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 = ...

Not Drawnto Scale(x - 2)cmDThe Diagram Shows Two Joined Rectangles.The Total Area Of The Compound ShapeABCDEF

Answers

Answer 1

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 :)


Related Questions

answer the following question

Answers

Answer:
2
Step-by-step explanation:
You get 8/4 and simplify down to 2

what is 4(2x+3) simplified using distributive property

Answers

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]

A drawing of a man is 4 inches high. The actual man is 64
inches tall. What is the scale factor for the drawing?

Answers

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.

While moving up on the rope-way, I noticed that the seat place in the opposite direction was numbered as 95. Behind it was number 0, then 1, 2 and so on. My seat place was numbered as 66. What number should I meet when I am in the middle of my one-way route?

Answers

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

Which of the following is the missing reason? Statements Reasons two thirds times x plus 7 equals negative 5 Given 2x 21 = â’15 Multiplication Property of Equality 2x = â’36 Subtraction Property of Equality x = â’18 ? Division Property of Equality Distributive Property Addition Property of Equality Subtraction Property of Equality.

Answers

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

What forms of the following equation in?

y=5x−3

Answers

5x-y=3
Not sure if it’s correct
the equation appears to in slope-intercept form

for future reference, slope-intercept form is written as: y=mx+b
m=slope and b=y-intercept

Simplify. √25a^2.
40 points but reported if troll.

Answers

I think that the answer is 5a.
The square root of 25 is 5 and the square root of a^2 is a.
Hope this helps and if possible could I please have the brainliest answer?

Ethan and Alex ordered 1,263 pizzas for the school. They wanted to share them equally with each class.If there are 34 classes, how many pizzas will each class get?​

Answers

each class will get about 37 pizzas

Which of these shapes have an area

Answers

I pretty sure the answer is c

Answer:

Shape 2 and 3

Step-by-step explanation:

shape 1 is not enclosed so it cannot have area

1.1046 rounded to the nearest whole number

Answers

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

Write an equation in slope-intercept form that describes the line through the points (-2,6) and (3, 1).

Answers

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

PLEASE HELP! WILL MARK BRAINLIEST!!!

Answers

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

If x = 1 and y = 2 is a solution to the simultaneous equation ax + by = 2 and bx + a^(2)y = 10, find the possible values of a and b.

Answers

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.

What is an equation ?

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

please solve quickly for 50 points

Answers

A: 208cm
B: 27cm
C: 30,000cm

Hope this helps!

help please! very important

Answers

I believe the answer would be 74 cups or 91

if f(x)= 3x+1 and g(x)= x^2-6 FIND (f+g)(x)

Answers

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

i need help on this assignment

Answers

Answer:

the answer is 10

Step-by-step explanation:

by the why want to be friends??

Answer:

10

Step-by-step explanation:

Choose the inequality that could be used to solve the following problem.

Three times a number is at most negative six.

(A) 3x ≤ -6

(B) 3x < -6

(C) 3x ≥ -6

(D) 3x > -6​

Answers

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

two expressions that are equivalent to 5.75 ÷ 1.15.

Answers

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.

james scored 30 out of 90 in a music test.he scored 48 out of 150 in drama test scored 35 out of 120 in an art test.in which test james score the highest​

Answers

Answer:

music test

Step-by-step explanation:

divide each one and find the highest answer.

Factor the expression using the GCF. (algebraic expressions, just dont subtract 18-12=6 its incorrect. please answer asap!!!! )


18 - 12 = ?

Answers

Factoring the GCF would make the answer 6… Double check with your teacher because it’s literally 6

Evelyn can run 3 miles in 40 minutes

Answers

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

Calculate 18.75 x 11.54 a) exact value b. corrected to 1 d.p c. corrected to 2 s.f

Answers

Step-by-step explanation:

18.75 x 11.54

= 216.375

216.375 is the correct answer

A hot air balloon went from an elevation of 4,060 feet to an elevation of 3,120 feet in 40 minutes. What was its rate of descent?

Answers

Answer:

23.5 feet per minute is the rate

Select the correct answer.

You're trying to determine how much money it would cost to hire a lawn mowing company to cut your grass. Your yard

measures 8,712 square feet. The lawn mowing company charges a base rate of $30, plus $20 for every tenth of an

acre. You determine that it will cost $70 to hire the lawn mowing company. Which sentence best describes this price

estimate?

A. The price should be $50 because you have a 0.1 acre yard.

B. The price should be $50 because you have a 0.2 acre yard.

C. The price should be $90 because you have a 0.3 acre yard.

D.

The price estimate is accurate,

Answers

It’s B because C is too much and A is to little for the correct answer

The half life of a radioactive substance is 10 years. If 64 grams are placed in a
container, how much will remain after 50 years?

Answers

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.

determine whether Δ def to Δ HIG is a reflection, translation, rotation, or glide reflection

what are the reflection line, translation rule. center and angle or rotation or glide translation rule and reflection line?


A. Rotation, 180°, about ( -0.5, 0)

B. glide reflection, translate 8 units to the right then reflect across the line y=4

C. Reflection, x=5

D. Rotation, 180, about (1,4)


20 Points

Answers

The answer is A. Rotation , 180 about (-0.5,0)

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



Please help me out kindda hard

Answers

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.

Have a good day :) !
360 mph . 144 divided by 6 equal 24 mph , so 24 times 15 will equal 360 .

Find the values of m and c if the straight line y=mx+c passes through the point (-2,5) and has a gradient of 4.

Answers

(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

PLEASE CAN SOMEONE HELP ME​

Answers

Answer:

u=ABCDEF

Step-by-step explanation:

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