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3 years ago

Find the slope of the line. Use the two points shown.

Mathematics

1 answer:

stellarik [79]3 years ago

5 0

Answer:

The slope is 2.

Step-by-step explanation:

slope = rise/run

= 1-(-5) / 2-(-1)

= 6/3 = 2

Therefore, the slope is 2.

You might be interested in

Find g. (-9)<br> g(+)= r^2 + 3r

oee [108]

Answer:

g(-9) = 64

Step-by-step explanation:

<u>Given function:</u>

g(r) = r² + 3r

g(-9) = (-9)² + 3(-9) = 81 - 27 = 64

7 0

3 years ago

Danielle’s aunt is 8 years than 3 times Danielle’s age. Her aunt is 34. Write an equation that relates Danielle’s age, a, to her

OverLord2011 [107]

Answer:

*Assuming that the question should read '8 years less than 3 times Danielle's age'*

Equation: 3a - 8 = 34, where 'a' = Danielle's age

Danielle's age (a) = 14

Step-by-step explanation:

Using key words and phrases from the problem, we can find Danielle's age by setting up an equation to solve for 'a'.

Since Danielle's aunt is '8 years less than 3 times Danielle's age' her aunt's age can be written as: 3a - 8. We also know her aunt is 34. So, the equation becomes:

3a - 8 = 34

Add 8 to both sides: 3a - 8 + 8 = 34 + 8 or 3a = 42

Divide both sides by 3: 3a/3 = 42/3

Solve for a: a = 14, so Danielle's age is 14 years old.

7 0

4 years ago

ASAP ASAP ASAP SHOW WORK TOO !!!!!!!!!!!!!!! thanks soo much

k0ka [10]

A.
(64x<span>² + 96x + 36) / (16x + 12)
= 4(16x</span><span>² + 24x + 9) / 4(4x + 3)
= 4*(4x + 3)(4x + 3) / 4(4x + 3)
= 4x + 3

b.
1.79 x 10^5 = 1.79 * 100,000 = 179,000

c.
(5.9736 x 10^24) + (4.8685 x 10^24)
= (5.9736 + 4.8685) x 10^24
= 10.8421 x 10^24
= 1.08421 x 10^25</span>

4 0

3 years ago

(Geometry course question) Explain why it is not possible to construct an equilateral triangle that has

Nutka1998 [239]

Answer:

√3 is irrational

Step-by-step explanation:

The location of the third point of a triangle can be found using a rotation matrix to transform the coordinates of the given points.

<h3 /><h3>Location of point C</h3>

With reference to the attached figure, the slope of line AC is √3, an irrational number. This means the line AC <em>never passes through a point with integer coordinates</em>. (Any point with integer coordinates would be on a line with rational slope.)

<h3>Equilateral triangle</h3>

The line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.

The math of it is this. For rotation of (x, y) counterclockwise 60° about the origin, the transformation matrix is ...

$\left[\begin{array}{cc}\cos(60^\circ)&\sin(60^\circ)\\-\sin(60^\circ)&\cos(60^\circ)\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}x'\\y'\end{array}\right]$

Cos(60°) is rational, but sin(60°) is not. For any non-zero rational values of x and y, the sum ...

cos(60°)·x + sin(60°)·y

will be irrational.

As in the attached diagram, if one of the coordinates of the rotated point (B) is zero, then one of the coordinates of its image (C) will be rational. The other image point coordinate cannot be rational.