Ask question

Ask question

All categories

4 years ago

9

Given f(x)=x2+14x+40 . Enter the quadratic function in vertex form in the box. f(x)=

1 answer:

sukhopar [10]4 years ago

6 0

We know that
the quadratic function in vertex form is--------------> y=a*(x-h)²+k

we have
f(x)=x²<span>+14x+40
y=</span>x²+14x+40

We can convert to vertex form by completing the square on the right hand side
y-40=x²+14x
y-40-49=x²+14x-49------> subtract 49 on BOTH sides to preserve the equality
y-40=(x²+14x+49)-49
y=(x²+14x+49)-49+40---------> y=(x+7)²-9

the answer is
the quadratic function in vertex form-----------> y=(x+7)²-9
<span>the vertex is the point (-7,-9)

</span>

You might be interested in

⚠️HELP DUE TODAY⚠️

IceJOKER [234]

Answer: (why is it 5 points?) Thats ok.

5 times what X is - 24 meaning whatever X is also by sry i don't make a lot of sense but i'm smart and know the answer. I will change it later after i find out which shouldn't take too long.

Step-by-step explanation:

Thanks, stay safe, have a great life! Byes! Brainliest then i will give answer! ;) :) :P XD :3 (: hehe :)

6 0

3 years ago

Clara went to a music store and brought some CDs and DVDs. She paid $14 for each CD and $17 for each DVD. Let x represent the nu

Effectus [21]

14x+17y= total spent

7 0

3 years ago

How many solutions does the following system of equations have? 2y=5x+4 y=3x+2 a. infinite many b.2 c.1 d.0

ella [17]

2y=5x+4
y= 3x+2

2(3x+2) = 5x+4
6x +4 = 5x+4
6x-5x=4-4
x=0-----------------------> y=3x+2
y=3(0)+2 = 0+2
y=2
solution (0,2) one point c.

8 0

3 years ago

A box with a square base and open top must have a volume of 157216 cm3. We wish to find the dimensions of the box that minimize

shepuryov [24]

Answer:

Base Length of 68cm
Height of 34 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 157216 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume $=x^2h=157216$

$h=\dfrac{157216}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{157216}{x^2}\\A(x)=x^2+4x\left(\dfrac{157216}{x^2}\right)\\A(x)=\dfrac{x^3+628864}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+628864}{x}\\A'(x)=\dfrac{2x^3-628864}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-628864}{x^2}=0\\2x^3-628864=0\\2x^3=628864\\x^3=314432\\x=\sqrt[3]{314432}\\ x=68$

Step 4: Verify that x=68 is a minimum value

We use the second derivative test

$If\:A(x)=\dfrac{x^3+628864}{x}\\A''(x)=\dfrac{2x^3+1257728}{x^3}\\$When x=68\\A''(x)=6$

Since the second derivative is positive at x=68, then it is a minimum point.

Recall:

$h=\dfrac{157216}{x^2}\\h=\dfrac{157216}{68^2}=34$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 68cm
Height of 34 cm.

3 0

3 years ago

If $396 is invested at an interest rate of 13% per year and is compounded continuously, how much will the investment be worth in

Vilka [71]

Answer: First option is correct.

Step-by-step explanation:

Since we have given that

Amount invested = $396

Interest rate = 13% per year

Time = 3 years

We will use the "Exponential growth formula" i.e.

$A=Pe^{rt}$

Here,

P denotes Principle amount

r denoted rate of growth

t denotes number of years,

So, it becomes

$A=396e^{0.13\times 3}\\\\A=396e^{0.69}\\\\A=\$584.88$

Hence, First option is correct.

3 0

3 years ago

Read 2 more answers