All categories

1 year ago

Which function has a Vertex at the origin f(x)= (x+4)^2, f(x) x(x-4), f(x)=(x-4)(x+4), f(x)=-x^2

1 answer:

Studentka2010 [4]1 year ago

7 0

First of all, we need to know what is the vertex means which is the maximum or minimum point of a parabola and the formula will be:
x=-b/2a
Where b and a from
f(x)=ax^2+bx+c
So do find which function has a vertex of origin. Let's find the vertex of all the function that we had:
f(x)=(x+4)^2
f(x)=(x+4)(x+4)
f(x)=x^2+8x+16
x=-b/2a
x=-8/2(1)
x=-8/2
x=-4
Not the right answer because the vertex needs to be origin which is x=0

f(x)=x(x-4)
f(x)=x^2-4x
x=-b/2a
x=-(-4)/2(2)
x=4/4
x=1
Not the right answer

f(x)=(x-4)(x+4)
f(x)=x^2-16
x=-0/2(1)
x=0
Yay! This is the right answer. As a result, f(x)=(x-4)(x+4) is your final answer. Hope it help!

You might be interested in

Beau buys a skateboard with a price tag of $82.50. The tax rate is 8%. How much does he pay, including tax

madam [21]

8% of $82.50 is $6.60 so 82.50 + 6.60 would equal $89.10 as the total

7 0

2 years ago

Judy’s measured potassium level varies according to the Normal distribution with μ = 3.8 and σ = 0.2 mmol/l. Let us consider wha

Basile [38]

Answer:

The blood potassium level L such that the probability is only 0.05 that the average of four measurements is less than L is 3.64.

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means of size n can be approximated to a normal distribution with mean $\mu$ and standard deviation, which is also called standard error $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 3.8, \sigma = 0.2, n = 4, s = \frac{0.2}{\sqrt{4}} = 0.1$

What is the blood potassium level L such that the probability is only 0.05 that the average of four measurements is less than L?

This is the value of X when Z has a pvalue of 0.05. So it is X when Z = -1.645.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$-1.645 = \frac{X - 3.8}{0.1}$

$X - 3.8 = -1.645*0.1$

$X = 3.64$

The blood potassium level L such that the probability is only 0.05 that the average of four measurements is less than L is 3.64.

8 0

2 years ago

Read 2 more answers

A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink on an average. Any overfill

ozzi

Answer:

d. The average is equal to 12 ounces.

Step-by-step explanation:

In this problem, the drink filling machine must be perfectly calibrated at 12 ounces since it needs to be shut down in cases of overfilling (mean > 12 ounces) and underfilling (mean < 12 ounces). Therefore, the correct approach would be to test if the mean is 12 ounces and the correct set of hypothesis would be:

$H_0:\mu=12\\H_a:\mu\neq 12$

The correct alternative is d. The average is equal to 12 ounces.

5 0

2 years ago

a barangay has 1000 individuals and its population doubles every 60 years. Give an exponential model for the barangay's populati

sdas [7]

Answer:

P(t) = 1000e^(0.01155)t

Step-by-step explanation:

Let the population of barangay be expressed according to the exponential formula;

P(t) = P0e^kt

P(t) is the population of the country after t years

P0 is the initial population

t is the time

If barangay has 1000 initially, this means that P0 = 1000

If the population doubles after 60years then;

at t = 60, P(t) = 2P0

Substitute into the formula

2P0 = P0e^k(60)

2 = e^60k

Apply ln to both sides

ln2 = lne^60k

ln2 = 60k

k = ln2/60

k = 0.01155

Substitute k = 0.01155 and P0 into the expression

P(t) = 1000e^(0.01155)t

Hence an exponential model for barangay's population is

P(t) = 1000e^(0.01155)t

7 0

2 years ago

Theo recorded the means and mean absolute deviations of his language arts and Biology scores. He found the difference in the mea

Rina8888 [55]

The answer is actually A.2 because I just took the test.

8 0

2 years ago

Read 3 more answers