Answer:
Step-by-step explanation:
Eight
590 = 1800 e^(-0.4t) Divide by 1800
0.32778 = e^(-0.4t) Put the value for e in the denominator.
0.32778 = 1 / e^(0.4t) Notice the sign's gone. Multiply both sides by e^(0.4t)
0.32778 *e^(0.4t) = 1 Divide by 0.32778
e^(0.4t) = 3.0508 Take the natural log of both sides.
0.4t = 1.11542 Divide both sides by 0.4
t = 2.78855
You should put this in the original equation to see if it checks. It does.
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Nine
3^(3 - 3x) + 6 = 42 Subtract 6 from both sides
3^(3 - 3x) = 36 Take the log of both sides.
(3 - 3x) ln(3) = ln 36
(3 - 3x) *1.098612 = 3.58352 Divide by 1.098612
3 - 3x = 3.26186 Subtract 3 from both sides
- 3x = 0.26186 Divide by - 3
x = - 0.087287
Since 1 km is 100,000 cm there are 39,400 inches in a kilometer
Equation in slope-intercept form is y = 2x - 6
Step-by-step explanation:
- Step 1: Given slope of the line, m = 2. Form an equation y = mx + b
⇒ y = 2x + b ---- (1)
- Step 2: The line passes through the point (4,2). So it will satisfy the equation. Find b by substituting x = 4 and y = 2.
⇒ 2 = 2 × 4 + b = 8 + b
⇒ b = -6
- Step 3: Form the slope-intercept equation.
⇒ y = 2x - 6
You are buying 2 items so let's use two different variables to represent each:
p = number of tubes of paint
b = number of disposable brushes
cost = price per item × number of items
Equations from information given:
4p + 0.50b = 20 ← from the first 2 sentences
2p = b ← if there are twice as many brushes as paint tubes you need 2 times paint tubes to equal number of brushes
Solve the problem by using substitution... 1b equals 2p so replace b with that:
4p + 0.50(2p) = 20
4p + 1p = 20 ← 0.50 is half so half of 2p is 1p
5p = 20 ← combine like terms
p = 4 ← divide both sides of the equation by 5
Recall the equation 2p = b replace p with 4
2(4) = b
8 = b
ANSWER:
You purchased 4 tubes of paint and 8 disposable brushes.
