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2 years ago

If f(x) = x2 − 6x + 19, complete the square and determine the minimum or maximum value of the function

Mathematics

1 answer:

lara31 [8.8K]2 years ago

8 0

Answer:

minimum value = 10

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form using completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 6x

f(x) = x² + 2(- 3)x + 9 - 9 + 19

= (x - 3)² + 10 ← in vertex form

with (h, k) = (3, 10 )

To determine maximum or minimum consider the value of a

• If a > 0 then minimum value of k

• If a < 0 then maximum value of k

Here a = 1 > 0, hence minimum value of k = 10

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Can somebody help me in this

DaniilM [7]

Answer:

Step-by-step explanation:

The 30-60-90 triangle has the shortest leg as x.

If there is no x you have to use the 2x or $x\sqrt{3}$

3 0

3 years ago

A breakfast cereal producer makes its most popular product by combining just raisins and flakes in each box of cereal. The amoun

yarga [219]

Using the normal distribution, it is found that there is a 0.9192 = 91.92% probability that the total amount of product is less than 575 g.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X.

When two normal variables are added, the mean is the sum of the means while the standard deviation is the square root of the sum of the variances.

In this problem, the product is composed by flakes and raisins, and we have that:

$\mu_F = 370, \sigma_F = 24, \mu_R = 170, \sigma_R = 7$

Hence, the distribution for the total amount of product has <u>mean and standard deviation</u> given by:

$\mu = \mu_F + \mu_R = 370 + 170 = 540$

$\sigma = \sqrt{\sigma_F^2 + \sigma_R^2} = \sqrt{24^2 + 7^2} = 25$

The probability that the total amount of product is less than 575 g is the <u>p-value of Z when X = 575</u>, hence:

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

$Z = \frac{575 - 540}{25}$

$Z = 1.4$

$Z = 1.4$ has a p-value of 0.9192.

0.9192 = 91.92% probability that the total amount of product is less than 575 g.

A similar problem is given at brainly.com/question/22934264

5 0

2 years ago

6. Compare 1⁄2 with 3⁄4 using ( <, >, =). A. None of the above B. 1⁄2 = 3⁄4 C. 1⁄2 < 3⁄4 D. 1⁄2 > 3⁄4

disa [49]

C. because 3/4 is more than 1/2.

5 0

2 years ago

the base of a right triangle is (x-5). The height of the triangle is (2x+1). The perimeter of the triangle is (7x+5). Find the a

Dovator [93]

Answer:

Area: (x^2)-(9x/2)-2 3rd side=4x+9

Step-by-step explanation:

First, let's find the third side. If all of the sums add up to 7x+5, then we can easily subtract the two sides that we do have.

2x+1+x-5=3x-4

Now, you have to ask yourself what added to 3x-4 can be equal to 7x+5.

It's 4x+9 because we combine like terms. That's the third side. Now, we should follow the formula for getting the area of triangle using the side lengths:

(2x+1)(x-5)/2=area of triangle

2x*x=2x^2

2x*-5=-10x

x*1=x

-5*1=-5

Now the total is 2x^2-9x-4 when you continue to combine like terms. Now all we have to do is divide by 2. So, the area is 2x^2-9x-4/2. You can simplify that. Answer is up top.

7 0

2 years ago

Custodian at Movie Theater

ollegr [7]

Answer:

1) A week: $151.74

2) A month : $606.96

3) A years : $7890.48

Step-by-step explanation:

Custodian at Movie Theater

pay:$9.95

per hours:

15.25 hours per week

How much do they make in

1) a- week

1 week = 15.25 hours

Hence,

1 hour = $9.95

15.25 hours = x

Cross Multiply

x = 15.25 × $9.95

x = $151.7375

Approximately = $151.74

2) A month

There are 4 weeks in a month

1 week = $151.74

4 weeks = x

Cross Multiply

x = 4 × $151.74

x = $606.96

3) A year

There are 52 weeks in a year

Hence,

1 week = $151.74

52 weeks = x

Cross Multiply

x = 52 × $151.74

x = $7890.48

Therefore, they made in :

1) A week: $151.74

2) A month : $606.96

3) A years : $7890.48

5 0

2 years ago