Simply the Expression.
​

First find the areas of the two separate rectangles where:

Area of rectangle = length x width

Area of the small rectangle = x(x–4)

Area of small rectangle = [tex]x^{2} -4x[/tex]

Area of big rectangle = (x–2)(2x+x)

Area of big rectangle = (x–2)(3x)

Area of big rectangle = [tex]3x^{2} -6x[/tex]

The total area of the compound shape is 36, therefore:

[tex]3x^{2} -6x +x^{2} -4x=36[/tex]

[tex]4x^{2} -10x-36=0[/tex] (collecting like-terms and by bringing the +36 to the other side)

By dividing this by 2, you get:

[tex]2(2x^{2} -5x-18)=0[/tex]

[tex]2x^{2} -5x-18=0[/tex]

To find the length of AB (x), solve the quadratic by either factorising, completing the square or by using the quadratic formula, etc to solve for x.

[tex]2x^{2} -5x-18=0[/tex]

[tex](2x-9)(x+2)=0[/tex]

[tex]x=\frac{9}{2}[/tex]

[tex]x=-2[/tex]

However, a length cannot be negative, so x must be [tex]\frac{9}{2}[/tex] or 4.5cm, so length AB = 4.5cm.

Hope this helps :)

Answer:

Step-by-step explanation:

If 10 less than 5 times a number is two more than 3 times the number, then the number is ​

10 - 5x = 2 + 3x

10 - 2 - 5x - 3x = 0

8 - 8x = 0

x = 1

---------------

check

10 - 5 * 1 = 2 + 3 * 1

5 = 5

the answer is good

Answer: 7.5

Step-by-step explanation: hope this help :)

Answer:

7.5

Step-by-step explanation:

hope this help you guys to answer the question

Answer:

y=-1/4x+1

Step-by-step explanation:

y-y1=m(x-x1)

y-3=-1/4(x-(-8))

y-3=-1/4(x+8)

y=-1/4x-8/4+3

y=-1/4x-2+3

y=-1/4x+1

Step-by-step explanation:

please mark me as brainlest

Answer:

4

Step-by-step explanation:

Answer: 4

Step-by-step explanation: 108/3 is 36, 36/3 is 12, and 12/3 is 4. :)

Step-by-step explanation:

radius of circle =5 cm

circumference of a circle =2πr

=2π×5

=10π=10×3.14

circumference=31.4 cm

Answer:

34 i think i got it really wrong but...

Step-by-step explanation:

Answer:

With its point on A, open the compass on point E

Answer:

1. 2/6

2. 1/3

3. 3/9

Step-by-step explanation:

I've learned this before

Answer: 14 miles

Step-by-step explanation: 3.5d+5+2.5d+3

Answer:

x = 600 pages

Step-by-step explanation:

Let the total books pages be x

Given that

Hank had read = 25% of x

25% of x = 150

=>  

Multiplying both sides by 4

=> x = 150 * 4

=> x = 600 pages

Step-by-step explanation:

There you go.

Answer:

C

Step-by-step explanation:

The reasonable estimate for the length of side DE is 3 units

Find the diagram of the question attached. The given triangle ABC and BDE are similar triangles.

Using the similarity theorem of a triangle, this is expressed as:

AC = DE

Using the pythagoras theorem to get the length of AC:

AB^2 = AC^2 + BC^2

5^2 + AC^2 + 4^2

AC^2 = 25 - 16

AC^2 = 9

AC= 3

Since AC = DE, hence the reasonable estimate for the length of side DE is 3 units

Learn more on similar shapes here: https://brainly.com/question/14285697

Answer:

5/3

Step-by-step explanation:

Answer:

x/3 ≤ 5

I'm not sure if this is what you were looking for. If not, please be more specific in your questions!

Answer:

48 ft 2

Step-by-step explanation:

The radius is 4 ft because it is half of the diameter.

3 * 4^2 = 3 * 16 = 48

Answer:

23

Step-by-step explanation:

x + x + 1 + x + 2 + x + 3 + x + 4 = 110

5x + 10 = 110

x = 20

4th number = x + 3

20 + 3 = 23

Step-by-step explanation:

[tex]{ \rm{a = c = \frac{2}{5} b}} \\ \\ { \rm{b = d = \frac{5}{2} a}}[/tex]

• Substitute:

[tex]{ \rm{ \frac{a + 3c + 4}{b + 3d + 10} = \frac{ \frac{2}{5} b + \frac{6}{5}b + 4 }{ b + \frac{15}{2} b + 10} }} \\ \\ = { \rm{ \frac{ \frac{8}{5} b + 4}{ \frac{17}{2}b + 10 } }} \\ \\ { \rm{}}[/tex]

Hi,

x² + 8x + 12 = 0

a= 1 ; b= 8 c= 12

∆ = b² - 4ac

∆ = 8² - 4*1*12

∆ = 64 - 4*12

∆ = 64 - 48

∆ = 16

∆>0 :

x1 = (-b-√∆)/2a = (-8-4)/2 = -12/2 = -6

x2 = (-b+√∆)/2a = (-8+4)/2 = -4/2 = -2

S= { -6 ; -2 }

x = -6

or x = -2

✅(•‿•)

Answer:

Step-by-step explanation:

x² + 8x + 12 = 0

➺ x² + 2x + 6x = 0

➺ x(x + 2) + 6(x + 2) =0

➺ (x + 6)(x + 2) = 0

Whether, x + 6 = 0

⠀⠀⠀⠀⠀➺ x = -6

⠀⠀or,⠀⠀⠀⠀ x + 2 = 0

⠀⠀⠀⠀⠀⠀➺ x = -2

Answer:

The answer is 10

Step-by-step explanation:

It is

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

12

Step-by-step explanation:

So Josh is 6 years older than kims age and the sum of the ages is less than 31, the greatest number that is less than 31 is 30 so we can use that.

We can make an equation out of this and solve it.

n+(n+6)=30

2n+6=30

2n=24

n=12

12 is the oldest Kim could be.

12+(12+6)=12+18=30.

Answer:

unit rate 1:8

Step-by-step explanation:

Answer:

the slope is stepper and the line is shifted up

Answer:100

Step-by-step explanation:

The question confuses you since there is no extra variable to help you which is you have to create it yourself.

Let's create a variable called 'y' and make it the empty angle inside the triangle and next to x + 30. Since at K it will always equal to 180° because x+30 + y = 180°, we can rearrange to make y alone which would be become:

[tex]y=-x-30+180[/tex] which then becomes [tex]y = -x+150[/tex].

Also since the inside sum of angles in a traingle is equal to 180°, this can be written as

[tex]180 = (x-40) +(x-30)+y[/tex]

if we replace y with the equation we get

[tex]180=(x-40)+(x-30) + (-x+150)[/tex]

which can be simplified to

[tex]180=x+80[/tex] because 2x-x = x and -70+150 = 80

If we rearrange to solve for x, we get:

[tex]x = 180-80[/tex] ⇒ [tex]x=100[/tex]

We can verify this by putting the value of x in both equation:

[tex]y = -100+150 = 50[/tex] angle at k

[tex]100-40=60[/tex] angle at j

[tex]100-30=70[/tex] angle at l

[tex]50+60+70=180[/tex] this match the rules of the sum of interior angle always equal 180°

Answer:

a box of 10 balls for $9?

Step-by-step explanation:

because u buy 10 tennis balls for 9 dollars and the first one is not true

becuase u buy 3 balls of tennis with 3 dollars and the last answer is right

becuase you buy 10 balls for 9 that means its 1 dollar less for 10 balls

hope it helps

answer is B. detrjrajaetkterjaejq

Answer:

77

Step-by-step explanation:

6x2 = 12

13x5 = 65

65+12 = 77

The answer is 77.