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noname [10]
3 years ago
8

Solve the simultaneous equation 3x²-xy=0, 2y-5x=1​

Mathematics
1 answer:
ratelena [41]3 years ago
4 0

Answer:

  (x, y) = (0, 1/2) or (1, 3)

Step-by-step explanation:

The first equation factors as ...

  x(3x -y) = 0

This has solutions x=0 and y=3x.

__

<u>x = 0</u>

Using this in the second equation gives ...

  2y -0 = 1

  y = 1/2

  (x, y) = (0, 1/2) is a solution

__

<u>y = 3x</u>

Using the expression for y in the second equation, we get ...

  2(3x) -5x = 1

  x = 1 . . . . . . . . . simplify

  y = 3x = 3 . . . . using x=1 in the first equation

  (x, y) = (1, 3) is a solution

_____

Interestingly, the (red line) graph of 3x^2 -xy = 0 produced by this graphing calculator has a "hole" at x=0, It says that point is (0, undefined). In a sense, y is undefined, in that it can be <em>anything</em>. A more appropriate graph would graph that equation as the two lines x=0 and y=3x.

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What steps would you use to plot (−3, −4, 0) in a 3-dimensional coordinate system?
eimsori [14]

Answer:

a. From the origin, move back 3 units and down 4 units

Step-by-step explanation:

Given:

The coordinates of a point in a 3-dimensional space is given as:

(-3, -4, 0)

The value of 'x' = -3

The value of 'y' = -4

The value of 'z' = 0

At the origin, the values of 'x', 'y', and 'z' are each equal to 0.

So, the coordinates of origin is (0, 0, 0). In order to reach the point (-3, -4, 0) from the point (0, 0, 0), we don't move along the z-axis as the 'z' value remains the same. We need to move along the 'x' and 'y' directions only.

Now, 'x' is equal to -3. Negative values of 'x' occur backwards from origin. So, we move back by 3 units. to reach the point (-3, 0).

Now, the value of 'y' is -4. Negative values of 'y' occur below the origin. So, we move down by 4 units to reach the point (-3, -4).

Therefore, the correct option is option (a)

A graph in 2 dimensional is shown in support of the answer.

8 0
4 years ago
Find the area of the rectangle:
kumpel [21]
10 ft and 2 because I did the math
6 0
3 years ago
Read 2 more answers
What is the equation, in slope-intercept form, of the line
Roman55 [17]
Y= 1/8 x + 10

You do 8-11/-16-8= -3/-24= 1/8 that’s your slope

Then to get y intercept you plug in ur slope and coordinates of (8,11) into point slope form. And you get that the y intercept is 10.
7 0
3 years ago
The average age of online consumers a few years ago was 24.1 years. As older individuals gain confidence with the​ Internet, it
love history [14]

Answer:

The correct option is (C).

Step-by-step explanation:

A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.  

It is a hypothesis of no difference.

It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.

Whereas the alternative hypothesis is a contradicting statement tot he null hypothesis. It is denoted by Hₐ.

In this case we need to test whether the average age of online consumers has increased or not.

From previous data we know that the average age of online consumers a few years ago was 24.1 years.

A one-sample mean test can be used to determine whether the mean age has increased or not.

The hypothesis for the test can be defined as follows:

<em>H₀</em>: The average age of online consumers is 24.1 years, i.e. <em>μ</em> = 24.1.

<em>Hₐ</em>: The average age of online consumers is more than 24.1 years, i.e. <em>μ</em> > 24.1.

Thus, the correct option is (C).

6 0
3 years ago
Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar pe
Alik [6]
The amount she has in hand, she can make 4 loaves of bread and 2 batches of muffins.
Hope this will help a lot!
4 0
3 years ago
Read 2 more answers
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