Answer: 8 batches
Step-by-step explanation:
To get the number of batches she made, we can just use proportion to solve it. But first, we need to convert 5 1/3 to improper fraction
5 1/3 = 16/3
Then we can now use the proportion to solve
2/3 cups = 1 batch
16/3 cups = x (note:5 1/3=16/3)
cross multiply
2/3 × x = 16 /3
2x/ 3 = 16/3
we need to make x the subject of the formula, to do that we will multiply each side of the equation by 3/2
2/3 × 3/2 x = 16/3 × 3/2
6x /6 = 48 / 6
x = 8
Therefore she made 8 batches of cookies.
Answer:
20x^3/4x7
20/4x^4
5/x^4
Step-by-step explanation:
xy = -1
x + y = 2
x + y = -2
- x - x
y = -x - 2
xy = -1
x(-x + 2) = -1
x(-x) + x(2) = -1
-x² + 2x = -1
+ 1 + 1
-x² + 2x + 1 = 0
-1(x²) - 1(-2x) - 1(-1) = 0
-1(x² - 2x - 1) = 0
-1 -1
x² - 2x - 1 = 0
x = -(-2) ± √((-2)² - 4(1)(-1))
2(1)
x = 2 ± √(4 - 4(-1))
2
x = 2 ± √(4 + 4)
2
x = 2 ± √(8)
2
x = 2 ± 2√(2)
2
x = 1 ± √(2)
x + y = 2
(1 ± √(2)) + y = 2
- (1 ± √(2)) - (1 ± √(2))
y = 1 ± √(2)
(x, y) = (1 ± √(2), 1 ± √(2))
The numbers that multiply to -1 and add to 2 are 1 ± √(2).
As a fraction, the exact answer is 5/6
In decimal form, the approximate answer is 0.8333
To get this answer, note how there are 5 ways to roll something that isn't a three (1,2,4,5,6) out of 6 ways total (1,2,3,4,5,6)
So you simply divide the two values to get 5/6 = 0.8333
The answer: m∡BCD = 130° .
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Explanation:
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m∡BCD = 9x - 5 = our answer.
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Note: (9x - 5) + (m∡C IN Δ ACB)= 180 ;
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Reason: all angles on straight line add up to 180.
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Note: In Δ ACB; m∡A + m∡B + m∡c = 180.
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Reason: All three angles in any triangle add up to 180.
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Given Δ ACB, we are given:
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m∡C= ?
m∡B = (4x + 5)
m∡A = 65
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So, given Δ ACB; m∡A + m∡B + m∡c = 180;
→Plug in our known values and rewrite:
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Given Δ ACB; 65 + 4x + 5 + (m∡c) = 180;
→Simplify, and rewrite:
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Given Δ ACB; 4x + 70 + (m∡c) = 180;
→Subtract "70" from each side of the equation; and rewrite:
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Given Δ ACB; 4x + (m∡C) = 110;
→Subtract "4x" from EACH SIDE of the equation; to isolate: "(m∡c)" on one side of the equation; and "solve in terms of "(m∡C)" ;
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Given Δ ACB' m∡C = 110 - 4x ;
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So, we know that: (110 - 4x) + (9x - 5) = 180; (since all angles on a straight line add up to 180.
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We can solve for "x".
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(110 - 4x) + (9x - 5) = 180;
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Rewrite as:
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(110 - 4x) + 1(9x - 5) = 180 ; (Note: there is an implied coefficient of "1"; since anything multiplied by "1" equals that same value).
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Note the "distributive property of multiplication":
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a*(b+c) = ab + ac ; AND:
a*(b - c) = ab - ac .
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So, +1(9x - 5) = (+1*9x) - (+1*5) = 9x - 5 ;
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So we can rewrite:
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(110 - 4x) + (9x - 5) = 180 ; as:
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110 - 4x + 9x - 5 = 180 ; We can simplify this by combining "like terms" on the "left-hand side" of the equation:
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110 - 5 = 105 ;
-4x + 9x = 5x;
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So, rewrite as: 5x + 105 = 180; Subtract "105" from EACH side; to get:
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5x = 75 ; Now, divide each side of the equation by "5";
to get: x = 15.
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Now, we want to know: m∡BCD; which equals:
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9x - 5 ; let us substitute "15" for "x"; and solve:
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9x - 5 = 9*(15) - 5 = 135 - 5 = 130.
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The answer: m∡BCD = 130°
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