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2 years ago

Determine the number of x-intercepts that appear on a graph of each function.f (x) = (x - 6)2(x + 2)2

Mathematics

2 answers:

Orlov [11]2 years ago

7 0

Short answer There are 2 places where the graph touches the x axis just as you said.
I take this to mean f(x) = (x - 6)^2*(x + 2)^2

There are two places where the graph touches the x axis but that is not an intercept.
When a graph just touches the x axis, that counts as a root. As the graph shows, these 2 places are
x = 6 and
x = - 2 is where they touch.

If you have a graphing calculator, you can see what this looks like for yourself. The window settings are
x min = - 3
x max = 7
y min = 0
y max = 250.

There is a local maximum between x = -2 and x = 6.
So the answer, once again is at x = -2 and x = 6 and that makes 2 roots for the equation.

Papessa [141]2 years ago

4 0

Answer:

f (x) = (x + 1)(x - 3)(x - 4)

= 3

f (x) = (x - 6)2(x + 2)2

= 2

f (x) = (x + 5)3(x - 9)(x + 1)

= 3

f (x) = (x + 2)(x - 1)[x - (4 + 3i )][x - (4 - 3i)]

= 2

hope this helps!

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A study of immunizations among school‑age children in California found that some areas had rates of unvaccinated school‑age chil

Rom4ik [11]

Answer:

Probability that none of the 20 children in such a classroom would be unvaccinated is 0.055.

Step-by-step explanation:

We are given that a classroom of 20 children in one such area where 13.5% of children are unvaccinated.

If there are no siblings in the classroom, we are willing to consider the vaccination status of the 2020 unrelated children to be independent.

The above situation can be represented through binomial distribution;

$P(X=r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,......$

where, n = number of trials (samples) taken = 20 children

r = number of success = none of the 20 children

p = probability of success which in our case is probability that

children are unvaccinated, i.e; p = 13.5%

Let X = Number of children that are unvaccinated

So, X ~ Binom(n = 20, p = 0.135)

Now, Probability that none of the 20 children in such a classroom would be unvaccinated is given by = P(X = 0)

P(X = 0) = $\binom{20}{0} \times 0.135^{0} \times (1-0.135)^{20-0}$

= $1\times 1 \times 0.865^{20}$

= 0.055

Hence, the probability that none of the 20 children in such a classroom would be unvaccinated is 0.055.

8 0

2 years ago

A sample of size 60 from one population of weights had a sample average of 10.4 lb. and a sample standard deviation of 2.7 lb. A

Olegator [25]

Answer:

z= 0.278

Step-by-step explanation:

Given data

n1= 60 ; n2 = 100

mean 1= x1`= 10.4; mean 2= x2`= 9.7

standard deviation 1= s1= 2.7 pounds ; standard deviation 2= s2 = 1.9 lb

We formulate our null and alternate hypothesis as

H0 = x`1- x`2 = 0 and H1 = x`1- x`2 ≠ 0 ( two sided)

We set level of significance α= 0.05

the test statistic to be used under H0 is

z = x1`- x2`/ √ s₁²/n₁ + s₂²/n₂

the critical region is z > ± 1.96

Computations

z= 10.4- 9.7/ √(2.7)²/60+( 1.9)²/ 100

z= 10.4- 9.7/ √ 7.29/60 + 3.61/100

z= 0.7/√ 0.1215+ 0.0361

z=0.7 /√0.1576

z= 0.7 (0.396988)

z= 0.2778= 0.278

Since the calculated value of z does not fall in the critical region so we accept the null hypothesis H0 = x`1- x`2 = 0 at 5 % significance level. In other words we conclude that the difference between mean scores is insignificant or merely due to chance.

3 0

2 years ago

Bryan earns $5.00 per lawn mowed and $5.00 per car washed. Let m be the number of lawns mowed and let c be the number of cars wa

Harrizon [31]

Answer:

5m+c

Step-by-step explanation:

4 0

2 years ago

Joanne has a goal of buying a townhome and saved for 5 years. She expected to have the down payment of $15,000 saved by now but

serg [7]

Answer:

Step-by-step explanation:

Average amount saved per year = $\frac{15,000}{5}$

=$ $3000$

So on average Joanne has saved $3000 per year. She only needs $2000 more which will not even take a year to save.

How many months it will take to save $2000:

$\frac{12}{3000} \times2000$

= $8$ Months.

It will only take Joanne 8 moths to save $2000.

If she really wants to buy the home now she can always go for a home loan scheme for $2000. Any interest rate less than 50% per year is fine as she can save $3000 per year.

6 0

2 years ago

Read 2 more answers

Which list correctly orders A, B, and C from least to greatest when A = –8, B = StartAbsoluteValue negative 6 EndAbsoluteValue,

vladimir2022 [97]

Answer:

A, B, C

Step-by-step explanation:

A = -8

B = |-6| = 6

C = |11| = 11

Least to greatest, negatives are the least and between 6 and 11, 11 is the greatest.