Ask question

Ask question

All categories

1 year ago

7

Olga buys tickets to a concert, She pays $27.7 for each ticket plus a handling fee of $5.50 for the order, The total cost is $14

4.25. How many tickets, n, Did Olga buy?
Equation is: 27.7n + 5.50 = 144.25

1 answer:

Blababa [14]1 year ago

6 0

Answer:

Step-by-step explanation:

1. 27.7n + 5.5 = 144.25

2. 27.7n = 138.75

3. n = 138.75/27.7

4. n = <em>about</em> 5.00903 or 2775/554

You might be interested in

A particle moving in a planar force field has a position vector x that satisfies x'=Ax. The 2×2 matrix A has eigenvalues 4 and 2

andrey2020 [161]

Answer:

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

Step-by-step explanation:

Consider the provided matrix.

$v_1=\begin{bmatrix}-3\\1 \end{bmatrix}$

$v_2=\begin{bmatrix}-1\\1 \end{bmatrix}$

$\lambda_1=4, \lambda_2=2$

The general solution of the equation $x'=Ax$

$x(t)=c_1v_1e^{\lambda_1t}+c_2v_2e^{\lambda_2t}$

Substitute the respective values we get:

$x(t)=c_1\begin{bmatrix}-3\\1 \end{bmatrix}e^{4t}+c_2\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-3c_1e^{4t}-c_2e^{2t}\\c_1e^{4t}+c_2e^{2t} \end{bmatrix}$

Substitute initial condition $x(0)=\begin{bmatrix}-6\\1 \end{bmatrix}$

$\begin{bmatrix}-3c_1-c_2\\c_1+c_2 \end{bmatrix}=\begin{bmatrix}-6\\1 \end{bmatrix}$

Reduce matrix to reduced row echelon form.

$\begin{bmatrix} 1& 0 & \frac{5}{2}\\ 0& 1 & \frac{-3}{2}\end{bmatrix}$

Therefore, $c_1=2.5,c_2=1.5$

Thus, the general solution of the equation $x'=Ax$

$x(t)=2.5\begin{bmatrix}-3\\1\end{bmatrix}e^{4t}-1.5\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

6 0

3 years ago

What is the solution to this system of equations?

maksim [4K]

Answer:x=3 y=1/2

Step-by-step explanation:

x+2y=4

2x-2y=5

Add both equations together

x+2x+2y-2y=4+5

3x+0=9

3x=9

Divide both sides by 3

3x/3=9/3

x=3

Substitute x=3 in x+2y=4

x+2y=4

3+2y=4

Collect like terms

2y=4-3

2y=1

Divide both sides by 2

2y/2=1/2

y=1/2

8 0

2 years ago

Where y=5x-7 and -3x-2y=-12 Write your answer as x,y

Mariulka [41]

Answer:

(x,y) = (2,3)

Step-by-step explanation:

y=5x-7 (i)

-3x-2y= -12

-(3x+2y)= -12

3x+2y= 12 (ii)

By putting the value of y from (i) in (ii)

3x+2(5x-7)=12

3x+10x-14=12

13x=12+14

13x= 26

x = $\frac{26}{13}$

x= 2

By putting the value of x in (i)

y= 5(2)-7

y= 10-7

y= 3

(x,y) = (2,3)

5 0

2 years ago

Which triangles in the diagram are congruent?

GenaCL600 [577]

Answer: triangle 1, triangle 2, and triangle 3

Step-by-step explanation:

Triangles 1 and 3 are congruent by SAS. So, by CPCTC, all three sides are congruent, making triangle 2 congruent to them as well by SSS.

4 0

1 year ago

Special right triangles

fiasKO [112]

Answer:

c

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers