Athena was completing a puzzle picture by connecting ordered pairs of points. Her next point is described below:

Find the intersection point between the lines of equations: 2x-y+6=0 and 2x+3y-6=0

Ugo [173]

Step-by-step explanation:

The two equation will intersect each other at the point which will be the solution of the given two equations , and the given equations are ,

$\implies 2x -y +6=0\\\\\implies 2x + 3y -6=0$

On subtracting the given equations we have,

$\implies -y - 3y +6 -(-6) = 0 \\\\\implies -4y = -12 \\\\\implies y = -12/-4\\\\\implies y = 3$

Put this value in any equation , we have ,

$\implies 2x -3 +6 =0\\\\\implies 2x = -3 \\\\\implies x =\dfrac{-3}{2} \\\\\implies x =-1.5$

Hence the lines will Intersect at ,

$\implies\underline{\underline{ Point=(-1.5, 3)}}$

8 0

2 years ago

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What is the sum of 1/8 + 5/16 + 3/8 9/32 13/32 9/16 13/16

den301095 [7]

11/16 sorry I’m stxxupid

6 0

2 years ago

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Find the area of the rectangle. Round the answer to the nearest whole number.

Fed [463]

Answer:

The area of the given rectangle is 51

Step-by-step explanation:

First we have to find the coordinates of the vertices of the rectangle.

Then the length and breadth of it using distance formula.

The distance d between points (x₁ , y₁) and (x₂ , y₂) is given by

$d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Finally calculate the area of rectangle using the formula,

Area of rectangle = Length * Breadth

From the given graph, we get the coordinates of the rectangle as

A(2,4) , B(-2,3) , C(1,-9) , D(5,-8)

Breadth, AB = $\sqrt{(-2-2)^{2}+(3-4)^{2}} = \sqrt{16+1} = sqrt{17}$

Length, BC = $\sqrt{(1+2)^{2}+(-9-3)^{2}} = \sqrt{9+144} = 3 sqrt{17}$

Now, Area of rectangle = Length * Breadth = AB * BC = √17 * 3√17 = 3 *17 = 51

∴ The area of the given rectangle is 51

7 0

3 years ago

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-w + 4(w+3) = -12 Please help

Ivahew [28]

Let's solve your equation step-by-step.−w+4(w+3)=−12Step 1: Simplify both sides of the equation.−w+4(w+3)=−12Simplify: (Show steps)3w+12=−12Step 2: Subtract 12 from both sides.3w+12−12=−12−123w=−24Step 3: Divide both sides by 3.3w3=−243w=−8Answer:w=−8

4 0

2 years ago

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I need to find the slope and y-intercept of this equation. I also need to convert it to slope intercept form. The equation is 3x

USPshnik [31]

Answer:

slope=-1/2

y intercept =-2

Step-by-step explanation:

what u have to do is get y on 1 side and 3x on the other, so take away 3x from both sides which leaves you with 6y = -3x -12. then divide both sides by 6 to get y on it's own so you have y= -1/2x -2. this formula is y=mx+c the m is always the slope and the c is always the y intercept

4 0

3 years ago