Multiply the following complex numbers:
(5+3i)(4+ 2i)
A. 14-22i
O B. 14+ 22i
O C. 26 - 22i
O D. 26 + 22i

Answer:

[tex] {x}^{2} + 9[/tex]

Step-by-step explanation:

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

Answer:

The answer is x² + 9.

Step-by-step explanation:

First, you have to get rid of bracket of square :

[tex] {(a + b)}^{2} \: ⇒ \: {a}^{2} + 2ab + {b}^{2} [/tex]

[tex] {(x + 3)}^{2} [/tex]

[tex] = (x + 3)(x + 3)[/tex]

[tex] = {x}^{2} + 6x + 9[/tex]

Next, you can simplify :

[tex] {x}^{2} + 6x + 9 - 6x[/tex]

[tex] = {x}^{2} + 9[/tex]

Answer:

Step-by-step explanation:

Given that  cos θ =7/11, cosec θ = 1/sinθ in trigonometry.

Based on SOH, CAH, TOA;

cosθ = adjacent/hypotenuse = 7/11

adjacent = 7 and hyp = 11

Since sinθ = opp/hyp, we need to get the opposite to be able to calculate sinθ.

Using pythagoras theorem to get the opposite;

[tex]hyp^{2} = adj^{2} + opp ^{2} \\opp = \sqrt{hyp^{2} - adj^{2} } \\opp = \sqrt{11^{2} - 7^{2}} \\opp = \sqrt{72} \\opp = 6\sqrt{2}[/tex]

sinθ = 6√2/11

cosecθ = 1/sinθ = 1/( 6√2/11)

cosecθ = 1/sinθ = 11/6√2

Note the error; cscθ[tex]\neq[/tex] 1/cosθ but cscθ = 1/sinθ

Answer:

5x^2/4

Step-by-step explanation:

5 times the cube of x divided by 4 times x

(5x^3)/4x=5x^2/4

Answer:

I'm not sure what the question is... but I'm guessing you have to put this in number form? If so, the answer would be 5x^3/4x

Step-by-step explanation:

When having a number times x instead of writing the multiplication sign you just put them next to each other. (5x)

When something is cubed that means it is to the power of three (5x^3)

Divided by four times x would be 4x

Hopefully I did this right and helped you!

Answer:

The answer is C.

Step-by-step explanation:

As you type into the calculator, you will get 0.707 :

cos(45) = √2/2

cos(45) ≈ 0.707 (3s.f)

Answer:

Sean

Step-by-step explanation:

We need to find how long Sofia spent mowing and then compare with the time Sean spent.

Sean mowed his lawn in 2 ½ hours.

Sofiia mowed her lawn for ¼ hours, then stopped. She did this 7 times. This means:

1/4 * 7 = 7/4 hours = [tex]1\frac{1}{4}[/tex] hours

Therefore, Sean spent more time mowing his lawn.

Step-by-step explanation:

The main goal is to separate the values on opposite sides of the equal sign.

2 + 2x = 3 + 2x

-2 -2 ⬅Subtract 2 from both expressions

2x = 1 + 2x

-2x - 2x ⬅Subtract 2x from both sides.

0 = 1

Answer:

0 does not equal 1, which means that this equation is inconsistent. In other words, there is no solution. 0 does not equal 1, so 2 + 2x does not equal 3 + 2x.

I hope this helps! :)

Answer:

x=−2/0

Step-by-step explanation:

Steps:

Let's solve for x.

2x+2y=2x

Step 1: Add -2x to both sides.

2x+2y+−2x=2x+−2x

2y=0

Step 2: Add -2y to both sides.

2y+−2y=0+−2y

0=−2y

Step 3: Divide both sides by 0.

00=−2y0x=−20

Answer: x=−2/0

Plz mark brainlies

Hope this helps

Answer:

  47°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation ...

  Cos = Adjacent/Hypotenuse

The side adjacent to ∠P is the one with P in its name: RP. The hypotenuse is the side opposite the right angle, the side without the right-angle vertex in its name: PQ. So, ...

  cos(∠P) = RP/PQ = 61/89

  ∠P = arccos(61/89) ≈ 46.733°

  ∠P ≈ 47°

Answer:

47 degrees

Step-by-step explanation:

Answer:

2(x+8)

Step-by-step explanation:

2x+16

2(x+8)

Answer:

unfactorable with real numbers

in the complex realm

(x-4i) (x+4i)

Step-by-step explanation:

x^2+16

We can only factor this with imaginary numbers

(x^2 - (-4i)^2)

This is the difference of squares

(x -4i) (x+4i)

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

y = [tex]\frac{3}{4}x+2[/tex]

Step-by-step explanation:

In the figure attached,

Graph of the line passes through the two points (0, 2) and (4, 5).

Let the equation of this line is y = mx + b

Here m = slope of the line

b = y-intercept

Since slope of the line passing through two points is represented by,

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

   = [tex]\frac{(5-2)}{(4-0)}[/tex]

   = [tex]\frac{3}{4}[/tex]

Y-intercept of the line 'b' = 2 units

Therefore, equation of the line will be,

y = [tex]\frac{3}{4}x+2[/tex]

Answer:

Total mean: 4.3

Step-by-step explanation:

(mean for home goals)

Mean: 2.5

(mean for away goals)

Mean: 1.8

it tells us to find the total games played all together..

so:

2.5 + 1.8 = 4.3

Answer:

$43.75 (65%)

Step-by-step explanation:

35% of 125= 43.75

.35 times 125+ 43.75

Answer:

78$

Step-by-step explanation:

Answer:

[tex]=2\sqrt{3}\\\mathrm{Decimal:\quad }\:3.46410[/tex]

Step-by-step explanation:

[tex]\frac{12\sqrt{2}}{2\sqrt{6}}\\\mathrm{Divide\:the\:numbers:}\:\frac{12}{2}=6\\=\frac{6\sqrt{2}}{\sqrt{6}}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a}=a^{\frac{1}{n}}\\\sqrt{6}=6^{\frac{1}{2}}\\=\frac{6\sqrt{2}}{6^{\frac{1}{2}}}\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\frac{6^1}{6^{\frac{1}{2}}}=6^{1-\frac{1}{2}}\\=\sqrt{2}\cdot \:6^{-\frac{1}{2}+1}\\\mathrm{Subtract\:the\:numbers:}\:1-\frac{1}{2}=\frac{1}{2}\\=6^{\frac{1}{2}}\sqrt{2}[/tex]

[tex]\mathrm{Apply\:radical\:rule}:\quad \:a^{\frac{1}{n}}=\sqrt[n]{a}\\6^{\frac{1}{2}}=\sqrt{6}\\=\sqrt{6}\sqrt{2}\\\mathrm{Factor\:integer\:}6=2\cdot \:3\\=\sqrt{2\cdot \:3}\sqrt{2}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}\\\sqrt{2\cdot \:3}=\sqrt{2}\sqrt{3}\\=\sqrt{2}\sqrt{3}\sqrt{2}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{a}=a\\\sqrt{2}\sqrt{2}=2\\=2\sqrt{3}[/tex]

Answer:

Step-by-step explanation:

[tex] \frac{ 12\sqrt{2} }{2 \sqrt{6} } [/tex]

Reduce the fraction with 2

[tex] = \frac{6 \sqrt{2} }{ \sqrt{6} } [/tex]

Simplify the expression

[tex] \frac{6}{ \sqrt{3} } [/tex]

Multiply the fraction by [tex] \frac{ \sqrt{3} }{ \sqrt{3} } [/tex]

[tex] \frac{6}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } [/tex]

To multiply the fractions, multiply the numerators and denominators separately

[tex] \frac{6 \sqrt{3} }{ \sqrt{3 \times \sqrt{3} } } [/tex]

When a square root of an expression is multiplied by itself, the result is that expression

[tex] \frac{6 \sqrt{3} }{3} [/tex]

Reduce the fraction with 3

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

Hope this helps...

Best regards!!

Answer:

-4

Step-by-step explanation:

khan academy

Answer:

10/20 for green, then 4/19 for blue. 10/20 * 4/19 = 2/19

Step-by-step explanation:

Explanation is above. If you need any more help let me know.

Answer:

1 mile.

Step-by-step explanation:

3/3 mile is equal to 1 mile.

Answer:

Joe walked his dog 1 mile.

Step-by-step explanation:

3/3 =1 mile.

Answer:

[tex]g^{-1}[/tex](x) = [tex]\frac{x+10}{5}[/tex]

Step-by-step explanation:

Given

g(x) = 5(x - 2)

let y = g(x) and rearrange making x the subject, that is

y = 5(x - 2) ← distribute

y = 5x - 10 ( add 10 to both sides )

y + 10 = 5x ( divide both sides by 5 )

[tex]\frac{y+10}{5}[/tex] = x

Change y back into terms of x with x = [tex]g^{-1}[/tex] (x) , thus

[tex]g^{-1}[/tex](x) = [tex]\frac{x+10}{5}[/tex]

Answer:

Step-by-step explanation:

Given the equation x + 5 = 1, to get the solution to the equation, we need to find the value of x

Step 1: Subtract 5 from both sides of the equation

x+5-5 = 1-5

x = 1-5

Step 2: Find the value of the unknown variable x

x = -4

The solution to the equation is x = -4

Answer:

y = 6x - 8

Step-by-step explanation:

line a: y = 6x- 5

10 = 6(3) - b

10 = 18 - b

10 - 18 = -b

-8 = -b

8 = b

Answer:

I) Y=5x

II) Y=50

III)X=12

Step-by-step explanation :

I) Y=5x

II) Y=5(10)

Y=50 when x=10

III)Y=5x

60=5x

X=60/5

X=12 when y=60

Hope this helps..

Answer:

[tex]34.5575191895[/tex]

Step-by-step explanation:

[tex]2\pi r(180/360)\\2\pi *11*1/2\\=11\pi[/tex]

The arc length of the semicircle is half the circumference i.e., 11π.

The circumference is the perimeter of a circle.

Formula of Circumference = 2πr.

= Arc length of a semicircle  

= half of the circle's circumference

= 2πr/2

= πr

=11r

Learn more about circumference here

https://brainly.com/question/4268218

#SPJ2

For this expression,a=15,b=7 and c=4

Good luck on your assignment

Answer:

y = 27.1

Step-by-step explanation:

We have the value of x:

x = 12

and we need to find the value of y in the expression:

y = x + 15.1

as we can see by the equation, the value of y depends on the value of x.

thus, we substitute x = 12 on the previous equation:

y = 12 + 15.1

y = 27.1

the value of y is 27.1

Answer:

The equation in slope-intercept form:

[tex]y = -3x - 4[/tex]

Step-by-step explanation:

Use the point-slope formula:

[tex]y-y_{1} = m (x-x_{1})[/tex]

Use the given slope [tex]-3[/tex] and point [tex](0,-4)[/tex] for the formula:

[tex]y + 4= -3 (x-0)[/tex]

-Then, you solve the formula:

[tex]y + 4 = -3 (x-0)[/tex]

[tex]y+4 - 4 = -3 (x-0) -4[/tex]

[tex]y = -3x - 4[/tex]

The equation, which is in slope-intercept form:

[tex]y = -3x - 4[/tex]

Answer:

D. y = -3x - 4

Step-by-step explanation:

→You can figure this out by using the point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y+4=-3(x-0)[/tex]

→Distribute the -3 to (x - 0):

y + 4 = -3x

→Subtract 4 from both sides:

y = -3x - 4

Answer:

Step-by-step explanation:

Our line's equation is;

2y = -8x + 12

Dividing throughout by 2 we get;

y = -4x + 6

The slope of our line = -4

We are to choose a line whose slope is -4 (from those four options)

A slope of -4 means that for every positive 1 move along the x-axis, there is a negative 4 move along the y-axis.

The line that satisfies this condition is the third line.

Answer:

In other words Its C

Step-by-step explanation:

The guy above and Edge 2020

Answer:

Ok, some theory first:

If we have more variables than linear independent equations, then we have infinite solutions.

If we have the same number of linearly independent equations and variables, we can have a unique solution or no solution.

we have no solution in cases where:

y = x + 3

y = x - 3

this leads to:

x + 3 = x - 3

+3 = -3

so this system has no solutions.

The first system of equations is:

y = x + 5

y = 2x + 5

Now, you can see that we have 2 variables, and 2 linear independent equations, this means that we have only one solution for this system

So here we have "One solution, the graph of these lines should intersect at one point" and the point is (0, 5)

The second system is:

y = x + 5 + x = 2x + 5

y = 2x+ 5

Both equations are the same, so here we have 2 variables and only one equation, this means that we have infinite solutions for this system.

here the correct option is the one that says "infinitely many solutions, both right side and left side are equivalent expressions"

Answer:

For y = x+5

      y=2x+5   It is one solution

For  y = X+5+X  and Y = 2X + 5   Infinitely Many Solutions both the right and left sides of the equations are equivalent expressions.  See photo below

Step-by-step explanation:

Answer:

4

4

4

4

Step-by-step explanation:

Answer:

height = 6 cm

base = 12 cm

Step-by-step explanation:

Let the base of the triangle is denoted by b

Let the height of the triangle is denoted by h

We are given that base of a triangle is twice that of its height,

b = 2h

Recall that area of a triangle is given by,

A = ½×b×h

We are given that area of the triangle is 36 cm²

36 = ½×b×h

Substitute b = 2h in the above equation

36 = ½×2h×h

36 = h×h

h² = 36

h = √36

h = 6 cm

Therefore, the height of the triangle is 6 cm

b = 2h

b = 2(6)

b = 12 cm

Therefore, the base of the triangle is 12 cm

Verification:

A = ½×b×h

A = ½×12×6

A = ½×72

A = 36 cm²

Hence proved

Answer:

50

Step-by-step explanation:

c = cell phone cost

t = 5c

computer = 2.5 t = 2.5 ( 5c) =12.5 c

The total = 925

c+t+ computer = 925

c + 5c+ 12.5c = 925

Combine like terms

18.5 c = 925

Divide each side by 18.5

18.5c /18.5 = 925/18.5

c = 50

Answer:

Step-by-step explanation:

From the end of the problem to the beginning of the problem (this is often how you need to "decipher" story problems...go at it backwards!), we see that the cost of everything Tony bought is, in the end, based on the cost of the cell phone. The TV is 5 times as much as the cell phone, and the computer is 2.5 times as much as the TV...which is based on the cell phone. So the cell phone is our "main" unknown. We'll call that x.

If the TV is 5 times the cell phone, then the

TV = 5x

If the computer is 2.5 times the TV, then the

computer = 2.5(5x) = 12.5x

The cost of all these added together is 925.  Therefore,

x + 5x + 12.5x = 925 and

18.5x = 925 so

x = 50

The cell phone cost $50. Choice G.