<u>We'll assume the quadratic equation has real coefficients</u>
Answer:
<em>The other solution is x=1-8</em><em>i</em><em>.</em>
Step-by-step explanation:
<u>The Complex Conjugate Root Theorem</u>
if P(x) is a polynomial in x with <em>real coefficients</em>, and a + bi is a root of P(x) with a and b real numbers, then its complex conjugate a − bi is also a root of P(x).
The question does not specify if the quadratic equation has real coefficients, but we will assume that.
Given x=1+8i is one solution of the equation, the complex conjugate root theorem guarantees that the other solution must be x=1-8i.
Answer:
20÷[18-{20-3(4)}]
120÷[18-[20-12]]
120÷[18-8]]
120÷10
12
Step-by-step explanation:
Answer:
<u>Radius: 12 units </u>
- Area: πr² = 3.14*12² = 452.16 square units
<u>Diameter: 16.8 units</u>
- Area: πd²/4 = 3.14*16.8²/4 = 221.5584 square units
<u>Radius: 3.4 units</u>
- Area: πr² = 3.14*3.4² = 452.16 square units
<u>Diameter: 10 units</u>
- Area: πd²/4 = 3.14*10²/4 = 78.5 square units
Answer:
You may or may not need to include the units.
A = 18x - 18
P = 6x + 6
Graph is attached below. (2, 18)
Step-by-step explanation:
Substitute the information we need, "l" and "w", into the formulas.
l is for length, 6cm.
w is for width, (3x - 3)cm.
Use the formula for area of a rectangle.
A = lw
A = (6)(3x-3)cm²
A = (18x - 18)cm² or 18x - 18
Use the formula for perimeter of a rectangle.
P = 2(l + w)
P = 2(6 + (3x - 3))cm
P = 2(3x + 3)cm
P = (6x + 6)cm or 6x + 6
Linear equations are written in the form y = mx + b, so we do not need to factor or further simplify the formulas.
To graph, first turn the "m" value into a fraction form.
8 -> 8/1
6 -> 6/1
You need two points to graph each line.
For each equation, the first point is on the y-axis at the "b" value. Then use the "m" in the equation to count the number of units up (numerator) and to the right (denominator).
The solution is (2,18)
Answer:
y =14
11x = 11*3.5 =38.5
3x+2y = 11x = 38.5
Step-by-step explanation:
The perimeter of a triangle is the sum of all three sides
3x+2y + 11x+y = 91
Combine like terms
14x +3y = 91
The lines mean the sides are equal
3x+2y = 11x
Simplify
Subtract 3x from each side
3x-3x+2y = 11x-3x
2y = 8x
Divide by 2
2y/2 = 8x/2
y = 4x
Substitute 4x in the first equation every time you see y
14x +3y = 91
14x +3(4x) = 91
14x+12x=91
26x = 91
Divide by 26
26x/26 =91/26
x = 3.5
Now we can find y
y = 4x
y = 4(3.5)
y = 14
We know x and y we can find the length of each of the sides
y =14
11x = 11*3.5 =38.5
3x+2y = 11x = 38.5