Removing the brackets gives 4a -2b +c -5c - a + 4b and then collect the like terms to get 3a + 2b - 4c
Answer:
Step-by-step explanation:
To find the number of inches, divide miles by 9.5.
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a) 24 miles = (24 mi)×(1 in)/(9.5 mi) = (24/9.5) in ≈ 2.526 in
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b) 24 miles + 16 miles = 40 miles = (40 mi)×(1 in)/(9.5 mi) = 40/9.5 in ≈ 4.211 in
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Comment on units conversion
I find it convenient to work units conversion problems by writing a fraction that is equal to 1 and multiplying by that to change units. My fraction has the "to" units in the numerator, and the "from" units in the denominator. That way, the unwanted units cancel when the multiplication is carried out.
The fraction is equal to 1 because the measurement in the numerator is equal to the measurement in the denominator.
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Some folks prefer proportions. If you do it that way, be sure "like" is matched with "like".
map inches/ground miles = 1/9.5 = x/24
route inches/scale inches = route miles/scale miles = x/1 = 24/9.5
Answer:
p = 1.5 and q = 9
Step-by-step explanation:
Expand the right side then compare the coefficients of like terms on both sides, that is
4(x + p)² - q ← expand (x + p)² using FOIL
= 4(x² + 2px + p²) - q ← distribute parenthesis
= 4x² + 8px + 4p² - q
Comparing coefficients of like terms on both sides
8p = 12 ( coefficients of x- terms ) ← divide both sides by 8
p = 1.5
4p² - q = 0 ( constant terms ), that is
4(1.5)² - q = 0
9 - q = 0 ( subtract 9 from both sides )
- q = - 9 ( multiply both sides by - 1 )
q = 9
The ratio is:
Chlorine : Water = 1 : 10
m ( Water ) = 15 ounces
m ( Chlorine ) = x
x : 15 = 1 : 10
10 x = 15 * 1
10 x = 15
x = 15 : 10
x = 1.5 ounces
Answer:
We need to add 1.5 ounces of Chlorine for the correct ratio.
Answer: False
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Explanation:
I'll use x in place of p.
The original equation 10x^2-5x = -8 becomes 10x^2-5x+8 = 0 after moving everything to one side.
Compare this to ax^2+bx+c = 0
We have
Plug those three values into the discriminant formula below
d = b^2 - 4ac
d = (-5)^2 - 4(10)(8)
d = 25 - 40*8
d = 25 - 320
d = -295
The discriminant is negative, which means we have no real solutions. If your teacher has covered complex or imaginary numbers, then you would say that the quadratic has 2 complex roots. If your teacher hasn't covered this topic yet, then you'd simply say "no real solutions".
Either way, this quadratic doesn't have exactly one solution. That only occurs when d = 0. Therefore, the original statement is false.
