7 + 9y < -3 (y

Factor x^2a^2 + 3xa^2 + 2a^2. Show your work.

kotegsom [21]

$x^2a^2 + 3xa^2 + 2a^2= \\ a^2(x^2+3x+2)= \\a^2(x^2+2x +x+2)= \\a^2(x(x+2)+(x+2))= \\a^2(x+2)(x+1)$

4 0

3 years ago

Leon drew a life cycle of Insect M as shown below.

tankabanditka [31]

Step-by-step explanation:

Larval mosquitoes breath through trachea in their siphons. This is a structure analogous to the snorkel on a diesel electric submarine. It allows for gas exchange with the atmosphere while the remainder of the insect is submerged. The opening of the siphon is hydrophobic so it won’t get wet and blocked by water. This works well to keep the siphon and the trachea open under normal conditions. Oil when poured on water forms a thin film. When there are mosquitos in that water, when their siphons contact the oil layer, the oil wets and blocks their siphons and suffocates the mosquitoes. This works against most, but not all mossies, as evolution is an amazing process. Some mosquitoes (Mansonia, Coquilletidia) have a siphon designed to penetrate the air vessels in aquatic plants and they don’t need to come to the surface to breath like other mossies. So oil won’t work on these genera.

3 0

3 years ago

Jason designs a rectangular sandbox. He models the perimeter of the sandbox using the expression 8l+2, where l is the length of

inn [45]

Answer:

A .The expression 2l+2(3l+1) shows the width is 1 more than 3 times the length.

Step-by-step explanation:

p = 8l + 2

Length = l

Width:

2w = p - 2l

2w = (8l + 2) - 2l

2w = 6l + 2

w = 3l + 1

Therefor w is 3 times the length plus 1

7 0

2 years ago

A is an m×n matrix.Check the true statements below:A. The kernel of a linear transformation is a vector space.B. If the equation

Bess [88]

Answer:

Results are (1) True. (2) False. (3) False. (4) True. (5) True. (6) True.

Step-by-step explanation:

Given A is an $m\times n$ matrix. Let $T :U\to V$ be the corresponding linear transformationover the field F and $\theta$ be identity vector in V. Now if $x\in Ker( T)\implies T(x)=\theta$ .

(1) The kernel of a linear transformation is a vector space : True.

Let $x,y\in Ker( T)$ , then,

$T(x+y)=T(x)+T(y)=\theta+\theta=\theta\impies x+y\in Ker( T)$

hence the kernel is closed under addition.

Let $\lambda\in F, x\in Ker( T)$ , then

$T(\lambda x)=\lambda T(x)=\lambda\times \theta=\theta$

$\lambda x\in Ker(T)$ and thus Ket(T) is closed under multiplication

Finally, fore all vectors $u\in U$ ,

$T(\theta)=T(\theta+(-\theta))=T(\theta)+T(-\theta)=T(\theta)-T(\theta)=\theta$

$\implies \theta\in Ker(T)$

Thus Ker(T) is a subspace.

(2) If the equation Ax=b is consistent, then Col(A) is $\mathbb R^m$ : False

if the equation Ax=b is consistent, then Col(A) must be consistent for all b.

(3) The null space of an mxn matrix is in $\mathbb R^m$

: False

The null space that is dimension of solution space of an m x n matrix is always in $\mathbb R^n$ .

(4) The column space of A is the range of the mapping $x\to Ax$

: True.

(5) Col(A) is the set of all vectors that can be written as Ax for some x. : True.

Here Ax will give a linear combination of column of A as a weights of x.

(6) The null space of A is the solution set of the equation Ax=0.

: True

5 0

2 years ago

Use Green's Theorem to calculate the circulation of F =2xyi around the rectangle 0≤x≤8, 0≤y≤3, oriented counterclockwise.

Tamiku [17]

Green's theorem says the circulation of $\vec F$ along the rectangle's border $C$ is equal to the integral of the curl of $\vec F$ over the rectangle's interior $D$ .

Given $\vec F(x,y)=2xy\,\vec\imath$ , its curl is the determinant

$\det\begin{bmatrix}\frac\partial{\partial x}&\frac\partial{\partial y}\\2xy&0\end{bmatrix}=\dfrac{\partial(0)}{\partial x}-\dfrac{\partial(2xy)}{\partial y}=-2x$

So we have

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_D-2x\,\mathrm dx\,\mathrm dy=-2\int_0^3\int_0^8x\,\mathrm dx\,\mathrm dy=\boxed{-192}$

6 0

3 years ago

7 + 9y < -3 (y - 5) + 4