Answer:
19. Opposite of a Difference ↔ E. -(8 - 3·m) = 3·m - 8
20. Opposite of a sum ↔ A. -[(-r) + 2p] = -(-r) - 2p
21. Opposite of an Opposite ↔ F. -1[ -1(9 - 2w)] = 9 - 2w
22. Multiplication by 0 ↔ B. 160 - (3d + 2)(0) = 160 - 0
23. Multiplication by ↔ D. -1 -(4r + 3s) + t = (-1)(4r + 3s) + t
21. Distributive property ↔ C. 5(2 - x) = 10 - 5x
Step-by-step explanation:
19. Opposite of a difference is the difference of the opposites
20. Opposite of a sum is the sum if the opposites
21. Opposite of an opposite is the original number
22. Multiplication by 0- The result of multiplication by 0 is 0
23. Multiplication by -1 results in the change in sign of a number
24. Distributive property - Multiplying the sum or difference of two numbers by a number, will have the same result as multiplying each each of the addends by the number individually and adding the product together.
Step-by-step Answer:
Step 1:
Extract factor(s) common to all terms.
In this case, the HCF is 3, so the expression is written
-12x^2+45x+12 = -3(4x^2-15x-4)
The negative sign was also exrracted to give a positive leading coefficient, which is easier to work with.
Step 2, group the coefficient in such a way that there is a common factor.
Leaving the factor -4 for the moment, and concentrate on the coefficients in parentheses, write the original expression as
4x^2 - 15x -4
= 4x^2 -16x
+ x -4
= 4x*(x-4) + 1*(x-4)
extract (x-4) as a common factor
= (x-4)(4x+1)
Step 3:
Combine all the factors to get
-3(x-4)(4x+1)
=3(4-x)(4x+1)
as the complete factoring of the given expression.
Answer:
1. Triangle: B = 47.0° , C = 103.05° , c = 2.53 cm
2. Lake: c = 1105.31 ft
Step-by-step explanation:
Law of Sine Formula:
Given: A = 30° , a = 1.3 cm , b = 1.9 cm
Solving for sin(B). Cross Multiply.
B = sin^-1( 
)
B ≈ 46.9509202
B = 47.0°
Solve for C°
A° + B° + C° = 180°
30° + 46.95° + C° = 180°
C° = 180° - 30° - 46.95°
C° = 103.05°
Solve for sin(C)
Cross Multiply
C ≈ 2.532850806
C = 2.53 cm
Law of Cosine Formula: 
Given: a = 850 ft , b = 960 ft , C=75°
Solve for c.
c ≈ 1105.308698
c = 1105.31 ft
Answer:
its the same above
Step-by-step explanation:
1.81437 :) .................................................................................................. woopsie
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