What is the vertex of x2 + 8x + 12?

Answer:

k ≈ - 0.069

Step-by-step explanation:

Given

A = 800 [tex]e^{kt}[/tex]

Substitute A = 400 and t = 10 into the equation

400 = 800 [tex]e^{10k}[/tex] ( divide both sides by 800 )

0.5 = [tex]e^{10k}[/tex] ( take the ln of both sides )

ln [tex]e^{10k}[/tex] = ln0.5

10k lne = ln0.5 [ lne = 1 ]

10k = ln 0.5 ( divide both sides by 10 )

k = [tex]\frac{ln0.5}{10}[/tex] ≈ 0.069 ( to the nearest thousandth )

Answer:

Step-by-step explanation:

400 = 800 * e^(k*t)

What are the units of t? I'm taking it as years.

Divide by 800

400/800 = e^(k*10)

1/2 = e^(k*10)

ln(1/2) = ln(e)^(k*10)

ln(1/2) = k*10 * ln(e)

ln(e) = 1

-0.69314 = k*10

-0.069314 = k

Check

A = 800 e^(-0.069314*10)

A = 800 e^(-0.69314)

A = 800 * 0.50000359

A = 400.0028722

Which is close enough to 400

Answer:

x = -7 or 7

Step-by-step explanation:

x² - 49 = 0

→ Factorise

( x + 7 ) ( x - 7 )

→ Solve

x = -7 or 7

Answer:

(x + 7) (x - 7) = 0

x + 7 = 0 and x - 7 = 0

So, x = +7 and -7

Hope this helps!

Answer:

Step-by-step explanation:

since 3 is outside the parenthesis (n + 2) you multiply the 3 by the n and the 2 and

3n + 6

next subtract the 6 and add the 6 to the other side

3n - 6 = 6

3n = 6

n = 2

Answer:

1. 21%   2.  70%

Step-by-step explanation:

1. 21 out of 100 are filled in

2. 7/10 are filled in

Answer:

11

Step-by-step explanation:

Answer:

Around 0.40

Step-by-step explanation

If she doubles the gift every year, do 18x2=36, 36 rounds to 40 or 0.40.

The total of all the gifts on the girl's 18th birthday given from her grandma for this considered case is  evaluated as 2621.43 dollars

Lets suppose the geometric sequence has its initial term is [tex]a[/tex], multiplication factor is  r, then, its sum is given as:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

The sequence would look like [tex]a, ar, \cdots, ar^{n-1},\cdots[/tex]

For this case, we are specified that:

That shows that the gift amounts each year will form a geometric sequence where a = 1, and r = 2 (as amounts are doubled).

The gift amounts would look like:

[tex]\\1, 2, 4, \cdots\\or\\1, 2\times 1, 2^2 \times 1, \cdots[/tex]

We have to find these terms' sum till 18th term(18th term is the gift of her 18th birthday).

Thus, we have: n = 18, a = 1, and r = 2.

The sum will be:

[tex]S_n = \dfrac{a(r^n-1)}{r-1} = \dfrac{1(2^{18}-1)}{2-1} = 2^{18} - 1 = 262143 \: \rm cents[/tex]

There are 100 cents in 1 dollars,

Thus, 1 cent = 0.01 dollars,

and thus, 262143 cents form 2621.43 dollars.

Thus, the total of all the gifts on the girl's 18th birthday given from her grandma for this considered case is  evaluated as 2621.43 dollars

Learn more about sum of terms of geometric sequence here:

https://brainly.com/question/1607203

Answer:

B.

Step-by-step explanation:

It only has one base and it's a pentagon. Therefore, it's a pentagonal pyramid.

Answer:

C. Reflection over x- axis, down 6 right 3

Step-by-step explanation:

Answer:

The angles are proportional and the side lengths are proportional.

Step-by-step explanation:

Savaas Realize

Answer:

yes it is good luck with your work

Answer:

$7500

Step-by-step explanation:

Given

[tex]I = 525[/tex]

[tex]R = 3.5\%[/tex]

[tex]T =2[/tex]

Required

The Principal

This is calculated using:

[tex]I =PRT[/tex]

Make P the subject

[tex]P = \frac{I}{RT}[/tex]

So, we have:

[tex]P = \frac{525}{3.5\% * 2}[/tex]

[tex]P = \frac{525}{7.0\%}[/tex]

[tex]P = 7500[/tex]

Answer:

4

Step-by-step explanation:

You can divide both numbers by four and get an even answer

Answer:

4

Step-by-step explanation:

Answer:

A. 130°

Step-by-step explanation:

Answer:130

Step-by-step explanation:

I just finished the quiz :)

Answer:

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{x +2}{4}=8}[/tex]

[tex]\large\textsf{MULTIPLY 4 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{x +2}{4}\times4=8\times4}[/tex]

[tex]\large\textsf{CANCEL out: 4}\times\large\textsf{4.}[/tex]

[tex]\large\textsf{KEEP: 8}\times\large\textsf{4 because it helps you solve for x}[/tex]

[tex]\mathsf{8\times4=\bf 32}[/tex]

[tex]\large\text{New equation: \textsf{x + 32 = \bf 32}}[/tex]

[tex]\large\textsf{x + 2 = 32}[/tex]

[tex]\large\textsf{SUBTRACT 2 to BOTH SIDES}[/tex]

[tex]\mathsf{x +2-2=32-2}[/tex]

[tex]\large\textsf{CANCEL out: 2}-\large\textsf{2 because that gives you 0}[/tex]

[tex]\large\textsf{KEEP: 32}-\large\textsf{2 because that helps you solve for x}[/tex]

[tex]\large\textsf{New EQUATION: \mathsf{x = 32 - 2}}[/tex]

[tex]\mathsf{x = 32 - 2}[/tex]

[tex]\large\textsf{Simplify above and you have your result to this equation}[/tex]

[tex]\mathsf{32-2=\bf 30}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf x =30}}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Hi, there your answer will C. 85pi ft^2

Step-by-step explanation:

pi(5)(12)+pi(5)^2

60pi+25pi

85pi ft^2

Hope this helps :)

An

Step-by-step explanation:

Cx+y s 100

Answer:

All the inequalities that model the constraints for this situation:

(d) x + y < 200 ;

(e) 0.75 x + 0.50 y ≥ 100

Step-by-step explanation:

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

As, x represent the number of candy bars sold & y represent the number of bags of chips sold.

It is given that,

price for one candy bar =  $0.75

also, price for one dag of chips = $0.50

So, price for 'x' candy bar =  $0.75x

also, price for 'y' of chips = $0.50 y

Is is mentioned in question, the sale of candy bar and bag of chips shoud be atleast $100.  

the First ineqaulity be,

0.75 x + 0.50 y ≥100

(which should the sales of candy baar and dag of chips be equal to 100 dollar or greater than 100 dollar)

Now, the second situation

Again, it is mentioned in the question is number of units (candy bar and dag of chips)  should be not more than 200 units.

the second inequality be,

x+ y < 200

(which shows that number of candy bar and dag of chips should be less than 200 units.)

All the inequalities that model the constraints for this situation

(d) x + y < 200

(e) 0.75 x + 0.50 y ≥100

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ2

To find the total cost you need to multiply the hourly rate by the number of hours they work and add the fixed fee.

C = 17h + 15

Answer:

240 million

Step-by-step explanation:

I took the application

Answer:

Center = (-1, 1)

Radius = 3

Graphing form

(x + 1)² + (y - 1)² = 3²

General form

x² + y² + 2x - 2y - 7 = 0

Step-by-step explanation:

Center = (-1, 1)

Radius = 3

Graphing form

(x + 1)² + (y - 1)² = 3²

General form   \Expand graphing form\

(x² + 2x + 1) + (y² - 2y + 1) - 9 = 0

Rearrange

x² + y² + 2x - 2y - 7 = 0

Answer:

B

Step-by-step explanation:

Answer:

5.831

Step-by-step explanation:

Distance between both given points=Lenght=5.831

Answer:

0

Step-by-step explanation:

Anything multiplied by 0 is 0. sorry if i did it wrong

Answer:

C

Step-by-step explanation:

1. The domain is the x-value of a function.

2. In that image, the x-values are the numbers on the left of each parenthesis.

3. You should put the domains in increasing order, so the final answer is -2, 0, 2, 4.