(2j+7)(2j−7)
=(2j+7)(2j+−7)
=(2j)(2j)+(2j)(−7)+(7)(2j)+(7)(−7)
=4j2−14j+14j−49
=4j2−49
In the metric system, each of the common kinds of measure -- length, weight, capacity -- has one basic unit of measure. To measure smaller amounts, divide the basic unit into parts of ten, a hundred, or a thousand, and so on. To measure larger amounts, multiply the basic unit by ten, a hundred, or a thousand, and so on.
Length:
1 kilometer (km) = 1000 meters (m)
1 centimeter (cm) = .01 meter (m)
1 millimeter (mm) = .001 meter (m)
Weight:
1 kilogram (kg) = 1000 grams (g)
1 milligram (mg) = .001 gram (g)
Capacity:
1 milliliter = .001 liter (l)
-2 = - x + x^2 -4 => x^2 - x - 4 + 2 = 0
x^2 - x - 2 = 0
a is the coefficient of x^2 => a = 1
b is the coefficient of x => b = - 1
c is the constant term => c = - 2
quadratic equation: [- b +/- √(b^2 - 4ac) ] / 2a =
= { 1 +/- √[ (-1)^2 - 4(1)(-2)] } / (2(1) = { 1 +/- √ (1 + 8) } / 2 = {1 +/- √9} / 2 =
= { 1 +/- 3} / 2
Beetle liked broccoli
worm liked tomato
snail liked corn
ladybug likes carrots
beetle likes peas
The correct question is
<span>
Penelope determined the solutions of the quadratic function by completing the square.f(x) = 4x² + 8x + 1
–1 = 4x² + 8x
–1 = 4(x² + 2x)
–1 + 1 = 4(x² + 2x + 1)
0 = 4(x + 2)²
0 = (x + 2)²
0 = x + 2
–2 = x
What error did Penelope make in her work?
we have that
</span>f(x) = 4x² + 8x + 1
to find the solutions of the quadratic function
let
f(x)=0
4x² + 8x + 1=0
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(4x² + 8x)=-1
Factor the
leading coefficient
4*(x² + 2x)=-1
Complete the square Remember to balance the equation
by adding the same constants to each side.
4*(x² + 2x+1)=-1+4 --------> ( added 4 to both sides)
Rewrite as perfect squares
4*(x+1)²=3
(x+1)²=3/4--------> (+/-)[x+1]=√3/2
(+)[x+1]=√3/2---> x1=(√3/2)-1----> x1=(√3-2)/2
(-)[x+1]=√3/2----> x2=(-2-√3)/2
therefore
the answer is
<span>
Penelope should have added 4 to both sides instead of adding 1.</span>
