Ask question

Ask question

All categories

3 years ago

10

Coordinate plane with two lines graphed. The equations of the lines are y equals negative two-thirds x plus four and the other l

ine is y equals two-thirds x. Determine the number of solutions the system of linear equations has and the solution(s) to the equations represented by these two lines? The system of equations has 0 solutions, because the graph has no point of intersection. The system of equations has infinite number of solutions and all real numbers satisfy both equations. The system of equations has 1 solution and it is (3, 2). The system of equations has 1 solution and it is (3, 0).

1 answer:

miss Akunina [59]3 years ago

3 0

Answer:

Step-by-step explanation:

y = -2/3x + 4

y = 2/3x

2/3x = -2/3x + 4

4/3x = 4

4x = 12

x = 3

y = 2/3(3)

y = 2

(3,2) one solution

option 3

You might be interested in

What is the portion of the quadratic formula under the square root sign

Gelneren [198K]

Portion under square root sign:

= (b^2 - 4*a*c).

8 0

3 years ago

Find dy/dx when y = Ln (sinh 2x). A. 2 cosh 2x B. 2 sech 2x C. 2 coth 2x D. 2 csch 2x

givi [52]

The function given is a composite function. Let's work from the outside in:
$y=(ln(sinh(2x)))$

First step:
$\frac{d}{dx}[y]= \frac{d}{dx}[ln(sinh(2x))]$

Now, let's work it out:
$\frac{dy}{dx} = \frac{1}{sinh(2x) } * \frac{d}{dx}[sinh(2x)]$

Next step:
$\frac{dy}{dx} = \frac{1}{sinh(2x) } * cosh(2x) * \frac{d}{dx}[2x]$

Next step:
$\frac{dy}{dx} = \frac{1}{sinh(2x) } * cosh(2x) *2$

Simplify:
$\frac{dy}{dx} = \frac{2cosh(2x)}{sinh(2x) }$

Simplify further:
$\frac{dy}{dx} = 2 (\frac{cosh(2x)}{sinh(2x)})$

Remember that:
${\frac{cosh(x)}{sinh(x)} = coth(x)$

So, your final answer is:
$\boxed{ \frac{dy}{dx} = 2coth(2x) }$

So, your answer is C. Hope I could help you!

8 0

3 years ago

Mrrafil [7]

Comparing with the original expression, the value that will go into the green box is 5

<h3>Exponents and indices</h3>

Given the indices expression below;

$\frac{4^{-5}}{4^4}$

Since 4^-5 is equivalent to 1/4^5, hence the given expression will be equivalent to;

$\frac{1}{4^5\times4^4}$

Comparing with the original expression, the value that will go into the green box is 5

Learn more on exponent here: brainly.com/question/11975096

#SPJ1

7 0

1 year ago

The combined height of one for tree and one pine tree is 21 meters. The height of 4 for trees stacked on top of each other is 24

slamgirl [31]

Answer:

The height of the fir tree is <u>9 meters</u> tall and the pine tree is <u>12 meters</u>.

Step-by-step explanation:

Given:

Note :→ there is a mistake it is <u>fir tree</u> not for tree.

The combined height of one fir tree and one pine tree is 21 meters.

The height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree.

Now, to find how tall are the types of trees.

Let the height of one fir tree be $x$ .

And the height of one pine tree be $y$ .

So, the combined height of one fir tree and one pine tree:

$x+y=21.$

$y=21-x.$ .........( 1 )

Now, as given the height of 4 for trees stacked on top of each other is 24 meters taller than one pine tree:

$4x=y+24.$

Putting the value of equation (1) in the place of $y$ :

$4x=21-x+24$

<em>Adding both the sides $x$ we get:</em>

$5x=21+24.$

$5x=45.$

<em>Dividing both the sides by 5 we get:</em>

$x=9\ meters.$

<em>So, the height of one fir tree = 9 meters.</em>

Now, putting the value of $x$ in equation (1) we get:

$y=21-9$

$y=12\ meters.$

<em>Thus, the height of one pine tree = 12 meters.</em>

Therefore, the fir tree is 9 meters tall and the pine tree is 12 meters tall.

6 0

3 years ago

What is the volume of a square pyramid that is 8 feet tall with base edges of 3 feet?

Dennis_Churaev [7]

Answer : 8 ft
Explanation :
You can find the volume of a regular square pyramid using the formula volume = base area × height / 3. Hope it helps.

8 0

2 years ago