Answer:
112
Step-by-step explanation:
Aaron = y
Victoria = x
y = 14 +x
126 = 14 + x
x = 112
Victoria sold 112 boxes of cookies
Answer:
See below
Step-by-step explanation:
a = 15 sqrt 2 sin 45
= 15 sqrt 2 * sqrt( 2 ) /2 = 15 * 2 /2 = 15
sin 60 = a/c
sqrt(3)/2 = 15/c
c = 15 / ( sqrt(3)/2) = 30 / sqrt 3 = 30 sqrt 3 /3 = 10 sqrt 3
percent of water is: 32/80*100= 40%
Set of equations that can be used to calculate rate for each plumber:
2A+8B+8C = 1,400 --- (1)
4A+7B+10C = 1,660 --- (2)
3A+9B+9C = 1,660 --- (3)
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2*(1) - (2)
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4A+16B+16C = 2,800
4A+7B+10C = 1,660 -
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9B+6C = 1,140 --- (4)
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3(2) -4(3)
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12A+21B+30C = 4,980
12A+36B+36C = 6,600 -
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-15B-6C = -1,620 --- (5)
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(4) + (5)
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9B+6C = 1140
-15B-6C = -1620 +
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-6B = -480 => 6B = 480 => B = 480/6 = 80
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Using (4), 9(80)+6C = 1140
720+6C = 1140 => 6C = 1140-720 = 420 => C = 420/6 = 70
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Using (1), 2A+8(80)+8(70) = 1400
2A+640+560 =1400 => 2A = 1400-640-560 = 200 => A = 200/2 = 100
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The rates are:
A = $100
B = $80
C = $70
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On Thursday, number of calls: A = 4 hrs, B = 6 hrs, C = 3 hrs
Money earned = 4*100+6*80+3*70 = $1,090
Answer:
(x - 8)(2x + 3)
Step-by-step explanation:
To factor a polynomial of the form
ax² + bx + c,
follow these steps:
1) Multiply ac together.
2) Find 2 factors of ac that add to b. Call these factors p and q.
3) Break up the middle term of the polynomial into px + qx.
4) Factor by grouping.
Now let's follow the steps above with your problem.
You are given the polynomial
2x² - 13x - 24,
so a = 2, b = -13, and c = -24
1) Find ac.ac is the product 2(-24) = -48
2) Now we need to find 2 factors of -48 that add to b, -13.
I know that 48 = 3 × 16, so if we use -16 and 3 for the two numbers, we have
-16 + 3 = -13
and -16 × 3 = -48.
3) Now we break up the middle term of the polynomial, -13x, into -16x + 3x.
The polynomial is now
2x² - 16x + 3x - 24
4) We factor the polynomial by grouping. To factor by grouping, you factor a common factor out of the first 2 terms and factor out a common factor out of the last two terms.
2x² - 16x + 3x - 24 =
= 2x(x - 8) + 3(x - 8)
We now see the common factor of x - 8, so we factor that out.
= (x - 8)(2x + 3)
Answer: (x - 8)(2x + 3)
