All categories

4 years ago

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

1 answer:

8 0

Please indicate exponentiation using " ^ " Thanks.

f(x)=x2+14x+40 => f(x)=x^2+14x+40

Next, complete the square:

f(x)=x^2+14x+ 49 - 49 +40 = (x+7)^2 - 9

Write this in the form y = (x+7)^2 - 9 or y + 9 = (x+7)^2
Comparing this result to y = a(x-h)^2 + k, we see that h = -7 and k=-9

In vertex form, the equation is y + 9 = (x+7)^2 and the vertex is at (-7, -9).

You might be interested in

List all prime fractors of the composite number 50

Misha Larkins [42]

The factors of 50 are 1, 2, 5, 10, 25 and 50. The factors of a number can be found by determining which numbers evenly divide into a given number.

3 0

3 years ago

A tank is filled at a constant rate. 10 minutes after filling is started, the tank contains 4.8L of water. After 35 minutes the

Mashcka [7]

Answer:

Part A)

0.1 liters per minute.

Part B)

There was initially 3.8 liters of water.

$\displaystyle V(t) = 0.1(t - 10) + 4.8$

Part C)

562 minutes.

Step-by-step explanation:

A tank is filled at a constant rate. After 10 minutes, the tank contains 4.8 L of water and after 35 minutes, the tank contains 7.3 L of water.

Part A)

We can represent the current data with two points: (10, 4.8) and (35, 7.3). The x-coordinate is measured in minutes since the tank began to be filled and the y-coordinate is measured in how full the tank is in liters.

To find the rate at which the tank is being filled, find the slope between the two points:

$\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(7.3)-(4.8)}{(35)-(10)} = \frac{2.5}{25} = 0.1$

In other words, the rate at which the tank is being filled is 0.1 liters per minute.

Part B)

To find the function of the volume of the tank, we can use the point-slope form to first find its equation:

$\displaystyle y - y_1 = m( x - x_1)$

Where m is the slope/rate of change and (x₁, y₁) is a point.

We will substitute 0.1 for m and let (10, 4.8) be the point. Hence:

$\displaystyle y - (4.8) = 0.1(x - 10)$

Simplify:

$\displaystyle y = 0.1(x-10) + 4.8$

Since y represent how full the tank is and x represent the time in minutes since the tank began to be filled, we can substitute y for V(t) and x for t. Thus, our function is:

$\displaystyle V(t) = 0.1(t - 10) + 4.8$

The initial volume is when t = 0. Evaluate:

$\displaystyle V(0) = 0.1 ((0) - 10) + 4.8 = 3.8$

There was initially 3.8 liters of water.

Part C)

To find how long it will take for the tank to be completely filled given its maximum capacity of 60 liters, we can let V(t) = 60 and solve for t. Hence:

$60 = 0.1(t - 10) + 4.8$

Subtract:

$55.2 = 0.1(t - 10)$

Divide:

$552 = t - 10$

Add. Therefore:

$t = 562\text{ minutes}$

It will take 562 minutes for the tank to be completely filled.

8 0

3 years ago

Is Zero a Positive Number or a Negative Number or a Neutral Number?

sergeinik [125]

Its a neutral number cause it has no value since its worth nothing at all, when u add it with something the number ur adding it with will be that number instead of 0, (like for ex 2 + 0 = 2) 0 cant be positive since on a number line its not on the right and it cant be negative since its not on the left, so its neutral in the middle.

4 0

3 years ago

Read 2 more answers

Anybody know the answer?

german

The answer 1 because because 1-cosx^2 =sinx^2 and cotx^2+1=cscx^2 =1/sinx^2 and sinx^2/sinx^2=1
Hope, help and Heal.

5 0

3 years ago

Can you help me!!!!!!!!

liubo4ka [24]

Answer:

Step-by-step explanation:

8 0

3 years ago

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

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