Mathematics College

8. Given: AD perpendicullar DB, DB perpendicullar BC, AB = CD Prove: AB||DC​

8. Given: AD Perpendicullar DB, DB Perpendicullar BC, AB = CD Prove: AB||DC

Answers

Answer 1

Step-by-step explanation:

Angle ADB = Angle CBD = 90° (given)

Side AB = Side DC (given)

Common side DB / BD

By HL congruence, triangles ABD and CDB are congruent.

Therefore Angle ABD = Angle CDB

=> Line AB is parallel to Line DC (Z angles)

Related Questions

16 is what percent of 20?

Answers

Answer:

3.2

Step-by-step explanation:

16/20 = 0.8
0.8 * 100 = 80
Solution: 80%

A music store marks up the instruments it sells by 30%.
If the price tag on a trumpet says $104, how much did the store pay for it?

Answers

A. $ 58.50

B. $ 80

C. No, it did not mark up 30%.

Step-by-step explanation:Since,

A. We have,

Mark up percentage = 30%

Actual price = $ 45,

B. We have,

SP = $ 104,

C.  We have,

AP = $ 75,

SP = $100,

Thus, mark up percentage =

= 33.33 %

Hence, store did not mark up the price by 30%.

Pls help me with this ASAP

Answers

The answer is the first option, 3/1

Find the value of x. Everything is in the photo.

Answers

Answer:

27

Step-by-step explanation:

Note that since VX and XZ are both line segments, <VWX and <XYZ both equal 180 (also known as a straight angle). Also, note that the sum of the angles in a triangle are 180 degrees. Now, let’s start.

Finding angles of the triangle:

<WYX = <XYZ - <WYZ = 180 - 4x

<XWY = <XWV - <VWY = 180 - 6x

Using the sum of angles in a triangle and substituting these values in:

180 = <X + <WYX + <XWY = 90 + (180 - 4x) + (180-6x) = 450 - 10x

270 = 10x

27 = x

We are done! I hope this helps! :)

Where did the 45% come from. It states 55% in question

Answers

Answer:

is this a question......

Lourdes recorded in this table the change in her dog's weight, in ounces, each month. Which statement can be suppor by the data in the table? Change in Dog's Weight January February March April May +6 +4 -2 +1 -5

A) Lourdes dog gained weight in more months than it lost weight because there are more positive numbers than ne numbers.

B) Lourdes' dog lost weight in more months that it gained weight because the digit 5 is the greatest digit and it is a ne number.

C) Lourdes dog gained weight every month because it is getting older.

D) Lourdes dog lost weight every month because the change in May is a negative number.​

Answers

Answer:

A). Lourdes dog gained weight in more months than it lost weight because there are more positive numbers then negative numbers

The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years. a. Find the probability that a cat will live to be older than 14 years. b. Find the probability that a cat will live between 14 and 18 years. c. If a cat lives to be over 18 years, would that be unusual? Why or why not? d. How old would a cat have to be to be older than 90% of other cats?

Answers

Answer

a. 0.856

b. 0.78071

c. It is not unusual

d. 13.65 years old

Step-by-step explanation:

The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years.

We solve this question using z score formula:

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

a. Find the probability that a cat will live to be older than 14 years.

For x > 14 years

z = 14 - 15.7/1.6

z = -1.0625

Probability value from Z-Table:

P(x<14) = 0.144

P(x>14) = 1 - P(x<14) = 0.856

b. Find the probability that a cat will live between 14 and 18 years.

For x = 14 years

z = 14 - 15.7/1.6

z = -1.0625

Probability value from Z-Table:

P(x = 14) = 0.144

For x = 18 years

z = 18 - 15.7/1.6

z= 1.4375

Probability value from Z-Table:

P(x = 18) = 0.92471

The probability that a cat will live between 14 and 18 years is calculated as:

P(x = 18) - P(x = 14)

0.92471 - 0.144

= 0.78071

c. If a cat lives to be over 18 years, would that be unusual? Why or why not?

For x > 18 years

z = 18 - 15.7/1.6

z= 1.4375

Probability value from Z-Table:

P(x<18) = 0.92471

P(x>18) = 1 - P(x<18) = 0.075288

Converting this to percentage:

0.075288 × 100 = 7.5288%

Hence, 7.5288% of the cats live to be over 18 years. Hence, it is not unusual.

d. How old would a cat have to be to be older than 90% of other cats?

From the question above, 10% of the cats would be older than 90% of other cats.

Hence, we find the z score of the 10th percentile

= -1.282

Hence,

-1.282 = x - 15.7/1.6

Cross Multiply

-1.282 × 1.6 = x - 15.7

- 2.0512 = x - 15.7

x = 15.7 -2.0512

x = 13.6488 years old

Approximately = 13.65 years old

At 5:00 p.m., Antonio turned on the oven. While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period. The oven remained at 400°F for 45 minutes until Antonio turned it off. It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m. Which statement best explains whether or not the temperature in the oven is a function of the time?

Answers

Answer: It is a function because at any given time the oven was exactly one temperature.

Step-by-step explanation:

It is given that:

At 5:00 p.m., Antonio turned on the oven.

The oven remained at 400°F for 45 minutes until Antonio turned it off.

It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m.

Which substitution method should be the best used to solve which system of equations

Answers

Answer: 6x+2y=1

Step-by-step explanation:

because it just is

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