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3 years ago

Solve the system of linear equations by elimination. x+4y=6 −x−2y=−4

Mathematics

1 answer:

REY [17]3 years ago

3 0

Answer:

(x , y) = (2 , 1)

Step-by-step explanation:

// Solve equation [1] for the variable x

[1] x = -4y + 6

// Plug this in for variable x in equation [2]

[2] -(-4y+6) - 2y = -4

[2] 2y = 2

// Solve equation [2] for the variable y

[2] 2y = 2

[2] y = 1

// By now we know this much :

x = -4y+6

y = 1

// Use the y value to solve for x

x = -4(1)+6 = 2

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2 years ago

Solve sin 0 + 1 = cos20 on the interval 0 ≤ 0 < 2pi. Show work please!

yan [13]

Answer:

$\theta=\frac{\pi}{2},\frac{3\pi}{2}\frac{2\pi}{3}\frac{4\pi}{3}$

Step-by-step explanation:

You need 2 things in order to solve this equation: a trig identity sheet and a unit circle.

You will find when you look on your trig identity sheet that

$cos(2\theta)=1-2sin^2(\theta)$

so we will make that replacement, getting everything in terms of sin:

$sin(\theta)+1=1-2sin^2(\theta)$

Now we will get everything on one side of the equals sign, set it equal to 0, and solve it:

$2sin^2(\theta)+sin(\theta)=0$

We can factor out the sin(theta), since it's common in both terms:

$sin(\theta)(2sin(\theta)+1)=0$

Because of the Zero Product Property, either

$sin(\theta)=0$ or

$2sin(\theta)+1=0$

Look at the unit circle and find which values of theta have a sin ratio of 0 in the interval from 0 to 2pi. They are:

$\theta=\frac{\pi}{2},\frac{3\pi}{2}$

The next equation needs to first be solved for sin(theta):

$2sin(\theta)+1=0$ so

$2sin(\theta)=-1$ and

$sin(\theta)=-\frac{1}{2}$

Go back to your unit circle and find the values of theta where the sin is -1/2 in the interval. They are:

$\theta=\frac{2\pi}{3},\frac{4\pi}{3}$

7 0

2 years ago

Segments AB, EF, and CD intersect at point C, and angle ACD is a right angle. Find the value of g. Please help me

iogann1982 [59]

Answer:

37 degree

Step-by-step explanation:

AB = 180 it is a straight line

ACD = 90 degree

DE+ DCB are complimentary angles they add up to 90 they dont need to be next to each other.

DE = 53 deg

DCB = 90-53= 37 degree

g = 37 and F is its vertical angle as they share the same corner point and lay opposite each other and each have same angle 37 degree.

8 0

3 years ago