What is the unit rate to the nearest cent per ounce if there is size is pint and the quantity is 16oz and the price is $3.98

Find the real numbers x and y if -3+ix^2y and x^2+y+4i are conjugate of each other. Pls solve with the steps

Firdavs [7]

ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y

For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions.

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the

x²y = -4 ... (I)

Condition 2: Real parts are the same

x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

x²y = -4 ... (I)
x² + y = -3 ... (II)

We can rearrange equation (II) so that we have

y = -3 - x² ... (II)

Substituting into equation (I)

x²y = -4 ... (I)
x²(-3 - x²) = -4
-3x² - x⁴ = -4
x⁴ + 3x² - 4 = 0
(x² + 4)(x² - 1) = 0
(x² + 4)(x-1)(x+1) = 0

Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

y = -3 - x² ... (II)
y = -3 - (±1)²
y = -3 - 1
y = -4

So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:

-3 + ix²y
= -3 + i(±1)²(-4)
= -3 - 4i

x² + y + 4i
= (±1)² - 4 + 4i
= 1 - 4 + 4i
= -3 + 4i

They result in conjugates

4 0

3 years ago

Read 2 more answers

On Monday morning, a school cafeteria had 97.88 gallons of milk. At lunch, the students drank 8

AlekseyPX

Answer:

89.88 gallons of milk

Step-by-step explanation:

97.88-8=89.88

4 0

3 years ago

I just need examples of these things, I have to make my own problems and solve them:

poizon [28]

1) x+17=20
x-10=30

2) x/4=20
x/30=2

3) 4(x+5)=40

4) x+3.2=6

5) A pizza place sells pizza for $5 per box. If I had $20 how many pizzas can I buy in all? (5x=20)

Hope this helps! Have a wonderful day.

6 0

3 years ago

One side of a triangle is 2 times the second side. The third side is 5 ft longer than the second side. The perimeter of a triang

TiliK225 [7]

Answer:

The length of each side of triangle are 19 ft, 24 ft and 38 ft.

Step-by-step explanation:

Let the length of second side be x.

Now given:

Length of first side is 2 times length of second side.

Length of first side = 2x

Also, Length of third side is 5 ft longer than the second side.

Length of third side = 5+x

Perimeter of triangle = 81 ft.

We need to find the length of each side.

Now perimeter of triangle is sum of all three sides of triangle.

Therefore;

Perimeter of triangle = Length of first side + length of second side + Length of third side.

$2x+x+5+x=81 ft\\4x+5=81ft\\4x= 81 -5 ft\\4x = 76ft\\x= \frac{76}{4} = 19 ft$

Length of Second Side = 19 ft.

Length of First side = $2x= 2\times19 = 38 ft$

Length of Third side = $5+x= 5+19=24ft$

Hence the Length of triangles are 19 ft,38 ft,24 ft.

3 0

3 years ago

Helpppppppoo!!!!!!!!!!!!!!!!!!!!!!!

Andru [333]

I want to say its 6 but I'm not sure. sorry

8 0

2 years ago