Answer:
5+6-8
Step-by-step explanation:
Let's solve this problem step-by-step.
6+0.1x=0.15x+8
Step 1: Simplify both sides of the equation.
0.1x+6=0.15x+8
Step 2: Subtract 0.15x from both sides.
0.1x+6−0.15x=0.15x+8−0.15x
−0.05x+6=8
Step 3: Subtract 6 from both sides.
−0.05x+6−6=8−6
−0.05x=2
Step 4: Divide both sides by -0.05.
-0.05x/-0.05=2/-0.05
So, the answer for this problem is x=-40
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
I assume by starting value, you mean y-intercept. The y-intercept is 15
To find this, we need to use slope intercept form and the given information to find it.
y = mx + b ----> plug in the known values
9 = -3/4(8) + b
9 = -6 + b
15 = b
Therefore, the starting value is 15.
