Roots can be written as fraction exponents. An exponent of 1/2 means the square root.

$(12 x^{4})^{1/2} = \sqrt{12 x^{4} } \\ \\ \sqrt{12 x^{4} } = \sqrt{3*4*x^{2}*x^{2}} = 2x^{2} \sqrt{3}$

8 0

3 years ago

The volume of a 10 ounce box of cheerios is 258.75in3. the length of the box is 4 inches less than the height and the width is 3

Marina86 [1]

Answer:

Height of the box = 11.5 in

Step-by-step explanation:

Let h be the height of the box.

Assuming the volume of the Box is $258.75\ in^3$ .

Given:

Length = Height - 4 = h - 4

Width = 3 in

We need to find the height of the box.

Solution:

We know that the volume of the box.

$Volume = Length\times height\times width$

Substitute all given value in above formula.

$258.75 = (h-4)\times h\times 3$

Rewrite the equation as:

$258.75 = 3h(h-4)$

$258.75 = 3h^2-12h$

$3h^2-12h-258.75=0$

whole equation divided by 3.

$h^2-4h-86.25=0$

Use quadratic formula with $a = 1, b = -4,c=-86.25$

$h=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}$

Put these a, b and c value in above equation.

$h=\frac{-(-4)\pm \sqrt{(-4)^{2}-4(1)(-86.25)}}{2(1)}$

$h=\frac{4\pm \sqrt{16+345}}{2}$

$h=\frac{4\pm \sqrt{361}}{2}$

$h=\frac{4\pm 19}{2}$

For positive sign

$h=\frac{23}{2}$

h = 11.5 in

For negative sign

$h=\frac{-15}{2}$

h = -7.5

We take positive value of h.

Therefore, the height of the box h = 11.5 in

4 0

3 years ago

SOME ONE PLEASE HELP WITH THIS MATH QUIZ PLASE HONEST AWNSERS!!!

Liula [17]

Answer:

1. d 2. d 3. a

Step-by-step explanation:

1. factor

((w-4)(w-6))/((w-5)(w-6))+8/(w-5)

solve

(w-4)/(w-5)+8/(w-5)

(w+4)/(w-5), so d

2.factor

((b+2)(b-4))((b+2)(b-1))-6/(b-1)

solve

(b-4)/(b-1)-6(b-1)

(b-10)/(b-1), so d

3. (2/5t-3/3t)/(1/2t+1/2t)

(2/5t-1/t)/(2/2t)

(2/5t-1/t)/(1/t)

t(2/5t-1/t)

2/5-1=-3/5, so a

7 0

2 years ago