Perfect square trinomial:
(a – b)2 = (a – b)(a – b) = a2 – 2ab + b2
Find the product of (k – 9)2 using the perfect square trinomial rule shown on the left.



The product (k – 9)2 can also be written as
.

The product is k2 –
k +
.

Answers:

=====================================================

Explanation for part (a)

Consider four slots labeled A,B,C,D.

We have

We started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440

You can use the nPr permutation formula as an alternative method

[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]

in this case n = 18 and r = 4. The exclamation marks indicate factorial.

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

Explanation for part (b)

Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.

Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.

There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)

73440/24 = 3060

You could use the nCr combination formula to get the same result

[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]

where n = 18 and r = 4 are the same from last time.

The connection between nPr and nCr is this

[tex]_nC_r = \frac{_nP_r}{r!}[/tex]

which can be rearranged into

[tex]_nP_r = r!*\left( _nC_r \right)[/tex]

these formulas are handy to help us go back and forth between nCr or nPr.

If the order of the choices is relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 73440.

If the order of the choices is not relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 3060.

Combination is a way of selecting items from a collection where the order of arrangement is not relevant.

It is given by:

[tex]^nC_r[/tex] = n! / r! (n-r)!

Permutation is a way of selecting items from a collection where the order of the arrangement is relevant.

It is given as:

[tex]^nP_r[/tex] = n! / (n-r)1

We have,

Number of distinct colors = 18

Number of colors to be chosen = 4

The number of ways the four colors be chosen when the order is not relevant:

= [tex]^{18}C_4[/tex]

= 18! / 4! 14!

= 18 x 17 x 16 x 15 / 4 x 3 x 2

= 3060

The number of ways the four colors be chosen when the order is relevant:

= [tex]^{18}P_4[/tex]

= 18! / 14!

= 18 x 17 x 16 x 15
= 73440

Thus,

If the order of the choices is relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 73440.

If the order of the choices is not relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 3060.

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Answer:

14,977.8946

Step-by-step explanation:

Answer:

[tex]slope = \frac{y2 - y1}{x2 - x1} \\ slope = \frac{10 - 5}{20 - 15} \\ = \frac{5}{5} \\ = 1[/tex]

Answer:

The answer is just re look at the question A

Answer

THE ANSWER IS A

Step-by-step explanation:

Answer:

Step-by-step explanation:

first: x+(1/4)

second: (-1/3 )x +1/4

third: (3/4)x +1/3

Answer:

75

Step-by-step explanation:

Given data

First term= 87

Second term= -12

Hence,

87 + (-12)

open bracket

+*-= -

= 87 -12

=75

Therefore the equivalent is 75

Answer:

60 ft³

Step-by-step explanation:

GIVEN :-

TO FIND :-

FACTS TO KNOW BEFORE SOLVING :-

Volume of a cube = Length × Width × Height

SOLUTION :-

In the question , all the dimensions of the cube is given. So,

Volume of the cube = 5 × 4 × 3 = 60 ft³

Based on the calculation, the volume of the box is 60 cubic feet.

To find the volume of a box, you need to multiply its length, width, and height. In this case, the dimensions of the box are given as:

Length = 3 ft

Width = 4 ft

Height = 5 ft

To calculate the volume, multiply these dimensions together:

Volume = Length × Width × Height

Volume = 3 ft × 4 ft × 5 ft

Volume = 60 cubic ft

Therefore, the volume of the box is 60 cubic feet.

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Answer:earthy

Step-by-step explanation:vuinh

Answer:  

f

−

1

(

x

)

=

x

−

12

5

Step-by-step explanation:

Answer:

the answer is a!

Step-by-step explanation:

Answer:

w

Step-by-step explanation:

The inputs (x) have the different variables in order for it to be a function.

Answer: 107/100x

1.07x

Step-by-step explanation:

Since the price of the model is x dollars, and she also has to pay a 7% tax, the amount that Leila will pay in total for the model will be the addition of the price of the model and the tax. This will be:

= x + (7% × x)

= x + (7/100 × x)

= x + (0.07 × x)

= x + 0.07x

= 1.07x

This can also be 107/100x

Answer:i dont know

Step-by-step explanation:

Answer:

610 m^2

Step-by-step explanation:

Area of the shaded region = area of the outer rectangle - area of the inner rectangle

Area of the outer rectangle

l = 42

b = 25

a = l*b = 42*25 = 1050m^2

Area of the inner rectangle

l = 22

b = 20

a = l*b = 22*20 = 440m^2

Therefore, the area of the shaded region is = 1050 - 440

                                                                         = 610m^2

Thank You

Hope u understood

Please mark as the brainliest

Sn = a(1-r^n)/(1-r)

Sn= 8(1-1/4096)/3= 2.67

Answer:

x=28.8

Step-by-step explanation:

using cosine

cos x= adjacent/hypotenuse

cos x = 71/81

cos x = 0.8765

make x subject of the formula

x= cos^-1 0.8765

x= 28.77699973

x≈ 28.8

The required value of x is 28.8 degrees for the right triangle.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The right triangle is given in the question, as shown

We have to determine the value of x for the triangle.

As we know the cosine ratio is:

cos x = adjacent/hypotenuse

As per the question, substitute the known values in the above ratio,

cos x = 71/81

Apply the division operation,

cos x = 0.8765

Solve for x, and we get

x= cos⁻¹ (0.8765)

x = 28.77699973

x ≈ 28.8

Thus, the required value of x is 28.8 degrees.

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Answer:

40-10=30

Step-by-step explanation:

x-10=30

we are going to flip the problem which would make it addition so you would do 10+30=X and we can fill in the blank of x equalling 40 because 10+30 is 40

Answer:

x = 40

Step-by-step explanation:

x - 10 = 30

=> x = 30 + 10

=> x = 40

Answer:

LHS,

hope it helps.

Answer:

91% markup

Step-by-step explanation:

$43.20 divided by 36 is $1.20 per package

if Green Foods is selling one package for $2.29 then they are marking each package up by $1.19

if you take the difference of the per carton prices (82.44-43.20) and divide it by 43.20, you get a 91% markup

Answer:

.......

Step-by-step explanation:

Jahlan, simple interest means that interest is paid every year on the original $4000.

To find 2% of 4000, you multiply 4000(.02) = $80.

Since the interest is the same, 3(80) = $240.

Answer:

[tex]14 \ 100 \1800[/tex]

Answer:

[tex]Area =55.4ft^2[/tex]

Step-by-step explanation:

Given

The attached rhombus

Required

The area

First, calculate the length of half the vertical diagonal (x).

Length x is represented as the adjacent to 60 degrees

So, we have:

[tex]\tan(60) = \frac{4\sqrt 3}{x}[/tex]

Solve for x

[tex]x = \frac{4\sqrt 3}{\tan(60)}[/tex]

[tex]\tan(60) = \sqrt 3[/tex]

So:

[tex]x = \frac{4\sqrt 3}{\sqrt 3}[/tex]

[tex]x = 4[/tex]

At this point, we have established that the rhombus is made up 4 triangles of the following dimensions

[tex]Base = 4\sqrt 3[/tex]

[tex]Height = 4[/tex]

So, the area of the rhombus is 4 times the area of 1 triangle

[tex]Area = 4 * \frac{1}{2} * Base * Height[/tex]

[tex]Area = 4 * \frac{1}{2} * 4\sqrt 3 * 4[/tex]

[tex]Area =2 * 4\sqrt 3 * 4[/tex]

[tex]Area =55.4ft^2[/tex]

Answer:tanQ=

adjacent

opposite

​

=

24

7

​

≈0.2917≈0.29

Step-by-step explanation:

trust me bro

The value of the tangent of ∠Q is 0.96.

One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.

We have,

∠S=90°, SR = 7, QS = 24, and RQ = 25.

Using Trigonometry

tan Q = P/ B

tan Q= 24/ 25

tan Q = 0.96

Thus, the value of tan Q is 0.96.

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Answer:

10.5

Step-by-step explanation:

Answer: 1238.916

Step-by-step explanation:

A = (Bh)/3

B = 14.7 x 14.7

The area of a pyramid is the formula at the top. B in the formula at the top is the Base. The reason it is capitalized is because B is also a formula. You need to find the area of the base of the pyramid and plug it into the equation. It this case, the base is equal to the second equation above.

Answer:

270 m²

Step-by-step explanation:

LA = (3+6+3+6)×15

= 18×15 = 270 m²

Answer:

Area of shaded part = 113 mm² (Approx.)

Step-by-step explanation:

Given:

Diameter of Semi-circle = 24 mm

Find:

Area of shaded part

Computation:

Radius of semi-cicrle = Diameter of Semi-circle / 2

Radius of semi-cicrle = 24 / 2

Radius of semi-cicrle = 12 mm

So,

Radius of small circle = 12 / 2

Radius of small circle = 6 mm

Area of shaded part = Area of semi circle - Area of small circle

Area of shaded part = [πR² / 2] - [πr²]

Area of shaded part = [(3.14)(12)² / 2] - [(3.14)(6)²]

Area of shaded part = [(3.14)(144) / 2] - [(3.14)(36)]

Area of shaded part = 226.08 - 113.04

Area of shaded part = 113.04

Area of shaded part = 113 mm² (Approx.)

Answer:

x = 18.4

y = 35º

Step-by-step explanation:

cos∅ = adj/hyp

cos49 = x/28

28cos49 = x

x = 18.4

tany = opp/adj

tany = 19/27

y = arctan19/27

y = 35º