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3 years ago

What is the graph of the inequality? 4x + 2y ≤ 6

Mathematics

2 answers:

lbvjy [14]3 years ago

8 0

The graph is Y= 2x + 3

frozen [14]3 years ago

6 0

Answer:

Graph Attached.

Step-by-step explanation:

Given: $4x+2y\leq 6$

We need to draw the graph of linear inequality.

First we write inequality as equality and then make table of x and y

New equation: $4x+2y=6$

x y

0 3

1 1

2 -1

Now, we take test point (0,0) to verify the shaded region.

$4(0)+2(y)\leq 6$

$0\leq 6$

TRUE

Now we plot the points on graph and then draw graph.

Please see the attachment for graph.

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-x=-y+2 and 3y+4=2x solve using matrices

MissTica

$\begin{cases}-x=-y+2\\3y+4=2x\end{cases}\implies\begin{cases}x-y=-2\\2x-3y=4\end{cases}$

In matrix form, this is

$\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-2\\4\end{bmatrix}$

The coefficient matrix has determinant

$\begin{vmatrix}1&-1\\2&-3\end{vmatrix}=-3+2=-1\neq0$

so it has an inverse, which is

$\begin{bmatrix}1&-1\\2&-3\end{bmatrix}^{-1}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}$

Multiply both sides by the inverse matrix:

$\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}-2\\4\end{bmatrix}$

$\implies\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-10\\-8\end{bmatrix}$

so that $x=-10$ and $y=-8$ .

8 0

3 years ago

The bar graph shows the number of contracts Company X gained each year from 2002 to 2006. Over which of the periods was the aver

vodomira [7]

Answer:

02-04 I think 10+5/2= 12.5 for average

Maybe 02-03 for 10

Step-by-step explanation:

5 0

3 years ago

X3−2=10 help plz i need help

Norma-Jean [14]

X=4
This is because
(4)3-2=10
12-2=10
10=10
This makes the statement true!
Hope this helps have a good day!

6 0

3 years ago

Which fraction can be replaced with 0 when estimating with fractions?

____ [38]

Answer:

None

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

PLEASE HELP! I feel horrible and I'm crying so hard right now. This is due.

Lady bird [3.3K]

Answer:

Step-by-step explanation:

surface area of a rectangular prism = 2lw + 2lh + 2wh

Where l = length, w = width and h = height

The box has the following dimensions

length = 5 in

width = 3 in

height 2 in

Using these dimensions, we plug in the values into the formula

$SA=2(5*3)+2(5*2)+2(3*2)\\5*3=15\\15*2=30\\5*2=10\\10*2=20\\3*2=6\\6*2=12\\SA=30+20+12\\30+20+12=62$

Hence, the surface area = 62

3 0

2 years ago