Maths Problem. I can't quite explain it, could you help please? Thanks for every good answer. All shown on the picture :)

Answer:

2(cos30°+isin30°)

Step-by-step explanation:

Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.

On converting the rectangluar to polar form of the complex number;

x = rcosθ and y = rsinθ

Substituting in the rectangular form of the comlex number above;

z = rcosθ + irsinθ

z = r(cosθ+isinθ)

r is the modulus of the complex number and θ is the argument

r =√x²+y² and θ = tan⁻¹y/x

Given the complex number in rectangular form z = -(3)^1/2 - i

z = -√3 - i

x = -√3 and y = -1

r = √(-√3)²+(-1)²

r = √3+1

r = √4

r = 2

θ = tan⁻¹ (-1/-√3)

θ = tan⁻¹ (1/√3)

θ = 30°

Hence the complex number in polar form will be z = 2(cos30°+isin30°)

Answer:

28

Step-by-step explanation:

All angle measures must add up to 180. x + 85 + 67 = 180; x = 28

For any triangle, the three angles always add to 180 degrees

85+67+x = 180

x+152 = 180

x = 180-152

x = 28

Answer:

2/13

Step-by-step explanation:

In a standard deck of cards, there are 52 cards total, 4 kings, and 4 queens.

Probability is calculated by (number of favorable outcomes)/(number of possible outcomes), so our probability would be 8/52, which can be simplified to 2/13.

Hope this helps!

Answer:

Step-by-step explanation:

Let L be the length of this rectangle

The length of a rectangle is 2 feet less than four times the width

● L+2 = 4w

The area of this rectangle is 38.2 ft^2

● L*w = 38.2

The system of equations is

L+2 = 4w => L-4w =2

L*w = 38.2 => L= 38.2/w

Replace L by 38.2/w in L-4w =2

● L-4w = 2

● (38.2/w)-4w = 2

●(38,2-4w^2)/w = 2

● 38.2-4w^2 = 2w

● 38.2-4w^2-2w = 0

● -4w^2-2w+38.2 =0

Multiply by -1 to reduce the - signs

● 4w^2+2w-38.2 =0

This is a quadratic equation so we will use the discriminant

□□□□□□□□□□□□□□□□□

The discriminant is b^2-4ac

● b= 2 (2w)

● a= 4 (4w^2)

● c= -38.2 (the constant term)

b^2-4ac =2^2-4*4*(-38.2) = 615.2 > 0

The discriminant is positive so we have two solutions w and w' :

●●●●●●●●●●●●●●●●●●●●●●●●

w= (-2-24.8)/8 = -3.35

24.8 is the root square of 615.2(the discriminant)

●w is negative

● a distance is always positive so this value isn't a solution

w'= (-2+24.8)/8 =2.85 > 0

So this value is a solution for our equation

■■■■■■■■■■■■■■■■■■■■■■■■■■

w= 2.85 feet

Answer:

w=3.35

Step-by-step explanation:

The length of a rectangle is two feet less than four times the width:

length=4W-2

A=L*W

A=(4W-2)(W)

38.2=4W^2-2W

4W^2-2W-38.2=0  complete the square to find the solution add term(b/2)²

4W²-2W+1/4=38.2+1/4

4(W²-W/2+1/16)=38.45

4(w-1/4)^2=38.45

(w-1/4)²=38.45/4=9.6125

w-1/4=+ or -√9.6125 ( since it is width it has to be positive

w=√9.6125+1/4 = 3.35

Answer:

Third term=4

Step-by-step explanation:

Given:

C(n)=4/9(-3)^n-1

Find the third term

Let n=3

Substitute n=3 into the equation

C(n)=4/9(-3)^n-1

C(3)=4/9(-3)^3-1

Step 1: evaluate the power 3-1

C(3) = 4/9(-3)^2

Step 2: evaluate (-3)^2

C(3) = 4/9(9)

It can be rewritten as

C(3) = 4/9*9

9 numerator will strike 9 denominator out leaving 4

C(3)=4

Therefore, the third term=4

C(3)=4

Answer:

Hey there!

He can create 7 plates at most, with one carrot cake and one marble cake on each plate.

Hope this helps :)

Step-by-step explanation:

Answer:

The answer is C.) (2, -5)

Answer:

4.25%

Step-by-step explanation:

Commision =  441.30 - 375 = 66.30

Commision is based on  = 6560-5000 = 1560

Rate of Commision = (in decimal) 66.30/1560 = 0.0425  

Rate of Commision = 0.0425  * 100 =   4.25 %

Answer:

Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2

Step-by-step explanation:

The image is attached below

For the triangular sides of the roof, area is

A = [tex]\frac{1}{2}bh[/tex]

where b is the base = 4 ft

h is the vertical height = 2.24 ft

A =  [tex]\frac{1}{2}*4*2.24 =[/tex] 4.48 ft^2

for the two faces we have 2 x 4.48 ft^2 = 8.96 ft^2

For the rectangular sections of the roof, area is

A = [tex]lh[/tex]

where [tex]l[/tex] is the length of the rectangle = 5 ft

h is the height of the rectangle = 3 ft

A = 5 x 3 = 15 ft^2

For the two rectangular faces, we have 2 x 15 ft^2 = 30 ft^2

For the bottom face, area is

A = [tex]lw[/tex]

where [tex]l[/tex] is the length of the house = 5 ft

w is the width of the house = 4 ft

A = 5 x 4 = 20 ft^2

Surface area of the roof of the dog kennel is

8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2

Answer:

Step-by-step explanation:

Since the sequence is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

d = 6

a = 2

n = 12

So the 12th term of the sequence is

A(12) = 2 + (12-1)6

= 2 + 11(6)

= 2 + 66

Hope this helps you

Answer:

1

Step-by-step explanation:

Answer:

44 units²

Step-by-step explanation:

For triangles: (bases and heights of both triangles are equal)

Base = 4 units, height = 3 units

For trapezoid:

Base 1 = 5 units, base 2 = 3 units, height = 8 units

Area of figure = Area of two triangles + Area of trapezoid

= 2 *1/2 * base * height + 1/2(base 1+ base 2) *height

=4*3 + 1/2(5+3)*8

= 12 + 8*4

= 12 + 32

= 44 units²

The required area of the figure shown in the graph is given as 44 square units.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

here,
The area of the given figure  is given as,
Area = Area of 1 + Area of 2 + Area  3 + Area 4
Area = length × width + [1/2× base × height] + [1/2× base × height] + [1/2× base × height]

Area = 8 × 3 + 1/2 × 4 × 3 + 1/2 × 4 × 3 + 1/2 × 8 × 2
Area = 44 square units.

Thus, the required area of the figure shown in the graph is given as 44 square units.

Learn more about the surface area here: https://brainly.com/question/2835293

#SPJ6

Answer:

Take a line segment AB = 2 units (consider 1 unit = 2 cm) on x-axis.

Draw a perpendicular on B and construct a line BC = 1 unit length.

Join AC which will be √5 (Pythagoras theorem). Take A as center, and AC as radius draw an which cuts the x-axis at point E.

The line segment AC represents √5 unit

Answer:

27

Step-by-step explanation:

3 cubed=3✖️3✖️3=27

Answer:

3³ = 3 × 3 × 3 = 9 × 3 = 27

Hope this helps you

Answer:

hi you can solve this sum by 4×side formula

Step-by-step explanation:

plz solve and check you equation

Answer:

I hope it helps you......

Answer:

The coordinates of the triangle, (3, 6), (3, -3), and (3, 3), dilated by a magnitude of 3 is;

(9, 18), (9, -9), and (9, 9)

Step-by-step explanation:

The vertices of the given triangle are;

(3, 6), (3, -3), and (3, 3)

A dilation with a magnitude of 3 can be found as follows;

For each value of the x, and y-coordinates of the vertices, we multiply by the magnitude of dilation

As an example, the coordinate of the points on a line, (x₁, y₁) and (x₂, y₂), dilated by a scale factor of m, will become, (m·x₁, m·y₁) and (m·x₂, m·y₂)

Therefore, we have foe a magnitude of 3;

(3, 6), (3, -3), and (3, 3) becomes, (3×3, 3×6), (3×3, 3×(-3)), and (3×3, 3×3)

(9, 18), (9, -9), and (9, 9).

Answer:

(9, 18), (9, -9), and (9, 9)

Step-by-step explanation:

Answer:

[tex] f = 12.7 [/tex]

Step-by-step explanation:

Given:

<H = 94°

FG = h = 15

<F = 58°

GH = f = ?

Use the law of sines to find f:

[tex] \frac{f}{sin(F)} = \frac{h}{sin(H)} [/tex]

[tex] \frac{f}{sin(58)} = \frac{15}{sin(94)} [/tex]

[tex] \frac{f}{0.848} = \frac{15}{0.998} [/tex]

[tex] \frac{f}{0.848} = 15.03 [/tex]

Multiply both sides by 0.848

[tex] \frac{f}{0.848}*0.848 = 15.03*0.848 [/tex]

[tex] f = 15.03*0.848 [/tex]

[tex] f = 12.74544[/tex]

[tex] f = 12.7 [/tex] (nearest tenth)

Answer:

n = 4

Step-by-step explanation:

4(2n + 3) = 44

Expand the brackets.

4(2n) + 4(3) = 44

8n + 12 = 44

Subtract 12 on both sides.

8n + 12 - 12 = 44 - 12

8n = 32

Divide both sides by 8.

(8n)/8 = 32/8

n = 4

Answer:

y = 250

Step 1:

To solve, we plug in 50x for y.

[tex]50x=200+10x[/tex]

Then, we subtract the 10x from the right side. Our goal is to get the x by itself first.

[tex]40x=200[/tex]

Then, we divide both sides by 40, since we have to get the x by itself.

[tex]\frac{40x}{40}=x\\\\\frac{200}{40} =5[/tex]

x = 5

Step 2:

Now that we found x, we plug in 5 to the original equation and solve from there.

[tex]y=200+10(5)\\y=200+50\\y=250[/tex]

y = 250

Answer:

740 m^2

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

SQUARE:

The area of the square is:

[tex]9x^2-12x+4[/tex]

Factor it:

[tex]=9x^2-6x-6x+4\\=3x(3x-2)-2(3x-2)\\=(3x-2)(3x-2)\\=(3x-2)^2[/tex]

Remember that all four sides of a square is equal. The area is simply the side squared. Therefore, all four sides of the square measure (3x-2).

RECTANGLE:

[tex]25x^2-16y^2\\[/tex]

Factor it. This resembles the difference of two squares, where:

[tex](x-a)(x+a)=x^2-a^2[/tex]

[tex]25x^2-16y^2\\=(5x)^2-(4y)^2\\=(5x-4y)(5x+4y)[/tex]

This cannot be simplified further. Note that the sides of rectangles doesn't necessarily have to be the same.

The dimensions of the rectangle is:

(5x-4y) by (5x+4y)

Answer:

Step-by-step explanation:

1. the area of square is 9x^2-12x+4 square units

shortcut: (a-b)^2= a^2-2ab+b^2

then simplify 9x^2-12x+4 to (3x-2)^2

area of square = s^2

then side equals sqrt((3x-2)^2)

s = (3x-2) units

2. the area of rectangle is (25x^2-16y^2) square units

shortcut: (a^2-b^2) = (a-b)(a+b)

then simplify (25x^2-16y^2) to (5x-4y)(5x+4y) square units

one side is: (5x-4y) units

one side is (5x+4y) units

Step-by-step explanation:

We need to find the value of k so that the triangle with vertices (1, -1), (-4,2k) and (-k, – 5) is 24 sq. units.

The area of triangle is given by :

[tex]A=\dfrac{1}{2}\times [x_1(y_2-y_3)-x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]

Here,

x₁ = 1, y₁ = -1, x₂ = -4, y₂ = 2k, x₃ = -k and y₃ = -5

So,

[tex]24=\dfrac{1}{2}\times [1(2k-(-5))-(-4)((-5)-(-1))+(-k)((-1)-(2k))][/tex]

We need to solve the above equation,

[tex]48=[1(2k-(-5))-(-4)((-5)-(-1))+(-k)((-1)-(2k))][/tex]

On solving the above equation we get the value of k as :

k = 4.7

Answer:

Step-by-step explanation:

The quotient of two numbers is 305.4. Find the quotient if the divisor decreases 2 times and the divisor increases 3 times

x/y = 305.4

3x/(y/2) = 6x/y = 6*305.4 = 1832.4

Note that the question will be deleted soon because it is posted in a language other than English.

Обратите внимание, что вопрос будет удален в ближайшее время, потому что он размещен на языке, отличном от английского.

Answer: X

Step-by-step explanation:

Answer:

1.25

Step-by-step explanation:

8x² -38x + 35 = 0

8x² - 10x - 28x + 35 = 0

2x(4x - 5)-7(4x - 5) = 0

(4x−5)(2x−7) = 0

4x - 5 = 0 or 2x - 7 = 0

x = 5/4 or x = 7/2

x = 1.25 or 3.5

Smallest value being = 1.25

Answer:

BD

Step-by-step explanation:

to find the longest segment in a triangle, first find the largest angle and the line opposite to it is the largest segment:

in this case it is angle BCD and the segment opposite is BD

Answer:

3,500 tons

Step-by-step explanation:

We know that 1,400 tons is 2/5 of the Consolidated Brick Company's output.

This means that 1/5 must be equal to 700 tons if 2/5 is 1,400.

So, we can find the total output by multiplying 700 by 5, since 700 is 1/5 of the total.

700(5) = 3,500 tons

Answer:

Does this sample provide convincing evidence that the machine is working properly?

Yes.

Step-by-step explanation:

Normal distribution test:

[tex]$z=\frac{x- \mu }{ \frac{\sigma}{\sqrt{n}} }=\frac{ (x-\mu)\sqrt{n}}{\sigma} $[/tex]

Where,

[tex]x: \text{ sample mean}[/tex]

[tex]\sigma: \text{ standard deviation}[/tex]

[tex]n: \text{ sample size determination}[/tex]

[tex]\mu: \text{ hypothesized size of the screw}[/tex]

[tex]$z=\frac{(1.476-1.5)\sqrt{200} }{0.203 } $[/tex]

[tex]$z=\frac{(-0.024)10\sqrt{2} }{0.203 } $[/tex]

[tex]z \approx -1.672[/tex]

Once the significance level was not given, It is usually taken an assumption of a 5% significance level.

Taking the significance level of 5%, which means a confidence level of 95%, we have a z-value of [tex]\pm 1.96[/tex]

Therefore, we fail to reject the null. It means that the hypothesis test is not statistically significant: the average length is not different from 1.5!