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On the surface, it seems easy. Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42?

Answer:

third option

Step-by-step explanation:

Using De Moivre's theorem

([tex]\sqrt{3}[/tex] + i)³ , then

| [tex]\sqrt{3}[/tex] + i |

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

= [tex]\sqrt{3+1}[/tex] = [tex]\sqrt{4}[/tex] = 2

arg([tex]\sqrt{3}[/tex] + i) = [tex]tan^{-1}[/tex]( [tex]\frac{1}{\sqrt{3} }[/tex] ) = [tex]\frac{\pi }{6}[/tex]

Thus

([tex]\sqrt{3}[/tex] + i)³

= 2³ [ cos(3 ×[tex]\frac{\pi }{6}[/tex] ) + isin( 3 × [tex]\frac{\pi }{6}[/tex] ) ]

= 8 [ cos([tex]\frac{\pi }{2}[/tex]) + isin([tex]\frac{\pi }{2}[/tex] ) ]

Answer:

C

Step-by-step explanation:

Step-by-step explanation:

60° + 60° + x + x = 180°. (Sum of angles in a triangle = 180°)

Therefore 2x = 60° and x = 30°.

Answer:

Step-by-step explanation:

2x + 60 = (180 - 60)

x = (180-120)/2

x = 30

Answer: 4

Step-by-step explanation: just did it myself

Answer:

$14.80

Step-by-step explanation:

18.50 * 0.20 = 3.70

Then

18.50 - 3.70

Yo I am not 100% sure. I have 90% sure that it is right answer though.

If that isn't one of your answer choices then it means it is 3.70.

Answer:

-6(-3)​=18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

6 x 3 = 18 bc neg x neg = pos

Answer:

35

Step-by-step explanation:

Answer:

y = 35°

Step-by-step explanation:

if the lines are parallel, the alternate interior angles theorem applies ("if a transversal intersects two parallel lines then alternate interior angles are congruent"). so since we know that the lines are parallel, the alternate interiors are congruent so 70=2y. from there, divide both sides by 2 to isolate y (division property of equality) and y=35.

Answer:

2

Step-by-step explanation:

So let's call the time she needs to catch up "x", and so Terry's rate would be x-6 since he left home 6 hours earlier. Then we multiply the rates to get 20x - 120 = 80x. The answer is -2, but we can just say 2.

Checking our answer, that means if it took Sally 2 hours, it took Terry 8 hours for he left home 6 hours earlier. So 8 times 20 = 160km traveled. 2 times 80 = 160km traveled. Same distance.

Answer:

They are not congruent.

The lines or the marks show that each side is congruent. If you compare the sides to where the angle is, you will see that it is not congruent.

Answer:

114

Step-by-step explanation:

25 + 25 + 64 = 114

Answer:

The first fraction is between 27 and 28, closer to 28. The second fraction is between 3 and 4, closer to 4. Compatible numbers in division are numbers that can be divided mentally. 28 divided by 4 is 7. The quotient will be around 7.

Step-by-step explanation:

Hope this helps,

Please give brainliest if you like my answer

Have a great day

Answer:

750

Step-by-step explanation:

The length and width of the swimming pool is 50feet and 30 feet respectively.

The amount of space covering the outside of a three dimensional space is called surface area.

surface area = length × breadth

According to the given question

The length of the rectangular swimming pool is 20 feet greater than the width.

and, the surface area of the pool is 1,500 square feet.

Let the width of the rectangular pool be x.

⇒ length of the pool = 20+x

therefore,

surface area of pool = length × breadth

⇒1500 = x×(20+x)

⇒[tex]1500= 20x+x^{2}[/tex]

⇒[tex]x^{2} +20x-1500=0[/tex]

⇒[tex]x^{2} +50x-30x-1500=0[/tex]

⇒[tex]x(x+50)-30(x+50)=0[/tex]

⇒[tex](x-30)(x+50)=0[/tex]

⇒x=30 and -50(not possible)

⇒x=30 feet

so, the width of the pool is 30 feet.

⇒ length of the pool = x+20 = 30+20 = 50 feet.

Hence, the length of the pool is 50 feet and width of the pool is 30 feet.

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This question is based on the concept of polar form.Therefore, the expression in polar form is [tex]\bold {z = \sqrt{10(cos108.43\; + \; i \; sin108.43)}}[/tex]

Given the following complex numbers in:

w = 2(cos(90°) + i sin (90°))

As we know that,

sin 90 degree = 1

cos 90 degree = 0

Put these values in given equation,

We get,

w = 2(0+i(1))

w = 2(0)+2i

w = 0+2i

Hence the value of w in rectangular form is  0+2i .

Now solving for z:

z =√2(cos(225°) + i sin(225°))

z = √2(-1/√2+ i (-1/√2))

z = -√2/√2 - √2(-1/√2)i

z = -1 + 1i

Therefore, the value of z in rectangular coordinate is -1+ 1i.

Now solving for  w + z:

w + z = 0+2i + (-1+1i)

w+z = 0+2i-1+i

w+z = -1+3i

Write w+z in polar form,

Get the modulus

|w+z| = √(-1)²+3²

|w+z| = √1+9

|w+z| =  √10

Get the modulus

= tan^-1(-3)

= -71.56

[tex]\Theta[/tex] = 180 - 71.56

[tex]\Theta[/tex] = 108.43

Therefore, the expression in polar form is,[tex]\bold{z = \sqrt{10(cos108.43\; + \; i \; sin108.43)}}[/tex]

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Answer:

Step-by-step explanation:

A. 1i

B.315

C.315

Hope this helps!

Answer: None of the lines are parallel to one another

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

Explanation:

Solve each equation for y

Line a:

4y+x = 8

4y = -x+8

y = (-x+8)/4

y = (-x/4) + (8/4)

y = (-1/4)x + 2

This equation is in the form y = mx+b with slope m = -1/4

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

Line b:

2y+x = 4

2y = -x+4

y = (-x+4)/2

y = (-x/2) + (4/2)

y = (-1/2)x + 2

The slope is m = -1/2. It is not parallel to line a because parallel lines must have the same slope (but different y intercept).

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

Line c:

2y = -3x+6

y = (-3x+6)/2

y = (-3x/2) + (6/2)

y = (-3/2)x + 3

The slope here is m = -3/2. it is not parallel to line a, and it is not parallel to line b either for similar reasons discussed above.

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

In summary, none of the three lines are parallel to one another. The graph below visually confirms this. Each pair of lines intersects at exactly one location, showing they cannot be parallel.

Answer: 56/33

Step-by-step explanation: Tan= Opposite over Adjacent or O/A

Answer:

A

Step-by-step explanation:

CAUSE MATH

I GOT THE SAME QUESTION AND GOT IT CORRECT. YEET :))))))))

The expression represents the number of hours in w weeks and d days is 168 W + 24 d.

The correct option is (C).

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

We know the number days in a week = 7

and, the number of hour in a day = 24

So, number of hour in a week = 24 x 7 = 168

Then, the expression number of hours

= 168 W + 24 d

where W is the weeks and d is days.

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Answer:

Total time taken = 27 min

Step-by-step explanation:

Given:

Started game time = 10:44 AM

Ending game time = 11:11 AM

Find:

Total time taken

Computation:

Total time taken = Ending game time in min - Started game time in min

Total time taken = [11x60 + 11] - [10x60 + 44]

Total time taken = 671 - 644

Total time taken = 27 min

Answer:

ratio is line from center to end of the circle

Step-by-step explanation:

Answer:

$4.80/2sodas

4.80/2=2.40

C. 2.40 per soda

Answer: -2 2/3 or -8/3

i dont think it right i only could do the first one i dint know the last one cuz ...

Answer:

Step-by-step explanation:

30 is half or 60

45 is half of 90

1:2 ratio

Answer:

x = [tex]\frac{15}{2}[/tex] , x = 1

Step-by-step explanation:

(a)

[tex]\frac{4x-1}{2}[/tex] = x + 7 ( multiply both sides by 2 to clear the fraction )

4x - 1 = 2x + 14 ( subtract 2x from both sides )

2x - 1 = 14 ( add 1 to both sides )

2x = 15 ( divide both sides by 2 )

x = [tex]\frac{15}{2}[/tex]

(b)

3x + 2 = [tex]\frac{2x+13}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

9x + 6 = 2x + 13 ( subtract 2x from both sides )

7x + 6 = 13 ( subtract 6 from both sides )

7x = 7 ( divide both sides by 7 )

x = 1

Answer:

Step-by-step explanation:

Hh

Answer:

you pay $26.25

you save $48.75

Step-by-step explanation:

Trust

Answer:

it would be 1/1000 assuming only 1 ticket sold to 1 person each; if a person bought more than 1 ticket then there odds of winning increase

Step-by-step explanation:

The probability of winning the car is 0.001.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

Given that, a raffle sells 1000 tickets for $35 each to win a new car.

Here, we know that there is a total of 1000 tickets. If there is only one car, then definitely only one wins the raffle. The probability of winning is also dependent on the number of tickets one will purchase. But for this problem, we are going to assume that only one raffle can be bought by one person. Thus, the probability of winning a new car is simply

P(E)= Number of raffle tickets one can buy/Total number of raffle tickets

= 1/1000

= 0.001

Therefore, the probability of winning the car is 0.001.

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Answer:

The resulting function is [tex]g(x) = \log_{2} (x+5)-4[/tex].

Step-by-step explanation:

Let [tex]f(x)[/tex] a real function, we define the following function operations:

Horizontal translation

[tex]g(x) = f(x + a)[/tex] (1)

If [tex]a > 0[/tex], then horizontal translation is to the left, otherwise it is to the right.

Vertical translation

[tex]g(x) = f(x) + a[/tex] (2)

If [tex]a> 0[/tex], then vertical translation is upwards, otherwise it is downwards.

Knowing that [tex]f(x) = \log_{2}x[/tex] and [tex]g(x)[/tex] is the result of translating [tex]f(x)[/tex] four units downwards and five units to the left. Then, we find that:

[tex]g(x) = \log_{2} (x+5)-4[/tex]

The resulting function is [tex]g(x) = \log_{2} (x+5)-4[/tex].