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3 years ago

A system of equations is shown below.

Mathematics

1 answer:

prisoha [69]3 years ago

5 0

Given:

The system of equations is

$y=1.5x-3$

$y=1.5x+4$

To find:

The true statement about the given system of equations.

Solution:

The slope intercept form of a line is

$y=mx+b$

Where, m is the slope and b is the y-intercept.

We have,

$y=1.5x-3$

$y=1.5x+4$

On comparing these two lines with slope intercept form, we get

$m_1=1.5,b_1=-3$

$m_2=1.5,b_2=4$

Since the slopes of the lines are equal but the y-intercepts are different, therefore, the two lines are parallel and the system has no solution.

Therefore, the correct option is A.

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The coordinates of point A are (p, q) and coordinates of point B are (p+2q, q+2p). Provide your complete solutions and proofs in

Dafna1 [17]

Answer:

The mid-point (p + q , q + p) of AB is the same distance from the x-axis and the y-axis

Step-by-step explanation:

* Lets explain how to solve the problem

- Any point will be equidistant from the x-axis and the y-axis must have

equal coordinates

- Ex: point (4 , 4) is the same distance from the x-axis and the y-axis

because the distance from the x-axis to the point is 4 (y-coordinate)

and the distance from the y-axis and the point is 4 (x-coordinate)

- If (x , y) is the mid-point of a segment its endpoints are

$(x_{1},y_{1})$ and $(x_{2},y_{2})$ , then

$x=\frac{x_{1}+x_{2}}{2}$ and $y=\frac{y_{1}+y_{2}}{2}$

* Lets solve the problem

∵ Point A has coordinates (p , q)

∵ Point B has coordinates (p + 2q , q + 2p)

- The mid-point of AB is (x , y)

∵ $x=\frac{p+p+2q}{2}$

∴ $x=\frac{2p+2q}{2}$

- Take 2 as a common factor from the terms of the numerator

∴ $x=\frac{2(p+q)}{2}$

- Divide up and down by 2

∴ x = p + q

∵ $y=\frac{q+q+2p}{2}$

∴ $y=\frac{2q+2p}{2}$

- Take 2 as a common factor from the terms of the numerator

∴ $y=\frac{2(q+p)}{2}$

- Divide up and down by 2

∴ y = q + p

∴ The mid point of AB is (p + q , q + p)

- p + q is the same with q + p

∵ The x-coordinate of the mid point of AB is p + q

∵ The y-coordinate of the mid point of AB is q + p

∵ p + q = q + p

∴ The coordinates of the mid-point of AB are equal

- According the explanation above

∴ The mid-point (p + q , q + p) of AB is the same distance from the

x-axis and the y-axis

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3 years ago

Please help with this problem i need to show my work

Damm [24]

Answer:

2/7 .2857

Step-by-step explanation:

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if you know that 7 x 8=56, how can you use the commutative property of multiplication to find the product of 8 x 7 ?

Fofino [41]

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4 years ago

Using the segment addition postulate, which is true? A number line going from negative 9 to positive 9. A closed circle appears

MArishka [77]

Answer:

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Step-by-step explanation:

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If point C divides segment BD into BC and CD, then the sum of those two segments will match the whole.

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Which property was used to simplify the expression?

Montano1993 [528]

Answer:

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Step-by-step explanation:

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