Answer:
x = 20
Step-by-step explanation:
The three angles make up a straight line.
A straight line has 180 degrees.
x + 3x + 100 = x80 Combine
4x + 100 = 180 Subtract 100 from both sides
4x = 180 - 100
4x = 80 Divide by 4
x = 80/4
x = 20
A points location will change after you add a negative value to the y coordinate even if you leave the x coordinate the name because you are changing the value of the y coordinate. For example, if you have (4,6) as a coordinate and then change it to (4,-6), the coordinate will now just be on the other side of the x axis
It costs $3.63 more for the gold die than the gold plated die.
The volume of each half of the die is given by the formula
V=1/3s³.
This means the total volume is V = 2(1/3s³) = 2(1/3(2³)) = 16/3 = 5.33 mm³.
For the solid gold die, we know that it weighs 0.02g per mm³:
5.33(0.02) = 0.1066g
Gold costs $40.38 per gram:
40.38(0.1066) = $4.30
For the plastic die, plastic weighs 0.01 g per mm³:
0.01(5.33) = 0.0533g
Plastic costs $10 per gram:
0.0533(10) = 0.533 ≈ $0.54.
We also need to find the surface area, as it will be painted. Each face is an equilateral triangle; the area of a triangle is given by the formula
A = 1/2bh
We need to use the Pythagorean theorem to find the height. The height will be one leg and 1/2 of the base will be the other; the slanted side will be the hypotenuse:
h² + (1/2(2))² = 2²
h² + 1² = 2²
h² + 1 = 4
h² = 3
h = √3
The area of the triangle would then be A = 1/2bh = 1/2(2)(√3) = √3. There are 8 such faces on the die, so the total surface area would be 8√3 = 13.86mm².
Paint costs $0.01 per mm²:
13.86(0.01) = 0.1386 ≈ $0.14
Together the cost for the plastic is 0.14+0.53 = $0.67.
The difference between it and the cost for the gold die is 4.30 - 0.67 = $3.63.
Answer: The numbers are: <u>x = 34, y = 12</u>
Step-by-step explanation:
Lets say the numbers are x and y. The two equations are:
x+y=46
x= 3y-2
Next you use substitution for x in the first equation which brings you to
3y-2 + y = 46 which simplyfies to:
4y - 2 = 46
4y = 48
48 / 4 = 12
y = 12
Then you plug back y=12 in either of the equation to solve for x:
x = 3y - 2
x = 3(12) - 2 = 36 - 2 = 34
x = 34, y = 12
Answer:
14 inches of the original length of ribbon is left.
Step-by-step explanation:
It is given that the total length of ribbon is 32 inches.
It is also given that he cuts six 3-inch pieces from the original length. This means:
6*3 = 18 inches
18 inches are cut from the total length of ribbon.
So the remaining ribbon will be:
= 32-18 = 14 inches
Hence,
14 inches of the original length of ribbon is left.
