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2 years ago

15

On a coordinate plane, 2 lines are shown. Line P Q has points (negative 5, 3) and (5, 1). Line R S has points (negative 4, negat

ive 2) and (0, negative 4).
Which statement best explains the relationship between lines PQ and RS?
They are parallel because their slopes are equal.
They are parallel because their slopes are negative reciprocals.
They are not parallel because their slopes are not equal.
They are not parallel because their slopes are negative reciprocals.

2 answers:

Doss [256]2 years ago

8 0

Answer:

the correct answer is c

Step-by-step explanation:

Edu2020

Romashka-Z-Leto [24]2 years ago

3 0

Given:

Line P Q has points (-5, 3) and (5, 1).

Line R S has points (-4, -2) and (0, -4).

To find:

The relationship between lines PQ and RS.

Solution:

If a line passing through two points, then the slope of line is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Line P Q has points (-5, 3) and (5, 1). So, slope of line PQ is

$m_1=\dfrac{1-3}{5-(-5)}$

$m_1=\dfrac{-2}{5+5}$

$m_1=\dfrac{-2}{10}$

$m_1=\dfrac{-1}{5}$

Line R S has points (-4, -2) and (0, -4). So, slope of line RS is

$m_2=\dfrac{-4-(-2)}{0-(-4)}$

$m_2=\dfrac{-4+2}{0+4}$

$m_2=\dfrac{-2}{4}$

$m_2=\dfrac{-1}{2}$

Slopes of two parallel lines are equal.

$m_1\neq m_2$

They are not parallel because their slopes are not equal.

Therefore, the correct option is C.

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There are 360 people in my school. 15 take calculus, physics, and chemistry, and 15 don't take any of them. 180 take calculus. T

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Answer:

150 students take physics.

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of this set.

I am going to say that:

-The set A represents the students that take calculus.

-The set B represents the students that take physics

-The set C represents the students that take chemistry.

-The set D represents the students that do not take any of them.

We have that:

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

In which a is the number of students that take only calculus, $A \cap B$ is the number of students that take both calculus and physics, $A \cap C$ is the number of students that take both calculus and chemistry and $A \cap B \cap C$ is the number of students that take calculus, physics and chemistry.

By the same logic, we have:

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

This diagram has the following subsets:

$a,b,c,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C), D$

There are 360 people in my school. This means that:

$a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) + D = 360$

The problem states that:

15 take calculus, physics, and chemistry, so:

$A \cap B \cap C = 15$

15 don't take any of them, so:

$D = 15$

75 take both calculus and chemistry, so:

$A \cap C = 75$

75 take both physics and chemistry, so:

$B \cap C = 75$

30 take both physics and calculus, so:

$A \cap B = 30$

Solution:

The problem states that 180 take calculus. So

$a + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 180$

$a + 30 + 75 + 15 = 180$

$a = 180 - 120$

$a = 60$

Twice as many students take chemistry as take physics:

It means that: $C = 2B$

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$B = b + 75 + 30 + 15$

$B = b + 120$

-------------------------------

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

$C = c + 75 + 75 + 15$

$C = c + 165$

----------------------------------

Our interest is the number of student that take physics. We have to find B. For this we need to find b. We can write c as a function o b, and then replacing it in the equations that sums all the subsets.

$C = 2B$

$c + 165 = 2(b+120)$

$c = 2b + 240 - 165$

$c = 2b + 75$

The equation that sums all the subsets is:

$a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) + D = 360$

$60 + b + 2b + 75 + 30 + 75 + 15 + 15 = 360$

$3b + 270 = 360$

$3b = 90$

$b = \frac{90}{3}$

$b = 30$

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$B = b + 75 + 30 + 15$

$B = 30 + 120$

$B = 150$

150 students take physics.

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