Two basketballs are thrown along different paths. Determine if the basketballs’ paths are parallel to each
other, perpendicular or neither. Explain your reasoning.

o The first basketball is along the path 3x + 4y = 12
o The second basketball is along the path -6x – 8y = 24

Answers

Answer 1

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:

[tex]\displaystyle 3x+4y=12[/tex]

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

[tex]4y=-3x+12[/tex]

And divide both sides by four:

[tex]\displaystyle y=-\frac{3}{4}x+3[/tex]

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

The second basketball is modeled by:

[tex]-6x-8y=24[/tex]

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

[tex]-8y=6x+24[/tex]

And divide both sides by negative eight:

[tex]\displaystyle y=-\frac{3}{4}x-3[/tex]

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.


Related Questions

Who knows the answer

Answers

Answer:

46 is the answer

Step-by-step explanation:

because 154-108=46

please help me solve

please show how you got the answer

Answers

Answer:

Based on the linear relation shown above, when the y coordinate is 3, the x coordinate is 8.

Step-by-step explanation:

This is because every time you add an input of 2, you subtract an output of 4.

Basically in the x value you add 2 while in the why value you subtract 4.

(2, 13) (4, 9) (6, 5) (8, 1)

Answer:

8

Step-by-step explanation:

Can someone help me?It's urgent and thank you!

Answers

Answer:

5 is added to the product of 4 and 3

Work out the size of angle x
Pls help thx !

Answers

Answer:

83

Step-by-step explanation:

not sure tho____________

Answer:

83 degrees

Step-by-step explanation:

The exterior angle of a triangle can be find by adding up the two inner angles that are not adjacent, so

43 + x = 126

x = 83 degrees

Second way

exterior angle + inner angle = 180

126 + inner angle = 180

inner angle = 54

the sum of the inner angles of a triangle is 180 degrees

54 + 43 + x = 180

97 + x = 180

x = 83 degrees

How many liters are equivalent to 25 ml​

Answers

Answer:

0.025 liters

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

0.025 liters

Step-by-step explanation:

PLEASE HELP
IT SAYS IN PROGRESS BUT ITS COMPLETED WHAT DO I DO???!!!!

Answers

Answer:

click on it and double check that all questions are 100% complete if so wait because it is quite possible it is a glitch this sort of thing happens often no need to be alarmed

Step by step pls thanks

Answers

The choose (d)

1/2(x+1)

x²–25/x²+6x+5 / 2x-10

(x+5)(x-5)/ (x+1)(x+5) / 2(x-5)

Remove (x+5) from the first fraction

(x-5)/(x+1) / 2(x-5)

(x-5) / 2(x-5)(x+1)

Remove (x-5)

1/2(x+1)

I hope I helped you

Good luck ^_^

Find the next two terms of each sequence.

1.) -16, 8, -4, 2, ...

2.) 1, 4, 9, 16, 25, ...​

Answers

Answer:

1)=-1;1

2)=36;49

Step-by-step explanation:

1.)aqui la secuncia es dividir en -2

2.)aqui la secuencia es sumar numeros impares es decir:+3;+5;+7 etc

HII GUYS DON'T WORRY I ONLY HAVE 3 MORE QUESTIONS LEFT I'M SO SORRY FOR BOTHERING YOU GUYS I'M SORRY THANK YOU FOR THE PEOPLE WHO HELP ME. <3​

Answers

Answer:

Hello! answer: 96

Step-by-step explanation:

I will find the area of each face separately and add them up so... for the triangles those would both be 6. the rectangle on the bottom would be 28 and the rectangle standing up would be 21 now for the triangle on top that would be 35. now we would just add these up so...

6 + 6 + 28 + 21 + 35 = 96 Therefore the surface area is 96 Hope that helps!

6 g of butter is used for making a cupcake. How many such cakes can be made by using 3 kg of butter?

Answers

Answer: 500

Step-by-step explanation:

Given

6 g butter is required to make a cupcake

If there is 3 kg butter

We know, 1 kg is equivalent to 1000 g i.e. 3 kg is 3000 gm

No of cup-cakes made

[tex]\Rightarrow \dfrac{3000}{6}=500\ \text{cupcakes}[/tex]

Stefan sells Jin a bicycle for $149 and a helmet for ​$19. The total cost for Jin is 140% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend​ originally? How much money did he make by selling the bicycle and helmet to​ Jin?

Answers

Answer:

$120

$48

Step-by-step explanation:

total amount Jin spent = cost of bicycle + cost of helmet

$149 + $19 = $168

This equation can be derived from the question :

1.4 x t = 168

where t = total cost Stephan spent on the helmet and bicycle

t = 168/1.4 = $120

Profit = selling price - cost price

$168 - $120 = $48

Discover the rate of change (slope) of these two points. (-4,5) and (5,-4).​

Answers

Answer:

-1

Step-by-step explanation:

y2-y1/x2-x1

-4-5/5- -4

-9/9

-1

Here is an expression: 3 ⋅ 2^t. Evaluate the expression when t is 4.

Answers

Answer:

48

Step-by-step explanation:

3 ⋅ 2^t

3 * 2^4

3*16

48

does anyone get this ?

Answers

Answer and Step-by-step explanation:

i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1

Since we know this, we can go to the last instance of the multiply of 4.

For this question, it is 12. 2 more after twelve is 14. Since it is 2, it would be -1.

D. -1 -- This is the answer.

#teamtrees #PAW (Plant And Water)

7.) There are about 9,987,000 people that live in Michigan. How do you write
9,987,000 in scientific notations?
a.) 99.87 x 105
b.)9.987 X 105
c.) 9.987 x 107
d.) 9.987 X 106

Answers

D.) 9,987,000 becomes 9.987 x 10^6

Please helppppppp me

Answers

Answer:

13

Step-by-step explanation:

< W = <V            Given

WV = 8              Given

XV = 13              Given

Find XW

In an isosceles triangle if you are given the length of one of the sides opposite one of the two equal angles, then the side opposite the other equal angle is equal to the given side.

In sort XV = 13. < V = <W   XW = 13

Here Tran posted it

Answers

Step-by-step explanation:

1. I estimate that the error in measuring the area of the lot is about 10% so we write the area as 400 sq ft +- 10%, which means that the lot can be as small as 360 sq ft or as large as 440 sq ft. We tack on 15% more on the number of pieces of sod to account of the plot's irregularities. Since each piece of sod is 2 sq ft, the number of pieces we must get is 440/2 = 220 pieces +- 15% or 253 pieces

2. The nominal value is jus the average weight which is 59.5 g. The tolerance is (3.5g/59.5g)×100% = 5.88% and the measurement range is from 56g to 63g.

It requires a minimum of ____ points to make up a plane

Answers

Answer:

2

Explanation: A plane contains at least three non-collinear points. If two points lie in a plane, then the line containing them lies in the plane. If two planes intersect, then their intersection is a line.

answer

Three points not lying on the same line define one and only one plane that they all belong to

What is an equation of the line that passes through the points (-5,6) and (7,6)?​

Answers

The y values are not changing so y = 6 describes the line

A jewelry box has a volume of 240 in cubic in. Its height is 12 inches, its width x in inches and its length ( x + 8) inches.

Answers

Answer:

Width of the box = 2 inches

Step-by-step explanation:

Volume of a box = length × width × height

Volume of the box = 240 cubic inches

Length of the box = (x + 8) inches

Width of the box = x inches

Height of the box = 12 inches

Volume of a box = length × width × height

240 = (x + 8) * x * 12

240 = (x² + 8x) * 12

240 = 12x² + 96x

12x² + 96x - 240 = 0

x² + 8x - 20 = 0

Solve quadratic equation using factorization method

x² + 10x - 2x - 20 = 0

x(x + 10) -2(x + 10) = 0

(x + 10) (x - 2) = 0

x + 10 = 0 OR x - 2 = 0

x = -10 OR x = 2

Width of the box can not be a negative value

Therefore,

Width of the box = 2 inches

A• 3.7

B• 3.8

C• 5.3

D• 5.4

Answers

Answer:

D 5.4

Step-by-step explanation:

The pythagoras theorem states that a² + b² = c²

2² + 5² = ?²

4 + 25 = ?²

29=?²

? =

[tex] \sqrt{29} [/tex]

? = 5.4 rounded 2 sig fig one decimal place

Which of the following is a composite number?
Ο Α. Ο
O B. 19
O C. 63
O D. 1

Answers

Answer: The letter C

Option C is correct, 63 is the composite number.

What is Number system?

A number system is defined as a system of writing to express numbers.

Composite numbers are numbers that have more than two factors.

0 is not a composite number.

19 is a prime number because it is divided by itself so it is not a composite number.

63 is a composite number because it has more than two factors.

The factors of 63 are 1, 7 , 9

1 is not a prime number as it does not have factors.

Hence, Option C is correct, 63 is the composite number.

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ7

You purchase 75 shares of stock at $15 per share. The next day the stock drops 3%; however, a week later it increases in value by 7%. If you immediately sell your 75 shares, how much will you gain or lose (a) in dollar amount and (b) in percent?

Answers

Answer:

You have gained $43 and the value increased by 3.8%

Step-by-step explanation:

You would 75 times 15 = $1125

then you would do 1125 times 97% = 1091.25

now you would do 1091.25 times 107% = estimation of 1168

then you would do 1168/1125 which is estimated to 1.038 and you would convert that into a percentage = 103.8%

You would do 1168 - 1125 = $43 and 103.8 - 100 = 3.8%

In Hackensack High School, the ratio of students to teachers is 9 to 2. If there
are 90 teachers at the High School, how many students are there?

Answers

I guess the answer is 405.

Because the value of 1 is 45 and 2×45 =90

9×45=405.

Hope it helps you:)

Step-by-step explanation:

students : Teachers

9 : 2

? : 90

students = 9 x 90 ÷ 2

students = 405

1 of 5
The ratio of boys to girls in a class is 4:3. There are 35 students in the class. How many
students are girls?

Answers

Answer:

15 girls

Step-by-step explanation:

[tex]\frac{4}{3}[/tex]  has 7 per "unit group" 35/7 = 5

so the ratio would be [tex]\frac{20}{15}[/tex]

the question states ratio is [tex]\frac{boys}{girls}[/tex]

thus 20 boys , and 15 girls

What is the x-intercept of the line shown below? Enter your answer as a coordinate pair.

Answers

Answer:

(1,0)

Step-by-step explanation:

The correct answer is (1, 0)

Please help will give branliest

Answers

-2x+8y-3

Hope this helps! :)

Answer:

-2x + 8y -3

Step-by-step explanation:

-2x = -2x

2y + 6y = 8y

-3  = -3

Plssssssssss Answer 100% sure will mark as brainlist

Find the angle measure x in the following ​

Answers

Answer:

Step-by-step explanation:

2x+15+x+10+3x+5=180 degree(sum of interior angles of a triangle)

6x+30=180

6x=180-30

x=150/6

x=25

therefore the value of x is 25 degree.

X=5/2
This is apparently an equalateril triangle so we can take any two angles and make them equal

x+10=3x+5
5=2x
5/2=x

*double check

Evaluate the function
f(8) + g(-1) for the functions f(x) = -2x + 9 and g(x) = x²-2

Answers

Answer:

- 8

Step-by-step explanation:

To evaluate f(8) substitute x = 8 into f(x)

f(8) = - 2(8) + 9 = - 16 + 9 = - 7

Similarly for g(- 1)

g(- 1) = (- 1)² - 2 = 1 - 2 = - 1

Then

f(8) + g(- 1) = - 7 + (- 1) = - 7 - 1 = - 8

What is the value of the expression, written in standard form?

Answers

Answer:

200

Step-by-step explanation:

6.6/3.3 = 2

10^-2 / 10^-4 = 10^2

10^2 = 100

2 x 100 = 200

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