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2 years ago

Y = 3x + 15 3x + 3y = 9

Mathematics

1 answer:

Zina [86]2 years ago

4 0

Answer:

$\Large\boxed{x=-3}$ $\Large\boxed{y=6}$

Step-by-step explanation:

Given the system of equations

$1)~y=3x+15$

$2)~3x+3y=9$

Divide 3 on both sides of the 2) equation

$3x+3y=9$

$3x\div3+3y\div3=9\div3$

$x+y=3$

Current system

$1)~y=3x+15$

$2)~x+y=3$

Substitute 1) equation into the 2) equation

$x+(3x+15)=3$

Combine like terms

$x+3x+15=3$

$4x+15=3$

Subtract 15 on both sides

$4x+15-15=3-15$

$4x=-12$

Divide 4 on both sides

$4x\div4=-12\div4$

$\Large\boxed{x=-3}$

Substitute the x value into one of the equations to find the y value

$y=3x+15$

$y=3(-3)+15$

$y=-9+15$

$\Large\boxed{y=6}$

Hope this helps!! :)

Please let me know if you have any questions

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Sin(A+B) sin(A-B) /sin^A Cos^B=1-cot^A Tan^B

telo118 [61]

In order to prove

$\dfrac{\sin(x+y)\sin(x-y)}{\sin^2(x)\cos^2(x)}=1-\cot^2(x)\tan^2(y)$

Let's write both sides in terms of $\sin(x),\ \sin^2(x),\ \cos(x),\ \cos^2(x)$ only.

Let's start with the left hand side: we can use the formula for sum and subtraction of the sine to write

$\sin(x+y)=\cos(y)\sin(x)+\cos(x)\sin(y)$

and

$\sin(x-y)=\cos(y)\sin(x)-\cos(x)\sin(y)$

So, their multiplication is

$\sin(x+y)\sin(x-y)=(\cos(y)\sin(x))^2-(\cos(x)\sin(y))^2\\=\cos^2(y)\sin^2(x)-\cos^2(x)\sin^2(y)$

So, the left hand side simplifies to

$\dfrac{\cos^2(y)\sin^2(x)-\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}$

Now, on with the right hand side. We have

$1-\cot^2(x)\tan^2(y)=1-\dfrac{\cos^2(x)}{\sin^2(x)}\cdot\dfrac{\sin^2(y)}{\cos^2(y)} = 1-\dfrac{\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}$

Now simply make this expression one fraction:

$1-\dfrac{\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}=\dfrac{\sin^2(x)\cos^2(y)-\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}$

And as you can see, the two sides are equal.

6 0

4 years ago

If you graph both sides of the equation 2(2x + 3) = 4x + 6, what will the graph look like? The graphs never intersect. The graph

koban [17]

The graphs are identical and intersect at infinitely many points.

This is because 2(2x+3) is the same as 4x+6
Distribute the outer 2 to each term inside
2 times 2x = 4x
2 times 3 = 6
So 2(2x+3) simplifies to 4x+6
Or you can think of 4x+6 factoring to 2(2x+3)

8 0

4 years ago

A student used the equation below to create a table.

Leokris [45]

Answer:

(-2, 1)

Step-by-step explanation:

Putting in -2 as an input basically means plugging in -2 in the place of x

So it would result in this

y = -3(-2) - 5

Remember that multiplying a negative number by another negative number results in a positive number

y = 6 - 5

y = 1

So we have

x = -2

y = -1

Making the answer (-2, 1)

3 0

3 years ago

Chaney deposits $1435.73 into a savings account that pays a simple annual interest rate of 1.32%. How much interest will she ear

Aneli [31]

Answer:

Interest Chaney earns after 3 years is $56.85

Step-by-step explanation:

Given:

Amount deposited = $1435.73

Simple annual interest rate = 1.32% = 1.32/ 100 = 0.0132

To find: Interest after 3 years

We know that the formula to calculate the interest amount is

Simple interest (S.I.) = $\frac{Prt}{100}$

where,

P is the initial amount deposited

r is the rate of simple interest in percentage

t is the time in years for which interest is to be calculated

Substituting the known values in the formula, we get

S.I = $\frac{1435.73 x 1.32 x 3}{100}$

= 56.85

Hence the interest Chaney earns after 3 years is $56.85

8 0

3 years ago

Once again, I can’t figure it out. Can you help me again

malfutka [58]

Cross multiply: 20 * b = 45 * 34

Simplifying: 20 * b = 45 * 34

Multiply 45 * 34: 20b = 1530

Solving: 20b = 1530

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Divide each side by '20': b = 76.5

Simplifying: b = 76.5

3 0

3 years ago