The point P divides the join of (2,1) and (-3, 6) in the ratio 2:3. does P lie on the line x-5y+15=0?PLEASE ANSWER FAST IT IS KINDA URGENT...

Answers

Answer 1

Answer: x= [ 2*(-3)+ 3*(2)/( 2+3) = 0
y = [ 1*3+ 6*2 ]/2+3 = 3
so P is( 0,3 )
if it lies on the line x+ 5y = 15 then this point should satisfy the equation
so 0 + 5*3 = 15
so Plies on the given line x - 5y + 15 = 0

Answer 2

Answer: $A=(2;1)\ \ \ and\ \ \ B=(-3;6)\ \ \ \Rightarrow\ \ \ \overrightarrow {AB}=[-3-2;\ 6-1]=[-5;\ 5]\n\nP=(x_P;\ y_P)\ \ \ \Rightarrow\ \ \ \overrightarrow {AP}=[x_P-2;\ y_P-1]\n\nthe\ ratio\ \ is\ \ 2:3\n\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \Rightarrow\ \ \ \overrightarrow {AP}= (2)/(5) \cdot \overrightarrow {AB}=(2)/(5)\cdot[-5;\ 5]=[(2)/(5)\cdot(-5);\ (2)/(5)\cdot5]=[-2;\ 2]$

$\overrightarrow {AP}=[x_P-2;\ y_P-1]\ \ \ \ and\ \ \ \ \overrightarrow {AP}=[-2;\ 2]\n\n.\ \ \ \ \ \ \ \ \ \ \Rightarrow\ \ \ x_P-2=-2\ \ \ \ and\ \ \ \ y_P-1=2\n\n.\ \ \ \ \ \ \ \ \ \ \Rightarrow\ \ \ x_P=0\ \ \ \ \ \ \ \ \ \ \ and\ \ \ \ y_P=3\ \ \ \Rightarrow\ \ \ P=(0;\ 3)\n\nthe\ line:\ x-5y+15=0\n\nfor\ P=(0;\ 3)\ \ \ \rightarrow\ \ \ 0-5\cdot3+15=-15+15=0\n\nThe\ point\ P\ lies\ on\ the\ line.$

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Answers

Answer: x ≤ 5 or x > 7

Step-by-step explanation:

First, we will write an equation for the left side. It's a closed dot going to the left (less than) of 5.

x ≤ 5

Next, we will write the right side. It's an open dot going to the right (greater than) of 7.

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Lastly, we will combine these to create our compound inequality.

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Step-by-step explanation:

What is the graph of the inequality 3x+2y>-5

Answers

Answer:

The graph is shown in attachment.

Step-by-step explanation:

we have to draw a graph of the inequality

3x+2y>-5

The following steps are:

Step 1: Rearrange the equation such that "y" is on the left side and rest on the right.

3x+2y>-5

⇒ $2y>-5-3x$ ⇒ $y>(1)/(2)(-5-3x)$

Step 2: Plot the $y>(1)/(2)(-5-3x)$ line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)

. Here, dashed line is drawn.

Step 3: Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).

The graph is shown in attachment.

the graph above is how the inequality looks. I highly recommend you download an app called "desmos" for any questions you have about graphs.

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Answers

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