because distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}]$

Taking square on both the sides , we get

$(x-6)^2+7^2=14^2\\\\\Rightarrow\ x^2+6^2-2(6)x+49=196\\\\\Rightarrow\ x^2+36-12x=147\\\\\Rightarrow\ x^2-12x=111\\\\\Rightarrow\ x^2-12x-111=0$

Using quadratic formula : $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\dfrac{12\pm\sqrt{(-12)^2-4(1)(-111)}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{144+444}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{588}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{2^2\times7^2\times3}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm14\sqrt{3}}{2}\\\\\Rightarrow\ x=6\pm7\sqrt{3}$

so, $(6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0)$ are the required points.

since $\sqrt{3}=1.732$

so, $(6+7(1.732),0)\text{ and }(6-7(1.732),0)$ are the required points.

i.e. (18.124,0) and ( -6.124,0) are the required points.

3 0

3 years ago