The quadratic equation in its generic form is:
ax2 + bx + c
To complete squares we must add the following term:
(b / 2) ^ 2
The equation is:
ax2 + bx + c + (b / 2) ^ 2
We have the following equation:
x ^ 2 - 5x + k = 7
By completing squares we have:
x ^ 2 - 5x + (-5/2) ^ 2 = 7 + (-5/2) ^ 2
Rewriting:
x ^ 2 - 5x + 6.25 = 7 + 6.25
Answer:
A constant term should be used to complete the square is:
6.25
Answer:
- sin C=h/a
- substitution property of equality
- commutative property of multiplication
Step-by-step explanation:
Because two points determine a line, you can draw altitude BD perpendicular to AC with height h. By the definition of a sine ratio, <u>sin(C) = h/a</u>, which can be rearranged into a·sin(C) = h. The area of △ABC is A=1/2bh. The <u>substitution property of equality</u> can be used to write A=1/2b(a sinC), which becomes A=1/2ab(sinC) by the <u>commutative property of multiplication</u>.
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The mnemonic SOH CAH TOA reminds you that the sine ratio is ...
Sin = Opposite/Hypotenuse
Here, the side of the right triangle opposite angle C is designated "h", the height of ∆ABC. The hypotenuse of that right triangle is side "a". So ...
sin(C) = h/a
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The substitution property of equality lets you replace any expression with its equal. Here, we have h=a·sin(C), so we can use a·sin(C) in place of h in the formula for triangle area:
1/2bh = 1/2ba·sin(C)
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The commutative property of multiplication lets you rearrange the order of the factors in a product, so ...
ba = ab
and
A = 1/2ba·sin(C) = 1/2ab·sin(C)
Answer:
±sqrt( H *f•c)= L
Step-by-step explanation:
H=L^2/f•c
Multiply each side by fc
H *fc=L^2/f•c * fc
H *f•c=L^2
Take the square root of each side
±sqrt( H *f•c)= sqrt(L^2)
±sqrt( H *f•c)= L
Cost of fuel = 30% of $400 000 = 30/100 x 400000 = $120 000
Fuel amount = $120 000/$1.5 = 80 000 liters
new cost of fuel = 80000 x $1.6 = $144 000
increase in cost = 144000 - 120000 = $24000
So the increase in petrol price increases the operating cost by $24000
