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2 years ago

Solve the equation 4n2 − 16n − 84 = 0 by completing the square.

Mathematics

1 answer:

melomori [17]2 years ago

8 0

4n² - 16n - 84 = 0

Multiply both sides by 1/4 :

n² - 4n - 21 = 0

Add 21 to both sides:

n² - 4n = 21

Complete the square by adding 4 to both sides:

n² - 4n + 4 = 25

(n - 2)² = 25

Solve for n :

n - 2 = ± √25

n - 2 = ± 5

n = 2 ± 5

Then n = 2 + 5 = 7 or n = 2 - 5 = -3.

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What kind of fraction is 8/3

Wewaii [24]

improper you need to simplify which would become 2 and 2/3

3 0

3 years ago

Adaline is designing a garden in the shape of a 45º-45º-90º triangle, with an area of 32 ft2. To the nearest foot, how much fenc

wel

Answer:

27 ft

Step-by-step explanation:

Given: A garden in the shape of a 45º-45º-90º triangle.

Area of triangle= 32 ft²

As given dimension of triangle, we understand that it is a right angle and triangle and since two angles are equal, therefore two sides of triangle are also equal.

∴ Base and height will be equal.

Assuming base is also as "h"

Now, finding the length of base and height by using area of triangle formula.

Area of triangle= $\frac{1}{2} \times base\times height$

⇒ $32= \frac{1}{2} \times h\times h$

Multiplying both side by 2

⇒ $64= h^{2}$

Square rooting both side, remember; √a²= a

⇒ $\sqrt{64} = h$

∴ h= 8 feet

Hence, both base and height of right angle triangle is 8 feet.

Next, finding total fencing required to enclose the garden.

Perimeter of garden is equal to the amount of fencing required by Adaline.

Therefore, finding the length of hypotenous of triangle too.

Using pythogorean theoram.

$h^{2} = a^{2} +b^{2}$ , where a is the height and b is the base of triangle.

⇒ $h^{2}= 8^{2} +8^{2}$

⇒ $h^{2} = 128$

Square rooting both side

⇒ $h= \sqrt{128}$

∴ h= 11.3 feet

Perimeter of garden= $base+height+hypotenous$

⇒ Perimeter of garden= $8+8+11.3= 27.3\ feet$ $\approx 27\ feet$

Hence, 27 feet fencing is required to enclose the garden.

3 0

3 years ago

Read 2 more answers

An empty cup in the shape of a cylinder is being filled with water . The cup is filled at constant rate . The table below shows

KatRina [158]

<h2>Explanation:</h2><h2></h2>

Hello! Remember you have to write complete questions in order to get good and exact answers. I'll help you to understand this problem, but I have to assume some things.

We know that the empty cup in the shape of a cylinder is being filled with water. Suppose the volume of this cylinder is:

$V=450cm^3$