All categories

3 years ago

Two basketballs are thrown along different paths. Determine if the basketballs’ paths are parallel to each

Mathematics

1 answer:

Paul [167]3 years ago

3 0

Answer:

Since the slopes of the two equations are equivalent, the basketballs' paths are parallel.

Step-by-step explanation:

Remember that:

Two lines are parallel if their slopes are equivalent.
Two lines are perpendicular if their slopes are negative reciprocals of each other.
And two lines are neither if neither of the two cases above apply.

So, let's find the slope of each equation.

The first basketball is modeled by:

$\displaystyle 3x+4y=12$

We can convert this into slope-intercept form. Subtract 3<em>x</em> from both sides:

$4y=-3x+12$

And divide both sides by four:

$\displaystyle y=-\frac{3}{4}x+3$

So, the slope of the first basketball is -3/4.

The second basketball is modeled by:

$-6x-8y=24$

Again, let's convert this into slope-intercept form. Add 6<em>x</em> to both sides:

$-8y=6x+24$

And divide both sides by negative eight:

$\displaystyle y=-\frac{3}{4}x-3$

So, the slope of the second basketball is also -3/4.

Since the slopes of the two equations are equivalent, the basketballs' paths are parallel.

You might be interested in

Bob is six years older than his sister, and the sum of their ages is 32. how old is bob?/search?q=david+is+38+years+old+and+his+

erica [24]

Bob's age is 22
And her sisters age is 14
If you'll add 22&14 the answer would be 36
And if you'll subtract 22&14 the answer would be 6

4 0

4 years ago

I have to find out if there equivalent? 96 miles on 4 gallons,380 miles on 15 gallons?

erik [133]

24 miles is 1 gallon so 360 miles is 15 gallons + 24 is 384 miles so they are not equivalent!

6 0

3 years ago

Read 2 more answers

Find the value of y.

Phoenix [80]

$\boxed{y=6\sqrt{3}}$

<h2>Explanation:</h2>

For a better understanding of the problem I've built up two triangles from the given triangular shape. So these two triangles are similar. Therefore, we can solve this problem by using ratios and corresponding sides in this way:

$\frac{x}{3}=\frac{12}{x} \\ \\ x^2=36 \\ \\ x=\sqrt{36} \\ \\ x=6$

But our goal is to find y. Let's call w the height of the small triangle, then:

$w=\sqrt{6^2-3^2}=3\sqrt{3}$

Applying the concept of ratios again:

$\frac{y}{w}=\frac{x}{3} \\ \\ y=w \left(\frac{x}{3}\right) \\ \\ y=3\sqrt{3}\left(\frac{6}{3}\right) \\ \\ \boxed{y=6\sqrt{3}}$

<h2>Learn more:</h2>

Right triangle: brainly.com/question/10684799

#LearnWithBrainly

4 0

3 years ago

This table shows the number of marbles in a bag by color. If one marble is randomly selected from the bag, what is the

ratelena [41]

Answer:

p(blue or red) = 0.52 = 52%

Step-by-step explanation:

total number of marbles = 7 + 10 + 14 + 19 = 50

number of blue marbles = 7

number of red marbles = 19

number of blue or red marbles = 7 + 19 = 26

p(blue or red) = 26/50

p(blue or red) = 0.52 = 52%

3 0

3 years ago

Read 2 more answers

A nugget of gold is placed in a graduated cylinder that contains 85 mL of water.the water level rises to 225 mL after the nugget

Rufina [12.5K]

To get the volume of an object, one of the oldest techniques is to fill a container with water of which we know the volume (in this case 85mL), and drop the object in. The water will rise and show a new volume (225mL). If we subtract the old volume (85) from the new volume (225), we will get the volume of the object (225 - 85 = 140).

8 0

4 years ago