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3 years ago

Using the completing-the-square method, rewrite f(x) = x2 - 8x + 3 in vertex form.

Mathematics

1 answer:

Leto [7]3 years ago

5 0

Answer:

Step-by-step explanation:

Given

f(x) = x² - 8x + 3

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 8x

x² + 2(- 4)x + 16 - 16 + 3

(x - 4)² - 13 ← in vertex form → B

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True or False:

Naya [18.7K]

we can check if a given sequence is geometric or not by checking the terms present in it ,

Let us find ratio of each term with it's previous term

if that ratio comes out same for every two consecutive terms then it is a geometric sequence , otherwise it is not geometric sequence .

Let us work on first one : given is : -1,1,-1,1.............

second term/ first term = 1/-1 = -1

third term/ second term = -1/1 = -1

fourth term / third term = 1/-1 = -1

fifth term/ fourth term = -1/1 = -1

because that ratio is same so it is a geometric sequence .

* let us now work with second sequence .

second term/ first term = -6/-2 = 3

third term/ second term = -18/ -6 = 3

fourth term / third term = -54 / -18 = 3

hence this is also geometric sequence .

Answer : both are geometric sequence .

6 0

3 years ago

A line passes through the points (-8, 1) and (-1, 6). A second line passes through the points (-3,0) and (-8,-5). What is the po

finlep [7]

$\begin{gathered} y=mx+b \\ m=\frac{6-1}{-1+8}=\frac{5}{7} \\ 6=\frac{5}{7}(-1)+b \\ 6+\frac{5}{7}=b \\ b=\frac{42+5}{7}=\frac{47}{7} \\ y=\frac{5}{7}x+\frac{47}{7} \end{gathered}$

For the second line

$\begin{gathered} y=mx+b \\ m=\frac{-5-0}{-8+3}=\frac{-5}{-5}=1 \\ 0=1(-3)+b \\ b=3 \\ y=x+3 \end{gathered}$

The intersection will be

$\begin{gathered} y=\frac{5}{7}x+\frac{47}{7} \\ x+3=\frac{5}{7}x+\frac{47}{7} \\ x-\frac{5}{7}x=\frac{47}{7}-3 \\ \frac{7x-5x}{7}=\frac{47-21}{7} \\ \frac{2x}{7}=\frac{26}{7} \\ 14x=182 \\ x=\frac{182}{14} \\ x=13 \\ \\ y=13+3=16 \end{gathered}$

Therefore, the point of intersection is (13, 16)

6 0

1 year ago

The cost in dollars of producing x vehicles for a company is given by C(x)=1200x+5500

GarryVolchara [31]

The rate of change represents the variable production cost rate. The production cost is increased in 1200 units per each additional manufactured car.

<h3>Interpretation of a linear function</h3>

Let be $C$ and $x$ the production cost and the number of vehicles produced, it there is a linear relationship between the two variables, then we have the following formula:

$C(x) = \dot r \cdot x + C_{o}$ (1)

Where:

$C_{o}$ - Fixed production costs.
$\dot r$ - Variable production cost rate.

In a nutshell, the rate of change represents the variable production cost rate. The production cost is increased in 1200 units per each additional manufactured car. $\blacksquare$

To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/8223651

7 0

3 years ago

Hey please help me if you can I would appreciate it

PolarNik [594]

This is a division problem.
You need to divide 51/2 by 3/2.

$\dfrac{51}{2} \div \dfrac{3}{2} =$

$= \dfrac{51}{2} \times \dfrac{2}{3}$

$= \dfrac{51 \times 2}{2 \times 3}$

$= \dfrac{102}{6}$

$= 102 \div 6$

$= 17$

Answer: Choice D.

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3 years ago

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Art [367]

Answer:

4 im pretty sur

Step-by-step explanation:

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3 years ago