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3 years ago

Simplify.

Mathematics

2 answers:

Semmy [17]3 years ago

7 0

The answer will be D 15m+2n

grigory [225]3 years ago

7 0

First one is 15m+2n, you have to add (or subtract) all the same familys

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A total of 715 tickets were sold for the school play. They were either adult tickets or student tickets. There were 65 more stud

Sergeeva-Olga [200]

Answer:

There were 423 adult tickets sold.

Step-by-step explanation:

Let x = the number of adult tickets sold

Let x + 65 = the number of student tickets sold

x + x + 65 = 715

2x = 715

x = 357.5

x + 65 = 422.5 (round up)

6 0

3 years ago

Read 2 more answers

Solve each system of equations algebraically. For each one, explain what the solution (or lack thereof) tells you

Paul [167]

Answer:

a: no solutions

b: (2, 3)

Step-by-step explanation:

In both equations, the slope of x is the same, but the y-intercept is not, which means they are parallel. Therefore, this system of equations has no solutions.

Since both of the equations are equal to y, we can set them equal to each other:

$\frac{1}{2}x^2+1= 2x-1\\x^2 + 2 = 4x - 2\\x^2-4x+4=0$

We can solve by factoring (by finding a number that multiplies to 4 and adds up to -4):

(x-2)^2 = 0

x = 2

Now, to find y, plug-in x to any of the equations:

y = 2*2-1 = 3

Therefore, the solution to this system of equation is (2, 3)

I hope this helped.

4 0

3 years ago

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

A pencil cost $1.20 and a pen cost $2.90. Jasmiah bought an equal number of such pencils and pens. She spent $32.30 more on the

garri49 [273]

Answer:

Step-by-step explanation:

hope it helps good day.

3 0

2 years ago

Read 2 more answers

Please Answer!! Thanx❤️

katrin2010 [14]

Answer:

the answer is 8.5

Step-by-step explanation:

divide 85 by 10 to get 8.5 for all the dimension

8 0

3 years ago