Answer:
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Step-by-step explanation:
Answer:
B) 43.758
Step-by-step explanation:
Starting from the right side of the decimal point, the places are:
tenths
hundredths
thousands
Each time, you add a zero to the previous number (10 to 100 to 1000, etc), therefore the third decimal would be the thousandths place. If the next figure is a 5 or above, you round up, to the next decimal.
Answer:
Here, 
, hence the quadratic equation has two distinct real roots.
Step-by-step explanation:
Given quadratic equation is 
.
Let, the quadratic equation is 
[where, 
are the constants]
The Discriminant 
Case 
: 
, if the discriminant is greater than 
, it means the quadratic equation has two real distinct roots.
Case 
: 
, if the discriminant is less than , it means the quadratic equation has no real roots.
Case 
: 
, if the discriminants is equal to , it means the quadratic equation has two real identical roots.
Now,
we have , where 
∴
Here, , hence the quadratic equation has two distinct real roots.
Simplifying
9 + 7x = 7x2
Solving
9 + 7x = 7x2
Solving for variable 'x'.
Combine like terms: 7x2 + -7x2 = 0
9 + 7x + -7x2 = 0
Begin completing the square. Divide all terms by
-7 the coefficient of the squared term:
Divide each side by '-7'.
-1.285714286 + -1x + x2 = 0
Move the constant term to the right:
Add '1.285714286' to each side of the equation.
-1.285714286 + -1x + 1.285714286 + x2 = 0 + 1.285714286
Reorder the terms:
-1.285714286 + 1.285714286 + -1x + x2 = 0 + 1.285714286
Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + -1x + x2 = 0 + 1.285714286
-1x + x2 = 0 + 1.285714286
Combine like terms: 0 + 1.285714286 = 1.285714286
-1x + x2 = 1.285714286
The x term is -1x. Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.
Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1.
First find the slope:
The slopes of perpendicular lines must multiply to -1.
-9m = -1 ----> m = 1/9
Next, use point-slope form:
y - y1 = m(x-x1) , where given point (0,5) is (x1,y1)
y - 5 = (1/9)(x - 0)
Finally, solve for y to put it in slope-intercept form:
y = (1/9)x + 5
