Solve equation 4(k-6)-(3k +2)=-5

to solve the equation |x-9|=0.5x, kiana graphed the functions f(x)=|x-9| and g(x)=0.5x on the same set of coordinate axes. She t

Pani-rosa [81]

Answer:

The answer is the option D

$f(6)=g(6)$ and $f(18)=g(18)$

Step-by-step explanation:

we have

$f\left(x\right)=\left|x-9\right|$

$g(x)=0.5x$

we know that

The solution of the system of equations is the intersection point both graphs

Using a graphing tool

see the attached figure

The solution are the points $(6,3)$ and $(18,9)$

therefore

The solution of the equation $\left|x-9\right|=0.5x$ are

$x=6, x=18$

so

For $x=6$

$f\left(6\right)=\left|6-9\right|=3$

$g(6)=0.5(6)=3$

$f(6)=g(6)$

For $x=18$

$f\left(18\right)=\left|18-9\right|=9$

$g(18)=0.5(18)=9$

$f(18)=g(18)$

therefore

$f(6)=g(6)$ and $f(18)=g(18)$ because the intersection points are common points for both graphs

5 0

3 years ago

Read 2 more answers

When you climb a rope , you change what energy into what energy

vredina [299]

Potential energy on the ground to kinetic energy climbing the rope to gravitational potential energy at the top of the rope

4 0

4 years ago

Simplify (x + 2/ x^2 + 2x -3) / (x + 2/x^2 - x)

rjkz [21]

Answer:

The simplest form is x/(x + 3)

Step-by-step explanation:

* To simplify the rational Expression lets revise the factorization

of the quadratic expression

* To factor a quadratic in the form x² ± bx ± c:

- First look at the c term

# If the c term is a positive number, and its factors are r and s they

will have the same sign and their sum is b.

# If the c term is a negative number, then either r or s will be negative

but not both and their difference is b.

- Second look at the b term.

# If the c term is positive and the b term is positive, then both r and

s are positive.

Ex: x² + 5x + 6 = (x + 3)(x + 2)

# If the c term is positive and the b term is negative, then both r and s

are negative.

Ex: x² - 5x + 6 = (x -3)(x - 2)

# If the c term is negative and the b term is positive, then the factor

that is positive will have the greater absolute value. That is, if

|r| > |s|, then r is positive and s is negative.

Ex: x² + 5x - 6 = (x + 6)(x - 1)

# If the c term is negative and the b term is negative, then the factor

that is negative will have the greater absolute value. That is, if

|r| > |s|, then r is negative and s is positive.

Ex: x² - 5x - 6 = (x - 6)(x + 1)

* Now lets solve the problem

- We have two fractions over each other

- Lets simplify the numerator

∵ The numerator is $\frac{x+2}{x^{2}+2x-3}$

- Factorize its denominator

∵ The denominator = x² + 2x - 3

- The last term is negative then the two brackets have different signs

∵ 3 = 3 × 1

∵ 3 - 1 = 2

∵ The middle term is +ve

∴ -3 = 3 × -1 ⇒ the greatest is +ve

∴ x² + 2x - 3 = (x + 3)(x - 1)

∴ The numerator = $\frac{(x+2)}{(x+3)(x-2)}$

- Lets simplify the denominator

∵ The denominator is $\frac{x+2}{x^{2}-x}$

- Factorize its denominator

∵ The denominator = x² - 2x

- Take x as a common factor and divide each term by x

∵ x² ÷ x = x

∵ -x ÷ x = -1

∴ x² - 2x = x(x - 1)

∴ The denominator = $\frac{(x+2)}{x(x-1)}$

* Now lets write the fraction as a division

∴ The fraction = $\frac{x+2}{(x+3)(x-1)}$ ÷ $\frac{x+2}{x(x-1)}$

- Change the sign of division and reverse the fraction after it

∴ The fraction = $\frac{(x+2)}{(x+3)(x-1)}*\frac{x(x-1)}{(x+2)}$

* Now we can cancel the bracket (x + 2) up with same bracket down

and cancel bracket (x - 1) up with same bracket down

∴ The simplest form = $\frac{x}{x+3}$

5 0

4 years ago

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Carla is practicing her land surveying skills at her college campus. She knows the famous "triangle courtyard," shown in the fig

Zarrin [17]

I also would think that it would be C 116,06

3 0

3 years ago

Find the square root of 3.24

PtichkaEL [24]

Answer:

1.8 or 9/5

Step-by-step explanation:

.................................

3 0

3 years ago