Answer:
1. b ∈ B 2. ∀ a ∈ N; 2a ∈ Z 3. N ⊂ Z ⊂ Q ⊂ R 4. J ≤ J⁻¹ : J ∈ Z⁻
Step-by-step explanation:
1. Let b be the number and B be the set, so mathematically, it is written as
b ∈ B.
2. Let a be an element of natural number N and 2a be an even number. Since 2a is in the set of integers Z, we write
∀ a ∈ N; 2a ∈ Z
3. Let N represent the set of natural numbers, Z represent the set of integers, Q represent the set of rational numbers, and R represent the set of rational numbers.
Since each set is a subset of the latter set, we write
N ⊂ Z ⊂ Q ⊂ R .
4. Let J be the negative integer which is an element if negative integers. Let the set of negative integers be represented by Z⁻. Since J is less than or equal to its inverse, we write
J ≤ J⁻¹ : J ∈ Z⁻
Based on the multiplication property of equality, the statement that completes the proof is: C. CD = b(sin A) and CD = a(sin B).
<h3>What is the Multiplication Property of Equality?</h3>
The multiplication property of equality is given as, if a/b = y, then a = yb. Both sides of the equation is multiplied by the same value.
In step 5 where the multiplication property of equality is applied, we would have:
sin(A) = CD/b
Multiply both sides by b
sin(A) × b = CD/b × b
b(sin A) = CD
CD = b(sin A)
This same property is applied to sin B = CD/a to get CD = a(sin B).
Therefore, the missing statement is: C. CD = b(sin A) and CD = a(sin B).
Learn more about the multiplication property of equality on:
brainly.com/question/1978763
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• Given the table of values, you can identify these points:
If you plot them on a Coordinate Plane, you get:
As you can observe, it is a Linear Function.
• The equation of a line in Slope-Intercept Form is:
Where "m" is the slope of the line and "b" is the y-intercept.
In this case, you can identify in the graph that:
Therefore, you can substitute that value and the coordinates of one of the points on the line, into this equation:
And then solve for "m", in order to find the slope of the line.
Using this point:
You get:
Therefore, the equation for the data in Slope-Intercept Form is:
Hence, the answer is:
• It represents a Linear Function.
,
• Equation:
Answer:x = 75
Step-by-step explanation:y=105 - 5 = 100 ft
z=125 ft
dz/dt=2 ft/sec
by using Pythagorean Theorem, we find x
x^2 + 100^2 = 125^2
x = 75
