Answer:
We know our answer is correct because 11 + 12 + 13 equals 36 as displayed Below
Explanation
3X + 3 = 36 3X + 3 - 3 = 36 - 3 3X = 33 3X/3 = 33/3 X = 11 Which means that the first number is 11, the second number is 11 + 1 and the third number is 11 + 2. Therefore, three consecutive integers that add up to 36 are 11, 12, and 13. 11 + 12 + 13 = 36 We know our answer is correct because 11 + 12 + 13 equals 36 as displayed above. Therefore, three consecutive integers that add up to 36 are 11, 12, and 13. 11 + 12 + 13 = 36
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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
Answer:
-9
Step-by-step explanation:
-3x+y=-7
-3x+y-2
-7-2=-9
Answer:
Step-by-step explanation:
Assuming this complete problem: "A cell tower is located at (-8, 4) and transmits a circular signal that covers three major cities. The three cities are located on the circle and have the following coordinates: G (-4, 7), H (-13, 4), and I (-8, -1). Find the equation of the circle"
For this case the generla equation for the circle is given by:
From the info we know that the tower is located at (-8, 4) so then h = -8 and k = 4, so then we need to find the radius. So we have the equation like this:
If the 3 points are on the circle then satisfy the equation. We can use the first point (-4,7) and if we replace we can find the value for 
So then 
And if we replace the second point we got this:
And for the third point we have:
And we got the same result.
So then our final equation is given:
Answer:
6 papayas and 11 pineapples
Step-by-step explanation:
So, we need to find an answer of how many papayas and pineapples she bought, and we only spent $48.
So, papayas are $2.50 each, and Pineapples are $3.00 each and we only bought 17 fruits total.
lets try 8 papayas, and 9 Pineapples.
$2.50 x 8 = $20.00 total on Papayas
$3.00 x 9 = $27.00 total on Pineapples.
That would only be $47 spent total.
Lets try 10 papayas and 7 pineapples.
$2.50 x 10 = $25.00
$3.00 x 7 = $21.00
That would only be a total of $26 spent.
Lets try 6 papayas and 11 pineapples.
$2.50 x 6 = $15.00
$3.00 x 11 = $33.00
This would be a total of $48 spent.
