Answer: 18 quarts
Step-by-step explanation:
Quantity of sparkling water and gape juice are used in proportion in the recipe.
Let x= quantity of sparkling water when 9 quarts of grape juice is used.
Then,
Hence, 18 quarts of sparkling water is required to mix with 9 quarts of grape juice.
A=43°
B=82°
c=28
1) A+B+C=180°
Replacing A=43° and B=82° in the equation above:
43°+82°+C=180°
125°+C=180°
Solving for C. Subtracting 125° both sides of the equation:
125°+C-125°=180°-125°
C=55° (option B or C)
2) Law of sines
a/sin A=b/sin B=c/sin C
Replacing A=43°, B=82°, C=55°, and c=28 in the equation above:
a/sin 43°=b/sin 82°=28/sin 55°
2.1) a/sin 43°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 43°:
sin 43°(a/sin 43°)=sin 43°(28/sin 55°)
a=28 sin 43° / sin 55°
Using the calculator: sin 43°=0.681998360, sin 55°=0.819152044
a=28(0.681998360)/0.819152044
a=23.31185549
Rounded to one decimal place
a=23.3
2.2) b/sin 82°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 82°:
sin 82°(b/sin 82°)=sin 82°(28/sin 55°)
b=28 sin 82° / sin 55°
Using the calculator: sin 82°=0.990268069, sin 55°=0.819152044
b=28(0.990268069)/0.819152044
b=33.84903466
Rounded to one decimal place
b=33.8
Answer: Option B) C=55°, b=33.8, a=23.3
More than 3,529.41176 which rounds up to 3,500.
The answer
if Marco wants to create a new circle using GX as a radius,
so GX = r = 10 cm + 16 cm = 26 cm
the area of a circle is
A = pie x r², so the new circle's area should be A = pie x 26² = 676 pie cm²
the true answer is
<span>D. 676 pie cm2</span>
Rational expression refers to a fraction in which the numerator and denominator are polynomials.