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4 years ago

Write an equation for each line in point-slope form and then convert it to standard form

Mathematics

1 answer:

asambeis [7]4 years ago

5 0

Answer:

x + 2y = 14
2x -y = 13

Step-by-step explanation:

I find it easier to work with the given standard-form equation. The parallel line will have the same x- and y-coefficients and a new constant. That constant can be found by substituting the given x- and y-values into the left-side expression:

x + 2y = 8 + 2·3 = 14

The parallel line is x + 2y = 14.

The perpendicular line will have the x- and y-coefficients swapped and one of them negated. (In standard form, the x-coefficient is positive, so in this case it is convenient to negate the y-coefficient.) Then the perpendicular line through (8, 3) is ...

2x -y = 2·8 -3 = 13

The perpendicular line is 2x - y = 13.

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A trumpet has a length of 140cm. The first valve lowers the root note by two semitones (f1/f0 = 2-2/12) and the second valve low

Alexxandr [17]

Answer:

a. 17.145cm

b. 8.325cm

c. 0.846

d. 2.896

Step-by-step explanation:

It is known that frequency is inversely proportional to length.

Case 1: The player presses only the first valve.

f₁/fo = 2^{-2/12} = lo/l₁

given that lo= 140cm.

l₁ = 2^{2/12}lo = 157.145

change in length:

l₁ - lo = 157.145 - 140 = 17.145cm

Case 2: The player presses only the second valve.

f₂/fo = 2^{-1/12} = lo/l₂

l₂ = 2^{1/12}lo = 148.325cm

l₂ - lo= 148.325-140 = 8.325cm

Case 3: The player presses both the first and second valve.

Change in length is the sum of change in length when they are individually pressed.

l₃ - lo = 17.145+8.325 = 25.47cm

l₃ = 25.47cm+lo = 165.47cm

f₃/fo = 2^{-n/12} = lo/l₃

f₃/fo = 2^{-n/12} = 140/{165.47 = 0.846

2^{-n/12} = 0.846\Rightarrow n/12 = -log(0.846)/log(2) = 0.2413

n = 0.2413*12 = 2.896

5 0

3 years ago

F(x) =x^2 what is g(x)

In-s [12.5K]

Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”. The function g (x) is called an inner function and the function f (x) is called an outer function.

6 0

3 years ago

Translations, rotations, and reflections are rigid transformations. What can you conclude about the measures of sides and angles

Alexeev081 [22]

After a translation, the measures of the sides and angles on any triangle would be the same since translation only involves changing the coordinates of the vertices of the triangle.
After a rotation, the measures of the sides and angles of a triangle would also be the same. Similar to translation, the proportion of the triangle is unchanged after a rotation.
After a reflection, the triangle's sides and angles would still be the same since reflection is a rigid transformation and that proportion of the sides and angles are not changed.

8 0

3 years ago

Answer please answer

const2013 [10]

Answer:

4 liters

Step-by-step explanation:

8/2 8 divided by 2 is 4 how do I know this, because if its per apple juice then we have to find out what can get me per apple juice, you just basically had to divde it by its own number

6 0

3 years ago

Indicate the equation of the line through (2, -4) and having slope of 3/5.

Kamila [148]

Y = mx + b

y = 3/5(x) + b

-4 = 3/5(2) + b

-4 = -2.4 + b

b = -4 + 2.4

b = -1.6 (-8/5)

y = 3/5x - 8/5.

4 0

3 years ago

Read 2 more answers