Adding and Subtracting Polynomials

the line with a slope of 1/3 and a y- intercept of - 15 intersects the line passing through which of these pairs of points?

stich3 [128]

Answer:

Options (C), (D) and (E)

Step-by-step explanation:

Slope of the given line = $\frac{1}{3}$

Any line having same slope will be parallel to the given line otherwise the lines will intersect.

Therefore, we will find the slope of the lines passing through two points given in the options.

Option A

Slope of the line passing through (12, -13) and (15, -12)

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

= $\frac{-13+12}{12-15}$

= $\frac{1}{3}$

Therefore, both the lines are parallel having no point of intersection.

Option B

Slope = $\frac{-9+7}{18-24}$

= $\frac{1}{3}$

Both the lines are parallel having no point of intersection.

Option C

Slope = $\frac{-20+21}{15-18}$

= $-\frac{1}{3}$

Therefore, both the lines will intersect.

Option D

Slope = $\frac{-15+14}{30-36}$

= $\frac{1}{6}$

Both the lines will intersect each other.

Option E

Slope = $\frac{-11+10}{24-30}$

= $\frac{1}{6}$

Both the lines will intersect each other at a point.

Options (C), (D) and (E) are the correct options.

6 0

3 years ago

C bisects AB. If AC = 8x - 1 and BC = 4x + 19, what is the length of AB?

tensa zangetsu [6.8K]

The length of AB is 78 units.

<h3>What is a Line Segment?</h3>

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure is given below shows a line segment AB , where the length of line segment AB refers to the distance between its endpoints, A and B.

Given that C is the midpoint of AB

AC = 8x - 1 and BC = 4x + 19,

A______________C______________B

⇒ AB = AC+ BC

Since C is the bisects of AB, So AC = BC

⇒ AB = AC+ BC

⇒ AB = 2AC

Substitute the values of If AC = 8x - 1 and BC = 4x + 19,

⇒ 8x - 1 = 4x + 19,

Rearranging the terms in the above equation,

⇒ 8x - 4x = 1 + 19,

⇒ 4x = 20,

⇒ x = 20/4,

⇒ x = 5

So AB = 2AC

⇒ AB = 2(8x - 1) = 16x -2

Substitute the value of x = 5 in the above equation,

⇒ AB = 16(5) -2

⇒ AB = 78

Hence, the length of AB is 78 units.

Learn more about the line segment here:

brainly.com/question/25727583

#SPJ1

8 0

1 year ago

How might snakes running out of food affect other organisms such as hawks? please help

marissa [1.9K]

Answer:

The population of Hawks and other species would likely start to edge off.

Step-by-step explanation:

Commonly, a Food Chain is dependent on all the parts of it sataying at a perfect point. If the food that the Snakes eat starts to run out, more of them will die off. With less Snakes, the Hawks will then have less food, and that continues throughout the chain. The same thing would happen if there was too much food, except instead of the populations of species dying off, the Snake population would spike.

3 0

3 years ago

How do I do this I don’t get it

masya89 [10]

Answer: The answer would be 17/10.

Step-by-step explanation: You would divide Marvin's miles by Nathan's miles to find your answer.

8 0

3 years ago

A social studies teacher orders several large maps for his classroom. The maps are to be shipped in a cylindrical

makvit [3.9K]

A.) 36 inches is the right answer

7 0

3 years ago