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3 years ago

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.

x = 0

Using this in the second equation gives ...

2y -0 = 1

y = 1/2

(x, y) = (0, 1/2) is a solution

y = 3x

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 anything. A more appropriate graph would graph that equation as the two lines x=0 and y=3x.

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7 0

3 years ago

The right rectangular prism is made up of 48 cubes. Each cube has an edge length of inch. What is the volume of this prism?

Gnesinka [82]

Given:

The right rectangular prism is made up of 48 cubes.
Each cube has an edge length of 1/4 inch.

$~$

To Find:

What is the volume of this prism?

$~$

Solution:

$~$

Using formula: 

$~$

$\sf \pmb {Volume \: of \: cube = {(side)}^{3} }$

$~$

Substituting values in the formula:

$~$

$\sf \longrightarrow \dfrac{1}{4} \times \dfrac{1}{4} \times \dfrac{1}{4}$

$\sf \longrightarrow \dfrac{1}{64} \: {inch}^{3}$

$~$

Now,

Volume of 48 such cubes = Volume of 1 cube × 48 cubes

$~$

$\sf \longrightarrow \dfrac{1}{64} \times 48$

$\sf \longrightarrow \dfrac{48}{64}$

$\sf \longrightarrow \dfrac{3}{4} \: {inch}^{3}$

$~$

Hence,

Volume of prism is 3/4 inch^3

7 0

2 years ago

Determine if the sequence is arithmetic. If it is, find the common difference. 1) 35, 32, 29, 26, ... 2) −3, −23, −43, −63, ...

vekshin1

1) Yes, it is arithmetic, the common difference is -3. To find this, subtract any number from the number after it.

32 - 35 = -3

2) yes, it is arithmetic, the common difference is -20. To find this, subtract any number from the number after it.

-23 - -3 = -20

3) yes, it is arithmetic, the common difference is -30. To find this, subtract any number from the number after it.

-64 - -34 = -30

4) yes, it is arithmetic, the common difference is -10. To find this, subtract any number from the number after it.

-40 - -30 = -10

yes, it is arithmetic, the common difference is -2. To find this, subtract any number from the number after it.

-9 - -7 = -2

yes, it is arithmetic, the common difference is 5. To find this, subtract any number from the number after it.

14 - 9 = 5

4 0

3 years ago

Help pls ill mark brainlist and follow u

KATRIN_1 [288]

Answer:

area of the shaded figure

$\frac{1}{2} \times 3 \times 10 \\ 15 \: {cm}^{2}$

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3 years ago

Read 2 more answers

Please help with this worksheet I don’t know any of it

sammy [17]

Answer:

4. 1/25

5. 1/16

6. 2/9

7. 5/567

8. 1/40

9. 2/175

10. 1/30

11. 2/5

12. 9/8

13. 4/3

14. 1

Step-by-step explanation:

sorry I only know how to do 4-14. I hope this helps you.

4 0

3 years ago

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

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