Answer:
4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
6−4x=6x−8x−2
6+−4x=6x+−8x+−2
−4x+6=(6x+−8x)+(−2)(Combine Like Terms)
−4x+6=−2x+−2
−4x+6=−2x−2
Step 2: Add 2x to both sides.
−4x+6+2x=−2x−2+2x
−2x+6=−2
Step 3: Subtract 6 from both sides.
−2x+6−6=−2−6
−2x=−8
Step 4: Divide both sides by -2.
−2x−2=−8−2
x=4
here is a link:
https://www.mathpapa.com/algebra-calculator.html?q=6-4x%3D6x-8x-2.
Answer:
Step-by-step explanation:
1) find the total candies
7 + 8 + 5 + 9 = 29
2) a probability can be expressed with a fraction whose denominator is the total candies, while the numerator represents the candies that we want to find
- red = 7/29
- blue = 8/29
- yellow = 5/29
- green = 9/29
3) compound probability
(red + blue)/29 = 15/29
(yellow + green)/29 = 14/29
(blue + yellow + green)/29 = 22/29
Answer:
a = length of the base = 2.172 m
b = width of the base = 1.357 m
c = height = 4.072 m
Step-by-step explanation:
Suppose we want to build a rectangular storage container with open top whose volume is 12 cubic meters. Assume that the cost of materials for the base is 12 dollars per square meter, and the cost of materials for the sides is 8 dollars per square meter. The height of the box is three times the width of the base. What’s the least amount of money we can spend to build such a container?
lets call a = length of the base
b = width of the base
c = height
V = a.b.c = 12
Area without the top:
Area = ab + 2bc + 2ac
Cost = 12ab + 8.2bc + 8.2ac
Cost = 12ab + 16bc + 16ac
height = 3.width
c = 3b
Cost = 12ab + 16b.3b + 16a.3b = 12ab + 48b² + 48ab = 48b² + 60ab
abc = 12 → ab.3b = 12 → 3ab² = 12 → ab² = 4 → a = 4/b²
Cost = 48b² + 60ab = 48b² + 60b.4/b² = 48b² + 240/b
C(b) = 48b² + 240/b
C'(b) = 96b - 240/b²
Minimum cost: C'(b) = 0
96b - 240/b² = 0
(96b³ - 240)/b² = 0
96b³ - 240 = 0
96b³ = 240
b³ = 240/96
b³ = 2.5
b = 1.357m
c = 3b = 3*1.357 = 4.072m
a = 4/b² = 2.172m
A = 1/2bh...for h
multiply both sides by 2
2A = bh
now divide both sides by b
(2a)/b = h
a) ∠PQR=65° (alternate interior angles theorem)
∠PRQ = 60° (linear pair)
x = 55° (angles in a triangle add to 180°)
b) ∠APQ and ∠PQR are congruent alternate interior angles.
