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Brrunno [24]
3 years ago
13

Factor over the complex numbers: 36x2 + 9.

Mathematics
1 answer:
ludmilkaskok [199]3 years ago
4 0

36x^2+9=(6x)^2-(-9)=(6x)^2-(-3^2)\\\\=(6x)^2-(3i)^2=(6x-3i)(6x+3i)\\\\\text{Used:}\\a^2-b^2=(a-b)(a+b)\\\\i^2=-1

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On Friday, Carlotta had 6/8 of her paper left to write. She wrote 2/6 of the paper on Saturday and ¼ of the paper on Sunday. At
alukav5142 [94]

Answer:

\frac{1}{6}

Step-by-step explanation:

<u>Skills needed: Fraction Subtraction, Least Common Denominator (LCD)</u>

1) \frac{6}{8} - \frac{2}{6} - \frac{1}{4} is the operation you would do.

--> You would do this because, Carlotta has \frac{6}{8} of the paper left, and does one fraction amount (\frac{2}{6}) on Saturday & does another fraction amount (\frac{1}{4}) on Sunday.

-->  Using subtraction is the best way

2) Now, we need to figure out the Least Common Denominator for all 3 fractions.

8,6,4 are the denominators.

The lowest number that is a factor of all them is 24.

So, it would then become \frac{18}{24} - \frac{8}{24} - \frac{6}{24}

This would become: \frac{18-8-6}{24} (18-8-6 = 4)

So then: \frac{4}{24} is your answer.

This simplifies into \frac{1}{6}.

Hope this helps and have a nice day!! :) :]

5 0
3 years ago
Which statement is false about the line whose equation is y=-2x-5?
Evgen [1.6K]
What are the choices
5 0
3 years ago
a Sam purchases a home for $1, 240, 500. Each year the value of the home appreciates by 3%. What is the value of the home after
OleMash [197]

Answer:

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Step-by-step explanation:

6 0
2 years ago
Solve for x.
Ivahew [28]
ANSWER

x=\frac{2-\sqrt{10}} {3}

or

x=\frac{\sqrt{10}+2} {3}

We have

3x^2-4x-2=0

Since we cannot factor easily, we complete the square.

Adding 2 to both sides give,

3x^2-4x=2

Dividing through by 3 gives

x^2-\frac{4}{3}x= \frac{2}{3}

Adding (-\frac{2}{3})^2 to both sides gives

x^2-\frac{4}{3}x+(-\frac{2}{3})^2= \frac{2}{3}+(-\frac{2}{3})^2

The expression on the Left Hand side is a perfect square.

(x-\frac{2}{3})^2= \frac{2}{3}+\frac{4}{9}

\Rightarrow (x-\frac{2}{3})^2= \frac{10}{9}

\Rightarrow (x-\frac{2}{3})=\pm \sqrt{\frac{10}{9}}

\Rightarrow (x)=\frac{2}{3} \pm {\frac{\sqrt{10}}{3}

Splitting the plus or minus sign gives

x=\frac{2- \sqrt{10}} {3}

or

x=\frac{\sqrt{10}+2} {3}
3 0
3 years ago
Read 2 more answers
Question
Jobisdone [24]

Answer:

The light bulb will reach the ground 1.25 seconds after it is dropped.

Step-by-step explanation:

We know that for an object that is in the air, the only force acting on it will be the gravitational force (where we are ignoring the air resistance)

Then the acceleration of the object is the gravitational acceleration, 32.17 ft/s^2

Then the acceleration of the light bulb is:

A(t) = (-32.17 ft/s^2)

Where the negative sign is because the acceleration is downwards.

Now, to get the velocity equation, we need to integrate the acceleration over time, we will get:

V(t) = (-32.17 ft/s^2)*t + V0

Where V0 is the initial velocity of the light bulb. Because it is dropped, the initial velocity will be zero, then V0 = 0m/s, then the velocity equation is:

V(t) =  (-32.17 ft/s^2)*t

Finally, to get the position equation we need to integrate again, we will get:

P(t) = (1/2)*(-32.17 ft/s^2)*t^2 + P0

Where P0 is the initial height of the object, and in this case, we know that it is equal to 25 ft.

Then the position equation is:

P(t) = (1/2)*(-32.17 ft/s^2)*t^2 + 25ft

The object will hit the ground when P(t) = 0 ft, then we need to solve that equation for t:

P(t) =  (1/2)*(-32.17 ft/s^2)*t^2 + 25ft = 0 ft

          25 ft =  (1/2)*(32.17 ft/s^2)*t^2

         2*25ft = (32.17 ft/s^2)*t^2

           50ft =  (32.17 ft/s^2)*t^2

         √( 50ft/(32.17 ft/s^2)) = t = 1.25 s

The light bulb will reach the ground 1.25 seconds after it is dropped.

8 0
3 years ago
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