For a system of two linear equations it is always true that if one equation is a linear combination of another, then the system will have infinite solutions.

Suppose we have the following system:

$ax + by = c\\dx + hy = f$

If there is a number n for which it is fulfilled that

$= n *$

Then the system has infinite solutions.

In this case the system is:

$x + 2y=10\\3x+6y =30$

Observe that:

$= \frac{1}{3}*$

Then $n =\frac{1}{3}$

The system has infinite solutions

5 0

3 years ago

What are the powers of 3 through 1000? AND DONT JUST SAY A FEW I NEED ALL OF THEM

galben [10]

Answer:

1, 3, 9, 27, 81, 243, 729

Step-by-step explanation:

The powers of 3 are:

$3^0 = 1$

$3^1 = 3$

$3^2 = 9$

$3^3 = 27$

$3^4 = 81$

$3^5 = 243$

$3^6 = 729$

$3^7 = 2187$

And so on...

So through 1000: 1, 3, 9, 27, 81, 243, 729

3 0

4 years ago

Find the product (a^2-b)(5a^2+6b)

Pie

Answer:

5a^4+a^2b−6b^2

Step-by-step explanation:

1. Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd.

5a^4+6a^2b−5ba^2−6b^2

2. Collect like terms.

5a^4+(6a^2b−5a^2b)−6b^2

3. Simplify.

5a^4+a^2b−6b^2

7 0

3 years ago

What is the least angle measure by which this figure can be rotated so that it maps onto itself?

evablogger [386]

its would be 360 as its not symmetrical.

6 0

4 years ago

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