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Elden [556K]
3 years ago
8

Simplify -4b + (-9k) -6 - 3b + 12

Mathematics
1 answer:
Olenka [21]3 years ago
6 0

Answer:

-7b-9k+6

Step-by-step explanation:

-4b+(-9k)-6-3b+12

(-4b-3b)+(-9k)+(-6+12)

-7b+(-9k)+6

-7b-9k+6

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(9x²+24x-8)-(5x²+3x+10)
motikmotik

Answer:

4x^2 + 21x - 18

Step-by-step explanation:

(9x^2+24x-8)-(5x^2+3x+10)

9x^2+24x-8-5x^2-3x-10

9x^2 - 5x^2 = 4x^2

24x - 3x = 21x

-8 - 10 = -18

Answer: 4x^2 + 21x - 18

8 0
3 years ago
Write any 4 laws of exponents.<br>​
emmainna [20.7K]

         \rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}

       <em>Write any 4 laws, or properties, of exponents.</em>

<em />

<em>        </em>\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}

\Large\text{Law number 1:-}

\Large\text{$a^n*a^m=a^{n+m}$}

\Large\text{It states that:-}

                        When we multiply together numbers with the same base,

                         we add the exponents.

\Large\text{Law number 2:-}

\Large\text{$a^m:a^n=a^{m-n}$}

\Large\text{It states that:-}

                     When we divide numbers with the same base, we

                     subtract the exponents.

\Large\text{Law number 3:-}

\Large\text{$(\displaystyle\frac{x}{y}) ^n=\frac{x^n}{y^n}$}

\Large\text{It states that:-}

                 If we have a fraction to a power, we raise the numerator and

               the denominator to that power.

And then last but not least,

\Large\textit{Law number 4:-}

\Large\text{$a^{-m} =\displaystyle\frac{1}{a^m}$}

\Large\text{It states that:-}

                   If we have a number with a negative exponent, we flip it over.

<h3>Good luck with your studies.</h3>

#TogetherWeGoFar

\rule{50}{1}\smile\smile\smile\smile\smile\smile\rule{50}{1}

6 0
2 years ago
Read 2 more answers
If Asher plays each of the remaining seasons for which he is eligible, what is the average number of doubles he needs to hit per
PtichkaEL [24]

Answer:

the

Step-by-step explanation:

6 0
3 years ago
Solve the equation15=2y-5
Lesechka [4]
15 = 2Y - 5
20 = 2Y
10 = Y
5 0
3 years ago
Y''+y'+y=0, y(0)=1, y'(0)=0
mars1129 [50]

Answer:

y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form ay''+by'+cy=0.

Given: y''+y'+y=0

Let y=e^{rt} be it's solution.

We get,

\left ( r^2+r+1 \right )e^{rt}=0

Since e^{rt}\neq 0, r^2+r+1=0

{ we know that for equation ax^2+bx+c=0, roots are of form x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} }

We get,

y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}

For two complex roots r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta, the general solution is of form y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )

i.e y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )

Applying conditions y(0)=1 on e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right ), c_1=1

So, equation becomes y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )

On differentiating with respect to t, we get

y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )

Applying condition: y'(0)=0, we get 0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}

Therefore,

y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )

3 0
3 years ago
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