Ask question

Ask question

All categories

1 year ago

11

Write f(x) = 2x2 44x + 185 in vertex form. to write f(x) = 2x2 44x + 185, factor out from the first two terms. next, form a perf

ect square trinomial keeping the value of the function equivalent: f(x) = 2(x2 22x + 121) + 185 242 the function written in vertex form is f(x) = (x )2 + .

2 answers:

Leona [35]1 year ago

7 0

The function is:
f ( x ) = 2 x² - 44 x + 185
f ( x ) = 2 ( x² - 22 x + 121 - 121 ) + 185 =
= 2 ( x² - 22 x + 121 ) - 242 + 185 =
= 2 ( x - 11 )² - 57
Answer:
The vertex is ( 11, - 57 ) and the vertex form is: f ( x ) = 2 ( x - 11 )² - 57

RUDIKE [14]1 year ago

7 0

Answer:

To write f(x) = 2x2 – 44x + 185, factor out 2 from the first two terms.

Next, form a perfect square trinomial keeping the value of the function equivalent:

f(x) = 2(x2 – 22x + 121) + 185 – 242

The function written in vertex form is f(x) = 2 (x – 11 )2 + -57.

You might be interested in

A recent article in Business Week listed the "Best Small Companies." We are interested in the current results of the companies'

Sindrei [870]

Answer:

(i) The estimated regression equation is;

$\hat y$ ≈ 1.6896 + 0.0604·X

The coefficient of 'X' indicates that $\hat y$ increase by a multiple of 0.0604 for each million dollar increase in sales, X

(ii) The estimated earnings for the company is approximately $4.7096 million

(iii) The standard error of estimate is approximately 29.34

The high standard error of estimate indicates that individual mean do not accurately represent the population mean

(iv) The coefficient of determination is approximately 0.57925

The coefficient of determination indicates that the probability of the coordinate of a new point of data to be located on the line is 0.57925

Step-by-step explanation:

The given data is presented as follows;

$\begin{array}{ccc}Sales \ (\$million)&&Earning \ (\$million) \\89.2&&4.9\\18.6&&4.4\\18.2&&1.3\\71.7&&8\\58.6&&6.6\\46.8&&4.1\\17.5&&2.6\\11.9&&1.7\end{array}$

(i) From the data, we have;

The regression equation can be presented as follows;

$\hat y$ = b₀ + b₁·x

Where;

b₁ = The slope given as follows;

$b_1 = \dfrac{\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}{\Sigma(x_i - \overline x)^2}$

b₀ = $\overline y$ - b₁· $\overline x$

From the data, we have;

${\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}$ = 364.05

$\Sigma(x_i - \overline x)^2}$ = 6,027.259

$\overline y$ = 4.2

$\overline x$ = 41.5625

∴ b₁ = 364.05/6,027.259 ≈ 0.06040059005

b₀ = 4.2 - 0.06040059005 × 41.5625 ≈ 1.68960047605 ≈ 1.69

Therefore, we have the regression equation as follows;

$\hat y$ ≈ 1.6896 + 0.0604·X

The coefficient of 'X' indicates that the earnings increase by a multiple of 0.0604 for each million dollar increase in sales

(ii) For the small company, we have;

X = $50.0 million, therefore, we get;

$\hat y$ = 1.6896 + 0.0604 × 50 = 4.7096

The estimated earnings for the company, $\hat y$ = 4.7096 million

(iii) The standard error of estimate, σ, is given by the following formula;

$\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu \right )^{2} }{n - 1}}$

Where;

n = The sample size

Therefore, we have;

$\sigma =\sqrt{\dfrac{6,027.259 }{8 - 1}} \approx 29.34$

The standard error of estimate, σ ≈ 29.34

The high standard error of estimate indicates that it is very unlikely that a given mean value within the data is a representation of the true population mean

(iv) The coefficient of determination (R Square) is given as follows;

$R^2 = \dfrac{SSR}{SST}$

Where;

SSR = The Sum of Squared Regression ≈ 21.9884

SST = The total variation in the sample ≈ 37.96

Therefore, R² ≈ 21.9884/37.96 ≈ 0.57925

The coefficient of determination, R² ≈ 0.57925.

Therefore, by the coefficient of determination, the likelihood of a new introduced data point to located on the line is 0.57925

6 0

2 years ago

A 250-kVA, three-phase, 480-volt transformer requires 75 gallons of insulating oil to keep it properly cooled. How many liters i

Dennis_Churaev [7]

This problem can be directly solved by using a conversion factor. Simple research will tell us that 1 gallon contains about 3.78 Liter. Therefore the volume in Liter is:

volume = 75 gallons * (3.78 Liter / gallon)

<span>volume = 283.5 Liters</span>

7 0

1 year ago

Which polynomial correctly combines the like terms and expresses the given polynomial in standard form?

dimaraw [331]

Answer:

D) n^6 - 6m^6 + 7mn^5 + 14m^2n^4 -5m^3 n^3

Step-by-step explanation:

The given polynomial is 8mn^5 -2m^6 +5m^2 n^4 - m^3 n^3 + n^6 - 4m^6 + 9m^2n^4 -mn^5 - 4m^3n^3

Now we have to identify the like terms and simplify.

Like terms are nothing but the terms which have the same variables with same powers.

= (8mn^5 - mn^5) -2m^6 - 4m^6 + 5m^2 n^4 + 9m^2 n^4 - m^3n^3 - 4m^3n^3 +n^6

Now combine the like terms

= 7mn^5 - 6m^6 +14m^2 n^4-5m^3n^3 + n^6

It can be written in standard form

= n^6 - 6m^6 + 7mn^5 + 14m^2n^4 -5m^3 n^3

The answer is D)

Hope this will helpful.

Thank you.

6 0

1 year ago

Read 2 more answers

Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB =

FromTheMoon [43]

Answer:

Here is the question attached with.

$m\angle CEA =90 \ (deg)$

$m\angle BEF=135\ (deg)$

$\angle CEF$ is a straight line.

$\angle AEF$ is a right angled triangle.

Options $1,4,5,6$ are correct answers.

Step-by-step explanation:

⇒As $\ ray\ AE$ is ⊥ $FEC$ so it will forms right angled triangle then $m\angle CEA =90\ (deg)$ .

⇒Measure of $\angle BEF =135\ (deg)$ as $\angle BEF =\angle AEB +\angle AEF = (45+90)=135\ (deg)$ as $\angle AEB$ is the bisector of $\angle AEC$ ,meaning that $\angle AEB$ is half of $\angle AEC$ so $\angle AEB = 45\ (deg)$ .

⇒ $\angle CEF$ is a straight line as the angles measure over it is $180\ (deg)$ .

⇒Measure of $\angle AEF = 90\ (deg)$ from linear pair concept.

As $\angle CEA + \angle AEF = 180\ (deg)$ ,plugging the values of $m\angle CEA =90\ (deg)$ we have $\angle AEF = 90\ (deg)$ .

The other two options are false as:

$m\angle CEF=m\angle CEA + m\angle BEF = (90+135)=225$

it is exceeding $180\ (deg)$ whereas $\angle CEF$ is a

straight line.

And $m\angle CEB=2(m\angle CEA)$ is not true.

As $\angle CEA = 90\ (deg)$ and $\angle CEB=45\ (deg)$

So we have total $4$ answers.

The correct options are $1,4,5,6$ .

5 0

2 years ago

Read 2 more answers

Suppose we have two thermometers. One thermometer is very precise but is delicate and heavy (X). We have another thermometer tha

makvit [3.9K]

Answer:

Step-by-step explanation:

(a) H0: μ_D=0

Ha: μ_D ≠ 0

b) Find attached the solution

(c) By technology,

p - value = 0.4437

Hence, the p-value is 0.4437

8 0

1 year ago