Answer:
x = -1, y = 1
Step-by-step explanation:
Multiply the top equation by 2:
Leaving the bottom equation unchanged, add the two resulting equations to eliminate y, obtaining:
Solve this for x, and then substitute this value of x into the bottom equation. Finally, solve for y.
Answer:
A) 15x - 12
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
5x(3 - 12x) - 3(4 - 20x²)
<u>Step 2: Simplify</u>
- Distribute: 15x - 60x² - 12 + 60x²
- Combine like terms: 15x - 12
Answer:
A. 13.31' to the nearest hundredth.
B. 86.52' to the nearest hundredth.
Step-by-step explanation:
Part A>
The apotherm of a regular polygon is the distance of the line segment from the centre of the polygon to the midpoint of a side.
2 radii of this decagon joined to the endpoints of a side form an isosceles triangle with equal sides = 14 cm.
The apotherm is the altitude of this triangle. The vertex of the triangle has an angle of 360 / 10 = 36 degrees and the apotherm bisects this angle.
So using trigonometry on the right triangle formed:
cos 18 = x / 14 where x is the apotherm.
x = 14 cos 18
= 13.31' (answer).
Part B.
Using trigonometry on the right triangle again:
sin 18 = x/2 / 14 (where x is the length of a side of the hexagon)
x/2 = 14 sin 18
x = 2 * 14 sin 18
= 8.652'.
As a decagon has 10 sides the perimeter = 8.652 * 10
= 86.52' to the nearest hundredth.
Answer:
5
Step-by-step explanation:
Let the smallest integer equal x - 1, the next one equal x, and the last one equal x + 1.
4(x-1) = 3(x-1) + 6
x-1 = 5
x = 6
The smallest integer is x - 1, which is equal to 5. Thus, the smallest of the three integers is 5.