Explanation

  y-intercept = 4/-2 = 2/-1  = -2.00000 

ND18-1-2023

Explanation

Find the equation of line I using the two-point form:

(y - 5) / (8 - 5) = (x - (-3)) / (6 - (-3))

(y - 5) / 3 = (x + 3) / 9

y = (1/3)x + 6

Check which point lies on line I:

(0, 6): 6 = (1/3)(0) + 6 => True

Answer: (0, 6)

Explanation

Since the sum of the angles in a triangle is always 180 degrees, and two of the angles are already 60 degrees each, the third angle can be found by subtracting the sum of the two known angles from 180:

180 - (60 + 60) = 180 - 120 = 60

So, the third angle is also 60 degrees, making the triangle an equilateral triangle.

Explanation

1. • The height $h$ of the equilateral triangle is $\frac{\sqrt{3}}{2}x$.

   • Using the area formula for a triangle ($\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}$):

     $$\mathrm{<b><font\; color="\#0000ff">A</font></b>}<b><font\; color="\#0000ff">=</font></b>\frac{\mathrm{<b><font\; color="\#0000ff">1</font></b>}}{\mathrm{<b><font\; color="\#0000ff">2</font></b>}}<b><font\; color="\#0000ff">\times </font></b>\mathrm{<b><font\; color="\#0000ff">x</font></b>}<b><font\; color="\#0000ff">\times </font></b>\frac{\sqrt{\mathrm{<b><font\; color="\#0000ff">3</font></b>}}}{\mathrm{<b><font\; color="\#0000ff">2</font></b>}}\mathrm{<b><font\; color="\#0000ff">x</font></b>}<b><font\; color="\#0000ff">=</font></b>\frac{\sqrt{\mathrm{<b><font\; color="\#0000ff">3</font></b>}}}{\mathrm{<b><font\; color="\#0000ff">4</font></b>}}{\mathrm{<b><font\; color="\#0000ff">x</font></b>}}^{\mathrm{<b><font\; color="\#0000ff">2</font></b>}}$$

Explanation

The given inequalities define a region in the Cartesian plane:

a - δ ≤ x ≤ a + δ (horizontal bounds)

b - δ ≤ y ≤ b + δ (vertical bounds)

This region forms a square with:

Center at (a, b)

Side length of 2δ

The answer is A square.

Explanation

Skew lines are lines that are not parallel and do not intersect, and they exist in three-dimensional space.

They lie in different planes, unlike parallel or intersecting lines.

Explanation

 the average of the data is also known as the arithmetic mean.

Explanation

Let angle = $x$
Complement = $90 - x$, Supplement = $180 - x$
Given:

$$6(90 - x) = 2(180 - x) - 12 \ 540 - 6x = 360 - 2x - 12 \ 540 - 6x = 348 - 2x \ 192 = 4x Rightarrow x = 48$$

$$540-6x=360-2x-12$$

$$540-6x=348-2x$$

$$192=4x\Rightarrow x=48$$

Explanation

Angular velocity is positive when the rotation is counter clockwise and negative when it is clockwise

Explanation

To find the perimeter of a square, use the formula:

Perimeter = 4 × side length

= 4 × 7 = 28 cm