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3 years ago

Which two steps should be used first in solving the system of equations

Mathematics

2 answers:

Inessa05 [86]3 years ago

7 0

Answer:

The value of x , y using substitution method is 2 , 5

Step-by-step explanation:

Given as :

The two linear equation as

6 y - 4 x = 22 .......1

y + 2 x = 9

Let y = 9 - 2 x .......2

Now, using substitution method

Substitute the value of y from eq 2 into eq 1

i.e 6 × (9 - 2 x) - 4 x = 22

Or, 54 - 12 x - 4 x = 22

Or, 12 x + 4 x = 54 - 22

Or, 16 x = 32

∴ x = $\dfrac{32}{16}$

i.e x = 2

Now, Put the value of x into eq 2

∴ y = 9 - 2 x

So, y = 9 - 2 × 2

Or, y = 9 - 4

i.e y = 5

So, The value of x , y = 2 , 5

Hence, The value of x , y using substitution method is 2 , 5 Answer

Goryan [66]3 years ago

7 0

Answer:

first step : option B

second step : option D

Step-by-step explanation:

first, Solve the second equation for y and then substitute this value into the first equation.

after this, you will get the value of y then substitute this value in of the equations to get x.

so, option B will be the first step to solve and option D is the second step.

the other two steps are wrong.

this is a standard way to solve any 2 given equations with 2 variables.

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At the grocery store, Emily notices that it costs

Dmitriy789 [7]

Answer:

4.34

Step-by-step explanation:

2.48/40=0.062 per ounce

0.062 x 70 = 4.32 for 70 ounces

4 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 linear 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 trigonometric formulae are used to derive the half-angle 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 half 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 half 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 half 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 rectangular form to polar form are obtained by trigonometric 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 polar 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 rectangular 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 linear function y = 5 · x - 8, we proceed to use the following substitution 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 linear 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

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4 0

2 years ago

WILL GIVE BRAINLIEST AND 20 POINTS!

lianna [129]

Answer:

2.6

Step-by-step explanation:

24 ft. divided by 9 is 2.6666666666...

5 0

2 years ago

Read 2 more answers

What is the image point of (-6, 9) after a translation left 4 uints and down 1 unit?

Alex17521 [72]

Answer:

(-10,8)

Step-by-step explanation:

So our original point is (-6,9).

A translation of 4 units to the left means that the x-value would go left by 4. In other words, we subtract 4 to -6. We subtract because going to the left means that it's going to the negative direction.

A translation of down 1 unit means that the y-value would go down by 1. In other words, we subtract 1. Again, we subtract because going downwards means that it's going to the negative direction.

Therefore, the new point would be:

$(-6-4,9-1)\\=(-10,8)$

6 0

3 years ago

what is perpendicular to y= 3x -9 and passes through the point (3,1)

GREYUIT [131]

$(3,1) , \ \ y= 3x -9 \\ \\ The \ slope \ is :m _{1} =3 \\ \\ If \ m_{1} \ and \ m _{2} \ are \ the \ gradients \ of \ two \ perpendicular \\ \\ lines \ we \ have \ m _{1} \cdot m _{2} = -1 \\ \\3\cdot m_{2}=-1 \ \ /:3\\ \\ m_{2}=-\frac{1}{3}$

$\Now \ your \ equation \ of \ line \ passing \ through \ (3,1) would \ be: \\ \\ y=m_{2}x+b \\ \\1=-\frac{1}{ 3} \cdot3 + b$

$1=-1+b\\ \\ b=1+1\\ \\b=2 \\ \\ y =- \frac{1}{3}x+2$

6 0

3 years ago