Mathematics High School

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 = ...

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

Explain why the square root of a number is defined to be equal to that number to the 1/2 power.

Answers

Answer:

This is essentially a rule in the unit of radicals, where n✔️X^m = X^m/n. If the value of m is equal to n, as in 2✔️3^2 it would simply be 3^2/2 which is nothing but 3^1 = 3. Basically, the m value can be greater than n and or less than n, but if it is equal the m and n values cancel out. Hope this helped <3

on a winter monday in nepal, the temperature was -8F. by 1 pm, it was 27F. how many degrees did the temperature change?

Answers

Answer:

35 degrees.

Step-by-step explanation:

Answer:

35 degrees

Step-by-step explanation:

27 - 35 = -8

i believe X=4, but i could be wrong with the whole thing

Answers

Answer:

A. x = 4

B. RQ = 6

C. 48 square units

Step-by-step explanation:

A. 3x - 2 = 10

3x = 12

x = 12/3

B. a^2 + b^2 = c^2

8^2 + b^2 = 10^2

64 + b^2 = 100

b = sqrt (100 - 64

b = 6

C. Area of a triangle = (b*h)/2

b = (2)(6) = 12

Area = (12 * 8)/2 = 48 square units

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Answers

Answer:

3:7

Step-by-step explanation:

She has 3 tennis and 7 soccer

What is the equation of the line that passes through the point (-4,-2)(−4,−2) and has a slope of -\frac{1}{2}− 2 1 ?

Answers

Answer:

Question not clear. I cant see the value for slope.

Step-by-step explanation:

A total of 576 square tiles are needed to tile the floor of a square room
a) how many tiles fit along one wall of the room ?
b) how many square fit along the perimeter of the room ?

Answers

a) 24 tiles for along one wall of the room
b) there are 92 tiles along the perimeter

1. 81 1/2 x 27 1/3

2. 32x = 729

Answers

Answer:

Step-by-step explanation:

1. 1.811/2=3.622 271/3=813

3.622*813=2,944.686

this is number one

2. 32x=729

divide both sides by 32

32x=729/32=

22.78125 approximate=22.8 or 23

Find the slope of the line from the points and the graph.
15. (2,4) and (5, 13)
16. (4,5) and (9,-3)

Answers

(2,4) and (5,13) is m=-1/3 and (4,5) and (9,-3) is m=-8/5

Answer:

15. m=3 16. m=-8/5 or -1.6

Step-by-step explanation:

The formula for slope is m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

so for #15

[tex]\frac{13-4}{5-2}[/tex]=[tex]\frac{9}{3}[/tex]=3

and for #16

[tex]\frac{-3-5}{9-4}[/tex]=[tex]\frac{-8}{5}[/tex]=-1.6

Simplify -1-18
-
(18)
O - |18|
0-18
O 18

Answers

Answer:

simplify -1-18

Step-by-step explanation:

Subtract 18 from −1

− 19

A $500 prize is shared equally between Maxwell and
Lino.
What fraction of the money does Maxwell get?

Answers

Answer:

1/2 50% $250

Step-by-step explanation:

Answer:

250$, or in fraction form, 1/2

Step-by-step explanation:

There are 2 people, so divide 1 whole by 2. Which is .5, or 1/2

Write the word sentence as a Equation.

The difference between a number p and 6 is -14

Answers

Step-by-step explanation:

how do we find the difference between 2 numbers ? by subtracting one from the other.

p - 6 = -14

p = -8

Jan has a piece of yarn that is 6 1/2 feet long. She cuts off a piece that is 2 5/12 feet long. How much yarn does she have left?
A. 3 3/4 feet
B. 4 1/12 feet
C. 4 3/4 feet
D. 8 7/12 feet

Please keep answer simple, and no absurd, out of context answers, thank you!

Answers

The answer is b because all you have to do is just subtract if I am wrong so sorry

Select all relations that represent function

Answers

the first three i believe represent a function

HELP!! WITH MATH- Percent increase and decrease!! CHECK THE PHOTO! (I’LL GIVE BRAINLIEST TO THE RIGHT ANSWERS)

Answers

Answer: 1. 24

2. 32

3. 22

4. 16

5. 14

6. 34

7. 44

8. 30

9. 24

10. 50

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Replace * with a monomial in such a way, that the trinomial becomes a perfect
square.
*+12x+1

Answers

Answer: 36x^2

Step-by-step explanation:

Hi! I usually hate to use links, but I actually just answered this same question for someone else. I would copy and paste, but my copy and paste is screwing up the format making it super hard to read. I'm attaching the link instead. Hope this helps!

https://brainly.com/question/26017159?cb=1639960292092

Select all relations that represent function

Answers

Answer:

The last three are all functions.

The first one is not because by defenition of function, an x value cannot have two y values.

The second one is because a function f(x) is the same thing as y

The third one is because x value does not repeat, and that is all that matters.

The fourth one is a function too since x values do not have two y values

What is the slope of a line that passes through the points (5, 6) and (−11, 14)

Answers

Answer:

m = -1/2

Step-by-step explanation:

let me know if it helped

(too lazy to write a explanation)

If the only force acting on the player is gravity what is F in F=ma?

Answers

Answer:

F is the force due to gravity

Step-by-step explanation:

F is the force resulting from gravity acting on the player whose mass is m. 'a' is the acceleration due to gravity, about 9.8 meters/second².

Ricky scored 20 points in his first game and 18 points in his second game. He played three games during the week and averaged 21 points per game. How many points did he score in his third game?

Answers

Answer:

25 points

Step-by-step explanation:

21 x 3

-20

-18

Jessie has $120 saved and earns $40 each month in
allowance. Peter has $180 saved and earns $20 a month
in allowance. If they both save their entire allowances,
how long will it take before Jessie and Peter have saved
the same amount of money?

Answers

Answer:

3 months

Step-by-step explanation:

Jessie starts with $120 and get $40 a month

peter has $180 and get $20 a month

1 month passed Jessie now has $160 and Peter has $200

2 months passed Jessie now has $200 and Peter has $220

3 months passed Jessie now has $240 and Peter has $240

What is the equation for Having your boss pay you 10,000 a day for 3 full weeks

Answers

Answer:

210,000 units

Step-by-step explanation:

Let d represent each day

Let p represent amount paid

p = 10000x

If paid for 3 full weeks.

3 weeks is 3x7 =21 days so:

p = 10000x

p = 10000(21)

p = 210000 units

Answer:

210,000

Step-by-step explanation:

10,000x(3x7)

10,000x21=210,000

estimate the area of the following irregular shapes

Answers

Answer and Explanation: We will find the area of the given shape:

To find the area, we will count the number of squares of the shaded area.

While calculating the area for a more accurate estimate, we count the square as “1” if the shaded region covers more than half of each square. By counting the squares, the area is approximately 50 square units.

Use long division to find the quotient below. (8x^3-10x^2-19x-15)/(2x-5)

Answers

Answer:

4x2 + 5x + 3

Step-by-step explanation:

Help please serious answers only

Answers

Step-by-step explanation:

1 Use the Quadratic Formula.

x=\frac{2+2\sqrt{14}\imath }{30},\frac{2-2\sqrt{14}\imath }{30}

2+2



2−2



2 Simplify solutions.

x=\frac{1+\sqrt{14}\imath }{15},\frac{1-\sqrt{14}\imath }{15}



1−



Done

Guy and Jim work at a furniture store. Guy is paid $185 per week plus 3% of his total sales in dollars, X, which can be represented by g(x) = 185 +0.03x. Jim is paid $275 per week plus 2.5% of his total sales in dollars, x, which can be represented by f(x) = 275 +0.025%. Determine the value of x, in dollars, that will make their weekly pay the same.

Answers

Answer:

$18,000.

Step-by-step explanation:

When their weekly pay is the same:

185 + 0.03x = 275 + 0.025x

0.03x - 0.025x = 275 - 185

0.005x = 90

x =90/0.005

x = 18,000

Jon buys a shirt for $40 and then buys socks for $15. He lives in Maine and their
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Answers

Jon pays $40 and $15. This means that he pays a total of $55. You multiply the total cost by 0.05, which is $2.75. To convert a number to a percentage, multiply it by 100. So, 0.05 as a percent is equal to 5%.

His sales tax will be $2.75.

help mee plss 5 mins

Answers

Answer:

20 ft

Step-by-step explanation:

It is 20 ft because you use pathagoren therom.

a^2 + b^2 = c^2

Answer:

The question cut off but I'm assuming this is basically just a find the area of the shaded region type of question. First thing you need to do is calculate the areas of the right triangle and the rectangle. Subtract the area of the triangle from the area of the rectangle.

Area of rectangle: 8 x 7 = 56ft^2

Area of the triangle: (6 x 2)/2 = 6ft^2

Subtract 6ft^2 from 56ft^2 and you get:

56 - 6 = 50ft^2

Area of shaded region is 50ft^2

Which relationship has a zero slope? A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5) A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).

Answers

Answer:y =3 x=1 hope this helps :)

Step-by-step explanation:

What is the slope of the line that passes through the points (8, -4) and (6, 2)?
Write your answer in simplest form.

Answers

Answer:

-3

Step-by-step explanation:

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

m=(2-(-4))/(6-8)

m=(2+4)/-2

m=6/-2

m=-3

Sixteen is 64% of what number?

A. 12
B. 48
C. 32
D. 25

Answers

Answer:

D. 25

Step-by-step explanation:

16 divided by 64% is 25

Answer:

Step-by-step explanation:

Hope I helped you.

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