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3 years ago

How can I tell if a system of equations has one, no, or infinitely many solutions?

Mathematics

1 answer:

Fittoniya [83]3 years ago

7 0

Answer:

There are many ways to interpret if whether or not a system of equations has solutions or not. Here is one way that is most ideal for most, if not, all equations: using graphs.

If the graphs of the set of equations do NOT intersect, then there are no solutions (because no x or y value will ever make both equations true)
If the graphs of the set of equations DO intersect at one point, then ONLY that one point will make both equations true. (One solution)
If the graphs of the set of equations are identical on the graph, then there are infinite solutions that make both equations true.

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Consider the drawing shown below. Given the measure of angle ACD is

gayaneshka [121]

Answer:

150

Explanation:

3 0

3 years ago

given two terms in a geometric sequence find the 8th term and the recursive formula . a4=-12 and a5=-6

Crazy boy [7]

A geometric sequence is defined by a starting point, $a$ , and a common ratio $r$

The first term is $a$ , and you get every next term by multiplying the previous one by r.

So, our terms are

$\left[\begin{array}{c|c}a_1&a\\a_2&ar\\a_3&ar^2\\a_4&ar^3=-12\\a_5&ar^4=-6\end{array}\right]$

We can see that when we pass from $a_4$ to $a_5$ the number gets halved ( $-12 \mapsto -6$ )

This implies that the common ratio is $r = \frac{1}{2}$

So, the table becomes

$\left[\begin{array}{c|c}a_1&a\\a_2&\frac{1}{2}a\\a_3&\frac{1}{4}a\\a_4&\frac{1}{8}a=-12\\a_5&\frac{1}{16}a=-6\end{array}\right]$

So, we can derive the starting point from either $a_4$ or $a_5$ :

$\dfrac{1}{8}a = -12 \iff a = -12\cdot 8 = -96$

The sequence is thus

$\left[\begin{array}{c|c}a_1&-96\\a_2&-48\\a_3&-24\\a_4&-12\\a_5&-6\\a_6&-3\\\vdots&\vdots\end{array}\right]$

And the recursive formula is

$a_n = -\dfrac{96}{2^{n-1}}$

7 0

4 years ago

For problems 3 and 4, find the missing side of the triangle. Leave answers in simplest radical form.

maria [59]

Answer: 3. 4 $\sqrt{13}$ 4. $\sqrt{225}$

Step-by-step explanation:

8^2 + 12^3 = c^2

64 + 144 = c^2

208 = c^2

√208

$4\sqrt{13}$

The final answer is the square root of 208

8^2 + b^2 = 17^2

64 + b^2 = 289

-64 64

b^2 = 225

$\sqrt{225}$

7 0

3 years ago

A cat is watching a bird in a tree nearby the tree is approximately 20 feet from the cat ground distance if the cats line of sig

Elina [12.6K]

Answer:

X=20Tan(25)

Step-by-step explanation:

So because the cat is looking at the tree it is a strait line making a right triangle with the tree. The cat spots the bird 25 degrees up in the tree making a triangle. Then use SohCahToa, and because u have the adjacent side use Tangent because you are missing the opposite side of the angle. There are a few other ways to find it but that is the simplest way to perform this, GOOD LUCK!

3 0

3 years ago

A right rectangular prism has a length of 6 in., a width of 9 in., and a height of 10 in. What is the surface area of the prism?

Alisiya [41]

408 in^2
.......Hope it helps, Have a nice day:)

5 0

3 years ago