a line with a positive slope and a line with a negative slope are parallel. sometimes always or never?

Mathematics

1 answer:

otez555 [7]3 years ago

4 0

Answer:

Never

Step-by-step explanation:

This statement is never true. Parallel lines have the exact same slope in every instance. This means that if one is negative and one is positive, then they can never be the same.

You might be interested in

Find the gcf. 12 and 45 a. 180 b. 3 c. 45 d. 12

densk [106]

The greatest common factor of 12 and 45 is 3. So its B. 12.

7 0

3 years ago

A small garden measures 9 ft by 13 ft. A uniform border around the garden increases the total area to 192 ft square. What is the

victus00 [196]

The width of border is 1.5 feet

<h3>Solution:</h3>

Given that small garden measures 9 ft by 13 ft

A uniform border around the garden increases the total area to 192 ft square

To find: width of border

Let the width of border be "x"

Then the new measures of garden are (9 + 2x) feet and (13 + 2x) feet

The total area of garden = 192 square feet

$(9 + 2x)(13 + 2x) =192$

$117 + 18x + 26x + 4x^2 = 192\\\\4x^2 + 44x - 75 = 0$

Let us solve the above equation by quadratic formula

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Using the above formula,

For $4x^2 + 44x - 75 = 0$ , we have a = 4 ; b = 44 ; c = -75

Substituting the values of a = 4 ; b = 44 ; c = -75 in above quadratic formula we get,

$\begin{aligned}&x=\frac{-44 \pm \sqrt{44^{2}-4(4)(-75)}}{2 \times 4}\\\\&x=\frac{-44 \pm \sqrt{1936-1200}}{8}\\\\&x=\frac{-44 \pm \sqrt{3136}}{8}\\\\&x=\frac{-44 \pm 56}{8}\end{aligned}$

$\begin{aligned}&x=\frac{-44+56}{8} \text { or } x=\frac{-44-56}{8}\\\\&x=\frac{12}{8} \text { or } x=\frac{-100}{8}\\\\&x=1.5 \text { or } x=-12.5\end{aligned}$