Answer:
x = 9 ± √14
Step-by-step explanation:
x² − 18x + 67 = 0
Move the constant to the other side:
x² − 18x = -67
Take half of -18, square it, and add to both sides.
(-18/2)² = (-9)² = 81
x² − 18x + 81 = -67 + 81
x² − 18x + 81 = 14
Factor the perfect square:
(x − 9)² = 14
Solve for x:
x − 9 = ±√14
x = 9 ± √14
Answer:an expression to describe the total cost of a party is written as
y = 13.50p + 50
Step-by-step explanation:
The cost of renting the party room at a restaurant is $50.00. Snacks cost $13.50 per person. Assuming the total number of persons invited for the party is p, and the total cost of renting the party room is y. Therefore an expression to describe the total cost of a party is written as
y = 13.50p + 50
The $50 always remains constant
Step-by-step explanation:
they're is a neat little trick.
but first of all, "roots" means the 0 solutions of the equation. like
ax² + bx + c = 0
there are 2 solutions for x to make the whole expression equal 0.
these are the "roots".
now to the little trick :
when is a multiplication resulting in 0 ?
when at least one of the factors is 0.
and any quadratic expression can be written as multiplication of 2 factors. like
c(x - a)(x - b) = cx² - cax - cbx + cab
what are the "roots" or 0 points ?
either
c = 0
x - a = 0 | x = a
x - b = 0 | x = b
the leading coefficient = 3.
that means nothing else than c = 3.
root = 1 means (x - 1) is one factor.
root = -5 means (x + 5) is the other factor.
so, we have
3(x - 1)(x + 5) = 3x² + 12x - 15
and the equation is
3x² + 12x - 15 = 0
or
3x² + 12x = 15
No. If you divide 69 by 100 you would get 0.69. If you divided 6 by 10 you would get 0.6. Therefore 69/100 and 6/10 is not equivalent.
Answer:
15
proof on pic......................
