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2 years ago

Which choice is equivalent to the product below for acceptable values of X? sqrt 6x² * sqrt 18x²

Mathematics

1 answer:

Ymorist [56]2 years ago

5 0

The choice which is equivalent is $6x^2\sqrt{3}$ option B

<h3>How to determine the value</h3>

We have that;

$\sqrt{6x^2} * \sqrt{18x^2}$ where $x\geq 0$

First, we factorize the square root

= $\sqrt{2 * 3 * x^2 } . \sqrt{3 * 3 * 2 * x^2}$

Find the common factors

= $2 * 3 x^2\sqrt{3}$

= $6x^2\sqrt{3}$

Thus, the choice which is equivalent is $6x^2\sqrt{3}$ option B

The complete question is;

Which choice is equivalent to the product below for acceptable values of X? sqrt 6x² * sqrt 18x²

a. $6\sqrt{3x}$

b. $6x^2\sqrt{3}$

c. $6\sqrt{18x}$

d. $\sqrt{108x^2}$

Learn more about algebraic expressions here:

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Let $f(x) = x^2$ and $g(x) = \sqrt{x}$. Find the area bounded by $f(x)$ and $g(x).$

Anna [14]

Answer:

$\large\boxed{1\dfrac{1}{3}\ u^2}$

Step-by-step explanation:

Let's sketch graphs of functions f(x) and g(x) on one coordinate system (attachment).

Let's calculate the common points:

$x^2=\sqrt{x}\qquad\text{square of both sides}\\\\(x^2)^2=\left(\sqrt{x}\right)^2\\\\x^4=x\qquad\text{subtract}\ x\ \text{from both sides}\\\\x^4-x=0\qquad\text{distribute}\\\\x(x^3-1)=0\iff x=0\ \vee\ x^3-1=0\\\\x^3-1=0\qquad\text{add 1 to both sides}\\\\x^3=1\to x=\sqrt[3]1\to x=1$

The area to be calculated is the area in the interval [0, 1] bounded by the graph g(x) and the axis x minus the area bounded by the graph f(x) and the axis x.

We have integrals:

$\int\limits_{0}^1(\sqrt{x})dx-\int\limits_{0}^1(x^2)dx=(*)\\\\\int(\sqrt{x})dx=\int\left(x^\frac{1}{2}\right)dx=\dfrac{2}{3}x^\frac{3}{2}=\dfrac{2x\sqrt{x}}{3}\\\\\int(x^2)dx=\dfrac{1}{3}x^3\\\\(*)=\left(\dfrac{2x\sqrt{x}}{2}\right]^1_0-\left(\dfrac{1}{3}x^3\right]^1_0=\dfrac{2(1)\sqrt{1}}{2}-\dfrac{2(0)\sqrt{0}}{2}-\left(\dfrac{1}{3}(1)^3-\dfrac{1}{3}(0)^3\right)\\\\=\dfrac{2(1)(1)}{2}-\dfrac{2(0)(0)}{2}-\dfrac{1}{3}(1)}+\dfrac{1}{3}(0)=2-0-\dfrac{1}{3}+0=1\dfrac{1}{3}$

6 0

3 years ago

The base of a triangle prism shown is an isosceles triangle having a height of H cm, and an area of 36cm squared

Alika [10]

Answer:

the value of h on the diagram is 9cm

Step-by-step explanation:

area = 1/2 * base * height

a = 1/2*b*h

36=1/2*8*h

36=4h

since the 1/2 will multiply the 8

36=4h

multiply both sides by 4

h=9cm.

4 0

3 years ago

I'm thinking of a fraction that is equivalent to . The numerator is less than the denominator." What fraction is thinking of?

Vesna [10]

Answer:

Proper fraction

Step-by-step explanation:

If the numerator is less than the denominator , then it is proper fraction.

Example : $\frac{5}{8}, \frac{124}{1000}$

8 0

3 years ago

Which expressions are less than 7/8? Choose all answers that apply: 7/8 x 9/15 7/8 x 3/4 7/8 x 9/9 7/8 x 4/3

seraphim [82]

Question

Which expressions are less than 7/8? Choose all answers that apply:

a) 7/8 x 9/15

b) 7/8 x 3/4

c) 7/8 x 9/9

d) 7/8 x 4/3

Answer:

a) 7/8 x 9/15

b) 7/8 x 3/4

Step-by-step explanation:

We are asked to find which expression are least than 7/8

Solving 7/8 = 0.875

We would evaluate the given option one after the other.

a) 7/8 x 9/15

= 63/120 = 0.525

b) 7/8 x 3/4

= 21/32 = 0.65625

c) 7/8 x 9/9

= 7/8 × 1 = 7/8 = 0.875

d) 7/8 x 4/3

= 7/6 = 1.1666666667

Therefore, from the above calculation, the expressions are less than 7/8 are

option a) a) 7/8 x 9/15 and b) 7/8 x 3/4

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3 years ago

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irina [24]

the correct answer is B

7 0

3 years ago