triangle inequality proof
/a + b/ ≤ /a/ + /b/

Answers

Answer 1

Answer:

a^2+b^2+2|a||b|≥a2+b2+2ab(|a|+|b|)2≥|a+b|2(∵∀x∈R;x2=|x|2)∴|a|+|b|≥|a+b|\

Step-by-step explanation:


Related Questions

a science class has two times as many girls as it has boys. a. Describe possible numbers of boys and girls in the science class.

Answers

the ratio is 2:1 so there could be multiple answers. 12:6 etc.

Find the range of x that satisfies both inequalities.

Answers

Answer:

may I ask what type of algebra this is

Step-by-step explanation:

(-infinity,-1) the blue also has red there, so the image is correct.

Solve m+7=8
What dose m =

Answers

1 bru just making this up bend

An electronics hobbyist has three electronic parts cabinets with two drawers each.
One cabinet has NPN transistors in each drawer, while a second cabinet has PNP transistors in each drawer. The third cabinet has NPN transistors in one drawer and PNP transistors in the other drawer. The hobbyist selects one cabinet at random and withdraws a transistor from one of the drawers.
a) What is the probability that an NPN transistor will be selected?
b) Given that the hobbyist selects an NPN transistor, what is the probability that it came from the cabinet that contains both types?
c) Given that an NPN transistor is selected what is the probability that it comes from the cabinet that contains only NPN transistors?

Answers

Answer:

a) 0.5 = 50% probability that an NPN transistor will be selected.

b) 0.3333 = 33.33% probability that it came from the cabinet that contains both types

c) 66.67% probability that it comes from the cabinet that contains only NPN transistors

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

a) What is the probability that an NPN transistor will be selected?

1/3 probability that the first cabinet is chosen. This cabinet has two transistors, both of which are NPN, so 100% probability of selecting a NPN transistor.

1/3 probability that the second cabinet is chosen. This cabinet has two transistors, both of which are PNP, so 0% probability of selecting a NPN transistor.

1/3 probability that the second cabinet is chosen. This cabinet has two transistors, one of which is NPN, so 50% probability of selecting a NPN transistor.

So

[tex]p = \frac{1}{3}*1 + \frac{1}{3}*0 + \frac{1}{3}*0.5 = \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = 0.5[/tex]

0.5 = 50% probability that an NPN transistor will be selected.

b) Given that the hobbyist selects an NPN transistor, what is the probability that it came from the cabinet that contains both types?

Here we use the conditional probability formula.

Event A: NPN transistor

Event B: From the third cabinet.

50% probability that an NPN transistor will be selected, so [tex]P(A) = 0.5[/tex].

1/6 probability that it is from the third cabinet and NPN, so [tex]P(A \cap B) = \frac{1}{6}[/tex]

The desired probability is:

[tex]P(B|A) = \frac{\frac{1}{6}}{0.5} = 0.3333[/tex]

0.3333 = 33.33% probability that it came from the cabinet that contains both types.

c) Given that an NPN transistor is selected what is the probability that it comes from the cabinet that contains only NPN transistors?

Either it comes from the cabinet with only NPN transistors, or it comes from the cabinet with both types of transistors. The sum of the probabilities of these outcomes is 100%. So

x + 33.33 = 100

x = 66.67

66.67% probability that it comes from the cabinet that contains only NPN transistors

need help with geometry ​

Answers

Answer:

A 38

Step-by-step explanation:

Since all the angles make up a circle which is 360 degrees, we can subtract all of the angle measurements we know from 360, in this case

360-298-24=38

please look at the photo below or above

Answers

Answer:

[tex]Opposite =- \frac{4}{5}[/tex]

Step-by-step explanation:

Given

[tex]Number = \frac{4}{5}[/tex]

Required

Determine its opposite

To get the opposite of a number, we simply subtract it from 0.

So, we have:

[tex]Opposite =0 - \frac{4}{5}[/tex]

[tex]Opposite =- \frac{4}{5}[/tex]

Hence, the opposite is -4/5

I need help with this

Answers

Answer:

5√2

Step-by-step explanation:

With reference angle 45°

perpendicular (p) = 5

hypotenuse (h) = x

sin 45 ° = p / h

1/√2 = 5 / x

x = 5√2

Solve the quadratic equation 3x^2 + 2x - 4 = 0
Give your answers to 2 decimal places​

Answers

Answer:

3x^2+2x−4=0

Use the quadratic formula to find the solutions

−b±√b^2−4(ac)/2a

Substitute the values

a=3, b=2, and c=−4 into the quadratic formula and solve for x.

−2±√2^2−4⋅(3⋅−4)/2⋅3

Simplify.

x = −1±√13/3

The final answer is the combination of both solutions.

x= −1−√13/3,−1+√13/3

The result can be shown in multiple forms.

Exact Form:

x= −1−√13/3,−1+√13/3

Decimal Form:

x=0.86851709…,−1.53518375…

Step-by-step explanation:

Hope it is helpful......

pls help this is an ixl question and it really is hard

Answers

Answer:

It would be the first one... 10:25

Step-by-step explanation:

10/4=2.5

2.5*10=25

2.5*4=10

PLEASE HELP SOLVE THIS WUESTION SOLVE FOR y

Answers

Answer:

y = 5

Step-by-step explanation:

12^2 + y = 13^ 2

144 + y = 169

169 - 144 = 25

sqrt of 25 = 5

y = 5

Answer:

A, y=5

Step-by-step explanation:

I just did it right now

an electric wire which is 0.12 m long is cut into 3 pieces of the same length.How long is each pieces?​

Answers

Answer:

0.04m

Step-by-step explanation:

0.12/3=0.04

Answer:

Step-by-step explanation:

Total length of a wire = 0.12 m

If the wire is divided into 3 equal pieces then

Length of each piece

= 0.12 / 3

= 0.04 m

hope it helps :)

Find the x-amd y-intercepts of the equation x-y=1

Answers

Answer:

x=9

y=8

Step-by-step explanation:

x-y=1

x=9

y=8

9-8=1

Mr. White is renting a small truck for one week and a few additional days d. He does not have to pay a per mile fee. Evaluate the expression 280+80d to find how much he will pay for a ​9-day rental.​

Answers

You multiply 80 by the number of days (9) and then add 280 to it and there’s your answer 280+80 x 9=

The amount of money paid for the 9-day rental will be $1000.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Mr White is renting a small truck for one week and a few additional days d. He does not have to pay a per-mile fee. The expression is 280+80d.

The amount of money for a 9-day rental will be calculated as,

A = 280+80d

A = 280+(80 x 9)

A = $1000

Therefore, the amount of money paid for the 9-day rental will be $1000.

To know more about an expression follow

https://brainly.com/question/22040802

#SPJ2

Fill in the missing values:
a) 17 out of 85 = ? %
b) ? out of 90 = 17%
c) 1026 out of ? = 54%
d) 8.1% of 90 = ?
e) ? % of 50 = 90
f) 88% of ? = 154


Answers

Answers

a. 20%

b. 15.3

c. 1900

d. 7.29

e. 180

f. 175

Way to do

a. 17 out of 85 how many percentage?

17/85 × 100 = 20%

b. what is 17% of 90?

? /90 × 100 = 17? /90 = 17 : 100? /90 = 0.17? = 90 × 0.17 ? = 15.3

c. 1026 out of ? = 54%

1026/? × 100 = 541026/? = 0.54? = 1026 : 0.54? = 1900

d. 8.1% of 90 = ?

90 × 8.1/100 = 7.29

e. ?% of 50 = 90

50 × ?/100 = 90?/100 = 90:50?/100 = 9/5? = 9/5 × 100? = 180

f. 88% of ? = 154

? × 88/100 = 154? = 154 : 88/100? = 175

For moderators who see this

#Moderators please don't be mean, dont delete my answers just for approval from your senior or just to get the biggest moderation daily rank. This answer is long, how can you just instanly delete it? :(

Write the word sentences as an equation. Then solve the equation.

13 subtract from a number w is 15

An equation that represent this word sentences is ?

The solution is w = ?

Answers

the equation would be w-13=15

w=28

7 1/5 – 6 2/5 = ?
А. 1 1/5
в. 4/5
с. 1 4/5
D. 13 3/5

D)correct?

Answers

I think so it’s b but not sure 100%
[tex]\\ \boxed{ \huge \boxed{\tt{} Answer}}[/tex]

[tex]\tt{B}[/tex]

the answer is letter B

[tex]\frac{1}{5}[/tex] — 6[tex]\frac{2}{5}[/tex] = [tex]\frac{31}{5}[/tex] or [tex]\frac{4}{5}[/tex]

[tex] \\ \huge\boxed{\ddot\smile}[/tex][tex]\longrightarrow[/tex][tex] \\ \huge\boxed{\ddot\smile}[/tex]

Camille has already baked 1 cake, and she can bake 2 cakes with each additional stick of butter she buys. Write an equation that shows the relationship between the number of additional sticks of butter and the number of cakes y

Answers

Answer:

1+2x=y

Step-by-step explanation:

X: Number of sticks

Y= number of cakes

There is already one cake, so you must add one to the equation. You multiply x by two since 1 stick of butter (x) makes two cakes.

The angles of a triangle add up to 180 degrees.

The second angle is 20 degrees larger than the smallest angle.

The third angle is 3 times as big as the smallest angle.

Find the measure of the smallest angle (in degrees)

Answers

Answer: 32 degrees

Step-by-step explanation:

small angle : x

middle angle: x + 20

large angle: 3x

Form an equation: 5x + 20 = 180

5x = 180 - 20

5x = 160

x = 160/5

x = 32

(8x²-1) (3x²-4x+5) standard form​

Answers

Answer:

24x⁴ - 32x³ + 37x² + 4x - 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Distributive Property

Algebra I

Terms/CoefficientsExpand by FOIL (First Outside Inside Last)

Step-by-step explanation:

Step 1: Define

(8x² - 1)(3x² - 4x + 5)

Step 2: Expand

Distribute/FOIL:                                                                                              24x⁴ - 32x³ + 40x² - 3x² + 4x - 5Combine like terms:                                                                                       24x⁴ - 32x³ + 37x² + 4x - 5

Quadrilateral EFGH is inscribed in a circle as shown.
G
E
н
mZF = (4x + 10°, mZG = (2x - 5)º, and m_H = (3x - 5)°. What is the value of x?

Answers

F + H = 180

(4x+ 10) + (3x - 5) = 180
7x + 5 = 180
7x = 175
X = 25

The correct response is B.

The value of the variable 'x' will be 25. Then the correct option is B.

What is a cyclic quadrilateral?

If the quadrilateral is inscribed in a circle then the quadrilateral is known as a cyclic quadrilateral. And the sum of opposite angles of the quadrilateral is 180 degrees.

Quadrilateral EFGH is inscribed in a circle as shown. ∠F = (4x + 10)°, ∠G = (2x - 5)º, and ∠H = (3x - 5)°.

Angles ∠F and ∠H will be supplementary angles. Then the equation is given as,

∠F + ∠H = 180

4x + 10 + 3x - 5 = 180

7x = 175

x = 25

The value of the variable 'x' will be 25. Then the correct option is B.

More about the cyclic quadrilateral link is given below.

https://brainly.com/question/15061291

#SPJ2

Hello pls help me with two of these questions;)

Answers

Answer:

1-A-15

2-C

Step-by-step explanation:

7-21 is an increase by 3 times, so 5*3=15

The second is kinda blurry, so it's a little hard to explain.


Help need to do this in 10 min

List the integers that satisfy both these inequalities.
2x + 5 < 0
x>-8

Answers

Answer:

no satisfied

Step-by-step explanation:

because of the rules

Solve the following inequality.
(x-2)(x– 7)<0

Answers

The answer should be 2

43,451 rounded down to the nearest dollar

Answers

Answer:

$43,450

Step-by-step explanation:

The last dollar in the ones place is 1.

Since this is less than 5, we have to round down.

Which gets us to 43,450.

Hope this helps! :)

Which of the following states the conditions that the graph meets?
OX2
Ox22
Oys2
Oy22

Answers

B is correct
I just took it

Mohan has starts his Shop,during the first month following events that take place.

I. Mohan start business with cash Rs. 50,000, goods Rs. 10,000 and furniture Rs. 1,000.

II. Purchased goods for cash Rs. 30,000

III. Purchased goods on credit Rs. 20,000

IV. Sold goods (cost Rs. 10,000) for Rs. 12,000

V. Bought furniture on credit Rs. 2,000

VI. Paid cash to a creditor Rs. 15,000

VII. Sold goods to Sohan costing Rs. 1,500 for Rs. 1,800

VIII. Purchased household goods for Rs. 15,000, giving Rs. 5,000 in cash and balance through

a loan.

Required:

a) Analyze the transactions

a) Show the effect on accounting equation.

b) Record the transactions in journal entries

c) Post the journal entries

d) Prepares unadjusted trial balance.​

Answers

Answer:

Step-by-step explanation:

He will finally have an amount of 3,500 Rupees

All I want to know is the formula and I will do the rest...pls someone help me with the formula...

Answers

Hey in this type of questions there's no formula, you need to use your logic.

#Note that the full degree or a triangle is 180°

#The L in triangle is 90°

I see that you want to try to do it by yourself, i will give you the tips. to get the <BAD

#since <DAC is 90°, The ADB is 90° (180°-90°)

<BAD = 180° - 90° - 25° = 65°

Now, try to find <BCA yourself.

Tell me if you give up, i will tell you lol.

Nora is going to invest in an account paying an interest rate of 4.3% compounded continuously. How much would Nora need to invest, to the nearest dollar, for the value of the account to reach $7,600 in 20 years?

Answers

Answer:

P≈3216

3216

Step-by-step explanation:

Find the slope of the passing line through the points (-4,7) and (-9,4)

Answers

Answer:

m = 3/5

Step-by-step explanation:

Answer:

m = 3/5

Step-by-step explanation:

[tex]\frac{7-4}{-4-(-9)} = \frac{3}{5}[/tex]

PLEASE HELP ME WITH THIS I DONT UNDERSTAND I WILL MARK YOU AS BRAINLIEST IF YOU ANSWER CORRECTLYY PLS AND TY​

Answers

Answer:  To establish the strength of a linear association, first compute the correlation coefficient between the variables involved. The, examine the absolute value of the coefficient. A strong relationship has an absolute value of close to 1 (or approaching 1) while a weak relationship has an absolute value close to 0 (or approaching zero).

The data points will be clustered more tightly around the trend line if there is a weak linear association and less tightly if there is a strong one.

hope it helps

take care

Step-by-step explanation:

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