All categories

3 years ago

What is the solution of |9x - 36| = 9

Mathematics

1 answer:

mash [69]3 years ago

3 0

Answer:

x = 5

Step-by-step explanation:

1. |9x - 36| = 9

2. Add 36 to each side.

3. |9x| = 45

4. Divide 9 on both sides.

5. |x| = 5

6. Absolute Value of x.

7. x = 5

8. Theres your answer :)

You might be interested in

A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must

Feliz [49]

The base length that will maximize the area for such a window is 168.03 cm. The exact largest value of x when this occurs is 233.39 cm

Suppose we make an assumption that:

(x) should be the width of the rectangle base;
(h) should be the height of the rectangle

Also, provided that the diameter of the semi-circle appears to be the base of the rectangle, then;

the radius $\mathbf{r = \dfrac{x}{2}}$

and, the perimeter of the window can now be expressed as:

$\mathbf{x + 2h + \pi r = x + 2h + \dfrac{\pi x }{2}}$

$\mathbf{= \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h}$

Given that the perimeter = 600 cm

∴

$\mathbf{ \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h= 600}$

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x}$

Since h > 0, then:

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x>0}$

By rearrangement and using the inverse rule:

$\mathbf{ x< \dfrac{ 300}{\Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) } }$

$\mathbf{ x= \dfrac{ 1200}{\Big( 2 +\pi \Big) } }$

$\mathbf{ x= 233.39 \ cm }$

Thus, the largest length x = 233.39 cm

However, the area of the window is given as:

$\mathbf{A(x) = xh + \dfrac{1}{2} \pi r^2}$

$\mathbf{A = x \Big [ 300 - \Big ( \dfrac{1}{2}+\dfrac{1}{4} \Big) x \Big ] +\dfrac{1}{2}\pi \Big(\dfrac{x}{2} \Big )^2}$

$\mathbf{A (x) = 300x - \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ cm^2}$

Now, at maximum, when the area A = 0. Taking the differentiation, we have:

$\mathbf{\dfrac{d}{dx} 300x - \dfrac{d}{dx} \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ =0}$

$\mathbf{ 300 - 2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \ =0}$

Making x the subject of the formula, we have:

$\mathbf{x = \dfrac{1200}{4 +\pi}}$

x = 168.03 cm

Taking the second derivative:

$\mathbf{\dfrac{d}{dx} \Big [300 -2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \Big]}$

$\mathbf{= -2 \Big( \dfrac{1}{2}+\dfrac{\pi}{8}\Big )$

Therefore, we can conclude that the maximum area that exists for such a window is 168.03 cm

Learn more about derivative here:

brainly.com/question/9964510?referrer=searchResults

6 0

3 years ago

Calcola l'area di un rombo sapendo che il perimetro è 160 cm è la sua altezza misura 38,4 cm

AURORKA [14]

Answer:

41,6 cm

Step-by-step explanation:

Formula for Perimeter of a rhombus: P = 2L + 2H (H is the height, L the length)

Perimeter: 160 cm = 2L + 2(38,4 cm), or

160 cm + 76.8 cm + 2L, or

83.2 cm = 2L

and so the height (altezza) is H = 83.2 cm / 2 = 41,6 cm

4 0

3 years ago

A housekeeper had 4/5 of a spray bottle of a cleaning solution. He used 1/8 of the solution in a day.How much of the bottle did

valina [46]

Answer:

0.1

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

13/17% of a quantity is equal to what fraction of the quality

Nookie1986 [14]

Answer:

13/1700

Step-by-step explanation:

so you do 13/17 x 1/100 which is 13/1700 please mark brainliest

8 0

3 years ago

Read 2 more answers

4|n|-5=7 please help me solve

DedPeter [7]

I think you meant to type

4(n)-5=7.

4n = 7 + 5

4n = 12

n = 12/4

n = 3

3 0

3 years ago

Read 2 more answers