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3 years ago

A) Find an equation of the line:

Mathematics

1 answer:

nikklg [1K]3 years ago

6 0

A) y=-2x-2

y/x=slope -4/2=-2 y-intercept=b=-2 (put in y=mx=b form)

B) y=15/4x-1 or y=3.75x-1

C) y=-0.6664x-3(I DONT THINK THIS ONE IS RIGHT CHECK IT FIRST)

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hi, i dont undertand number 20 because i was absent in class today and i rerally need help, i will appraciate with the help, and

Mariulka [41]

Given:

The equation is,

$2\log _3x-\log _3(x-2)=2$

Explanation:

Simplify the equation by using logarthimic property.

$\begin{gathered} 2\log _3x-\log _3(x-2)=2 \\ \log _3x^2-\log _3(x-2)=2_{}\text{ \lbrack{}log(a)-log(b) = log(a/b)\rbrack} \\ \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \end{gathered}$

Simplify further.

$\begin{gathered} \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \\ \frac{x^2}{x-2}=3^2 \\ x^2=9(x-2) \\ x^2-9x+18=0 \end{gathered}$

Solve the quadratic equation for x.

$\begin{gathered} x^2-6x-3x+18=0 \\ x(x-6)-3(x-6)=0 \\ (x-6)(x-3)=0 \end{gathered}$

From the above equation (x - 6) = 0 or (x - 3) = 0.

For (x - 6) = 0,

$\begin{gathered} x-6=0 \\ x=6 \end{gathered}$

For (x - 3) = 0,

$\begin{gathered} x-3=0 \\ x=3 \end{gathered}$

The values of x from solving the equations are x = 3 and x = 6.

Substitute the values of x in the equation to check answers are valid or not.

For x = 3,

$\begin{gathered} 2\log _3(3^{})-\log _3(3-2)=2 \\ 2\log _33-\log _31=2 \\ 2\cdot1-0=2 \\ 2=2 \end{gathered}$

Equation satisfy for x = 3. So x = 3 is valid value of x.

For x = 6,

$\begin{gathered} 2\log _36-\log _3(6-2)=2 \\ 2\log _36-\log _34=2 \\ \log _3(6^2)-\log _34=2 \\ \log _3(\frac{36}{4})=2 \\ \log _39=2 \\ \log _3(3^2)=2 \\ 2\log _33=2 \\ 2=2 \end{gathered}$

Equation satifies for x = 6.

Thus values of x for equation are x = 3 and x = 6.

6 0

1 year ago

Stan made changes to

Lemur [1.5K]

Answer:

22%

Step-by-step explanation:

7 0

2 years ago

2/3 : 1 in its simplest form

slamgirl [31]

Answer:

2 : 3

Step-by-step explanation:

You need to show the ratio using the smallest whole numbers possible.

Multiply both numbers by 3.

2/3 : 1

2/3 × 3 : 1 × 3

2 : 3

5 0

2 years ago

what is 40% off of $712.00 please explain how you got your answer as if you were teaching me how to do it.

Vikentia [17]

Answer: $284.80

look when you are trying to find the percent of a number you need to turn the percent into a decimal then multiply the decimal by the number:

1st. 40% as a decimal is 0.40 because as a fraction 40% is 40/100 so that means that 1.00 is 100 and 0.40 is 40%

2nd. Next, you do 0.40 x 712.00 = or

712.00

x 0.40

______

$284.80

3 0

2 years ago

You invest $1000 in a 5-year savings bond that pays 8% annual interest on the principal. How much total interest will you have e

atroni [7]

8% of 1000 = 80
8% of 1080 = 86.4
8% of 1166.4 = 93.31
8% of 1259.71 = 100.77
8% of 1360.48 = 108.8
$1469.28
Rounded: $1469

3 0

3 years ago