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2 years ago

Which of the following represents graph of f(x) = (1/2)^x

Mathematics

2 answers:

Alona [7]2 years ago

6 0

heyy, I know you posted this on 2017 and got no answers yet, well i need it this answer and it wasn't here, so i know the answer

The answer is The first one

Thank u :)

Tatiana [17]2 years ago

5 0

Answer:

The first option is correct.

Step-by-step explanation:

The given function is

$f(x)=(\frac{1}{2})^x$ .... (1)

The general exponential function is

$f(x)=ab^x$ .... (2)

Where, a is initial value and b is the growth factor.

If b>1, then it is a growth function and its graph is an increasing curve.

If b<1, then it is a decay function and its graph is a decreasing curve.

On comparing (1) and (2) we get,

$b=\frac{1}{2}$

So, f(x) is a decreasing function.

Since f(x) is decreasing function, therefore the graph of the function decreases as the value of x increases. Option 1 is correct.

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Jack and his partner went to a party where four other couples were present. Every person shook hands with everyone else (other t

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Answer:

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2 years ago

If x equals 3 calculate the value of 2x squared plus x

Korolek [52]

2 × 3 = 6
6 squared = 36
36 + 3 = 39
Hope this helps!

6 0

2 years ago

Read 2 more answers

If you invest $4000 at 9% interest compounded annually, in how many years will you have $20,000. Give your answer the nearest te

Masteriza [31]

Answer:

18.7 years

Step-by-step explanation:

This is a compound interest problem and the following variables have been given;

Principal = 4000; this is the amount o be invested

APR = 9%; this is the compound interest to be earned

Accumulated amount = 20,000

We are required to determine the duration in years. We apply the compound interest formula;

$A=P(1+r)^{n}$

$20000=4000(1+\frac{9}{100})^{n}\\20000=4000(1.09)^{n}\\5=(1.09)^{n}$

The next step is to introduce natural logarithms in order to determine n;

$ln5=nln(1.09)\\n=\frac{ln5}{ln(1.09)}\\n= 18.675$

The number of years required is thus 18.7 years

6 0

3 years ago

In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.

solmaris [256]

Answer:

1. m∠R > 90°

2. m∠S + m∠T < 90°

4. m∠R > m∠T

5. m∠R > m∠S

Step-by-step explanation:

<h3>General strategy</h3>

prove the statement starting from known facts, or
disprove the statement by finding a counterexample

Helpful fact: Recall that the Triangle Sum Theorem states that m∠R + m∠S + m∠T = 180°.

Option 1. m∠R > 90°

Start with m∠R > m∠S + m∠T.

Adding m∠R to both sides of the inequality...

m∠R + m∠R > m∠R + m∠S + m∠T

There are two things to note here:

The left side of this inequality is 2*m∠R
The right side of the inequality is exactly equal to the Triangle Sum Theorem expression

2* m∠R > 180°

Dividing both sides of the inequality by 2...

m∠R > 90°

So, the first option must be true.

Option 2. m∠S + m∠T < 90°

Start with m∠R > m∠S + m∠T.

Adding (m∠S + m∠T) to both sides of the inequality...

m∠R + (m∠S + m∠T) > m∠S + m∠T + (m∠S + m∠T)

There are two things to note here:

The left side of this inequality is exactly equal to the Triangle Sum Theorem expression
The right side of the inequality is 2*(m∠S+m∠T)

Substituting

180° > 2* (m∠S+m∠T)

Dividing both sides of the inequality by 2...

90° > m∠S+m∠T

So, the second option must be true.

Option 3. m∠S = m∠T

Not necessarily. While m∠S could equal m∠T, it doesn't have to.

Example 1: m∠S = m∠T = 10°; By the triangle sum Theorem, m∠R = 160°, and the angles satisfy the original inequality.

Example 2: m∠S = 15°, and m∠T = 10°; By the triangle sum Theorem, m∠R = 155°, and the angles still satisfy the original inequality.

So, option 3 does NOT have to be true.

Option 4. m∠R > m∠T

Start with the fact that ∠S is an angle of a triangle, so m∠S cannot be zero or negative, and thus m∠S > 0.

Add m∠T to both sides.

(m∠S) + m∠T > (0) + m∠T

m∠S + m∠T > m∠T

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠T.

So, option 4 must be true.

Option 5. m∠R > m∠S

Start with the fact that ∠T is an angle of a triangle, so m∠T cannot be zero or negative, and thus m∠T > 0.

Add m∠S to both sides.

m∠S + (m∠T) > m∠S + (0)

m∠S + m∠T > m∠S

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠S.

So, option 5 must be true.

Option 6. m∠S > m∠T

Not necessarily. While m∠S could be greater than m∠T, it doesn't have to be. (See examples 1 and 2 from option 3.)

So, option 6 does NOT have to be true.

4 0

1 year ago

Do this and I’ll pay u I need help

frutty [35]

Answer:

"bring me my money"

Step-by-step explanation:

8 0

3 years ago