Not drawn
to scale
(x - 2)cm
D
The diagram shows two joined rectangles.
The total area of the compound shape
ABCDEF is 36 cm
2x cm
c
By considering the areas of the two rectangles,
show that 2x2 - 5x - 18 = 0 and hence find B
the value of length AB.
x cm
A
+
(x - 4)cm
Note: Please make sure your final line only shows your final answer written as AB = ...

Answer:

  8x +12

Step-by-step explanation:

The outside factor is applied to each term inside parentheses:

  4(2x +3) = 4(2x) +4(3) = 8x +12

[tex]\huge\boxed{Hi\:there!}[/tex]

To simplify this expression, we should use the Distributive Property.

It states that

a(b+c)=ab+ac

Let's use it:

4(2x+3)

8x+12

That's the answer.

[tex]\huge\boxed{\boxed{\boxed{Hope\:it\:helps!}}}[/tex]

[tex]\huge\bold{Good\:luck!}[/tex]

[tex]\huge\mathfrak{LoveLastsAllEternity}[/tex]

Answer:

a = - 2, [tex]\frac{9}{4}[/tex] , b = 2, - [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Since x = 1, y = 2 is a solution to the equations , then substitute these values into the 2 equations and solve for a and b

a + 2b = 2 → (1)

b + 2a² = 10 → (2)

In (1) subtract 2b from both sides

a = 2 - 2b → (3)

Substitute a = 2 - 2b into (2)

b + 2(2 - 2b)² = 10 ← expand parenthesis using FOIL

b + 2(4 - 8b + 4b²) = 10 ( simplify left side )

b + 8 - 16b + 8b² = 10 ( subtract 10 from both sides )

8b² - 15b - 2 = 0

Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term

product = 8 × - 2 = - 16 and sum = - 15

The factors are - 16 and + 1

Use these factors to split the b- term

8b² - 16b + b - 2 = 0 ( factor first/second and third/fourth terms )

8b(b - 2) + 1(b - 2) = 0 ← factor out (b - 2) from each term

(b - 2)(8b + 1) = 0

Equate each factor to zero and solve for b

b - 2 = 0 ⇒ b = 2

8b + 1 = 0 ⇒ 8b = - 1 ⇒ b = - [tex]\frac{1}{8}[/tex]

Substitute these values into (3) and evaluate for a

b = 2 ⇒ a = 2 - 2(2) = 2 - 4 = - 2

b = - [tex]\frac{1}{8}[/tex] ⇒ a = 2 - 2(- [tex]\frac{1}{8}[/tex] ) = 2 + [tex]\frac{1}{4}[/tex] = 2 [tex]\frac{1}{4}[/tex] = [tex]\frac{9}{4}[/tex]

The possible values of a and b are 8, -3 or 9/4 , -1/8 respectively.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equations are,

ax + by = 2            (1)

and bx + a²y = 10        (2)

Also, x = 1 and y = 2 are the solution of the equation,

Substitute x = 1 and y = 2in equation (1),

a(1) + b(2) = 2

a + 2b = 2       (3)

Further substitute x = 1 and y = 2 in equation (2),

b(1) + a²(2)  = 10  

2a² + b = 10         (4)

By solving equation (3) and (4),

The possible values of a are 8 and 9/4.

And possible value of b are -3 and -1/8.

To know more about Equation on:

brainly.com/question/187506

#SPJ2

Answer:

1

Step-by-step explanation:

Answer is 1

cuz nearest whole number, just check the next number that is nearest, that in this case is the decimal 1, hence, if it's 5 or above add a one to the whole number, if not then just write it as it is. in this case the nearest number is less than five so we just write it as 1.0000 or just 1

Answer:

u=ABCDEF

Step-by-step explanation:

The correct option is B. Distributive property

Given,

[tex]\frac{2}{3} x+7=-5\\[/tex]

On solving the above equation,

multiplying both sides by 3 we, get

[tex]2x+21=-15[/tex]

now subtracting 21 from both the sides,

[tex]2x=-36\\[/tex]

dividing both the sides by 2 we get,

[tex]x=-18[/tex]

Since in the above steps we follow all the giving property except the distributive property.

Hence the correct option is B. Distributive property.

For more details follow the link:

https://brainly.com/question/13130806

Answer:

-x² + 3x + 7

Step-by-step explanation:

• f(x) = 3x + 1

• g(x) = x² - 6

Then,

According to th' question :-

(f - g)(x) = f(x) - g(x)

= 3x + 1 - (x² - 6)

= 3x + 1 - x² + 6

= -x² + 3x + 7

Answer:

music test

Step-by-step explanation:

divide each one and find the highest answer.

Answer:

i think the answe is A and B hope this helps

Step-by-step explanation:

Have a nice day!

Answer:

5.75 / 1.15 = 5

5 is an answer.

10/2 is also an answer.

25/5 is also also an answer.

100/20 is also also also an answer.

Step-by-step explanation:

18.75 x 11.54

= 216.375

216.375 is the correct answer

AnswerAnswers in explaination

Step-by-step explanation

PART A ANSWER: equation 1) y=1155x+982 and 2) y+100x+1000 both have x model the number of years and y model the investment they made.

PART B answer: The two equations I solved for above

Part C: if she goes with the first plan and invest for 20 years she'll get 24082 dollars and if she invest in the second one she'll get 3000 dollars. As you can see there is a huge difference between the two

Answer:

23.5 feet per minute is the rate

Answer:

the answer is 10

Step-by-step explanation:

by the why want to be friends??

Answer:

10

Step-by-step explanation:

Answer:

y=-x+4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(1-6)/(3-(-2))

m=-5/(3+2)

m=-5/5

m=-1

y-y1=m(x-x1)

y-6=-1(x-(-2))

y-6=-(x+2)

y-6=-x-2

y=-x-2+6

y=-x+4

Hello there, there are multiple ways of solving this problem, let me show you.

[tex]{\huge{\boxed{\mathbb{QUESTION}}}}}[/tex]

A Freight Train Travels 144 miles in 6 hours. How Far will it travel in 15 hours?

_________________

For this problem I will show you 2 methods.

[tex]{\huge{\boxed{\mathbb{METHOD\:ONE}}[/tex]

Cross multiplication, cross multiplication involves algebra to use.

Let x be our answer for this problem. Here is our it would look like

[tex]\frac{6}{144}=\frac{15}{x}[/tex], now we will cross multiply, here is what it'd look like now.

[tex]6x=2160[/tex], then do simple algebra and divide both sides by 6. and then we get [tex]x=360[/tex] miles in 15 hours.

_________________

[tex]{\huge{\boxed{\mathbb{METHOD\:TWO}}[/tex]

For method two we can look for the unit rate. Also known as our rate for one.

divide 144 by 6 and we get 24, then multiply it by 15 and we get 360.

_________________

[tex]{\huge{\boxed{\mathbb{EXACT\:ANSWER}}[/tex]

360 miles in 15 hours.

Answer:

Step-by-step explanation:

The scale factor is the ratio between the man's actual height and the height of the drawing.

Scale = 64/4 = 16

Answer:

1/16

Step-by-step explanation:

the actual man is 16 times bigger than drawing.

Answer:

Shape 2 and 3

Step-by-step explanation:

shape 1 is not enclosed so it cannot have area

Answer:

I believe the answer is A

Step-by-step explanation:

three times x can be equal to, but never greater than -6

Answer:

A. 3x ≤ -6

Step-by-step explanation:

the sentence ‘3x is at most -6

means that the most 3x is allowed to be is -6

it can be -6 or any number less than -6

So, the phrase 3x is at most -6

’ means ‘

3x ≤ -6

Answer:

2 grams

Step-by-step explanation:

50 years is 5 half lives as 1 half life is 10 years.

64 divide 2 = 32-1 half life

32 divide 2 =16-2nd half life

16 divide 2 = 8-3rd half life

8 divide 2 = 4-4th half life

4 divide 2 = 2-5th half life

This means we will have 2 grams left of the radioactive substance after 50 years.

The seat in the middle of the one-way route is 34

The seats are given as:

[tex]First= 0[/tex] --- the first seat behind the seat number 95

[tex]Last= 66[/tex] --- my seat

The seat number half-way would be:

[tex]Half = \frac{Last - First}{2} + 1[/tex]

This gives

[tex]Half = \frac{66- 0}{2} + 1[/tex]

Subtract 0 from 66

[tex]Half = \frac{66}{2} + 1[/tex]

Divide 66 by 2

[tex]Half = 33 + 1[/tex]

Add 33 and 1

[tex]Half = 34[/tex]

Hence, the seat in the middle of the one-way route is 34

Read more about median at:

https://brainly.com/question/8892632

Answer:

m= 4.5 miles

Step-by-step explanation:

Let the number of miles Evelyn can run be m and can be modeled by the equation below

m= kx

Where x Is the Minutes

When m= 3

x= 40

3= k40

k= 3/40

If x= 60

m=3/40(60)

m = (60*3)/40

m= 180/40

m= 4.5 miles

(2,5) and (4,13)

y - y1 = y2 - y1

x - x1    x2 - x1

y - 5  = 13 - 5 = 8/2 = 4 x - 2     4 - 2

y - 5 = 4x - 8

y = 4x - 3

m = 4, c = -3