2. For all real numbers x and y, (2x + 3y)² = ?

Answer:

228573

Step-by-step explanation:

a = 219 (first term)

an = 2018 (last term)

Sn->Sum of n terms

Sn=n/2(a + an)         [Where n is no. of terms] -> eq 1

To find number of terms,

an = a + (n-1)d     [d->Common Difference] -> eq 2

d= 226-219 = 7

=> d=7

Substituting in eq 2,

2018 = 219 + (n-1)(7)

1799 = (n-1)(7)

1799 = 7n-7

1799 = 7(n-1)

1799/7 = n-1

257 = n-1

n=258

Substituting values in eq 1,

Sn = 258/2(219+2018)

    = 129(2237)

    = 228573

Answer:

1320

Step-by-step explanation:

Use the formula for sum of series, s(a) = n/2(2a + (n-1)d)

The terms increase by 6, so d is 6

a is the first term, -56

n is the terms you want to find, 33

Plug in the numbers, 33/2 (2(-56)+(32)6)

Simplify into 33(80)/2 and you get 1320

Answer:

abc is a triangle so ,

a is ( 9,6 )

b is ( 9,3 )

and c is ( 3,3 )

Answer:

Ekta and Preyal

Step-by-step explanation:

[tex]\\ \rm\Rrightarrow -30=5(x+1)[/tex]

[tex]\\ \rm\Rrightarrow -30=5x+5[/tex]

[tex]\\ \rm\Rrightarrow 5x=-30-5[/tex]

[tex]\\ \rm\Rrightarrow 5x=-35[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{-35}{-5}[/tex]

[tex]\\ \rm\Rrightarrow x=7[/tex]

Answer:

x = -7

Step-by-step explanation:

-30 = 5 (x -1 )

5 ( x + 1 ) =-30

5 (x + 1 ) = - 30

     5            5

x + 1 = -6

x + 1 -1 = -6 -1

x = - 7

Answer:

See Below (Boxed Solutions).

Step-by-step explanation:

We are given the two complex numbers:

[tex]\displaystyle z = \sqrt{3} - i\text{ and } w = 6\left(\cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12}\right)[/tex]

First, convert z to polar form. Recall that polar form of a complex number is:

[tex]z=r\left(\cos \theta + i\sin\theta\right)[/tex]

We will first find its modulus r, which is given by:

[tex]\displaystyle r = |z| = \sqrt{a^2+b^2}[/tex]

In this case, a = √3 and b = -1. Thus, the modulus is:

[tex]r = \sqrt{(\sqrt{3})^2 + (-1)^2} = 2[/tex]

Next, find the argument θ in [0, 2π). Recall that:

[tex]\displaystyle \tan \theta = \frac{b}{a}[/tex]

Therefore:

[tex]\displaystyle \theta = \arctan\frac{(-1)}{\sqrt{3}}[/tex]

Evaluate:

[tex]\displaystyle \theta = -\frac{\pi}{6}[/tex]

Since z must be in QIV, using reference angles, the argument will be:

[tex]\displaystyle \theta = \frac{11\pi}{6}[/tex]

Therefore, z in polar form is:

[tex]\displaystyle z=2\left(\cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6}\right)[/tex]

Part A)

Recall that when multiplying two complex numbers z and w:

[tex]zw=r_1\cdot r_2 \left(\cos (\theta _1 + \theta _2) + i\sin(\theta_1 + \theta_2)\right)[/tex]

Therefore:

[tex]\displaystyle zw = (2)(6)\left(\cos\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right) + i\sin\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right)\right)[/tex]

Simplify. Hence, our polar form is:

[tex]\displaystyle\boxed{zw = 12\left(\cos\frac{9\pi}{4} + i\sin \frac{9\pi}{4}\right)}[/tex]

To find the complex form, evaluate:

[tex]\displaystyle zw = 12\cos \frac{9\pi}{4} + i\left(12\sin \frac{9\pi}{4}\right) =\boxed{ 6\sqrt{2} + 6i\sqrt{2}}[/tex]

Part B)

Recall that when raising a complex number to an exponent n:

[tex]\displaystyle z^n = r^n\left(\cos (n\cdot \theta) + i\sin (n\cdot \theta)\right)[/tex]

Therefore:

[tex]\displaystyle z^{10} = r^{10} \left(\cos (10\theta) + i\sin (10\theta)\right)[/tex]

Substitute:

[tex]\displaystyle z^{10} = (2)^{10} \left(\cos \left(10\left(\frac{11\pi}{6}\right)\right) + i\sin \left(10\left(\frac{11\pi}{6}\right)\right)\right)[/tex]

Simplify:

Simplify using coterminal angles. Thus, the polar form is:

[tex]\displaystyle \boxed{z^{10} = 1024\left(\cos \frac{\pi}{3} + i\sin \frac{\pi}{3}\right)}[/tex]

And the complex form is:

[tex]\displaystyle z^{10} = 1024\cos \frac{\pi}{3} + i\left(1024\sin \frac{\pi}{3}\right) = \boxed{512+512i\sqrt{3}}[/tex]

Part C)

Recall that:

[tex]\displaystyle \frac{z}{w} = \frac{r_1}{r_2} \left(\cos (\theta_1-\theta_2)+i\sin(\theta_1-\theta_2)\right)[/tex]

Therefore:

[tex]\displaystyle \frac{z}{w} = \frac{(2)}{(6)}\left(\cos \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right) + i \sin \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right)\right)[/tex]

Simplify. Hence, our polar form is:

[tex]\displaystyle\boxed{ \frac{z}{w} = \frac{1}{3} \left(\cos \frac{17\pi}{12} + i \sin \frac{17\pi}{12}\right)}[/tex]

And the complex form is:

[tex]\displaystyle \begin{aligned} \frac{z}{w} &= \frac{1}{3} \cos\frac{5\pi}{12} + i \left(\frac{1}{3} \sin \frac{5\pi}{12}\right)\right)\\ \\ &=\frac{1}{3}\left(\frac{\sqrt{2}-\sqrt{6}}{4}\right) + i\left(\frac{1}{3}\left(- \frac{\sqrt{6} + \sqrt{2}}{4}\right)\right) \\ \\ &= \boxed{\frac{\sqrt{2} - \sqrt{6}}{12} -\frac{\sqrt{6}+\sqrt{2}}{12}i}\end{aligned}[/tex]

Part D)

Let a be a cube root of z. Then by definition:

[tex]\displaystyle a^3 = z = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]

From the property in Part B, we know that:

[tex]\displaystyle a^3 = r^3\left(\cos (3\theta) + i\sin(3\theta)\right)[/tex]

Therefore:

[tex]\displaystyle r^3\left(\cos (3\theta) + i\sin (3\theta)\right) = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]

If two complex numbers are equal, their modulus and arguments must be equivalent. Thus:

[tex]\displaystyle r^3 = 2\text{ and } 3\theta = \frac{11\pi}{6}[/tex]

The first equation can be easily solved:

[tex]r=\sqrt[3]{2}[/tex]

For the second equation, 3θ must equal 11π/6 and any other rotation. In other words:

[tex]\displaystyle 3\theta = \frac{11\pi}{6} + 2\pi n\text{ where } n\in \mathbb{Z}[/tex]

Solve for the argument:

[tex]\displaystyle \theta = \frac{11\pi}{18} + \frac{2n\pi}{3} \text{ where } n \in \mathbb{Z}[/tex]

There are three distinct solutions within [0, 2π):

[tex]\displaystyle \theta = \frac{11\pi}{18} , \frac{23\pi}{18}\text{ and } \frac{35\pi}{18}[/tex]

Hence, the three roots are:

[tex]\displaystyle a_1 = \sqrt[3]{2} \left(\cos\frac{11\pi}{18}+ \sin \frac{11\pi}{18}\right) \\ \\ \\ a_2 = \sqrt[3]{2} \left(\cos \frac{23\pi}{18} + i\sin\frac{23\pi}{18}\right) \\ \\ \\ a_3 = \sqrt[3]{2} \left(\cos \frac{35\pi}{18} + i\sin \frac{35\pi}{18}\right)[/tex]

Or, approximately:

[tex]\displaystyle\boxed{ a _ 1\approx -0.4309 + 1.1839i,} \\ \\ \boxed{a_2 \approx -0.8099-0.9652i,} \\ \\ \boxed{a_3\approx 1.2408-0.2188i}[/tex]

Answer:4 in each bad 2 left over

Step-by-step explanation:

Answer:

4 in each bag and 2 left over

Step-by-step explanation:

divide 14 by 3

3 goes into 14, 4 times

14 - 12 = 2

4 in each bag and then 2 left over

Answer:

divide, 2x+9

Step-by-step explanation:

got it right

[tex]\\ \sf\longmapsto m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{1-3}{-4-3}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{-2}{-7}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{2}{7}[/tex]

Points are (-7,6),(11,-4)

[tex]\boxed{\sf slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{-4-6}{11+7}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{-10}{18}[/tex]

[tex]\\ \sf\longmapsto m=-\dfrac{5}{9}[/tex]

Answer:

Step-by-step explanation:

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

9) Mark any two point on the line

(x₁ , y₁) = (3 , 3)   ;   (x₂, y₂) = (-4 ,1)

[tex]Slope =\frac{1-3}{-4-3}\\\\=\frac{-2}{-7}\\\\=\frac{2}{7}[/tex]

10) (x₁ , y₁) = ( -7 , 6)   ;   (x₂, y₂) = (11 ,-4)

[tex]Slope =\frac{-4-6}{11-[-7]}\\\\ =\frac{-4-6}{11+7}\\\\=\frac{-10}{18}\\\\=\frac{-5}{9}[/tex]

Answer:

9 years older

Step-by-step explanation:

The ratio of their ages is 8 : 5 = 8x : 5x ( x is a multiplier )

In 30 years their ages will be 8x + 30 and 5x + 30 and the ratio 6 : 5 , so

[tex]\frac{8x+30}{5x+30}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )

5(8x + 30) = 6(5x + 30) ← distribute parenthesis on both sides

40x + 150 = 30x + 180 ( subtract 30x from both sides )

10x + 150 = 180 ( subtract 150 from both sides )

10x = 30 ( divide both sides by 10 )

x = 3

Then

Michell is 8x = 8 × 3 = 24 years old

Connor is 5x = 5 × 3 = 15 years old

Mitchell is 24 - 15 = 9 years older than Connor

Answer:

-1

Step-by-step explanation:

I know that i^4 = 1

i^10 = i^4 * i^4 * i^2

     = 1 * 1 * i^2

We know that i^2 = -1

    =1 *1 *-1

    = -1

Answer:

Step-by-step explanation:

Question:

Max needs to purchase a car and  withdraws $100 from his bank. In a few days he withdraws another $50 to make same repairs. In total what is the change in his bank balance from theese two costs?

Solution:

(-100) + (-50) =

-150

Answered by G a u t h m a t h

3x+x^2=3x+x^2

3x-3x=x^2-x^2

which means x=0

Answer:

4+2x = 12

Step-by-step explanation:

sum means add an is means equal

4+2x = 12

Step-by-step explanation:

the sum of 4 and twice a number is 12:

The type of budget that would likely work best for Brody is biweeky budget.

Budget is an economic term that refers to the planning and advance formulation of expenses and income. The budget is a tool to organize expenses depending on the amount of money available.

The type of budget that would be best for Brody is a biweekly budget because he receives his payment every fifteen days (twice a month). So, he  can schedule his expenses each time he receives his payment, in this way he  does not spend all his money before he receives the next payment.

Additionally, weekly, monthly, and dairy are not correct options because they do not fit the time periods in which Brody receives payment for his services.

Learn more in: https://brainly.com/question/141889

Note:

This question is incomplete because options are missing, here are the options.

Daily budget

Biweekly budget

Monthly budget

Weekly budget

Answer:

11

Step-by-step explanation:

6+(2x+28)=x+23=-11 -> Answer can't be negative -> 11

Answer:

13

Step-by-step explanation:

Step-by-step explanation:

Given that,

We have to find the value of m∠E.

Here, two sides are equal, thus it is an isosceles triangle. As the two sides are equal, so their angles must be equal. So, ∠E and ∠D will be equal. Let us assume the measures of both ∠E and ∠D as x.

→ Sum of all the interior angles of ∆ = 180°

→ ∠E + ∠D + ∠F = 180°

→ 116° + x + x = 180°

→ 2x = 180° – 116°

→ 2x = 64°

→ x = 64° ÷ 2

→ x = 32°

Henceforth,

→ m∠E = x

→ m∠E = 32°

[tex] \\ [/tex]

~

Answer:

Step-by-step explanation:

Answer:

x6−24x5+240x4−1280x3+3840x2−6144x+4102

Step-by-step explanation:

I don't know if this is right or not but there ig?

please mark this answer as brainlist

Answer:

Slope is (1/4)

Step-by-step explanation:

The slope is calculated by (6-5)/(5-1)=1/4

Answer:  Choice A)  3x3

The 3x3 refers to the number of rows and the number of columns in that order.

As another example, this matrix

[tex]\begin{bmatrix}1 & 7 & 9\\13 & 41 & 2\\5 & 8 & 7\\92 & 3 & 5\end{bmatrix}[/tex]

is a 4x3 matrix because it has 4 rows and 3 columns.

Answer:

1) 6r+7=13+7r —> 7r–6r=7–13 —> r = – 6

2) 13–4x=1–x —> 4x–x=13–1 —> 3x=12 —> x=12/3 —> x=4

3)–7x–3x+2=–8x–8 —> –8x+7x+3x=2+8 —> 2x=10 –> x= 10/2 –> x= 5

4)–8–x=x–4x —> –x–x+4x=8 —> 2X=8 —> x= 8/2 —> x= 4

5) –14+6b+7-2b=1+5b —> 5b +2b –6b = –14+7–1 —> b=–8

6) n+2=–14–n —> n+n=–14–2 —> 2n = –16 —> n = – 16/ 2 —> n = – 8

7) n – 3n = 14 –4n —> n –3n + 4n = 14 —> 2n = 14 —> n = 14/ 2 —> n = 7

8) 7a – 3 = 3 + 6a —> 7a – 6a = 3 + 3 —> a = 6

9) 3(1–3x ) =2(–4x+7) —> 3 –9x = –8x+14 —> 9x–8x = 3–14 —> x = –11

10) –10 +x+4–5 =7x –5 —> 7x–x = –10+4–5 +5 —> 6x = –6 —> x= –6/6 —> x = –1

11) –8n +4(1+5n)=–6n–14 —> –8n +4 + 20n = – 6n– 14

20n –8n +6n= –14 –4 —> 18n = – 18 —> n = –18/18 —> n = –1

12) –6n–20=–2n +4(1–3n) —> –6n –20 = – 2n +4 –12n —> 12n +2n –6n = 4 +20 —> 8n =24 —> n = 24/8 —> n =3

I hope I helped you^_^

Answer:

1.

6r + 7 = 13 +7r

6r - 7r = 13-7

-r = 6

r = 6

2.

13 - 4x = 1-x

-4x +x = 1 -13

-3x = -12

x = -12 / -3

x = 4

3.

-7x - 3x + 2 = -8x -8

-10x +2 = -8x -8

-10x +8x = -8 -2

-2x = -6

x = -6 / -2

x = 3

4.

-8 - x  = x- 4x

-8 - x  = -3x

-x + 3x = -8

2x = -8

x = -8 / 2

x = -4

5.

-14 + 6b + 7 -2b = 1 + 5b

-7 + 4b = 1 + 5b

4b - 5b = 1 + 7

-b = 8

b = -8

6.

n + 2 = -14 -n

n + n = -14 -2

2n = - 16

n = -16 / 2

n = -8

7.

n - 3n = 14 -4n

-2n = 14 - 4n

-2n +4n = 14

2n = 14

n = 14 /2

n = 7

8.

7a - 3 = 3 + 6a

7a - 6a = 3 +3

a = 6

9.

3 ( 1 - 3x ) = 2 (-4x + 7)

3 - 9x = -8x +14

-9x +8x  = 14 - 3

-x = 11

x = -11

10.

-10 + x + 4 - 5 = 7x - 5

-10 +x -1 = 7x - 5

-11 + x = 7x - 5

-11 + 5 = 7x -x

-6 = 6x

x = -6/6

x = -1

11.

-8n + 4 ( 1 + 5n ) = -6n -14

-8n + 4 + 20n = -6n -14

12n +4 = -6n -14

12n  + 6n = -14 -4

18n = -18

n = -18/18

n = -1

12.

-6n - 20 = -2n + 4 ( 1 - 3n)

-6n - 20 = -2n + 4 - 12n

-6n - 20 = -14n +4

-20 -4 = -14n +6n

-24 = 8n

n = -24/8

n = -3

Answer:

6

BRAINLIEST, PLEASE!

Step-by-step explanation:

-19p - 2p + 16p + 12 = -18

-5p + 12 = -18

-5p = -30

p = 6

Answer:

p = 6

Step-by-step explanation:

Given

- 19p - 2p + 16p + 12 = - 18 ( simplify left side )

- 5p + 12 = - 18 ( subtract 12 from both sides )

- 5p = - 30 ( divide both sides by - 5 )

p = 6

Answer:

4

Step-by-step explanation:

1 5

2 10

3 15

4 20

i wrote it out

x+16=5x

16=4x

4=x

Marissa is currently four years old.

Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use.

Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.

Let's represent Marissa's current age "x".

According to the given question, in 16 years she will be five times older than she is today, which we can express as:

x + 16 = 5x

Solving for x, we can subtract x from both sides:

16 = 4x

Dividing both sides by 4, we get:

x = 4

Therefore, Marissa is currently 4 years old.

To learn more about the Algebra link is given below.

brainly.com/question/953809

#SPJ6

Step-by-step explanation:

Here,

| −34 |

= 34

As,

| | are absolute symbols so it's denote only the neutral number such as, | - 1 | = 1

Answer:

34

Step-by-step explanation:

|-34|

The absolute value bars means taking the non-negative value

|-34| = 34

Answer:

3x-3xy-2xy-5x+6. ( multiply the number that were outside the bracket)

By BODMAS rule...

= 3x-5x-3xy-2xy+6

= -2x-5xy+6

hope you understood...

Answer and Step-by-step explanation:

We are given an expression to simplify. According to PEMDAS

(Parenthesis, Exponents, Multiplication, Division, Addition, and Subtract [in that order]), we need to start with the parentheses first.

With what we are given, we need to multiply the value outside of the parenthesis to the values inside the parenthesis.

Start with the first set of terms in the expression.

3(x - xy)

We need to multiply 3 to the x and negative xy.

3x - 3xy

Now we go to the next set of terms in the expression.

-x(2y + 5)

Distribute the x (multiply) to the 2y and 5.

-2xy - 5x

Now, we combine like terms within the entire expression.

Combining like terms is essentially saying to combine the terms that have similar properties/values. We have values that have an x with it, and xy with it, and no variables with it. We can combine only the values with the x variable together, and the values with the xy variable can only be combined together. The values without the variables (if you have more than one), will combine only with each other.

3x - 3xy - 2xy - 5x + 6

____________________________________________

-5xy - 2x + 6   <- This is the final answer; the simplified version of the expression.

#teamtrees #PAW (Plant And Water)

Answer:

Step-by-step explanation:

Value of the car at the end of the first year = £9680

Depreciation = 12 %

Original price = £ x

If we reduce 12% of original price from x, we will get £9680

x - 12% of x  = £ 9680

[tex]x-\frac{12}{100}x=9680\\\\\\\frac{88}{100}x=9680\\\\x=9680*\frac{100}{88}\\\\x = 11000[/tex]

Original price  = £ 11000