Answer:
In the mid-19th century, the quest for control of the West led to the annexation of Texas and the Mexican–American War. ... This expansion led to debates about the fate of slavery in the West, increasing tensions between the North and South that ultimately led to the collapse of American democracy and a brutal civil war.
Step-by-step explanation:
Answer:
151 notes
Step-by-step explanation:
$85/1=85 notes
125/5=25 notes
150/10=15 notes
420/20=21 notes
500/100=5 notes
85+25+15+21+5=151 notes total
Answer:
a) f(16) = 42
b) f(16) = 54
c) f(16) = 162
d) f(16) = 30
Step-by-step explanation:
a) y = mx + b ∧ m = (f(8) - f(4))/(8-4) ⇒ m = (18 - 6)/(8 - 4) = 3
b = y - mx = 6 - 3(4) = 6 - 12 = - 6
f(16) = 3(16) - 6 = 42
b) y = kxⁿ ∧ f(4) = 6 = k4ⁿ ∧ f(8) = 18 = k8ⁿ ⇒ 18/6 = (k8ⁿ)/(k4ⁿ) ⇒ 3 = 2ⁿ
n = ㏑(3) / ㏑(2) ⇒ k = y/xⁿ ⇒ k = 6/4ⁿ = 2/3
f(16) = 2/3 × 16ⁿ = 54
c) y = aeᵇˣ ∧ f(4) = 6 = aeᵇ⁴ ∧ f(8) = 18 = aeᵇ⁸ ⇒ 18/6 = (aeᵇ⁸)/(aeᵇ⁴) ⇒ 3 = e⁴ᵇ
b = ㏑(3/4) ∧ a = y / eᵇˣ ⇒ a = 6 / e⁴ᵇ = 2
f(16) = 2eᵇ¹⁶ = 162
d) y = a㏑(bx) ∧ f(4) = 6 = a㏑(b4) ∧ f(8) = 18 = a㏑(b8)
⇒ 18 - 6 = a㏑(b8) - a㏑(b4) ⇒ 12 = a㏑(8b/4b) ⇒ a = 12 / ㏑(2)
f(4) = 6 = a㏑(4b) ⇒ b = (√2)/4
f(16) = a㏑(b16) = 30
The original inequality is -3x+4 > 19
Let's replace x with -4 and see what happens.
-3x + 4 > 19
-3(-4)+4 > 19
12+4 > 19
16 > 19
The last inequality is false, so the original inequality is false when x = -4.
This means x = -4 is not a solution to -3x + 4 > 19
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Let's plug in something larger. Let's say x = -3 which is one space to the right of -4 on the number line.
So we get...
-3x + 4 > 19
-3(-3) + 4 > 19
9 + 4 > 19
13 > 19
This doesn't work either. The value x = -3 is not a solution.
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Let's determine which x values will work by solving for x
-3x + 4 > 19
-3x + 4 -4 > 19-4 ... subtracting 4 from both sides
-3x > 15
-3x/(-3) < 15/(-3) ... divide both sides by -3; inequality sign flips
x < -5
The solution set consists of values smaller than -5
So values like {-6, -7, -8, -9, ...} and decimal values as well in that interval.
Answer:
Maybe Height and Width or Length I don't know