Secondary succession occurs following triggers such as logging, mining, wildfires, or

drought. The presence of soil nutrients allows for a faster recovery.

Hardwood trees

Pine trees

Perennials

and

grasses

Shrubs

Answer: a = -2  and  c = 7

Step-by-step explanation:

(this answer uses some basic calculus)

We know that [tex]f'(x) = 2ax + 4[/tex], and since [tex](1,9)[/tex] is a maximum of [tex]f[/tex], then [tex]f'(1) = 0[/tex]. That means [tex]2a + 4 = 0[/tex], so [tex]\boxed{a = -2}[/tex]. Then since [tex]f(1) = 9[/tex], we have [tex]-2(1)^2 + 4(1) + c = 9[/tex], so [tex]\boxed{c = 7}[/tex].

Answer:

a = -2

c = 7

Step-by-step explanation:

Given the quadratic function, f(x) = ax² + 4x + c, for which its vertex is the maximum point occurring at (1, 9), and b = 4.

Since the x-coordinate of the vertex, x = 1, can be calculated using the formula, [tex]x = \frac{-b}{2a}[/tex]:

We can substitute the value of the x-coordinate and b = 4 into the formula, and solve for the value of a:

[tex]x = \frac{-b}{2a}[/tex]

[tex]1 = \frac{-4}{2a}[/tex]

Multiply both sides by 2a:

(2a) 1 =  [tex]\frac{-4}{2a} (2a)[/tex]

2a = -4

Divide both sides by 2 to solve for a:

[tex]\frac{2a}{2} = \frac{-4}{2}[/tex]

a = -2

Therefore, the value of a = -2.

Next, to solve for c, substitute the coordinate values of the vertex, (1, 9) into the given quadratic function:

f(x) = ax² + 4x + c

9 = -2(1)² + 4(1) + c

9 = -2 + 4 + c

9 = 2 + c

Subtract 2 from both sides to isolate c:

9 - 2 = 2 - 2  + c

7 = c

In order to double-check the validity of our values for a and c, substitute a = -2, and c = 7 into the function, along with the coordinates of the vertex, (1, 9):

f(x) = -2x² + 4x + 7

9 = -2(1)² + 4(1) + 7

9 = -2 + 4 + 7

9 = 9 (True statement).

Therefore, the correct answers are: a = -2, and c = 7.

Answer:

E=10.353

Step-by-step explanation:

First plug in all the numbers: 1.960(31.25/[tex]\sqrt{35}[/tex])

solve: E=10.353

Step-by-step explanation:

I am not sure, what is the level of math for you currently.

do you do differentiation and derivatives already ?

because that is how I find "extreme points" and "turning points" of a function right away.

the vertex is the turning point for a quadratic parabola.

that means the point where the slope (= the first derivative) of the function is 0.

and that is also where the axis of symmetry is.

8x - 8 = 0

8x = 8

x = 1 (axis of symmetry).

y = 4×1² - 8×1 = 4 - 8 = -4

so, the vertex is (1, -4)

in case you don't understand derivatives yet, there is a shortcut for this for quadratic equations (fyi - in fact, the generic result of the first derivative) :

y = ax² + bx + c

the x value for the axis is then

x = -b/(2a)

in our case

a = 4

b = -8

x = - -8/8 = 8/8 = 1

and then y is calculated as above.

Answer:

-1.8 million. This means that the business likely spent a lot on production and generated very little sales during the first year.

Step-by-step explanation:

2.3 - 4.1= -1.8

Answer:

Unicorn a : 1,160, and Unicorn b : 290

Step-by-step explanation:

We can make this an equation

Unicorn a is 4x

Unicorn b is x

4x + x = 1,450

x = 290

Unicorn a : 4•290= 1160 years old

Unicorn b : is 290 years old

Hello there! :)

Parallel lines have identical slopes.

So if one line has a slope of 2, then the line parallel o it would have the same slope.

Now, use the Point-Slope form:

y-y1=m(x-x1)

y-3=2(x-(-2)

y-3=2x+4

y=2x+4+3

y=2x+7

Hope this helps!

~Just a cheerful gal

#CarryOnLearning

[tex]SilentNature :)[/tex]

Answer:

2%

Step-by-step explanation:

Answer:

I don’t know

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

because the x equals 7 and then the line would pass through (7,-3)

Answer:

3

Step-by-step explanation:

bookstore is two blocks east of town hall: 0+2=2

the hardware store is three blocks east of the bookstore: 2+3=5

the bank is eight blocks west of the hardware store: 5-8=-3

place an empty store in the opposite location of the bank: opposite of -3 is 3

Answer:

R is 4*Pi*R2

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Let's simply the given expression ~

Answer:

show the question

Step-by-step explanation:

6/6, simplified to 1,

negative slope so -1

Divide everything by half

Since she doubled the recipes, divide all by half.

1 cup of sugar / 2 = 1/2 cup of sugar

3 1/2 cups of flour / 2 = 7/2/2 cups of flour = 7/4 cups of flour or 1 3/4 cups of flour.

Answer:

Sugar: 1/2  Flour: 1 3/4

Step-by-step explanation:

1 cup of sugar

3 1/2 cups of flour

Since the recipe is doubled you'll divide the ingredients by 2.

Sugar: 1÷2=1/2

Flour: 3 1/2÷2=7/4

=1 3/4

Hope this helps :)

Answer:

(n/5)+4

Step-by-step explanation:

I think you were asking for the equation?

Answer:

X/5 + 4

Step-by-step explanation:

X is the “number”

Answer:

She ate 5/12 of carrot hope it's help

My ans is C

24 - 6x + 40 = 34

24+40 - 6x = 34

64 - 6x = 34

6x = 64-34

6x = 30

x = 5 ^^

A) S(x) = 18x + -36005

B) 18

C) 2013

Step-by-step explanation:

A. Take two pairs of points:

Find the rate of change:

This is the rate, $0.50 per minute

B. Take one pair of points (120, 40) to show the relationship between number of minutes and the cost:

A list of choices that appears on a computer screen when a person clicks on the menu title To print the document click on print in the file drop down menu

Answer:

Area= 100 inches square.

Step-by-step explanation:

4(x-1)=36

4x-4=36

4x=40

x=10

10×10=100

Answer:

Alex can jump 50 times in one minute.

Step-by-step explanation:

1.) Start off by creating your equation.

It says that Anna can jump 35 times in one minute. It continues to say, that this value IS 70% as many as Alexander can jump in one minute. Thus, your equation should look like this:

x represents the number of jumps Alexander can do in one minute

35 = 0.70x

2.) Solve for x

35 = 0.70x

35/0.70 = x

50 = x

I hoped this helped. Good luck!

You just have to underline the word that connects two sentences .

for example: In number 2. Sophia ate a lot. She is still hungry. These are two sentences the word 'yet' connects two sentences. that is called conjunction.

1.= under line so

2.= under line yet

3.= under line but

4.= under line so

32,760 is the answer!!