Triangle ABC has coordinates , A(1, 4) ; B(3,-2) ; C(4,2)

( simultaneous equations)

daser333 [38]

Answer:

See method below.

Step-by-step explanation:

m/n + n/3 = 2

2/m + n = 4

First eliminate the fractions by multiplying the first equation by 3n:-

3m + n^2 = 6n...........(1)

and the second equation by m:-

2 + mn = 4m..............(2)

Now we solve using substitution:-

From equation (2):-

4m - mn = 2

m = 2 / (4 - n)

Now substitute for m in equation (1):-

6/ (4 - n) + n^2 = 6n

6 + n^2(4 - n) = 6n(4 - n)

6 + 4n^2 - n^3 = 24n - 6n^2

n^3 - 10n^2 + 24n - 6 = 0

This will not factor so we could solve this using graphical software.

To find the values of the variable m we substitute the found values of n into one of the original equations and solve for m.

6 0

4 years ago

Joey pays $35.85 each month for his new stereo what does he pay each year

maks197457 [2]

ANSWER
$430.20

STEP BY STEP
there are 12 months in a year so multiply that number by 12.

Hope this helps

6 0

3 years ago

Read 2 more answers

Which statements are NOT true?

ser-zykov [4K]

Step-by-step explanation:

${2}^{ - 2} = \frac{1}{ {2}^{2} } = \frac{1}{4}$

but it's given = -4

which is incorrect

Again , 8^2 = 64

but it's given = √64

so option C and D are not true

8 0

3 years ago

Convert 65 cm/s to m/s

photoshop1234 [79]

Answer:

65 centimeters per second = 0.65 meter per second

Step-by-step explanation:

So, 65 centimeters per second = 65100 = 0.65 meter per second. To calculate a centimeter Per second value to the corresponding value in m/s, just multiply the quantity in cm/s by 0.01 (the conversion factor).

4 0

3 years ago

Read 2 more answers

For some constants a and b let \[f(x) = \left\{ \begin{array}{cl} 9 - 2x & \text{if } x \le 3, \\ ax + b & \text{if } x

Viktor [21]

Answer:

The value of a+b is 4.

Step-by-step explanation:

The given function is

$f(x) = \left\{ \begin{array}{cl} 9 - 2x & \text{if } x \le 3, \\ ax + b & \text{if } x > 3. \end{array} \right.$

It is given that for some constants a and b the function f has the property that f(f(x))=x for all x.

For x≤3,

$f(x)=9-2x$

For x>3,

$f(x)=ax+b$

At x=0,

$f(0)=9-2(0)=9$

$f(f(0))=f(9)\Rightarrow a(9)+b=9a+b$

Using property f(f(x))=x,

$f(f(0))=0$

$9a+b=0$ .... (1)

At x=1,

$f(1)=9-2(1)=7$

$f(f(1))=f(7)\Rightarrow a(7)+b=7a+b$

Using property f(f(x))=x,

$f(f(1))=1$

$7a+b=1$ .... (2)

Subtract equation (2) from equation (1).

$9a+b-(7a+b)=0-1$

$2a=-1$

Divide both sides by 2.

$a=-\frac{1}{2}$

Substitute this value in equation (1).

$9(-\frac{1}{2})+b=0$

$b=\frac{9}{2}$

The value of a is $-\frac{1}{2}$ and value of b is $\frac{9}{2}$ . The value of a+b is

$a+b=-\frac{1}{2}+\frac{9}{2}$

$a+b=4$

Therefore the value of a+b is 4.

5 0

3 years ago