Do perpendicular lines always have a slope that are negative reciprocals. Explain your answer

Answers

Answer 1

Answer:

Yes. parallel lines are known to have the same slope, but perpendicular lines will always have negative-reciprocal slopes.

Answer 2

This holds true for all lines that are not vertical or horizontal

This holds true for all lines that are not vertical or horizontal. A horizontal line has a slope of 0, and a vertical line has an undefined slope. These lines are perpendicular, but the rule of negative reciprocals does not apply because you cannot divide by zero.

Let’s prove that the product of the slopes of two perpendicular lines is -1.

Let’s consider two lines, Line 1 and Line 2, that are perpendicular to each other.

Line 1: Let’s say the slope of Line 1 is m1.

Line 2: Now, let’s consider Line 2 which is perpendicular to Line 1. Let’s say the slope of Line 2 is m2.

Since Line 1 and Line 2 are perpendicular, the angle between them is 90 degrees. Now, the tangent of the angle between two lines is equal to the absolute difference of their slopes divided by 1 plus the product of their slopes.

tan(90) = |m1 - m2| / (1 + m1*m2)

But we know that tan(90) is undefined, which implies that the denominator of the right side of the equation must be zero.

So, 1 + m1*m2 = 0, which implies that m1*m2 = -1.

Therefore, we have proved that the product of the slopes of two perpendicular lines is -1.


Related Questions

Lily offers embroidery services at her clothing store. She charges $2 for every letter plus a $6 setup fee. Which graph represents the cost of Lily's embroidery services?

Answers

Answer:

Ok so the way i see it lily would take $2 and $6 and multiply it by the price of the item say someone walks in and buy's a 5 letter's she'd first multiply 2x5 = 10 and then she'd multiply 6x5= 30 add the two 30 + 10 = 40.  If it isn't to much can you give me brainliest? if not a simple thanks will do!!!

~~ Night

Answer: lily would take $2 and $6 and multiply it by the price of the item say someone walks in and buy's a 5 letter's she'd first multiply 2x5 = 10 and then she'd multiply 6x5= 30 add the two 30 + 10 = 40. Brainliest?

Mr. Falcone’s pizza shop offers three sizes of pizza. The large pizza has a diameter 12 inches. What is the area of the large pizza in terms of pi ?

Answers

Answer:

37.68

Step-by-step explanation:

12 times 3.14

hope this helps

Answer:

113.04

Step-by-step explanation:

The diameter is 12 which means the radius is 6

The formula to find the area of a circle is A=π r²

r²=36

π=3.14

3.14×36=113.04

So your answer is 113.04

How many solutions does this linear system have?



y = y equals StartFraction 2 over 3 EndFraction x plus 2.x+ 2



6x – 4y = –10



one solution: (–0.6, –1.6)


one solution: (–0.6, 1.6)


no solution


infinite number of solutions

Answers

Answer:

one solution: (–0.6, 1.6)

Step-by-step explanation:

Given the system of equation,

y = [tex]\frac{2x}{3}+2[/tex]...(1)

6x – 4y = –10 ...(2)

Substituting equation 1 into 2 we have;

6x - 4(2x/3 +2)= -10

6x -8x/3 -8 = -10

Multiplying through by 3;

18x-8x-24=-30

10x=-30+24

10x = -6

Dividing both sides by 10

10x/10 = -6/10

x = -0.6

Substituting x = -0.6 into equation 1 to get the value of y we have;

y = 2(-0.6)/3 + 2

y = -1.2/3 + 2

y = -0.4+2

y = 1.6

This shows that the linear equation has only one solution. The solution is

x = -0.6 and y = 1.6

Answer:

its b

Step-by-step explanation:

hope this helped

A craftsman can sell 10 jewelry sets for $500 each. He knows
for each additional set he makes, the price of each set will decrease by $25. Hoy
many jewelry sets should he make if he wants to maximize his earnings?
jewelry sets

Answers

Answer:15

Step-by-step explanation:

Given

Craftsman sell 10 Jewelry set for $500 each

For each additional set he will decrease the price by $ 25

Suppose he sells n set over 10 set

Earning[tex]=\text{Price of each set}\times \text{no of set}[/tex]

Earning [tex]=(500-25n)(10+n)[/tex]

[tex]E=5000+500n-25n^2-250n[/tex]

differentiate to get the maximum value

[tex]\frac{dE}{dn}=-50n+250[/tex]

Equate [tex]\frac{dE}{dn}[/tex] to get maximum value

[tex]-50n+250=0[/tex]

[tex]n=\frac{250}{50}[/tex]

[tex]n=5[/tex]

Thus must sell 5 extra set to maximize its earnings.

I NEED HELP PLZ!!!! It’s important!

Answers

Answer: 24x^3 sqrt5x -4x^3 sqrt10x

Step-by-step explanation:

Show in the photo attached.

Answer:

24x to the power of 3 square root 5x-4x to the power of 3 square root 10x.

I hope this helps you, I tried my best!!

Please help me with answer I need help now

Answers

Answer:

7 + 2, i cant see the full question so im not sure

Step-by-step explanation:

Given: y=x^2-4x-12

A.) determine the roots/zero
(By factoring & setting the answer equal to zero)

B.) use h=-b/2a to get vertex

Answers

Answer:

see below

Step-by-step explanation:

y=x^2-4x-12

Set equal to 0 to find the zeros

0 =x^2-4x-12

Factor.  What 2 numbers multiply to -12 and add to -4

-6*2 = -12  

-6+2 = -4

0= (x-6) (x+2)

Using the zero product property

0=x-6         0 = x+2

x=6            x = -2

zeros: -2,6

Vertex

h = -b/2a = - (-4)/ 2(1) = 4/2 = 2

OR  Average the roots  (-2+6)/2 = 4/2 =2

The y coordinate is found by substituting into the equation

y = (2)^2 -4(2) -12

y = 4-8-12

y =-16

vertex : (2, -16)

Answer:

x = -2, 6

Vertex: (2,-16)

Step-by-step explanation:

x² - 4x - 12

x² - 6x + 2x - 12

x(x - 6) + 2(x - 6)

(x - 6)(x + 2) = 0

x = -2, 6

h = -(-4)/2

h = 4/2

h = 2

k = 2² - 4(2) - 12

k = 4 - 8 - 12

k = -16

Vertex: (2,-16)

Each of two urns contains green balls and red balls. Urn I contains 10 green balls and 14 red
balls. Urn II contains 4 green balls and 11 red balls. If a ball is drawn from each urn, what is
P(red and red)?

A.1/9
B.25/39
C.79/60
D.77/180

Answers

The probability of drawing a red ball from both urns is found by multiplying the probability of drawing a red ball from Urn I by the probability of drawing a red ball from Urn II. After simplification, the probability is [tex]\(\frac{77}{180}\)[/tex], which corresponds to answer choice D.

To calculate the probability of drawing a red ball from each of two urns, we must first determine the probability of drawing a red ball from Urn I, and then multiply that by the probability of drawing a red ball from Urn II. In Urn I, there are 14 red balls and a total of 24 balls (10 green + 14 red). So, the probability of drawing a red ball from Urn I is [tex]\(\frac{14}{24}\)[/tex].

In Urn II, there are 11 red balls and a total of 15 balls (4 green + 11 red). Hence, the probability of drawing a red ball from Urn II is [tex]\(\frac{11}{15}\)[/tex].

The joint probability of two independent events is the product of their individual probabilities, so to find the probability of drawing a red ball from both urns (P(red and red)), we multiply the two probabilities:

[tex]\(P(red \,\text{from Urn I}) \times P(red \,\text{from Urn II}) = \frac{14}{24} * \frac{11}{15}\)[/tex].

To simplify the calculation:

Simplify [tex]\(\frac{14}{24}\) to \(\frac{7}{12}\)[/tex].Multiply [tex]\(\frac{7}{12}\) by \(\frac{11}{15}\)[/tex].[tex]\(\frac{7}{12} \times \frac{11}{15} = \frac{77}{180}\)[/tex].

Therefore, the correct answer is D. 77/180.

factorise 4p + 6pq

step by step

answer fully please, thank you.​

Answers

Answer:

2p(2+3q)

Step-by-step explanation:

Find the Greatest Common Factor (GCF).

GCF = 2p2p

Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

2p(4p/2p + 6qp/2p)

simplify each term in parentheses.

2p(2+3q)

Your answer is 2p(2 + 3q).

First we can start by finding common factors in the coefficients, 4 and 6. 4 and 6 are both divisible by 2, so we can pull this out as our first factor:

2(2p + 3pq)

Now we can look for common factors regarding p and q. Both terms include p, but only one includes q, which means we can also pull the p out as another factor:

2p(2 + 3q)

The expression inside the parentheses cannot be factored anymore, so this is the final factorisation.

I hope this helps!

Enter the trigonometric equation you would use to solve for x in the following right triangle. Do not solve the equation.

Answers

Answer:

sin 70= x/8

Step-by-step explanation:

Opposite of 70 degrees is x and the hypotenuse is 8.

Sin is opposite over hypotenuse

Therefore, sin 70=x/8

A triangle has angles that measure 55°, 43°, and 82°. What kind of triangle is it?
A. obtuse
B. right
C. acute

Answers

Answer:

c. acute

Step-by-step explanation:

all angles are less than 90 degrees, so it is acute

Dominick drew a triangle on a map connecting his house, his school, and his favorite skate park. He used a scale on the map to determine that the height of the triangle that he drew represented 2 miles, and the base of the triangle that he drew represented 6 miles. What is the area of the triangle in square miles?

A triangle has points House, skate park, school. The height of the triangle is 2 miles and the base is 6 miles.

Use the formula for the area of a triangle, A = one-half b h, where A is the area of the triangle, b is the base, and h is the height.


Square miles

Answers

Answer is 6 square miles
Since you multiply 6x 2 and then divide it by 2 is equal to 6

Which elevation is lowest?

-80 m
220 m
-120 m
45 m

Answers

Answer:

I think its -120m

Step-by-step explanation:

Coz negatives are less than positives

C would be the answer because it’s the lowest number there due to the negative sign

A farmer plants corn and soybeans. This model shows the area reserved for each.

A model with 4 rows of 5 squares that represent corn and 4 rows of 3 squares that represent soybeans. Corn is 20 acres and soybeans is 12 acres.
(sorry theirs no picture)
Which expression is equivalent to the sum of the two areas?

4(5)(3)

5(4 + 3)

4(5 + 3)

(4 + 5)(4 + 3)

Answers

Answer:

C) 4 (5+3)

Step-by-step explanation:


If angle B measures 120 degrees, find
the Q
A.30 degrees
B.60 degrees
C.120 degrees
D.90degrees

Answers

Answer:

C. 120°

Step-by-step explanation:

There are two paralell lines, one is part of Angle B, and the other of Angle Q. Then there is a diagonal line, coming at the same angle from B all the way to Q, because the other two lines are paralell. It basically means if you were to slide the flat line which is connected to Q up the diagonal line, it would fit perfectly with it's parallel. So the two angles; Angle B and Angle Q; are the exact same.

Hope this helped! Good luck with future math problems :)

Answer:

The answer for this question is 120 degrees

Step-by-step explanation:

hiya! any help is appreciated!

Answers

I believe you go up one and to the right 2, although I’m not sure wha it’s asking

In a clothing store, 75% of the customers buy a shirt, 20% of the customers buy a pair of pants, and 15% of the customers by both the shirt and a pair of pants. If a customer is chosen at random what is the probability that he or she buys a shirt or a pair of pants?

Answers

Answer:

80%

Step-by-step explanation:

75% + 20% - 15% = 80%

The probability is 80%

The probability that he or she buys a shirt or a pair of pants is 80%.

What is Probability?

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given that in a clothing store, 75% of the customers buy a shirt, 20% of the customers buy a pair of pants, and 15% of the customers buy both the shirt and a pair of pants.

The percentage of customers who buy only shirt = 75% - 15% = 60%

The percentage of customers who buy only pant= 20% - 15% = 5%

The percentage of customers who buy both = 15%

Now, the probability that he or she buys a shirt or a pair of pants is,

Probability = 60% + 5% + 15% = 80%

Hence, the probability that he or she buys a shirt or a pair of pants is 80%.

Learn more about Probability:

https://brainly.com/question/795909

#SPJ2

Wich fraction is the largest? 8/6 8/4 9/6 5/7 6/9

Answers

Answer:

8/4

Step-by-step explanation:

8/4 is equal to 2 and the others equal less than 1 1/2 and 2

Answer:

8/4

Step-by-step explanation:

8/4 is 2

8/6 is 1.333

9/6 is 1.5

5/7 is .7142

6/9 is .666

The triangle shown below has an area of 25 units squared. What is the missing height?

Answers

Answer:

height = 5

Step-by-step explanation:

If area = (1/2)bh, the equation would be 25 = (1/2)10h.

The first step I'd do is multiply both sides by 2 to get rid of the (1/2). So, now the equation is 50 = 10h.

Divide both sides by 10, and you get h = 5! :D

Answer:

x=5 units

Step-by-step explanation:

Given:

A= 25

b=10

Find the height:-

[tex]\sf A=0.5\:bh[/tex]

[tex]\sf 25=0.5(10)h[/tex]

[tex]\sf 25=5h[/tex]

[tex]\sf 5h=25[/tex]

[tex]\sf \cfrac{5h}{5}=\cfrac{25}{5}[/tex]

[tex]\sf h=5[/tex]

Hope it helps!

Which expression has a term with a coefficient greater than 1?

A. M - 5 x3
B. 5/6m + 3
C. 5 + m
D. 5 + 3m

Answers

Answer:

D

Step-by-step explanation:

I'm sorry, but I don't know what option A is.

However, we are asked which expression has a coefficient greater than one. A coefficient is a number in front of a variable. D is the only one with a coefficient GREATER than 1, so that is the answer.

You can tell me if I did anything wrong! :)

what type of triangle is abc

Answers

Every Triangle is an abc triangle

Answer:

Isosceles triangle.

Step-by-step explanation:

-9
- 12 square root of 3

Answers

Answer:

b = 9

Step-by-step explanation:

A= 30°      a = 3[tex]\sqrt{3x}[/tex]

B =            b =

C = 90°     c =

find B first

90 + 30 = 120

180 - 120 = 60

B = 60°

Now, let's find b

use the Law of Sines

[tex]\frac{sin A}{a} = \frac{sin B}{b} \\\frac{sin 30}{3\sqrt{3} } = \frac{sin 60}{b}\\b = \frac{3\sqrt{3} sin 60 }{sin 30}\\b = 9[/tex]

why is this correct idkidkidkidkidkidk

Answers

Answer:

Step-by-step explanation:

because you go with you first answer bc its going to be right

Jose sells 12 cars 8 months if this trend continues how many cars can he expect to sell in 29 months

Answers

Answer:

He can expect to sell 43 more cars.

Step-by-step explanation:

So far he has 1.5 cars per month 12/8=1.5

If he continues this for 29 months 29x1.5=43.5

He will sell 43 cars

Hope this helps :)

3. Liam has a rectangular back
yard. He measured one side of the
yard and found it to be 85 feet and its
diagonal to be 117 feet. Determine, to
the nearest tenth of a foot, the length
of the other side of his back yard

Answers

Answer:

Length of the other side of the backyard is 80.4 feet.

Step-by-step explanation:

Let the dimensions of the Liam's rectangular backyard = 85 feet × a feet

Diagonal of the rectangle, AD = 117 feet

When we apply Pythagoras theorem in ΔABD,

AD² = AB² + BD²

(117)² = (85)² + BD²

a² = 13689 - 7225

a = √6464

  = 80.399 feet

a ≈ 80.4 feet

Therefore, length of the other side of the backyard is 80.4 feet.

solve the equation x-8=3x

Answers

Answer:

x = -4

Step-by-step explanation:

x - 8 = 3x

First, subtract x from both sides:

x - 8 = 3x

-x        - x

________

-8 = 2x

Then, divide both sides by 2:

-8 = 2x

-4 = x

Which set of drivers are progressing at the same pace

Answers

I dont know anything about these set of drivers

Iceberg lettuce is grown and shipped to stores for about 50 cents a​ head, and consumers purchase it for about 120 cents a head. Find the percent increase.


ANSWER FAST PLEASE

Answers

Final answer:

The percent increase in the price of iceberg lettuce is 140%.

Explanation:

To find the percent increase, we need to calculate the difference between the price at which iceberg lettuce is grown and shipped and the price at which consumers purchase it, and then divide that difference by the original price and multiply by 100.

Let's start by finding the difference:

Difference = Consumer price - Production price

Difference = 120 cents - 50 cents = 70 cents

Now, let's calculate the percent increase:

Percent Increase = (Difference / Production price) * 100

Percent Increase = (70 cents / 50 cents) * 100 = 140%

a sightseeing bus picks up a group of tourists at a hotel. it then travels 2 blocks north, 2 blocks eats , 1 block south,2 blocks east, and 1 block south. describes where the bus is in relation to the hotel.

(*It would mean a lot if you could answer*)​

Answers

Answer:

the hotel is four blocks west from the bus; the bus is four blocks east from the hotel.

The bus is 4 blocks east of the hotel.

Since a sightseeing bus picks up a group of tourists at a hotel, and it then travels 2 blocks north, 2 blocks east, 1 block south, 2 blocks east, and 1 block south, to determine where the bus is in relation to the hotel, the following calculation must be carried out:

North and South are antagonistic, the same as East and West  2 N + 2 E - 1S + 2E - 1S 2 N - 2S = 0 2E + 2 E = 4E

Therefore, the bus is 4 blocks east of the hotel.

Learn more in https://brainly.com/question/17249312

why is it not possible to make a right triangle using lengths of 10 feet, 60 feet, and 65 feet ?

Answers

C) is the correct answer

Answer:

the answer is C

Step-by-step explanation:

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