The answer is B

Starting zeros are not significant and so the number of significant digits starts from 3597. The 3 digits lands on 9 but the digit next to it is more than 5 (7) and so 1 is added to the 9 to make it 10 and so the 0 is written down and the 1 is added to the 5 next to it which makes it 6.

NOTE
Zeros between other digits are significant. Only starting zeros are insignificant. For instance 3.052306, all the zeros are significant because they are not starting zeros after a decimal point.

T ={ 2,3,5,7}

M ={1,3,5,7,9}

U {1,2,3,4,5,6,7,8,9,10}

T¹ is called T compliment, which means numbers found in universal set but can't be found in set T

M¹ is called M compliment, which means numbers found in universal set but can't be found in set M

T¹ = {1,4,6,8,9,10}

M ¹ = { 2,4,6,8,10}

T ¹ M ¹ = { 4,6,8,10}

Length of an arc = 22 cm

raduis =

π = 22⁄7

angle (∅)= ?

formular for length of an arc = ∅⁄360 x 2πr

since length of an arc =22 cm

r = 15 and π = 22⁄7

22 = π⁄360 X 2(22)⁄7 X 15

22 = π⁄360 X 44⁄7

22 = π⁄360 X 94.286

22 = 94.2860⁄360

22⁄0.262 = 0.2620⁄0.262

π =22⁄0.262

π = 84

The angle is 84 °

diffence of two squards

(27.63 - 12.37)(27.63 + 12.37)

610.4

Run it to three dicimal place

since 4 is less than 5 you maintian it

Commision on selling price let selling price of house = x

commision on selling price = x x 8⁄100

$0.08x

Eric share of the house = 17,760.00

Total selling price of the house = Agent commision + Eric share x = $117,760 + $0.80x

group like terms

x - 0.08x = 117,760.00

0.92x⁄0.92 = 117760⁄0.92

x = $178,000.000

The total selling price of the house is 128,000

Considering 2^a = √64

2^a = √64

what raise the power 2 will give you 64

2⁶ = √64

2^a = 2^61⁄2

since √ = 1⁄2

2a = 2^6(1⁄2)

divide 2 by 6

2^a = 2³⁽¹⁾

2^a = 2²

since the base arethe same we equate the exponent considering b⁄a = 3

b⁄a = 3

cross multiple

b⁄a = 3⁄l

b(1) = 3(a)

b =3a

since a = 3

b = 3(3)

b = 9

therefore a² + b² = 9² + 3²

81 + 9

90

C

NB: Change the mixed fractions to improper fractions

Explanation:

Multiply the whole number(A) by the denominator(c) and add the numerator(b) to the result(Axc). Divide everything by the denominator(c).

⇒ 2¹⁄₂ = ^{(2x2 + 1)}⁄₂ = ⁵⁄₂
⇒ 1¹⁄₂ = ^{(1x2 + 1)}⁄₂ = ³⁄₂

Concepts

a = a/₁
b = b/₁

Explanation:

Change the ÷ to x (multiplication). To do so:
Reciprocate the fraction at the right side of the ÷
Reciprocate means the top goes to the down and the down comes to the top

Explanation:

The numerators multiply each other over the denominators multiplying each other.

Thus the products of the numerators over the products of the denominators

Product means multiplication

Applying all the above concepts

Geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, none-one number called the common ratio

Rules

For the sequence a₁, a₂, a₃, a₄ ...

Where a₁ = first term

Where a₂ = second term

Where a₃ = third term

Where a₄ = forth term

r = a₂ / a₁ = a₃ / a₂ = a₄ / a₃

Where r = common ratio

Thus the common ratio (r) is the same for all calculations

Hence 4/x = 16/4

4/x = 4

Multiplying both sides by x

x x 4/ x = 4 x x

4x = 4

Dividing both sides by 4

x = 1

16/4 = y/16

4 = y/16

Multiplying both sides by 16

16 x 4 = y/16 x 16

y = 64

⇒ x:y = 1:64

Represent them by diagrams

First Ladder

Second Ladder

The angle θ can be calculated using any of SOH, CAH , TOA

SOH = sin θ = Opposite (O) / Hypotenuse (H)

CAH = cos θ = Adjacent (A) / Hypotenuse (H)

TOA = tan θ = Opposite (O) / Adjacent (A)

You have to know which of the sides are known (Adjacent, Opposite or Hypotenuse)

The hypotenuse is the side facing the right angle triangle (90^o), the ladder

The adjacent is the side adjacent to the angle θ, ground

The opposite is the side opposite (facing) the angle θ, the building

From both diagrams, the Opposite and Hypotenuse sides are known

Hence SOH can be used to calculate the angle

SOH = sin θ = Opposite / Hypotenuse

For the first ladder

Opposite = 8 m and Hypotenuse = 10 m

Hence sin θ = 8 m / 10 m = 8 / 10

For the second ladder

Opposite = h, Hypotenuse = 12 m

Hence sin θ = h m/ 12 m

Since the angle (θ) is the same as indicated in the question, it means the value of sin θ is the same for both the first and second ladders

Hence 8/10 = h/12

Multiply both sides by 12

12 x 8/10 = h

∴ h = 9.6

Considering ‣RPQ

Sum of interior angle is 180°

∠PRT + ∠RQP + ∠RPQ = 180

x+70+52 = 180

x+122 = 180

x =180 - 122

x=58°

Concept

(a+b)² = a²+2xaxb + b² = a²+2ab + b²
(a-b)² = a²-2xaxb + b² = a²-2ab + b²

Alternatively
(a+b)² = (a+b)x(a+b) [Expand and simplify]
(a-b)² = (a-b)x(a-b) [Expand and simplify]

⇒ (x-2)² = x²-2xxx2+2² = x²-4x+4
(x+1)² = x²+2xxx1+1² = x²+2x+1

(x-2)²+3 = (x+1)² - 6
x²-4x+4+3 = x²+2x+1 - 6
x²-4x+7 = x²+2x-5
x²-x²-4x-2x = -5 - 7
-6x = -12
^-6x⁄_-6 = ^-12⁄_-6
x = 2

3 can go into 48, hence express 48 as a multiplication of 3 and 16

√48 = √(16x3)

Applying √(axb) = √a x √b

⇒ √(16x3) = √16 x √3

√16 = 4

Hence √16 x √3 = 4 x √3 = 4√3

NB: 4√3 - √3 is similar to 4x - 3x, thus you can simplify like terms.

Express 72 too as a multiplication of 24 and 3 so we can cancel the √3 at the numerator and denominator

√72 = √(24 x 3) = √24 x √3

24 = 4 x 6

√24 = √(4 x 6) = √4 x √6

√4 = 2

√24 = 2 x √6 = 2√6

⇒ √72 = √(24 x 3) = √24 x √3 = 2√6 x √3

⇒ √72 /3√3 = 2√6 x √3 / 3√3

√3 cancels each other

Hence 2√6/3

y ∝ 1 / x

NB: Inversely = 1 / the relation

Varies directly = Relation 1 ∝ Relation 2

Find the constant of the relation

Let k = the constant

y = k x 1/x

When y = 6, x is 3

⇒ 6 = k/3

Multiplying both sides by 3

⇒ k = 6 x 3 = 18

Hence y = 18/x

When x = 9

⇒ y = 18 / 9 = 2

Trace any point on the graph where the line passes and use that x and y coordinates to substitute and find y

The line passes through the points (0,1), hence x = 0 and y = 1

y = d - x ⇒ 1 = d - 0 ⇒ 1 = d ⇒ d = 1

NB: The line also passes through the points (1,0), (4, -3 ). Any point on the line you use should arrive at the same answer

Since the angle of the polygon are five

It means the polygon is pentagon

interior angles of polygon = n-2x180⁄n

number of side (n) = 5

Interior angles of pentagon = (5-2)X180⁄5

=3X180⁄5

=540⁄5

108

since 180 is the interior

3x which is the smalllest angle

3x⁄3 = 108⁄3

x =60°

the smallest angle is 60°

Change the mixed fraction to an improper fraction.

Explanation:
Multiply the whole number(A) by the denominator(c) and add the numerator(b). Divide everything by the denominator(c).

⇒ 1¹⁄₁₅ = ^(1x15+1)⁄₁₅ = ¹⁶⁄₁₅

⇒ t - ⁹⁄₅ = -¹⁶⁄₁₅

Get ride of the denominators by multiplying both sides by the least common multiple(LCM)
The denominators are 5 and 15,5 can go into 15, hence the LCM is 15

tx15 -15x⁹⁄₅ = 15x-¹⁶⁄₁₅
15t - 27 = -16
15t = -16+27
15t = 11
^15t⁄₁₅ = ¹¹⁄₁₅
t = ¹¹⁄₁₅

Length = 15cm

width = x cm

If the side are double

New length = 15 X 2

30cm

New width = 2 X x

2x

2x

Area of new rectangular box = Length(L) X (W)

30cm X 2xcm

60x cm²

Move the z to the left side, + becomes - and - becomes +

E - z = kx²/2y

Multiply both sides by 2y to get rid of the 2y at the denominator

2y x (E-z) = kx²

2y(E-z) = kx²

Divide both sides by k

2y(E-z)/k = x²

To get rid of a square on an alphabet, take the square root of both sides

Thus

Change the decimal number to a standard form with a complete whole number
∴ 0.064 = 64 x 10^-3
⇒ (0.064)^-1/3 = (64 x 10^-3)^-1/3
Applying, (a x b)ⁿ = aⁿ x bⁿ ⇒ (64 x 10^-3)^-1/3 = 64^-1/3 x 10^{(-3 x -1/3)}
64^-1/3 x 10^{(-3 x -1/3)} = 64^-1/3 x 10¹
Note:-3 x -1/3, negatives cancels each other likewise the 3s
Change the 64 to an indices form in order to cancel the powers
64 = 2 x 2 x 2 x 2 x 2 x 2 = 2⁶
⇒ 64^-1/3 x 10¹ = (2⁶)^-1/3 x 10
3 goes into 6, 2 times ⇒ 6 x -1/3 = -2
∴ (2⁶)^-1/3 x 10 = 2^-2 x 10
Applying, a^-n = 1 / aⁿ
⇒ 2^-2 = 1 /2²
2² = 4
∴ 2^-2 x 10 = 1/4 x 10
Using 2 to cancel each other, 2 goes into 4, 2 times and 10, 5 times
⇒ 1/4 x 10 = 1/2 x 5 = 5/2
Note 1/2 x 5 = 1/2 x 5/1 , every number is divided by 1
Applying a/b x c/d = axc / bxd
⇒ 1/2 x 5/1 = 1 x 5 / 2 x 1 = 5/2
∴ (0.064)^-1/3 = 5/2

Expand the bracket

2x(x) +2y(x-y) +2x(x+y) 2y(x+y)

2x² - 2xy + 2xy + - 2y² + 2x² + 2xy - 2xy - 2y²

2x² - 2y² + 2x² + 2y²

Group like terms

2x² - 2y² - 2y²

factorize 4 out

4(x - y²)

(x - y²) = (x - y)(x + y)

4[(x - y)(x + y)]

∠ZXY = ∠ZOY = 70°

Length of an arc = Δ⁄2πr

since angle (Δ)π = 22⁄7 and r = 18cm

length of an arc =70⁄360 x 2 x 22⁄7 x 18

cancelation will take place here

70⁄360 x 2 x 22⁄7 x 18

1⁄18 x 22 x 18

22cm

class="remain-inline"> the subject.

Cross multiple:

5(5y – x) = 1(8y + 3X)

Expand the bracket:

25Y – 5X = 8Y + 3X

Group like terms and add:

25Y- 8Y = 3X + 5X

17Y = 8X

Divide through by 8.

Divide through by Y to make X the numerator

From the above diagram, the length of the arc becomes the circumference of the base of the cone.

radius of the circle = 22cm
θ = 60^o

NB: Unit of area = unit square (e.g cm²,m²) and unit of volume = unit cubic (e.g cm³, m³)

Run the decimal point to the right side to get whole number for easy calculation:

Cancellation will take place here, 5 will go into 15 (3times) and 189 will go into 567 (3times). Which will give us:

Group like terms:

Multiply like terms

Indices first law will be applied here. Which says

“If the bases are the same take one of the base and add the exponent:

Indices second law will be applied here. Which says

“If the bases are the same take one of the base and subtract the exponent:

9 x 10^{-6– (-5)}

9 x 10^-1

NB: Always leave your answer in standard form.

4b² – ab + (a + 9b)² – a²

step 1: Expand (a + 9b)² to give (a + 9b) (a + 9b)

4b² – ab + (a + 9b) (a + 9b) – a²

step 2: Expand the bracket:

=4b² – ab + a² + 18ab + 81b² – a²

step 3: Group like terms:

= 4b² + 81b² – ab + 18ab + a² - a²

= 4b² + 81b² – ab + 18ab

= 85b² + 17ab

step 4: Factorize 17b out:

= 17b(5b + a)

Notes

Arithmetic Progression

Is a sequence of numbers such that the difference between the consecutive terms is constant.

E.g The sequence 1,3,5,7,9.. is an arithmetic progression with a common difference of 2

a_n = a₁ + (n - 1)d

a_n = The value of the sequence number of on the n^th position.

a₁ = the first number in the sequence

d = the common difference

d = a_{n + 1} - a_n (The difference between two consecutive sequence numbers)

d is the same for all consecutive numbers used for the calculator.

Thus a_{n + 2} - a_{n + 1} = a_{n + 1} - a_n

For instance, the common difference for the sequence a₁, a₂, a₃, a₄, a₅, a₆ .... will be calculated as:
a₂ - a₁ = a₃ - a₂ = a₅ - a₄ = a₆ - a₅

NB: The common difference (d) is the higher sequence number value - lower previos sequence number.

For the sequence 1,3,5,7,9

⇒ d = 3 - 1 = 5 - 3 = 7 - 5 = 9 - 7 = 2

Summation of Arithmetic Progression

S_n = ⁿ/₂ (a₁ + a_n)

S_n = ⁿ/₂ [2a₁ + (n - 1)d]

If the last number is know the summation can also be writen as

S_n = ⁿ/₂ [a₁ + l]

where l = last term

Since Z = 8, x = 4, y = 1/8, substitute them in place of the variables.