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3 years ago

A line intersects the points

Mathematics

1 answer:

monitta3 years ago

3 0

The slope of this line in its simplest form is -3.

Given the following points:

Points on the x-axis = (7, 11)

Points on the y-axis = (6, -6)

To determine the slope of this line in its simplest form:

The slope of a line refers to the gradient of a line and it describes both the direction and steepness of an equation of a straight line.

Mathematically, the slope of a line is calculated by using this formula;

$Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the given parameters into the formula, we have;

$Slope, \;m = \frac{-6 - 6}{11 - 7}\\\\Slope, \;m = \frac{-12}{4}\\$

Slope, m = -3.

Read more on slope here: brainly.com/question/3493733

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3 years ago

There is a bag filled with 4 blue and 5 red marbles.

gavmur [86]

1) first pick red 5/9 blue 4/9

2) second pick when red has been picked red now becomes 4/8, blue stays 4/8

2) Second pick when blue has been picked blue now becomes 3/8, red stays 5/8

Mind you, you only need both different colours so:

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and first pick blue 4/9 x sec pick red 5/8 = 20/72

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3 years ago

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3 years ago

The outer and inner triangles are both equilateral and the circle touches all three sides of the outer triangle. If the area of

Brrunno [24]

Answer:

The area of outer Δ = 40 cm²

Step-by-step explanation:

∵ Area of the small triangle = 10 cm²

If we join the center of the circle with the 3 vertices of the inner Δ

These 3 segments are the radii of the circle

Now the inner triangle has 3 isosceles Δ their sides are r , r and s1 with vertex angle 120° ⇒ (360° ÷ 3 = 120°)

Where r is the radius of the circle and s1 is the side of the inner triangle

By using cosine rule

(s1)² = r² + r² - 2r²cos120 = r² + r² - 2r² (-0.5) = r² + r² + r² = 3r²

∴ s1 = r√3

∵ The radius of the circle ⊥ to the side of the outer Δ because the side of the outer Δ is a tangent to the circle

If we join a vertex of the outer Δ with the center of the circle

We will have a right angle triangle of two legs r and half s2 with angle 60° (120° ÷ 2 )between them ⇒ s2 is the side of outer Δ

∴ tan 60° = 1/2 (s2) ÷ r ⇒ √3 = 1/2 (s2) ÷ r = (s2)/2r

∴ s2 = 2r√3

∴ s2 : s1 = 2r√3 ÷ r√3 = 2 : 1

∴ The side of the outer Δ is double the side of the inner Δ

By using similarity ratio

A2/A1 = (s2/s1)² ⇒ A2 and A1 are the areas of outer and inner triangles

∴ A2 : A1 = (2/1)² = 4/1

∴ A2 = 4 A1

∴ A2 = 4 × 10 = 40 cm²

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3 years ago

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Answer:

Step-by-step explanation:

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