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4 years ago

Graph 6x-2y=2 ,9x-3y=1

Mathematics

1 answer:

enot [183]4 years ago

4 0

It's a linear function. We need only two points to draw a graph.

We choose any values of x and calculate the value of y.

$6x-2y=2\qquad|-6x\\\\-2y=-6x+2\qquad|:(-2)\\\\y=3x-1$

for x= 0 → y = 3(0) - 1 = 0 - 1 = -1 → (0, -1)

for x = 2 → y = 3(2) - 1 = 6 - 1 = 5 → (2, 5)

$9x-3y=1\qquad|-9x\\\\-3y=-9x+1\qquad|:(-3)\\\\t=3x-\dfrac{1}{3}$

for x = 0 → y = 3(0) - 1/3 = 0 - 1/3 = -1/3 → (0, -1/3)

for x = 2 → y = 3(2) - 1/3 = 6 - 1/3 = 5 2/3 → (2, 5 2/3)

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The chairlift at a ski resort rises a total of 2600 feet from where it starts. The angle of elevation is about 22.3 degrees. How

Monica [59]

Answer:

6852 feet .

Step-by-step explanation:

Refer the attached figure

The chairlift at a ski resort rises a total of 2600 feet from where it starts. i.e.AB = 2600 feet

The angle of elevation is about 22.3 degrees.i.e.∠ACB= 22.3°

We are supposed to find How far do riders travel on the lift i.e.AC

In ΔABC

We will use trigonometric ratio

$Sin\theta =\frac{Perpendicular}{Hypotenuse}$

$Sin22.3^{\circ} =\frac{AB}{AC}$

$AC=\frac{2600}{Sin22.3^{\circ}}$

$AC=\frac{2600}{0.379456159529}$

$AC=6851.9$

So, riders travel 6852 feet .

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3 years ago

Read 2 more answers

An isosceles triangle has a base with length 15 inches and two congruent sides with lengths of 15 inches each. Find the height o

SpyIntel [72]

An isosceles triangle is a special triangle having at least 2 equal sides equal. But in this case, since all sides are equal having a length of 15 inches, this is actually an equilateral triangle.

When you create a perpendicular bisector from the top vertex to the midpoint of the base, you get a right triangle with the hypotenuse equal to 15 inches, a base equal to half of 15 because it was bisected, and the height. Therefore, we use the pythagorean theorem. The solution would be

h = √(15)^2 +(15/2)^
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3 years ago

Davida bought a pair of earrings, each in the shape of an isosceles triangle with equal side lengths of 24 mm and a base length

zubka84 [21]

If the base is 11 mm the side lengths are 19 mm

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4 years ago

Stem of Equations<br> Substitute (2, 1) into x + 3y = 5 to get<br> =

algol [13]

Answer:

see below!!

Step-by-step explanation:

x + 3y = 5,

y = –x + 3

Substitute the point into each equation and verify that it is true

x + 3y = 5, 2 +3(1) = 5 5 = 5 true

y = -x +3 1 = -2+3 1=1 true

(2,1) is a solution

6 0

2 years ago

A sinusoidal function whose period is 4π, maximum value is 6, and minimum value is -2 has a y intercept of 6. What is the equati

IRINA_888 [86]

Equation of the function: f(x) = 4 sin (x/2) + 6.

<h3>What is sinusoidal function ?</h3>

The term sinusoidal is used to describe a curve, referred to as a sine wave or a sinusoid, that exhibits smooth, periodic oscillation. It is named based on the function y=sin(x).

Given: max value= 6, min value= -2, y-intercept= 6.

As, standard form f(x) = A sin (ωx +φ) + k,

where A is the amplitude, ω is the angular velocity with ω=2πf.

Now,

A = |6- (-2)/2|

A = |6 +2/2| = 8/2

A = 4

Also, ω:

The period of a sinusoidal is T = 1/f

so, f = 1 / T

ω = 2πf

ω = 2π ( 1/T) with T = 4π

ω = 2π (1/(4π) = 2π (2)

ω = 1/2

The y-intercept k = 6

So, equation with values A =4, ω = 1/2, k = 6, φ = 0.

f(x) = A f(x)

f(x) = A sin (ωx +φ) + k

f(x) = 4 sin (x/2) + 6.

Hence, equation of the function f(x) = 4 sin (x/2) + 6.

Learn more about this concept here:

brainly.com/question/26315885

#SPJ1

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2 years ago