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3 years ago

Equations with variables. Please explain it to me.

Mathematics

1 answer:

irinina [24]3 years ago

6 0

Answer:

Equation: 10x-12=6x-6

X: 3/2 or .5

Perimeter of square and triangle are both 3.

Step-by-step explanation:

Square:

4(2.5x-3) {The four represents the amount of sides}=

10x-12

Triangle:

3(2x-2)=

6x-6

Since they have the same perimeter the equation is

10x-12=6x-6

10x-6x=12-6

4x=6

x=1.5

Square pt 2:

4(2.5(3/2)-3)=

4(3.75-3)=

4(0.75)=

Triangle pt 2:

3(2(3/2)-2)=

3(3-2)=

3(1)=

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3 years ago

The coordinates of AB are A(-5, -1) and B(-2, -6). If AC : CB = 3 : 7, what are the coordinates of point C?

navik [9.2K]

$\text{Let the coordinates of AB are }A(-5,-1), \text{ and }B(-2, -6)\\
\\
\text{let the coordinate of th point C be (x, y), such that}\\
\\
AC:CB=3:7\\
\\
\text{By the section formula, we know that if P(x,y) lies on a line segment AB}\\
\text{where, }A(x_1,y_1), \ B(x_2,y_2)\text{ and satisfy the ratio, }AP:PB=m:n, \text{ then}$

$P=\left ( \frac{mx_2+nx_1}{m+n}, \ \frac{my_2+ny_1}{m+n} \right ).\\
\\
\text{So using this formula, we get for the given problem}\\
\\
C=\left ( \frac{3(-2)+7(-5)}{3+7}, \ \frac{3(-6)+7(-1)}{3+7} \right )\\
\\
\Rightarrow C=\left ( \frac{-6-35}{10}, \ \frac{-18-7}{10} \right )\\
\\
\Rightarrow C=\left ( \frac{-41}{10}, \ \frac{-25}{10} \right )\\
\\
\Rightarrow C=\left ( -4.1, \ -2.5 \right )$

Coordinates of the point C is: (-4.1, -2.5)

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