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3 years ago

Solve the equation. Show all steps in the solution2\3x + 1 = 5

Mathematics

2 answers:

lapo4ka [179]3 years ago

5 0

Answer: x=6

Step-by-step explanation:

problem: 2/3x + 1 =5

step 1: subtract 1 from both sides

2/3x+1-1=5-1 .... simplify .... 2/3x=4

step 2: multiply both sides by 3/2

x=6

Troyanec [42]3 years ago

3 0

Answer: $x=6$

Subtract 1 from both sides

$2/3x+1-1=5-1$

$2/3x=4$

Multiply both sides by 3/2

$(3/2)*(2/3x)=(3/2)*4\\x=6$

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Find the zero(s) of each function algebraically. f(x) = 8x-16

vodomira [7]

the zero(s) of function $f(x)=8x-16$ is x=2

Step-by-step explanation:

We need to find the zero(s) of function algebraically.

We are given: $f(x)=8x-16$

To find the zeros we put the function equal to zero.

$8x-16=0\\Solving:\\8x=16\\x=\frac{16}{8}\\x=2$

So, the zero(s) of function $f(x)=8x-16$ is x=2

Keywords: zero(s) of function

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3 years ago

x = c1 cos(t) + c2 sin(t) is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the seco

igomit [66]

Answer:

$x=-cos(t)+2sin(t)$

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

$a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0$

Will have a characteristic equation of the form:

$a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0$

Where solutions $r_1,r_2...,r_n$ are the roots from which the general solution can be found.

For real roots the solution is given by:

$y(t)=c_1e^{r_1t} +c_2e^{r_2t}$

For real repeated roots the solution is given by:

$y(t)=c_1e^{rt} +c_2te^{rt}$

For complex roots the solution is given by:

$y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)$

Where:

$r_1_,_2=\lambda \pm \mu i$

Let's find the solution for $x''+x=0$ using the previous information:

The characteristic equation is:

$r^{2} +1=0$

So, the roots are given by:

$r_1_,_2=0\pm \sqrt{-1} =\pm i$

Therefore, the solution is:

$x(t)=c_1cos(t)+c_2sin(t)$

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of $x(t)$ in order to find the constants $c_1$ and $c_2$ :

$x'(t)=-c_1sin(t)+c_2cos(t)$

Evaluating the initial conditions:

$x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1$

And

$x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2$

Now we have found the value of the constants, the solution of the second-order IVP is:

$x=-cos(t)+2sin(t)$

3 0

3 years ago

A prism is filled with 30 cubes with 1/2 unit side lengths. What is the volume of the prism in cubic units?

Vladimir [108]

The correct anwser would be 56

7 0

4 years ago

A company rents out 15 food booths and 22 game booths at the county fair. The fee for a food booth is $100 plus $9 per day. The

Tasya [4]

I'm not completely sure about this answer but here is what I got: 100•15=1500 for one day of the food booth. 50•22=1100 one day for the game booth. 1500+(x9) and 1100+(x8). (1500+x)+(1100+x)=x

8 0

4 years ago

Jordan spent 22% of his time doing math homework. If hw spent 11 minutes on his math homework. How many minutes did he spend on

Angelina_Jolie [31]

Jordan spends 50 minutes on his homework.

Step-by-step explanation:

Given,

Time spent on Maths homework = 11 minutes

This represents the 22% time of his total homework.

Let,

x be the total time spent on homework.

22% of x = 11

$\frac{22}{100}*x=11\\0.22x=11$

Dividing both sides by 0.22

$\frac{0.22x}{0.22}=\frac{11}{0.22}\\x=50$

Jordan spends 50 minutes on his homework.

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8 0

3 years ago

Solve the equation. Show all steps in the solution2\3x + 1 = 5​

Solve the equation. Show all steps in the solution2\3x + 1 = 5