Here are two rectangles the two rectangles are similar and the scale factor is

Please help me i need the answer right now. The lesson is Rational Root Theorem.

Debora [2.8K]

Step-by-step explanation:

1. The length is one more thrice it's width. The height is 4 more than it width. We can represent the

x+4.(3x+1)(x)
The volume is 720.
Volume of Rectangular prism is LxWXH. So the volume is equal to the terms all multiplied. which is

$(3x + 1)(x + 4)$

$(3 {x}^{2} + 13x + 4)x = 720$

Multiply it by x.

$3 {x}^{3} + 13 {x}^{2} + 4x = 720$

$3{x}^{3} + 13 {x}^{2} + 4 x - 720$

The possible roots

The possible roots are plus or minus is1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720. By a long list of substitution, 5 is a root. So this means that x=5. So the width has to be

$x = 5$

2. First. we apply the Rational Root Theorem so the possible roots are plus or minus 1,2,3,6.

Let check via synethic division to see which are roots.

Let try 1 and -1 first. If we plug 1 into the equation, we get

$1 - 2 - 5 + 6 = 0$

So 1 or (x-1) is a solution. Since it's a solution we can divide this into our original polynomial to get us a new polynomial that is more simplified. If we apply synthetic division, we get a new polynomial in

${x}^{2} - x - 6$

We can then factor this into

$(x - 3)(x + 2)$

So our roots or factors is

$(x - 1)(x - 3)(x + 2)$

6 0

3 years ago

Consider the function f(x, y) = x2 + xy + y2 defined on the unit disc, namely, d = {(x, y)| x2 + y2 ≤ 1}. use the method of lagr

Pani-rosa [81]

First we note that the partial derivatives vanish simultaneously at one point:

$\begin{cases}f_x=2x+y=0\\f_y=x+2y=0\end{cases}\implies(x,y)=(0,0)$

so there is one critical point within the region $D$ .

The Lagrangian is

$L(x,y,\lambda)=x^2+xy+y^2+\lambda(x^2+y^2-1)$

and has partial derivatives

$L_x=2x+y+2\lambda x$
$L_y=x+2y+2\lambda y$
$L_\lambda=x^2+y^2-1$

Set each partial derivative to 0 to find the possible critical points within the disk $D$ . Then we notice that

$yL_x=2xy+y^2+2\lambda xy=0$
$xL_y=x^2+2xy+2\lambda xy=0$
$L_\lambda=0\implies x^2+y^2=1$

$\implies xL_y-yL_x=x^2-y^2=0$

Since $x^2+y^2=1$ , we have

$x^2-y^2=x^2+y^2-2y^2=0\implies1=2y^2\implies y^2=\dfrac12\implies y=\pm\dfrac1{\sqrt2}$

And since $x^2-y^2=0$ , or $x^2=y^2$ , we also have

$x=\pm\dfrac1{\sqrt2}$

So we have four possible additional critical points to consider:

$f(0,0)=0$
$f\left(-\dfrac1{\sqrt2},-\dfrac1{\sqrt2}\right)=\dfrac32$
$f\left(-\dfrac1{\sqrt2},\dfrac1{\sqrt2}\right)=\dfrac12$
$f\left(\dfrac1{\sqrt2},-\dfrac1{\sqrt2}\right)=\dfrac12$
$f\left(\dfrac1{\sqrt2},\dfrac1{\sqrt2}\right)=\dfrac32$

It should be clear enough which of these correspond to the absolute extrema of $f$ over $D$ .

8 0

3 years ago

What ratios are equivalent with 7 : 4?

Bess [88]

Answer:

14 : 8

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The ratio of 2 nickels to 5 dollars is

Brums [2.3K]

The answer is 10/ten

4 0

3 years ago

Read 2 more answers

170 is 1/10 of 17 true or false

kobusy [5.1K]

The answer to this question would be true.

In this case, you are given a sentence containing a condition to fulfill. To answer this question, you need to understand the sentence and turn it into an equation then compare it with the condition. The equation for this question would be: 170 * 1/10= 17.
The answer is true because the result of 170 * 1/10 is 17

5 0

3 years ago