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3 years ago

Which of the following is not a zero of the function shown below?

Mathematics

2 answers:

Ierofanga [76]3 years ago

7 0

Answer:

Step-by-step explanation:

For a number to be a zero of the polynomial, the function has to be equal to 0 if we were to plug in the number into x.

Let's find each:

plugging in x = -2 into the function:

$2(-2)^4-(-2)^3-42(-2)^2+16(-2)+160\\=0$

so this is a zero.

Plugging in x = 2 into the function:

$2(2)^4-(2)^3-42(2)^2+16(2)+160\\=48$

This is NOT a zero

Plugging in x = 4 into the function:

$2(4)^4-(4)^3-42(4)^2+16(4)+160\\=0$

this is a zero

Plugging in x = -4 into the function:

$2(-4)^4-(-4)^3-42(-4)^2+16(-4)+160\\=0$

this is a zero

hence, x = 2 in NOT a zero, answer choice B is right

erica [24]3 years ago

5 0

Answer:

Step-by-step explanation:

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PLEASE HELP URGENT!! What single rigid transformation maps ABC onto A'BC'?

Feliz [49]

We notice that reflecting ABC with respect to the vertical red line, we get A'B'C'.

So, ABC is mapped onto A'B'C by a reflection.

Answer: Reflection

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3 years ago

Read 2 more answers

A cone and its dimensions are shown in the diagram. What is the volume of the cone in cubic inches?

Vinvika [58]

Answer:

The exact value of the volume is equal to

$V=19\frac{397}{512}\pi\ in^{3}$

Step-by-step explanation:

we know that

The volume of a cone is equal to

$V=\frac{1}{3}\pi r^{2} h$

we have

$D=5\frac{5}{8}\ in$

convert to an improper fraction

$D=5\frac{5}{8}\ in=\frac{5*8+5}{8}=\frac{45}{8}\ in$

$r=(45/8)/2=\frac{45}{16}\ in$

$h=7\frac{1}{2}\ in=\frac{7*2+1}{2}=\frac{15}{2}\ in$

substitute in the formula of volume

$V=\frac{1}{3}\pi (\frac{45}{16}^{2})(\frac{15}{2})=\frac{30,375}{1,536}\pi\ in^{3}$

Simplify

$\frac{30,375}{1,536}=\frac{29,184}{1,536}+\frac{1,191}{1,536}=19\frac{397}{512}$

substitute

$V=19\frac{397}{512}\pi\ in^{3}$

4 0

3 years ago

A container has 360 gallons ; daniel took 1/3 of water to give to the animals in the ranch; how many gallons of water are left?

Mrrafil [7]

Answer: 240 gallons

Step-by-step explanation:

From the question, we are informed that the container has 360 gallons and that Daniel took 1/3 of water to give to the animals in the ranch. Therefore, the amount of water that Daniel took will be:

= 1/3 × 360

= 120 gallons

Since we have 360 gallons at the beginning and Daniel has taken 120 gallons, the amount of gallons that'll be left will be:

= 360 - 120

= 240 gallons

8 0

3 years ago

An arithmetic sequence has t1=5 and t2=8 find tn and sn

RoseWind [281]

Answer:

$a_n=2+3n$

$\displaystyle S_n=\frac{7n+3n^2}{2}$

Step-by-step explanation:

<u>Arithmetic Sequences </u>

The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

$a_n=a_1+(n-1)r$

Where

an = nth term

a1 = first term

r = common difference

n = number of the term

The sum of the n terms of an arithmetic sequence is given by:

$\displaystyle S_n=\frac{a_1+a_n}{2}\cdot n$

We are given the first two terms of the sequence:

a1=5, a2=8. The common difference is:

r = 8 - 5 = 3

Thus the general term of the sequence is:

$a_n=5+(n-1)3=5+3n-3=2+3n$

$\boxed{a_n=2+3n}$

The formula for the sum is:

$\displaystyle S_n=\frac{5+2+3n}{2}\cdot n$

$\displaystyle S_n=\frac{7+3n}{2}\cdot n$

Operating:

$\boxed{\displaystyle S_n=\frac{7n+3n^2}{2}}$

4 0

3 years ago

Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an avera

slega [8]

Complete question is;

Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an average of 8.88 new words (words not used in the poet's other works). The standard deviation of the number of new words is 3. Now a manuscript with 6 new sonnets has come to light, and scholars are debating whether it is the poet's work. The new sonnets contain an average of 12.4 words not used in the poet's known works. We expect poems by another author to contain more new words, so to see if we have evidence that the new sonnets are not by our poet we test the following hypotheses.

H0 : µ = 8.88 vs Ha : µ > 8.88

Give the z test statistic and its P-value. What do you conclude about the authorship of the new poems? (Let a = .05.)

Use 2 decimal places for the z-score and 4 for the p-value.

a.What is z ?

b.The p-value is greater than ?

c. What is the conclusion? A)The sonnets were written by another poet or b) There is not enough evidence to reject the null.

Answer:

a) z = 2.87

b) P-value ≈ 0.0021

c) The sonnets were written by another poet

Step-by-step explanation:

We are given the hypothesis as;

Null hypothesis; H0 : µ = 8.88

Alternative hypothesis; Ha : µ > 8.88

We are also given;

Sample size; n = 6

Population Standard deviation; σ = 3

Sample mean; x¯ = 12.4

a) formula for z - value is;

z = (x¯ - µ)/(σ/√n)

z = (12.4 - 8.88)/(3/√6)

z = 2.87

b) we are given the significance value as α = 0.05.

From online p-value from z-score calculator attached and using z = 2.87; one tail distribution; α = 0.05, we have;

P-value = 0.002052

Approximating to 4 decimal places;

P-value ≈ 0.0021

c) The p-value is less than the significance level, thus we react the null hypothesis and conclude that the sonnets were written by another poet

5 0

3 years ago