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faltersainse [42]
3 years ago
7

Write an equation of a line whose graph is parallel to the graph of y=3x-10.

Mathematics
2 answers:
Rzqust [24]3 years ago
7 0
Y=3x plus or minus any number that is not 10.

The slope of your function has to stay 3x to be parallel with the function given. Just change the y-intercept (also known as the B value) to a number other than -10.
Diano4ka-milaya [45]3 years ago
5 0

Answer:  

The equation of line parallel to the given equation of line : y = 3x + 4

Step-by-step explanation:

The equation of the line is given to be :

y = 3x - 10

Now, on comparing the given equation of line with the standard equation of line in slope intercept form : y = mx + c

where m is the slope of the line

So, Slope of the given equation of line = 3

Now, Since parallel lines never intersect each other

⇒ The slope of parallel lines are equal to each other

So, The required equation of parallel line is of form : y = 3x + c

Hence, The equation of line parallel to the given equation of line : y = 3x + 4

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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
15 plus the quotient of 60 and w
Romashka [77]
15+60:w=15+\dfrac{60}{w}
6 0
2 years ago
Read 2 more answers
(-4, 8) and (6, 2). Slope
Setler79 [48]

Answer:

In order to go from the first point to the second, we need to rise from 4 to 7, i.e. by 3. We also need to run from -4 to -2, i.e. by 2. Therefore the slope is 32 .

Step-by-step explanation:

8 0
2 years ago
Solve the equation 2x^2 + 4x - 39 to the nearest tenth.
Virty [35]

Answer:

cant be solved, when you try to you get

-1+78 = 77

which is

77 = 77

1=1

So cannot be factored

Step-by-step explanation:

8 0
2 years ago
Jeff has $6000 in a savings account, has $15000 in investments, he owned a guitar worth $1000, he has $17000 left to pay on his
Law Incorporation [45]

Answer:

$200

Step-by-step explanation:

To find Jeff's net worth, we will deduct all his debts (liabilities) from his assets (his properties).

ASSETS

Savings Account - $6000

Investments - $15000

Guitar - $1000

TOTAL - $22000

LIABILITIES

Student loans - $17000

Credit Card Debt - $1200

Outstanding car payment - $3600

TOTAL - $21800

NET WORTH = Assets - Liabilities

NW = $22000 - $21800

NW = $200

His net worth is $200.

4 0
3 years ago
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