5. x=a+b+4 and anyz; bo when y=2; x=18 and when y=1; x=-3. Find tu
90​

Answer:

- 4 + 4√3 i, where a = -4 & b = 4√3

Step-by-step explanation:

z = 8 cis(2π/3)

z = 8 [cos(2π/3) + i sin(2π/3) ]

z = 8 [cos(π - π/3) + i sin(π - π/3)]

z = 8 [ - cosπ/3 + i sin(π/3)]

z = 8[ - 1/2 + i √3/2 ]

z = - 4 + 4√3 i [in a + bi form]

Note that: cis x = cosx + i sinx

Answer:

[tex]a + bi = - 4 + 4 \sqrt{3} i[/tex]

Step-by-step explanation:

we are given [tex]\displaystyle cis(\dfrac{2\pi}{3})[/tex]

recall complex number trigonometric form:

[tex] \displaystyle \: r( \cos( \theta) + i \sin( \theta) )[/tex]

we are already given that [tex]\theta=\dfrac{2\pi}{3}[/tex]

recall complex number rectangular form

[tex] \displaystyle \: a + bi[/tex]

where [tex]\displaystyle a=r\cos(\theta)\: and\: b=r\sin(\theta)[/tex]

let's work with a:

substitute the value of [tex]\theta[/tex] and r

[tex] \displaystyle \: a = 8 \times \cos( \frac{2\pi}{ 3} ) [/tex]

recall unit circle

so [tex]\cos(\dfrac{2\pi}{3})[/tex] should be in Q:II

[tex] \displaystyle \: a = 8 \times - \frac{1}{2} [/tex]

simplify multiplication:

[tex] \displaystyle \: a = - 4[/tex]

let's work with b:

substitute the value of [tex]\theta[/tex] and r:

[tex] \displaystyle \: b = 8\sin( \frac{3\pi}{2} ) [/tex]

recall unit circle so [tex]\sin(\dfrac{3\pi}{2})[/tex] should be in Q:II

[tex] \displaystyle \: b = 8 \times \frac{ \sqrt{3} }{2} [/tex]

simplify:

[tex] \displaystyle \: b = 4 \sqrt{3} [/tex]

so

[tex] \displaystyle \: b i= 4 \sqrt{3} i[/tex]

hence,

[tex]a + bi = - 4 + 4 \sqrt{3} i[/tex]

Answer:

The answer is 7

Step-by-step explanation:

2+8+9+9÷4=7

Answer:

c >  $16

Step-by-step explanation:

Since she already spent $14 from the original $30 then the value of C would be the following inequality.

c > 30 - 14

c >  16

Therefore, the additional amount she could spend needs to be greater than $16 in order for Fatema to actually spend more than the $30 she wanted to spend on gifts in total.

Answer:

independent variable is pens and dependent variable is $5 each Im pretty sure

Answer:

3500

hope this helps

Answer:

x=-4

Step-by-step explanation:

The angles have to equal eachother, so:

130=134+x

subract 134 from both sides

-4=x

Answer:

2¹⁰

Step-by-step explanation:

when the bAse the same

then,

we take them common and add their exponents.

Answer: [tex]2^{10}[/tex]

They give you the answer in the question. Multiply [tex]2^{3}[/tex] and [tex]2^{7}[/tex].

When multiplying exponents we add them.

Answer:

2 ( x + 1 ) = 64

x = 64 : 2 - 1

x = 31

The equation isn't true

Answer:

0.5398

Step-by-step explanation:

Given that :

Total possible numbers vice presidents invited = 7

Required number of vice presidents invited = 1

Probability that a certain vice president is invited ;

P(a certain V. P is invited) = required outcome / Total possible outcomes

P(a certain V. P is invited) = 1/ 7

P(1 of the V. P's hasn't been invited to attend any of the last 4 games)

Then ; it means any of the remaining (7 - 1) = 6 has been invited ;

Hence,

P(1 of the V. P's hasn't been invited to attend any of the last 4 games) = ((7-1) / 7)^4

Likelihood that it could be due to chance :

(6/7)^4 = 0.5397750

= 0.5398

1) A graph is linear when the line on a graph is a straight line with no curves.

2) A proportional graph means that as x increases, y increases and when x decreases, y decreases and their ratio always stays the same.

3) (I don't know what type of equation you mean but this is my guess)

Division is the last step of an equation.

Answer:

Weight of circles = 10

Step-by-step explanation:

Say the circle's weight is x

Since there is one triangle and one square on the left, we know that is 16 pounds

Since there are 5 squares on the right, we know that is 36 pounds

Knowing that the circle weight variable is x, we can make an equation

16+3x=36+x

Simply solve for x now

Answer:

3

Step-by-step explanation:

to get enough pie for 32 people, each of the 4 pies would need to be 8 slices. since they each get 1 of 8 it would be 1/8

Answer:

TIME REMAINING

54:28

The battle that resulted in both a Confederate victory and the death of General “Stonewall” Jackson was

Step-by-step explanation:

TIME REMAINING

54:28

The battle that resulted in both a Confederate victory and the death of General “Stonewall” Jackson was

Answer:

360

Step-by-step explanation:

144/2=72

5×72=360

...........

Answer:

a. The 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is (0.54, 0.588). This means that we are 95% sure that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is between these two bounds.

b. Because this confidence interval is entirely above 0.5, the interval is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

Sample of 1,664 adult Americans, 939 people in the sample would have given themselves a grade of A or B in personal finance.

This means that [tex]n = 1664, \pi = \frac{939}{1664} = 0.5643[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5643 - 1.96\sqrt{\frac{0.5643*0.4357}{1644}} = 0.54[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5643 + 1.96\sqrt{\frac{0.5643*0.4357}{1644}} = 0.588[/tex]

The 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is (0.54, 0.588). This means that we are 95% sure that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is between these two bounds.

(b) Is the confidence interval from part (a) consistent with the statement that a majority of adult Americans would give themselves a grade of A or B?

Yes, because the confidence interval is entirely above 0.5.

Because this confidence interval is entirely above 0.5, the interval is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.

Answer:

11.8 meters

Step-by-step explanation:   ʕ ˵• ₒ •˵ ʔ

Answer:

[tex]b = 0.3[/tex]

Step-by-step explanation:

Given

[tex]V = ab^t[/tex]

See attachment for graph

From the graph

V = 20 when t = 0

This implies that:

[tex]V = ab^t[/tex]

[tex]20 = ab^0[/tex]

[tex]20 = a * 1[/tex]

[tex]20 = a[/tex]

[tex]a = 20[/tex]

Also:

V = 4 when t = 1.5

So:

[tex]4 = ab^{1.5[/tex]

Substitute 20 for a

[tex]4 = 20 * b^{1.5[/tex]

Divide by 20

[tex]0.2 =b^{1.5[/tex]

[tex]b^{1.5} = 0.2[/tex]

Take 1.5th root of both sides

[tex]b = 0.34199518933[/tex]

[tex]b = 0.3[/tex] --- approximated

Answer:

Perimeter: 50.27

Area: 201.06

Step-by-step explanation:

The perimeter (circumference) is radius times pi times 2

This would be 8 times pi tomes 2 and when you do that you get 50.27

For the area you would do radius squared times pi

This would be 8 squared times pi which is 201.06

Hope this is helpful

- Please mark brainliest :)

Answer:

i

Step-by-step explanation:

my name is Aisha let's play

Explanation is in the file

tinyurl.com/wpazsebu

The solution to the equation 5x - 4 = 2x + 20 is x = 8 which can be determined by simplification process.

To solve for x in the equation 5x - 4 = 2x + 20, we can follow these steps:

Start by isolating the x terms on one side of the equation. We can do this by subtracting 2x from both sides:

(5x - 2x) - 4 = (2x - 2x) + 20]

Simplifying:

3x - 4 = 20

Next, isolate the constant term on the opposite side of the equation by adding 4 to both sides:

(3x - 4) + 4 = 20 + 4

Simplifying:

3x = 24

Finally, solve for x by dividing both sides of the equation by 3:

(3x)/3 = 24/3

Simplifying:

x = 8

Therefore, the solution to the equation 5x - 4 = 2x + 20 is x = 8.

To know more about  "equation."  here

https://brainly.com/question/29174899

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Full Question-

Solve for x in the given equation  5x-4  =  2x+20​

Answer:

B. because there are too many side lengths to be a triangle

Answer:

That would be 19! / 10!, which is 33522128640

If to create a CD 9 songs are needed and user have 19 songs then he can create 33522128640 such CD's if solving through permutations.

It is basically an arrangement of objects in a certain order.It is expressed as n[tex]P_{r}[/tex] and it is equal to n!/(n-r)!.

We have been given that user have 19 songs and 1 CD is made from 9 songs so the number of CD's which can be made is basically the number of ways these 9 songs are arranged from 19 songs in CD's. So, the number of CD's will be 19[tex]P_{9}[/tex]=19!/(19-9)!

=19!/10!

=19*18*17*16*15*14*13*12*11*10!/10!

=19*18*17*16*15*14*13*12*11

=335322128640 CD's

Hence 335322128640 CD's can be made from 19 songs by the user.

Learn more about permutations at https://brainly.com/question/1216161

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Answer:

x=7, y=-1. (7, -1).

Step-by-step explanation:

2x+4y=10

-2x+y=-15

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

5y=-5

y=-5/5

y=-1

2x+4(-1)=10

2x-4=10

2x=10+4

2x=14

x=14/2

x=7

Answer:

a

Step-by-step explanation:

a

Answer:

6(x + 9) (x + 9)

or

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

Step-by-step explanation:

[tex]468 + 108x + 6x^{2} \\6x^{2} +108x + 468[/tex]

Greatest common factor of 6, 108, and 486:

6 x 1 = 6

6 x 18 = 108

6 x 81 = 486

GCF: 6

so:

[tex]6(x^{2} +18x +81)[/tex]

[tex]x^{2} +18x + 81[/tex]

factors to:

(x + 9) (x + 9)

because:

9 x 9 = 81

9 + 9 = 18

So:

It factors completely too:

6(x + 9) (x + 9)

or

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

9% is the answer trust me on this