Answer:
47.4 pounds
Step-by-step explanation:
First, find the height of the trapezoid. Draw the height DE. Quadrilateral ABED is a rectangle, then BE = 12 cm. Since BC = 20 cm, then EC = 20 - 12 = 8 cm.
Consider right triangle DEC. By the Pythagorean theorem,
The area of the trapezoid ABCD is
One can cover 
, then it is needed
cans
One can costs 19.75 pounds, then 2.4 cans cost
pounds
Answer: -1 ± <em>i</em>√35
⁻⁻⁻⁻⁻⁻⁻⁻
6
Step-by-step explanation:
From the quadratic equation,
X = -b ±√b² - 4ac
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
2a
From the given equation, -3x² - x - 3 = 0
where a = -3, b = -1, c = -3
Now substitute for the values in the formula above
x = -(-1) ± √(-1)² - 4(-3)(-3)
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
2(-3)
x = 1 ± √ 1 - 36
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
-6
x = 1 ± √ -35
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
-6
x = -1 ± <em>i√35 this is because it has a negative root.</em>
<em> ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻</em>
<em> 6</em>
<em> The answer is b</em>
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
Answer:
the substitution method is one way to solve linear equation. the substitution method is when substitute the one y value with the other:
example :
x+y=10
y=10-x ( value of y)
2x+y=12 ( substitute the value of y in the equation )
2x+(10-x)=12
2x+10-x=12 ( now solve for x)
x=12-10
x=2 ( substitute the value of x in the equation x+y=10)
x+y=10
2+y=10
y=10-2
y=8
( i hope it helps)
