MATHEMATICS HIGH SCHOOL

Paul opened a bakery. The net value of the bakery (in thousands of dollars) ttt months after its creation is modeled by v(t)=2t^2-12t-14v(t)=2t 2 −12t−14v, left parenthesis, t, right parenthesis, equals, 2, t, squared, minus, 12, t, minus, 14 Paul wants to know what his bakery's lowest net value will be. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation.

Answers

Answer 1

Answer:

Given:

The net value of the bakery (in thousands of dollars) t months after its creation is modeled by

$v(t)=2t^2-12t-14$

Paul wants to know what his bakery's lowest net value will be.

To find:

The function in a different form (factored or vertex) where the answer appears as a number in the equation.

Solution:

Factor form is used to find the x-intercepts and vertex form is used to find the extreme values (maximum or minimum). So, here we need to find the vertex form.

We have,

$v(t)=2t^2-12t-14$

$v(t)=2(t^2-6t)-14$

Adding and subtract square of half of 6 in the parenthesis, we get

$v(t)=2(t^2-6t+3^2-3^2)-14$

$v(t)=2(t^2-6t+3^2)+2(-9)-14$

$v(t)=2(t-3)^2-18-14$ $[\because (a-b)^2=a^2-2ab+b^2]$

$v(t)=2(t-3)^2-32$

Vertex form:

$f(x)=a(x-h)^2+k$

where, (h,k) is vertex.

On comparing this equation with vertex form, we get the of the function is (3,-32).

Therefore, the vertex form is $v(t)=2(t-3)^2-32$ and the function has minimum value at (3,-32). It means, minimum net value of the bakery is -32 after 3 months.

Answer 2

Answer:

The vertex form is v(t) = 2(t - 3)² - 32 and the function has a minimum value at (3,-32). It means the minimum net value of the bakery is -32 after 3 months.

Given that,

Paul opened a bakery.

The net value of the bakery (in thousands of dollars) t months after its creation is modelled by the equation v(t) = 2t²- 12t - 14.

Paul wants to determine the bakery's lowest net value.

To rewrite the function in a different form,

Find the vertex of the quadratic equation.

The vertex form of a quadratic equation is given by,

v(t) = a(t-h)² + k,

Where (h, k) represents the coordinates of the vertex.

Proceed, v(t) = 2t² - 12t - 14,

v(t) = 2(t² - 6t) - 14,

v(t) = 2(t² - 6t + 3² - 3²) - 14

v(t) = 2(t - 3)² - 32

Vertex form:

v(t) = a(t-h)² + k,

where, (h,k) is vertex.

On comparing this equation with vertex form, we get the function is (3,-32).

Therefore,

The vertex form is v(t) = 2(t - 3)² - 32 and the function has a minimum value at (3,-32). It means minimum net value of the bakery is -32 after 3 months.

To learn more about quadratic equations visit:

brainly.com/question/30098550

#SPJ3

Related Questions

A rectangles length is 7 inches greater than its width. If the perimeter of the rectangle is 110 inches, find its length and width. I think it's w (w+7)=110
Sins = 8x2 and = 2x + a find 5- o
Alina measured a distance to be 2.18 miles. What is the margin of error?
Sunshine Honda sold 112 cars this month. If that is 40% greater than last month, how many cars were sold last month?
Use substitution to solve this system of equations:5x+y=10,y=x+4.

I would appreciate if u guys would help me rn.

Answers

Answer:

11 is 18.54 ft 12 is 351.86 cm 13 is 109.96 inches

Step-by-step explanation:

Explain how a number and its reciprocal are related

Answers

A number's reciprocal when multiplied by the original form of the number is, and always will be, 1.

PPPPPPPPPPPLLLLLLLLLLZZZZZZZ HELPPPPP I WILL GIVE 50 POINTS

Answers

Hello!

Reading these types of graphs can be difficult, but it displays the following numbers:

27, 30, 31, 43, 45, 49, 51, 58, 62, 64

To find mean, or average, you need to add up all of the numbers and divide by how many there are (10)

This will give you 46.

I hope this helps you and good luck!

Your answer should be 46.

Hope it helps!

Solve for x.

3x - 4 = 13

Answers

The solution of expression is,

⇒ x = 5.67

We have to given that;

Expression is,

⇒ 3x - 4 = 13

Now, We can simplify as;

⇒ 3x - 4 = 13

Add 4 both side, we get;

⇒ 3x - 4 + 4 = 13 + 4

⇒ 3x = 17

Divide by 3;

⇒ x = 17/3

⇒ x = 5.67

Thus, The solution of expression is,

⇒ x = 5.67

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

We want the value of x. Add 4 to both sides to cancel out the -4 on the left.
3x=17
Now divide both sides by 3 to get the answer.
x=5.66666667

What is the domain of y=4[x+2]

Answers

Answer:

$-\infty \:<x<\infty \:\nor\n\left(-\infty \:,\:\infty \:\right)$

Step-by-step explanation:

$\mathrm{Domain\:of\:}\:4\left(x+2\right)\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \n \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$