Answer:
ft/min is the rate of changing of width
Step-by-step explanation:
Given -
The area always remain constant i.2 2 square feet.
Height of the rectangle = 2 feet
Rate of changing of height = 6 feet per minute
Since area is constant
2 sq ft = (2 * 6) ft/min * 1 * x ft/min
x = ft/min
Answer: (3y - 5) • (2y - 3)
Step-by-step explanation: 6y2 - 10y - 9y - 15
2.1 Factoring 6y2-19y+15
The first term is, 6y2 its coefficient is 6 .
The middle term is, -19y its coefficient is -19 .
The last term, "the constant", is +15
Answer:
Step-by-step explanation:
we know that
The scale factor on a map is equal to
so
by proportion
Find how many miles are in the real life 
inches apart on the map
6x15= 90
9x20= 180
180+90= 270
270 - 25 = 245 dane has 245 stamps left
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
