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oksano4ka [1.4K]
3 years ago
6

The slope of the line whose equation is 3x - 2y = 4 is 2/3 3/2 -2

Mathematics
1 answer:
7nadin3 [17]3 years ago
6 0

Answer:

3/2

Step-by-step explanation:

The equation 3x-2y=4 can be written in the form of y=mx+c where m is the slope and c is the y intercept.

Therefore

2y=3x-4 and dividing both sides by 2 to have y at the LHS

y=3/2x-2

Therefore, 3/2 represents the gradient/slope

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Log4 x + log4 (x – 3) = 1 Solve the equation.
Natasha_Volkova [10]

Answer:

x is EQUIVALENT to 2.89

Step-by-step explanation:

7 0
3 years ago
Pls please help me ASAP!!!
oksian1 [2.3K]

Answer:

z = 0

Step-by-step explanation:

3 (z + 7) = 21

3z + 21 = 21

3z = 0

z = 0

8 0
2 years ago
1. Derive the half-angle formulas from the double
lilavasa [31]

1) cos (θ / 2) = √[(1 + cos θ) / 2], sin (θ / 2) = √[(1 - cos θ) / 2], tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) (x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°). The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) The <em>linear</em> function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

<h3>How to apply trigonometry on deriving formulas and transforming points</h3>

1) The following <em>trigonometric</em> formulae are used to derive the <em>half-angle</em> formulas:

sin² θ / 2 + cos² θ / 2 = 1                      (1)

cos θ = cos² (θ / 2) - sin² (θ / 2)           (2)

First, we derive the formula for the sine of a <em>half</em> angle:

cos θ = 2 · cos² (θ / 2) - 1

cos² (θ / 2) = (1 + cos θ) / 2

cos (θ / 2) = √[(1 + cos θ) / 2]

Second, we derive the formula for the cosine of a <em>half</em> angle:

cos θ = 1 - 2 · sin² (θ / 2)

2 · sin² (θ / 2) = 1 - cos θ

sin² (θ / 2) = (1 - cos θ) / 2

sin (θ / 2) = √[(1 - cos θ) / 2]

Third, we derive the formula for the tangent of a <em>half</em> angle:

tan (θ / 2) = sin (θ / 2) / cos (θ / 2)

tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) The formulae for the conversion of coordinates in <em>rectangular</em> form to <em>polar</em> form are obtained by <em>trigonometric</em> functions:

(x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) Let be the point (x, y) = (2, 3), the coordinates in <em>polar</em> form are:

r = √(2² + 3²)

r = √13

θ = atan(3 / 2)

θ ≈ 56.309°

The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°).

Let be the point (r, θ) = (4, 30°), the coordinates in <em>rectangular</em> form are:

(x, y) = (4 · cos 30°, 4 · sin 30°)

(x, y) = (2√3, 2)

The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) Let be the <em>linear</em> function y = 5 · x - 8, we proceed to use the following <em>substitution</em> formulas: x = r · cos θ, y = r · sin θ

r · sin θ = 5 · r · cos θ - 8

r · sin θ - 5 · r · cos θ = - 8

r · (sin θ - 5 · cos θ) = - 8

r = - 8 / (sin θ - 5 · cos θ)

The <em>linear</em> function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

To learn more on trigonometric expressions: brainly.com/question/14746686

#SPJ1

4 0
2 years ago
Find the missing number in the following pattern 12,24,72,288
konstantin123 [22]
12 × 2 = 24

24 × 3 = 72

72 × 4 = 288

288 × 5 = 1,440, and so on...

<span><span>Comments </span> <span>Report</span></span>
3 0
3 years ago
Can someone please help me answer this?
Lina20 [59]
DEF = BAC : x = 15 <==

once u allign ur triangles, u will see that there is a scale factor of 1.5.
6 * 1.5 = 9

1.5(x - 5) = 15
1.5x - 7.5 = 15
1.5x = 15 + 7.5
1.5x = 22.5
x = 22.5/1.5
x = 15 <==

6 0
3 years ago
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