Answer:
y = 5
General Formulas and Concepts:
<u>Alg I</u>
Point-Slope Form: y - y₁ = m(x - x₁)
Step-by-step explanation:
<u>Step 1: Define variables</u>
Point (-2, 5)
Slope <em>m</em> = 0
<u>Step 2: Write function</u>
y - 5 = 0(x + 2)
y - 5 = 0
y = 5
<u>Step 3: Identify</u>
y = 5 is a horizontal line.
Answer:
11 coins for $1.99
Step-by-step explanation:
The maximum total less than $2 is $1.99. It takes 11 coins to make that total. It would take 1 fewer if the nickel were not required.
Starting with the minimum required coins, which total $0.91, we need to add $1.08 using a minimum number of coins. To minimize the added coins, we start with the largest we can use without going over the total: 2×50¢ + 1×5¢ + 3×1¢. These 6 coins added to the required 5 coins give the desired total using 11 coins.
11 coins: $1.99 . . . . (3×50¢ +1×25¢ +1×10¢ +2×5¢ +4×1¢)
$1.99 is the highest possible total less than $2.00, and it takes a minimum of 11 coins to make that total.
Answer:
23 years
Step-by-step explanation:
Step 1: Calculate the rate constant (k) for the radioactive decay
A radioactive substance with initial concentration [A]₀ decays to 97% of its initial amount, that is, [A] = 0.97 [A]₀, after t = 1 year. Considering first-order kinetics, we can calculate the rate constant using the following expression.
ln [A]/[A]₀ = - k.t
k = ln [A]/[A]₀ / -t
k = ln 0.97 [A]₀/[A]₀ / -1 year
k = 0.03 year⁻¹
Step 2: Calculate the half-life of the substance
We will use the following expression.
= ln2/ k = ln 2 / 0.03 year⁻¹ = 23 years
Answer:
x=-2
Step-by-step explanation:
3x-8x = -5x
8+2= 10
5x = 10
simp: x=-2
