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3 years ago

Find the modulo class to which the number belongs for the given modulo system. 69, mod 15

1 answer:

3 0

The best and most correct answer among the choices provided by your question is letter C. 9.

<span>4*15+9 </span>

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After the drama club sold 100 tickets to a show, it had $300 in profit. After the next show, it had sold a total of 200 tickets

Alinara [238K]

Answer:

Option a : $y-300 = 4(x - 100)$

Step-by-step explanation:

Given :

The drama club sold 100 tickets to a show, it had $300 in profit.

The next show, it had sold a total of 200 tickets and had a total of $700 profit.

To Find : Equation models the total profit, y, based on the number of tickets sold, x

Solution :

For 100 tickets he had $300 in profit .

⇒ ( $x_{1} ,y_{1}$ )=(100,300)

For 200 tickets he had $700 in profit .

⇒ ( $x_{2} ,y_{2}$ )=(200,700)

We will use point slope form i.e.

$y-y_{1} = m(x - x_{1})$ --(A)

Now, to calculate m we will use slope formula :

$m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }$

$m = \frac{700 -300}{200-100}$

$m =4$

Now, putting values in (A)

$y-300 = 4(x - 100)$

Thus Option a is correct i.e. $y-300 = 4(x - 100)$

5 0

3 years ago

Read 2 more answers

The total number of people at a football game was 5600. Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.

rewona [7]

Answer:

1100 field-side tickets and 4500 end-zone tickets.

Step-by-step explanation:

Let x represent number of field side tickets and y represent number of end-zone tickets.

We have been given that the total number of people at a football game was 5600. We can represent this information in an equation as:

$x+y=5600...(1)$

$y=5600-x...(1)$

We are also told that Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.

Cost of x field side tickets would be $40x$ and cost of y end-zone tickets would be $20y$ .

The total amount of money received for the tickets was $134000. We can represent this information in an equation as:

$40x+20y=134000...(2)$

Upon substituting equation (1) in equation (2), we will get:

$40x+20(5600-x)=134000$

$40x+112000-20x=134000$

$20x+112000=134000$

$20x+112000-112000=134000-112000$

$20x=22000$

$\frac{20x}{20}=\frac{22000}{20}$

$x=1100$

Therefore, 1100 field side tickets were sold.

Upon substituting $x=1100$ in equation (1), we will get:

$y=5600-1100$

$y=4500$

Therefore, 4500 end-zone tickets were sold.

3 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

Write a whole number and a fraction greater than 1 to name the part filled. think 1 container = 1?

zvonat [6]

<span>A whole number greater than 1 could be 2,3,4,5... And so on. A fraction greater than 1 is any fraction where the top number (numerator) is greater than the bottom number (denominator) for example 7/5</span>

8 0

3 years ago

there are 36 roses and 27 carnations. anna is making flower arrangements using both flowers, if she made the maximum number of a

Genrish500 [490]

3 carnations, you find the lowest common multiple.

8 0

3 years ago