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3 years ago

Which of the following is an even function?

2 answers:

8 0

Even means g(-x)=g(x)
replace x with -x and see if it simplifies to original functin

g(-x)=(-x-1)²+1
g(-x)=((-1)(x+1))²+1
g(-x)=(x+1)²+1
nope

g(x)=2x²+1
g(-x)=2(-x)²+1
g(-x)=2x²+1
yep

we are done

answer is 2nd one

IrinaVladis [17]3 years ago

8 0

Answer:

2nd Option is correct.

Step-by-step explanation:

We need to find Even function from given functions.

Even function: Even function is a function which hold the following equation.

f(x) = f(-x) for all value of x.

Option 1).

g(x) = ( x - 1 )² + 1 = x² - 2x + 1 + 1 = x² - 2x + 2

put x = -x

g(-x) = (-x)² - 2(-x) + 2 = x² + 2x + 2

Since, g(x) ≠ g(-x)

This is not even function.

Option 2).

g(x) = 2x² + 1

put x = -x

g(-x) = 2(-x)² + 1 = 2x² + 1

Since, g(x) = g(-x)

This is even function.

Option 3).

g(x) = 4x + 2

put x = -x

g(-x) = 4(-x) + 2= -4x + 2

Since, g(x) ≠ g(-x)

This is not even function.

Option 4).

g(x) = 2x

put x = -x

g(-x) = 2(-x) = 2x

Since, g(x) ≠ g(-x)

This is not even function.

Therefore, 2nd Option is correct.

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Need answer asap.thanks

Marrrta [24]

Answer:

$0.46=\frac{23}{50}$

Step-by-step explanation:

To write any decimal as a fraction you divide by 1 and multiply by a number (ranging from 10, 100, 1000 etc.) that will make 0.46 a whole number, this will explain:

Let x = $\frac{0.46}{1}$

10x = $10*\frac{0.46}{1} =\frac{4.6}{10}$

100x = $100*\frac{0.46}{1}=\frac{46}{100}$ this is our perfect fraction, now we simplify later

100x - 10x = $\frac{46}{100} -\frac{4.6}{10}$

90x = $\frac{46}{100} -\frac{4.6}{10} =0$ this is to confirm both fractions are equal

x is the same as $\frac{0.46}{1}$ as $\frac{4.6}{10}$ as $\frac{46}{100}$ but here x = $\frac{46}{100}$ because a fraction has to have no decimals.

So 0.46 is equal any of these values, as a fraction, on the other hand, it's improperly equal to $\frac{46}{100} = \frac{23}{50}$ here I divided by 2 to bring down the proper fraction. (fraction at its simplest form)

6 0

3 years ago

At a certain charity fundraiser, some guests will be randomly selected to receive a gift. The probability of receiving a gift is

mixas84 [53]

Answer:

a) Your answer for part a (I got 3/28) is wrong.

Odds are always expressed as ratios after calculating. Therefore, the odds in favour of receiving a gift = 3:22

b) Your answer in part b(I got 7/9) is correct.

The probability of the box having a toy is 7/9.

Step-by-step explanation:

The question above has to do with odds and probability.

It is important to note that odds are expressed in the form of ratios while probabilities are expressed as fractions.

a) At a certain charity fundraiser, some guests will be randomly selected to receive a gift. The probability of receiving a gift is 3/25. Find the odds in favor of receiving a gift.(I got 3/28)

The formula for calculating odds from probability is Odds = Probability / (1 - Probability).

Probability = 3/25

Odds =(3/25)/(1 - 3/25)

= (3/25)/22/25

= 3/25 ÷ 22/25

= 3/25 × 25/22

= 3/22

Note that odds are always expressed as ratios.

Therefore, the odds in favour of receiving a gift = 3:22

Your answer for part a (I got 3/28) is wrong.

The correct answer is 3:22

b) A child has a box of candies which might have a toy inside. The odds against the box having a toy are 7/2. What is the probability of the box having a toy? I got 7/9.

The formula for calculating probability from odds is P = Odds / (Odds + 1).

Odds = 7/2 or 7:2

We convert the odds to fraction when calculating

Probability = Odds / (Odds + 1).

Probability = (7/2)/ (7/2 + 1)

Probability = (7/2)/9/2

Probability = 7/2 ÷ 9/2

= 7/2 × 2/9

= 7/9

Probability is always expressed as a fraction.

Therefore, the probability of the box having a toy is 7/9.

Your answer in part b(I got 7/9) is correct.

8 0

3 years ago

The cost of a floral bouquet after a discount is applied is represented by the function below, where x represents the number of

galina1969 [7]

The average rate of change over the interval $(12,24)$ is 2.17

Explanation:

Given that the cost of a floral bouquet after a discount is given by the function $f(x)=2.17x-10.00$

We need to determine the average rate of change over the interval $(12,24)$

The average rate of change can be determined using the formula,

$\frac{f(b)-f(a)}{b-a}$

where $a=12$ and $b=24$

Substituting the value of a and b in the function, we get,

$f(12)=2.17(12)-10.00$

$=26.04-10.00$

$=16.04$

$f(24)=2.17(24)-10.00$

$=52.08-10.00$

$=42.08$

Hence, substituting these values in the formula, we get,

$\frac{f(b)-f(a)}{b-a}=\frac{42.08-16.04}{24-12}$

Simplifying, we get,

$\frac{f(b)-f(a)}{b-a}=\frac{26.04}{12}$

Dividing, we have,

$\frac{f(b)-f(a)}{b-a}=2.17$

Thus, the average rate of change over the interval $(12,24)$ is 2.17

7 0

3 years ago

The garden has red roses.

Sauron [17]

Answer: Classic beauty.

Step-by-step explanation: ...

4 0

2 years ago

Algebraic terms are separated by ______.

wariber [46]

Answer: 2) +

Step-by-step explanation:

2) would be the correct answer because when a term is made up of a constant multiplied by a variable or variables, that constant is called a coefficient, so Algebraic terms are separated by a plus sign or +.

Hopefully this helps:)

4 0

3 years ago