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Travka [436]
3 years ago
15

Plot the x- and y- intercepts of the function.

Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
4 0

Answer:

y intercept = -2

x intercepts = -2,-1,1

Step-by-step explanation:

f(x) = x^3 + 2x^2 -x-2

Set this equation equal to zero to find the x intercepts.

Factoring by grouping

0 =x^3 -x   +2x^2 -2

   = x( x^2-1) +2(x^2-1)

Factoring out the (x^2-1)

0= (x^2-1) (x+2)

Factoring the first term using the difference of squares (a^2-b^2) = (a-b)(a+b)

0 = (x-1) (x+1) (x+2)

Using the zero product property

x-1 = 0  x+1  = 0  x+2 =0

x=1,  x=-1   x=-2

The x intercepts are -2, -1, 1


To find the y intercepts, set x=0

y = x^3 + 2x^2 -x-2

y = 0 -2

y = -2


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Given that f(X)=2X-5, find the value of X that makes f(X)=15
amid [387]
X=15 because 2(15) is 30-5 is 15
5 0
3 years ago
Read 2 more answers
Consider a collection of envelopes consisting of 1 red envelope, 3 blue envelopes, 2 green envelopes, and 3 yellow envelopes if
nasty-shy [4]

Answer:

the probability that at least one envelope is a yellow envelope is 16/21

Step-by-step explanation:

The probability that at least one envelope is a yellow envelope is P(Y);

P(Y) = 1 - P(Y)'

P(Y)' is the probability that no envelope is a yellow envelope.

Given;

red envelope = 1

blue envelopes = 3

green envelopes = 2

yellow envelopes = 3

Total = 9

Number of non-yellow envelope = 9 -3 = 6

(6 envelope are not yellow)

P(Y)' = P1 × P2 × P3

Since there is no replacement;

P(Y)' = 6/9 × 5/8 × 4/7

P(Y)' = 5/21

From equation 1;

P(Y) = 1 - 5/21

P(Y) = 16/21

the probability that at least one envelope is a yellow envelope is 16/21.

8 0
3 years ago
Hunter thought he purchased an umbrella for $60. The actual price of an Umbrella is $50. What is hunters percent error
Dima020 [189]
Error = 60-50/50 × 100
= 10/50 × 100
= 20 %
3 0
3 years ago
The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2inches.a. Wha
Charra [1.4K]

Answer:

a)P(X>66)=P(Z>1)=1-P(Z

b)P(\bar X >66)=P(Z>2)=1-P(Z

c) P(\bar X >66)=P(Z>10)=1-P(Z

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

2) Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(64,2)  

Where \mu=64 and \sigma=2

We are interested on this probability

P(X>66)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>66)=P(\frac{X-\mu}{\sigma}>\frac{66-\mu}{\sigma})=P(Z>\frac{66-64}{2})=P(Z>1)

And we can find this probability on this way:

P(Z>1)=1-P(Z

3) Part b

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

P(\bar X >66)=P(Z>\frac{66-64}{\frac{2}{\sqrt{4}}}=2)

And using a calculator, excel or the normal standard table we have that:

P(Z>2)=1-P(Z

4) Part c

P(\bar X >66)=P(Z>\frac{66-64}{\frac{2}{\sqrt{100}}}=10)

And using a calculator, excel or the normal standard table we have that:

P(Z>10)=1-P(Z

3 0
3 years ago
WILL GIVE BRAINLIEST, THANKS AND 5 STARS! PLEASE HELP! LOTS OF POINTS
irina [24]

First graph it

#1

Maximum height is the y coordinate of vertex

  • (2,144)

Max height

  • 144m

#2

Time is the x coordinate of vertex

  • 2s

#3

  • y is 0

\\ \rm\Rrightarrow -16t^2+64t+80=0

x intercepts are the solutions

  • (-1,0)U(5,0)

Take it positive

  • t=5s

#4

put in function

  • y=-16(1)+64+80=-16+144=128ft

8 0
2 years ago
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