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3 years ago

Solving 6x^2-24x-54 with quadratic formula

Mathematics

1 answer:

RoseWind [281]3 years ago

4 0

Answer:

x = 5.61 or -1.61

Step-by-step explanation:

$x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a}$

6x² - 24x - 54 = 0

6(x² - 4x - 9) = 0

x = [4+-√(4²)-4(1)(-9)]/2(1)

= (4+√52)/2

= 5.61

= (4-√52)/2

= -1.61

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A type of bacteria has a very high exponential growth rate of 80% every hour. If there are 10 bacteria, determine how many will

Lana71 [14]

<h3>There are 189 bacteria in 5 hours</h3><h3>There are 13382588 bacteria in 1 day</h3><h3>There are $10(1.8)^{168}$ bacteria in 1 week</h3>

Solution:

Given that,

A type of bacteria has a very high exponential growth rate of 80% every hour

There are 10 bacteria

The increasing function is given as:

$y = a(1+r)^t$

Where,

y is future value

a is initial value

r is growth rate

t is time period

From given,

a = 10

$r = 80 \5 = \frac{80}{100} = 0.8$

Determine how many will be in 5 hours

Substitute t = 5

$y = 10(1 + 0.8)^5\\\\y = 10(1.8)^5\\\\y = 10 \times 18.89568\\\\y \approx 188.96$

y = 189

Thus, there are 189 bacteria in 5 hours

Determine how many will be in 1 day ?

1 day = 24 hours

Substitute t = 24

$y = 10(1 + 0.8)^{24}\\\\y = 10(1.8)^{24}\\\\y = 10 \times 1338258.84\\\\y = 13382588.45\\\\y \approx 13382588$

Thus, there are 13382588 bacteria in 1 day

Determine how many will be in 1 week

1 week = 168

Substitute t = 168

$y = 10(1 + 0.8)^{168}\\\\y = 10(1.8)^{168}$

Thus there are $10(1.8)^{168}$ bacteria in 1 week

6 0

3 years ago

(x+11)(2x-8) as a trinomial

Alborosie

Answer:

2x^2+14x-88

Expand the equation

6 0

2 years ago

A plumbing supply company has fixed costs of $9,000 per month and average variable costs of $9.30 per unit manufactured. The com

nekit [7.7K]

Answer:

8710 units

Step-by-step explanation:

Step 1: Write all the data

Fixed cost: $9000

Average variable cost: 9.3 per unit

Total cost: 90,000

Total units: x

Step 2: Find the total variable cost

Average variable cost is per unit so it has to be multiplied by the number of units to find the total variable cost.

Total variable cost = average variable cost per unit x number of units

Total variable cost = 9.3x

Step 3: Make the formula for finding x

Total cost = total fixed cost + total variable cost

90,000 = 9000 + 9.3x

81000 = 9.3x

x = 8709.67

Rounded off to 8710 units

3 0

4 years ago

Help with Geometry ,please

suter [353]

Answer:look at the angle bro and you got the angle just look at it good enough

Step-by-step explanation:

4 0

3 years ago

Find x in DEF A. 6 B. 6 (square root 2) C. 6 (square root 3) D. 12

netineya [11]

Answer:

B. 6√2

Step-by-step explanation:

We can use the Pythagorean Theorem to solve this out. The Pythagorean Theorem states that for any right triangle with the shortest sides (called legs) as a and b and the longest side (called the hypotenuse) as c:

a² + b² = c²

Here, a = b = 6, so:

6² + 6² = c²

36 + 36 = c²

72 = c²

c = √72 = 6√2

Now, we see the answer is B.

However, there's a trick to solving these kinds of problems. Notice that DEF is both an isosceles triangle and a right triangle. We call these 45-45-90 triangles because those are the angles of the triangle.

One characteristic of these types of triangles is that their leg to leg to hypotenuse ratio is 1 : 1 : √2, always. We could apply that here. We see that the legs are 6, so we could find the hypotenuse simply by multiplying 6 by √2, and we would get 6√2, which is exactly the value we obtained above.

Thus, the answer is B.

4 0

4 years ago