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Elan Coil [88]
3 years ago
15

Consider the equation 5x-2y=3. If possible, find a second linear equation to create a system of equations that has: Exactly one

solution Exactly two solutions No solutions Infinitely many solutions

Mathematics
2 answers:
nekit [7.7K]3 years ago
4 0
A) One solution: 5x +2y = 0 . . . . (any line with a different slope)

b) Two solutions: not possible

c) No solutions: 5x -2y = 0 . . . . (any different line with the same slope)

d) Infinitely many solutions: 10x -4y = 6 . . . . (any other equation for the same line)
GenaCL600 [577]3 years ago
3 0

Answer with explanation:

1.⇒ The given equation is

  5x-2y=3

For one solution ,you should write linear equation in such a way

ax+by=c, such that

  \frac{5}{a}\neq \frac{-2}{b}\neq \frac{3}{c}

So, the linear equation will be

→3x+4y=8

You can write many more by yourself.

2.⇒Exactly two solutions

The two lines intersect at only one point.So,there are no such lines which has two point of Intersection.

3.⇒No solutions

It means the two lines will never intersect.

 For no solution ,you should write equation of line in such a way

ax+by=c, such that

  \frac{5}{a}=\frac{-2}{b}\neq \frac{3}{c}

So, the linear equation will be

→10x -4y=15

You can write many more by yourself.

4.⇒Infinitely many solutions

For Infinite number of solution ,you should write linear equation in such a way

ax+by=c, such that

  \frac{5}{a}=\frac{-2}{b}=\frac{3}{c}

→10x-4y=6

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Gnoma [55]

An attempt to divide by zero gives a contradictory result

A rule of algebra broken is <u>dividing by zero</u> (leading to a contradiction) and stating a finite result

Reason:

The given calculation is presented as follows;

1. a > 0, b > 0 given

2. a = b given

3. a·b = b²

4. a·b - a² = b² - a²

5. a·(b - a) = (b + a)·(b - a)

6. a = b + a

7. 0 = b

8. b = 2·b

9. 1 = 2

From line 4, the result are;

4. a·b - a² = b² - a² = 0

5. a·(b - a) = (b + a)·(b - a) = 0

On line 6, both sides where divided by (b - a) = 0, which should given an infinite result

Therefore, one rule of algebra broken is dividing by zero to get a finite result

In line 7, we have;

7. 0 = b

From 6. a = b + a, and a = b, we have;

8. b = 2·b

Therefore, line 9 should be;

9. 0 = 2·0; 0 = 0, given that we have;

1 × 0 = 0

2 × 0 = 0

∴ 1 × 0 = 2 × 0

However

  • 1 ≠ 2

In line 9., by dividing by b = 0, again, we have;

  • 9. 1 = 2 (a contradiction)

Therefore, one rule of algebra that is broken is <u>dividing by zero</u> and having a finite result

Learn more about the rules of algebra here:

brainly.com/question/11388301

5 0
3 years ago
A rectangular pyramid has a base area of 24in² and a volume of 48in³. What is the height of the pyramid?
alexgriva [62]

height of pyramid = 3*(V/A)

V=48in^3

A=24in^2

So 3*(48/24) = 3*2=6

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3 years ago
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For fun question
ZanzabumX [31]
Consider the function f(x)=x^{1/3}, which has derivative f'(x)=\dfrac13x^{-2/3}.

The linear approximation of f(x) for some value x within a neighborhood of x=c is given by

f(x)\approx f'(c)(x-c)+f(c)

Let c=64. Then (63.97)^{1/3} can be estimated to be

f(63.97)\approxf'(64)(63.97-64)+f(64)
\sqrt[3]{63.97}\approx4-\dfrac{0.03}{48}=3.999375

Since f'(x)>0 for x>0, it follows that f(x) must be strictly increasing over that part of its domain, which means the linear approximation lies strictly above the function f(x). This means the estimated value is an overestimation.

Indeed, the actual value is closer to the number 3.999374902...
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Answer: add a photo

Step-by-step explanation:

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Answer:

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