What is the product of the complex numbers below?
(2 - 3i)(1 + 7i)

A)-19+11i
B) 23-17i
C) -19-17i
D) 23+11i

Answer:

its less than <

Step-by-step explanation:

........

Answer:

>

Step-by-step explanation:

[tex]12 \times 1 \frac{2}{5} = 12 \times \frac{7}{5} = \frac{60}{5} \times \frac{7}{5} = \frac{420}{25} = 16 \frac{20}{25} [/tex]

Step-by-step explanation:

To find - How can you determine the number of solutions of a system

              of linear equations by inspecting its equations?

Proof -

There exists three types of solution for a system of linear equations.

1. No solution.

2. Unique solution.

3. Infinite many solutions.

Now,

Let the 2 linear equations are as follows :

y = ax + b

y = cx + d

1. For no solution -

a = c and b ≠d

For example-

y = -2x + 5

y = -2x  - 1

Subtract first equation from second , we get

y - y = -2x - 1 - ( -2x + 5)

⇒0 = -2x - 1 + 2x - 5

⇒0 = -6

Not possible

So, There exist no solution.

2. For unique solution -

a ≠ c and b , d can be any value

For example -

If b and d are same ,

y = 2x - 4

y = -3x - 4

Subtract equation 1st from 2nd , we get

y - y = -3x - 4 - ( 2x - 4)

⇒0 = -3x - 4 - 2x + 4

⇒0 = -5x

⇒x = 0

⇒y = 2(0) - 4 = -4

∴ we get

x = 0, y = -4

If b and d are different

y = 2x - 4

y = -3x + 5

Subtract equation 1st from second

y - y = -3x + 5 - 2x + 4

⇒0 = -5x + 9

⇒-5x = -9

⇒x = [tex]\frac{9}{5}[/tex]

⇒y =2([tex]\frac{9}{5}[/tex]) - 4 = [tex]\frac{18}{5} - 4 = \frac{18 - 20}{5} = -\frac{2}{5}[/tex]

∴ we get

x = [tex]\frac{9}{5}[/tex] , y = [tex]-\frac{2}{5}[/tex]

3. Infinitely many solution -

a = c and b = d

For example -

y = -4x + 1

y = -4x + 1

Subtract equation first from equation second

y - y = -4x + 1 - ( -4x + 1)

⇒0 = -4x + 1 + 4x - 1

⇒0 = 0

Satisfied

So, Infinite many solution possible.

9514 1404 393

Answer:

 2 nickels, 9 dimes

Step-by-step explanation:

When there are a number of overlapping shaded areas on the graph, I find it convenient to use the reverse of the inequalities. That makes the unshaded area the solution space. Here, the vertices of the triangular solution space are ...

  (2, 9), (2, 13), (6, 9)

Any of the grid points within (or on) this triangle is a possible solution. One of them is (2, 9) corresponding to 2 nickels and 9 dimes.

__

Three solutions are shown:

  (x, y) = (2, 9), (3, 10), (4, 11)

Answer:

66

Step-by-step explanation:

6x + 8y + 6

x=2

y=6

Replace the letters with the numbers:

6(2) + 8(6) +6

= 12 +48 + 6

= 66

Answer:

y= -6x+62

Step-by-step explanation:

y-y1=m(x-x1)

y-8=-6(x-9)

y-8=-6x+54

+8        +8

y= -6x+62

Answer:

Hiya!

Are there any answers I can choose from?

Thank you muchly,

        Pandora

Step-by-step explanation:

Answer:

7/ 36

Step-by-step explanation:

Roll of 2 fair six sided die :

Sample space = 6² = 36

Sum of 7:

(1,6) ; (6,1) ; (3,4) ; (4,3) ; (2,5) ; (5,2) = 6

Probability = required outcome / Total possible outcomes

Required outcome = 7

Total possible outcomes = 36

P(obtaining a sum of 7) = 7 / 36

Answer:

6.4

Step-by-step explanation:

Answer:$5.50

Step-by-step explanation:

22.50 -11.50= 11

soda and popcorn (2 items)

11/2= 5.50

Answer:

unsimplified : [tex]\frac{21}{225} or simplified: \: \frac{7}{75}[/tex]

Step-by-step explanation:

Work out : Look above at image.

Answer:

the answer is actually D

Step-by-step explanation:

this is for the the perso above .......

its ashamed what u do for points there r ppl out there that rlly need help :)

Answer:

D) got it on edge

Step-by-step explanation:

Answer:

Step-by-step explanation:

2.5(2 1/2) / 0.8(4/5)

Hope this helped!!

Answer:

The Pythagorean theorem consists of a formula a^2+b^2=c^2 which is used to figure out the value of (mostly) the hypotenuse in a right triangle. The a and b are the 2 "non-hypotenuse" sides of the triangle (Opposite and Adjacent).

Answer:

Step-by-step explanation:

Used t find missing side angles when two sides are present. For example, if you have a short leg and a long leg, you can use the Pythagorean Theorem to find the hypotaneus and vse versa, using it to find the short or long leg if the other two are given.

Answer:

we dont know what the equation equals yes im using this for free points im having a compition with my friend so ty im srry if i offended you

Step-by-step explanation:

Answer:

its c

Step-by-step explanation:

because i multuply

Answer:

320 cubic centimeters

Step-by-step explanation:

Multiply.

--

20 x 4 x 4 = 320

--

Finding Volume

Length x Width x Height = Volume

--

Answer: 79

Step-by-step explanation:

6 ÷ 3 + 9 x² - 4=79

Answer:

$2440

Step-by-step explanation:

a10 = a1 + (n-1)d <--- arithmetic sequence formula

a10 = 1000 + 9(160)

a10 = 2440

Answer:

2/7

Step-by-step explanation:

Answer:

86.6667% decrease

Step-by-step explanation:

Answer:

good luck

Step-by-step explanation:

Answer:

(5,3)

Step-by-step explanation:

you would move 3 to the right and 2 down

Answer:

376

Step-by-step explanation:

Answer: p < -3/5

Step-by-step explanation:

2p - 4 < -3p - 7

+3p       +3p

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

5p - 4 < -7

     +4   +4

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

5p < -3 (divide by 5)

p < -3/5

Answer:

Step-by-step explanation:

A side of the triangle must be shorter than the sum of the remaining two sides.

He cannot make a triangle with 3, 4, and 8.

Given:

In a right angle triangle ABC, [tex]\angle B=90^\circ,x=8.7\ m[/tex], and [tex]\theta = 45^\circ[/tex]

To find:

The value of AC.

Solution:

In a right angle triangle,

[tex]\cos \theta =\dfrac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos \theta =\dfrac{BC}{AC}[/tex]

[tex]\cos (45^\circ) =\dfrac{8.7}{AC}[/tex]

[tex]\dfrac{1}{\sqrt{2}}=\dfrac{8.7}{AC}[/tex]

On cross multiplication, we get

[tex]AC=8.7\times \sqrt{2}[/tex]

[tex]AC=12.30365799[/tex]

[tex]AC\approx 12.304[/tex]

Therefore, the measure of AC is 12.304 m.

Answer:

67.6

Step-by-step explanation:

area = 158/360 * 49 * pi = 67.56