X+2y=3 <br> 3x-2y=5<br> What is the solution to system of equations?

Sin theta+costheta/sintheta -costheta+sintheta-costheta/sintheta+costheta=2sec2/tan2 theta -1

sleet_krkn [62]

$\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}$

From Left side:

$\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)$

$\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}$

NOTE: sin²θ + cos²θ = 1

$\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}$

$\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}$

$\dfrac{2}{sin^2\theta-cos^2\theta}$

$\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}$

$\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}$

$\dfrac{2sec^2\theta}{tan^2\theta-1}$

Left side = Right side <em>so proof is complete</em>

8 0

3 years ago

Read 2 more answers

2/5 simplified to its lowest

Dmitry [639]

Answer:

Its already simplified.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

A college student needs 15 classes that are worth a total of 40 credits in order to complete her degree. The college offers both

mars1129 [50]

12 three credit classes and two 2 credit classes

EXPLINATION:

12x3=36
2x2=4

And when you add you’re products together you get you get 40

6 0

3 years ago

A rectangular piece of metal is 15 in longer than it is wide. Squares with sides 3 in long are cut from the four corners and the

ziro4ka [17]

Answer:

The original dimensions of the piece of metal are

Length: 36 inches

Width: 21 inches

Step-by-step explanation:

Let

x ----> the original length pf the piece of metal

y ----> the original width pf the piece of metal

we know that

$x=y+15$ ----> equation A

The volume of the box is equal to

$V=LWH$

we have

$V=1,350\ in^3$

$L=(x-3-3)=(x-6)\ in\\W=(y-3-3)=(y-6)\ in$

$H=3\ in$

substitute in the formula of volume

$1,350=(x-6)(y-6)(3)$ ----> equation B

substitute equation A in equation B

$1,350=(y+15-6)(y-6)(3)$

solve for y

$450=(y+9)(y-6)$

$y^2-6y+9y-54=450\\y^2+3y-504=0$

Solve the quadratic equation by graphing

using a graphing tool

The solution is y=21

Find the value of x

$x=21+15=36$

therefore

The original dimensions of the piece of metal are

Length: 36 inches

Width: 21 inches

5 0

3 years ago

Which graph shows the solution set of x^2+9x-22/x+4<_0

motikmotik

Answer:

The Tasty Beans Coffee House being planned for the corner of SE 12th and Main will ruin a perfectly nice neighborhood. Besides the fact that Tasty Beans already has coffee shops all over the city, it will pull business away from local coffee houses that have been here for decades. In addition, there is already a parking problem on that street, and the new business will just add to the congestion. They're planning a drive-up window, too, and that will mean a steady stream of traffic in a very high-volume area. Ask anyone walking down the street, and they'll tell you this is a bad idea. I speak for my whole neighborhood when I say, "Go away, Tasty Beans!"

Step-by-step explanation:

The Tasty Beans Coffee House being planned for the corner of SE 12th and Main will ruin a perfectly nice neighborhood. Besides the fact that Tasty Beans already has coffee shops all over the city, it will pull business away from local coffee houses that have been here for decades. In addition, there is already a parking problem on that street, and the new business will just add to the congestion. They're planning a drive-up window, too, and that will mean a steady stream of traffic in a very high-volume area. Ask anyone walking down the street, and they'll tell you this is a bad idea. I speak for my whole neighborhood when I say, "Go away, Tasty Beans!"

7 0

3 years ago

X+2y=3 3x-2y=5 What is the solution to system of equations?