solve the system using substitution 4x+3y=23 x-5=0

Answer:

  266

Step-by-step explanation:

There are (3 ft)^3 = 27 ft^3 in 1 cubic yard. Then 9.83 cubic yards will be ...

  (9.83 yd^3)(27 ft^3/yd^3) = 265.41 ft^3

265 sacks will not be enough. 266 sacks must be ordered.

Given nth term of an AP = 7-4n

Put n = 1 then t1 = 7-4(1) = 7-4 = 3

Put n = 2 then t2 =7-4(2) = 7-8 = -1

Common difference = t2-t1 = -1-3 = -4

[tex]z1=\stackrel{a}{3}+\stackrel{b}{3}i~~ \begin{cases} r = \sqrt{a^2+b^2}\\ r = \sqrt{18}\\[-0.5em] \hrulefill\\ \theta =\tan^{-1}\left( \frac{b}{a} \right)\\ \theta =\frac{\pi }{4} \end{cases}~\hfill z1=\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right] \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right]} {7\left[\cos\left( \frac{5\pi }{9} \right) i\sin\left( \frac{5\pi }{9} \right) \right]} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[\cos(\alpha)+i\sin(\alpha)]}{r_2[\cos(\beta)+i\sin(\beta)]}\implies \cfrac{r_1}{r_2}[\cos(\alpha - \beta)+i\sin(\alpha - \beta)] \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{\pi }{4}-\frac{5\pi }{9} \right)+i\sin\left( \frac{\pi }{4}-\frac{5\pi }{9} \right) \right] \\\\\\ \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{-11\pi }{36} \right) +i\sin\left( \frac{-11\pi }{36} \right) \right]\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{83\pi }{36} \right) +i\sin\left( \frac{83\pi }{36} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{z1}{z2}\approx 0.348~~ + ~~0.496i~\hfill[/tex]

The value of z1/z2 is √18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).

"A complex number is the sum of a real number and an imaginary number and it is of the form x + iy and is usually represented by z".

For the given situation,

z1= 3+3i and

z2= 7(cos(5π/9) + i sin (5π/9))

To divide the complex numbers, both should be in same form.

Convert z1 in polar form.

z is of the form x+iy, so, r=[tex]\sqrt{x^{2}+y^{2} }[/tex]

⇒[tex]r=\sqrt{3^{2}+3^{2} }[/tex]

⇒[tex]r=\sqrt{18}[/tex]

θ = [tex]tan^{-1}(\frac{b}{a} )[/tex]

⇒[tex]tan^{-1}(\frac{3}{3} )[/tex]

⇒[tex]tan^{-1}(1)[/tex]

⇒[tex]45[/tex]°

The polar form is of the form, z= r (cosθ + i sinθ),

⇒ z1 = [tex]\sqrt{18}[/tex] (cosπ/4 + isinπ/4)

The formula for dividing complex number is

z1/z2 = r1(cos θ1 + isin θ1) / r2(cos θ2 + isin θ2)

⇒ z1/z2 = r(cosθ + isinθ)

where, r = r1/r2 and θ = (θ1 - θ2)

z1/z2 = [tex]\sqrt{18}[/tex] (cos π/4 + isin π/4) / 7 (cos 5π/9 + isin 5π/9)

⇒ r = [tex]\sqrt{18}[/tex] / 7 and

θ = (π/4 - 5π/9 )

⇒ θ = (-11π/36)

cos(-θ) = cos θ

⇒cos( -11π/36 ) = cos ( 11π/36 )

sin(-θ) = -sin θ

⇒ sin ( -11π/36 ) = -sin ( 11π/36 )

Thus, z1/z2 = [tex]\sqrt{18}[/tex] / 7 (cos ( 11π/36 ) - isin ( 11π/36 ))

Hence we can conclude that the value of z1/z2 is

√18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).

Learn more about complex number here

https://brainly.com/question/19612663

#SPJ2

Answer:

Step-by-step explanation:

There are 4 tens.

There are 48 cards that are not a 10. The probability of drawing 1 of the 48 is

P(~10) = 48/52 which is quite high as you might imagine.

Explanation:

The general template of a sine function is

y = Asin(B(x-C))+D

The value of B is the only thing that determines the period T. We ignore every other term.

It turns out that T = 2pi/B which can be solved to B = 2pi/T

Plug in the given period of T = 8pi and compute to get

B = 2pi/T

B = (2pi)/(8pi)

B = 2/8

B = 1/4

This means that the term out front of the x is 1/4 and the equation must be [tex]y = \sin\left(\frac{1}{4}x\right)[/tex] which matches with answer choice B.

Answer: The simplified ratio is 4:3

Step-by-step explanation:

To find the ratio of the number of girls to the number of boys, we can divide the number of girls (28) by the number of boys (21) to get:

28 ÷ 21 = [tex]\frac{28}{21}[/tex]

Next, we can simplify the fraction further to get [tex]\frac{4}{3}[/tex], which equals 4:3.

Answer:

Angle 5

Step-by-step explanation:

Answer:

a = 11

Step-by-step explanation:

As all angles on a straight line must add up to 180°:

(9a + 6) + 75 = 180

9a + 6 + 75 = 180

9a + 81 = 180

Subtract 81 from both sides of the equation:

9a + 81 - 81 = 180 - 81

9a = 99

Divide both sides by 9 to isolate a:

9a ÷ 9 = 99 ÷ 9

a = 11

Hope this helps!

Answer:

[tex]a=11[/tex]

Step-by-step explanation:

These are supplementary angles, meaning they together make up the whole measure of the angle of a straight line. A straight line is 180°, so the sum of these has to be 180° too:

[tex](9a+6)+75=180[/tex]

Then just solve for a:

[tex]9a+6+75=180\\9a+81=180\\9a=99\\a=11[/tex]

Answer:

42x - 54 I think

Step-by-step explanation:

Just simplify it  

Answer:

112 in.³

Step-by-step explanation:

This box is a combination of two rectangular prisms:

bottom - 9 in. by 2 in. by 4 in.

top - 5 in. by 2 in. by 4 in.

total volume = 9 in. × 2 in. × 4 in. + 5 in. × 2 in. × 4 in.

total volume = 112 in.³

Answer:

its 112

Step-by-step explanation:

first see how it looks like 2 boxes on top of each other, break it into major parts then multiply depth by wighth by highth

Answer:

The value of the 5 in 50.89 is 100 times the value of the 5 in 261.58

Step-by-step explanation:

The 5 in 50.89 is in the 10's place

The 5 in 261.58 is in the 1/10's place

1/10(100) = 10

Answer:

1/52

Step-by-step explanation:

A deck has 52 cards and the probability of picking a specific one is 1/52, or 1.92%

If you are looking for the probability of a diamond, it is 1/4, or 25%

Answer: c

Step-by-step explanation: I JUST ANSWERED BOTH PARTs

Answer:

good day of school and➕➕ I have a great day of school and I have a great day☀☀☀ of school and➕➕ I

Answer:

x=7,4

Step-by-step explanation:

To reach a raise of $ 700, you can sell 20 entire cheesecakes and 63 slices, or 10 entire cheesecakes and 132 slices, or 15 entire cheesecakes and 98 slices.

To determine, if they want to raise at least $ 700, how many of each could they sell, listing three possible combinations of entire cheesecakes and slices of cheesecake the players could sell to reach their goal, the following calculation must be performed:

Therefore, to reach a raise of $ 700, you can sell 20 entire cheesecakes and 63 slices, or 10 entire cheesecakes and 132 slices, or 15 entire cheesecakes and 98 slices.

Learn more about maths in https://brainly.com/question/25903420

Answer:

Step-by-step explanation:

The conjugate of the given is:

Find their product:

Answer:

1)B 4 x 4 x 4 x 4

2)B 8292

Step-by-step explanation:

Answer:

the answer is

1. 11.33

2. 5.9

3. 8.1

This is the same as typing in 0.5x^7

Other equivalent forms are (1/2)x^7 or (x^7)/2

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

Work Shown:

[tex]\frac{d}{dx}\left[f(x^2)\right] = x^8\\\\f'(x^2)*\frac{d}{dx}(x^2) = x^8\\\\f'(x^2)*2x = x^8\\\\f'(x^2) = \frac{x^8}{2x}\\\\f'(x^2) = \frac{x^7}{2}\\\\f'(x^2) = \frac{1}{2}x^7\\\\f'(x^2) = \boldsymbol{0.5x^7}\\\\[/tex]

I used the chain rule on the second step. The chain rule will apply the derivative to the outer function f(x^2). Then we also apply the derivative to the inner function x^2 to get 2x, which is multiplied with f ' (x^2). From that point, we isolate f ' (x^2).

Side note: When applying the first derivative, it might help to think of f(x^2) as simply f(x) on a temporary basis.

Answer:  40 ounces or 0.3125 of a gallon

i didnt quite understand what you were asking but here is it broken down. :)

all real numbers except the 90 and 270 because of cosx

Answer:

a) 32km

b) 40 miles

Step-by-step explanation:

Answer:

44 ten-dollar bills

Step-by-step explanation:

Assume that all 124 bills are ten-dollar bills,

124 x $10 = $1240

Total Value of Money : $840

$1240 - $840 = $400

There are $400 worth of five-dollar bills,

$400 / 5 = 80 (The number of five-dollar bills)

Therfore the number of ten-dollar bills,

124 - 80 = 44

Let's check:

44 x $10 = $440

80 x $5 = $400

Total = $440 + $400

        = $840

Building a probability distribution, it is found that the expected value for both players is of 0.25 points.

In this problem, the four possible outcomes, considering Player A - Player B, are:

H - H

T - H

H - T

T - T

That is, considering a success as the number of heads, the distribution is:

[tex]P(X = 0) = 0.25[/tex]

[tex]P(X = 1) = 0.5[/tex]

[tex]P(X = 2) = 0.25[/tex]

For Player A, the earnings of each outcome are: -1, 0 and 2

Hence, the expected value is:

[tex]E_A(x) = -1(0.25) + 0(0.5) + 2(0.25) = 0.25[/tex]

For Player B, the earning of each outcome are: 2, 0 and -1.

Hence:

[tex]E_B(x) = 2(0.25) + 0(0.5) - 1(0.25) = 0.25[/tex]

The expected value for both players is of 0.25 points.

You can learn about expected value at https://brainly.com/question/24855677