Jill had a total score of 40 on 13 quizzes, so her average was
40/13 ≈ 3.08
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1 quiz @ 1 = total of 1
3 quizzes @ 2 = total of 6
4 quizzes @ 3 = total of 12
4 quizzes @ 4 = total of 16
1 quiz @ 5 = total of 5
total score = 1 + 6 + 12 + 16 + 5 = 40
total quizzes = 1 + 3 + 4 + 4 + 1 = 13
8 = 4w/3
8 = 4w/3
×3 = 4w×3
24= 4w ( the two 3s cross each other out)
÷4 = ÷4
8 = w ( the two 4s cross each other out)
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)
because 4x+20y=-36,so ( 4x+20y)/2=2x+10y=-18
(2x+10y)-(2x+5y)=-18-18
5y=-36
then y=-7.2
because 2x=18-5y
so x=(18-5y)/2=(18-5*(-7.2)）/2=27
If I am reading the equations correctly, they are:
5x - 14 = 3x AND 7x + 12 = x - 6
If this is correct, the first one would be worked out like this:
5x (- 5x) - 14 = 3x (- 5x)
- 14 = - 2x
- 14 (/ - 2) = - 2x (/ - 2)
7 = x
The second would be worked out like this:
7x + 12 (+ 6) = x - 6 (+ 6)
7x + 18 = x
7x (- 7x) + 18 = x (- 7x)
18 = - 6x
18 (/ - 6) = - 6x (/ - 6)
- 3 = x
I hope this is what you are looking for :)
