Combine like terms to create an equivalent expression 2/5m - 4/5

What is the approximate volume of a cone with a radius of 15 cm and a height of 4 cm? Round your answer to the nearest hundredth

vichka [17]

Answer:

Volume of a cone $=942.86cm^3$

Step-by-step explanation:

Given that the radius of a cone is 15cm and its height is 4cm

That is r=15cm and h=4cm

To find the volume of a cone :

volume of a cone $=\frac{\pi r^2h}{3}$ cubic units

Now substitute the values in the formula we get

volume of a cone $=\frac{(\frac{22}{7}) (15)^2(4)}{3}$

$=\frac{(\frac{22}{7}) (225)(4)}{3}$

$=\frac{19800}{21}$

$=942.857$

Now round to nearest hundredth

$=942.86$

Therefore Volume of a cone $=942.86cm^3$

6 0

3 years ago

Plz help

kvv77 [185]

Option C: $5 x(4 x+7)(3 x+2)$ is the possible expressions for length, width and height of the prism.

Explanation:

The volume of the rectangular prism is $60 x^{3}+145 x^{2}+70 x$

To determine the length, width and height of the rectangular prism, let us factor the expression.

Thus, factoring 5x from the expression, we have,

$5 x\left(12 x^{2}+29 x+14\right)$

Let us break the expression $12 x^{2}+29 x+14$ into two groups, we get,

$5x[\left(12 x^{2}+8 x\right)+(21 x+14)]$

Factoring 4x from the term $12 x^{2}+8 x$ , we get,

$5x[4 x(3 x+2)+(21x+14)]$

Similarly, factoring 7x from the term $21 x+14$ , we get,

$5x[4 x(3 x+2)+7(3x+2)]$

Now, let us factor out $3x+2$ , we get,

$5 x(4 x+7)(3 x+2)$

Hence, the possible expressions for length, width and height of the prism is $5 x(4 x+7)(3 x+2)$

Therefore, Option C is the correct answer.

8 0

3 years ago

Cos^2x+cos^2(120°+x)+cos^2(120°-x)<br>i need this asap. pls help me

o-na [289]

Answer:

$\frac{3}{2}$

Step-by-step explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

---------------------------------------------------------------

cos(120 + x) = cos120cosx - sin120sinx

= - cos60cosx - sin60sinx

= - $\frac{1}{2}$ cosx - $\frac{\sqrt{3} }{2}$ sinx

squaring to obtain cos² (120 + x)

= $\frac{1}{4}$ cos²x + $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

--------------------------------------------------------------------

cos(120 - x) = cos120cosx + sin120sinx

= -cos60cosx + sin60sinx

= - $\frac{1}{2}$ cosx + $\frac{\sqrt{3} }{2}$ sinx

squaring to obtain cos²(120 - x)

= $\frac{1}{4}$ cos²x - $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

--------------------------------------------------------------------------

Putting it all together

cos²x + $\frac{1}{4}$ cos²x + $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x + $\frac{1}{4}$ cos²x - $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

= cos²x + $\frac{1}{2}$ cos²x + $\frac{3}{2}$ sin²x

= $\frac{3}{2}$ cos²x + $\frac{3}{2}$ sin²x

= $\frac{3}{2}$ (cos²x + sin²x) = $\frac{3}{2}$

5 0

3 years ago

one x-intercept for a parabola is at the point (2, 0). use the quadratic formula to find the other x-intercept for the parabola

omeli [17]

Answer:

Step-by-step explanation:

There are 3 ways to find the other x intercept.

1) Polynomial Long Division.

Divide x^2 - 3x + 2 by the binomial x - 2, because by the Factor Theorem if a is a root of a polynomial then x - a is a factor of said polynomial.

2) Just solving for x when y = 0, by using the quadratic formula.

$x^2 - 3x + 2 = 0\\x_{12} = \frac{3 \pm \sqrt{9 - 4(1)(2)}}{2} = \frac{3 \pm 1}{2} = 2, 1$ .

So the other x - intercept is at (1, 0)

3) Using Vietta's Theorem regarding the solutions of a quadratic

Namely, the sum of the solutions of a quadratic equation is equal to the quotient between the negative coefficient of the linear term divided by the coefficient of the quadratic term.

$x_1 + x_2 = \frac{-b}{a}$

And the product between the solutions of a quadratic equation is just the quotient between the constant term and the coefficient of the quadratic term.

$x_1 \cdot x_2 = \frac{c}{a}$

These relations between the solutions give us a brief idea of what the solutions should be like.

6 0

3 years ago

There are 6,000 products at the store in one hour, 425 products are sold how products are left

wariber [46]

Answer:

5575

Step-by-step explanation:

its just subtraction you take the 6000 and subtract 425 and thats how you get whats left they try to trick you using the time im guessing correct me if im wrong

3 0

3 years ago

Combine like terms to create an equivalent expression 2/5m - 4/5 - 3/5m