Answer:
y-intercept of the line MN = 2
Standard form of the equation ⇒ x + y = 2
Step-by-step explanation:
Coordinates of the ends of a line MN → M(-3, 5) and N(2, 0)
Slope of a line = 
= 
= -1
Equation of the line MN passing through (-3, 5) and slope = -1,
y - 5 = (-1)(x + 3)
y - 5 = -x - 3
y = -x + 2
This equation is in the y-intercept form,
y = mx + b
where m = slope of the line
b = y-intercept
Therefore, y-intercept of the line MN = 2
Equation in the standard form,
x + y = 2
Though I almost broke my brain while solving what "-3 0 -2 5 0 9 2 5 3 0" means, I can tell you which statements is absolutely incorrect: it is "The function g(x) has a minimum value of 0" (it is incorrect because the maximum value is 9 as table provides).
To solve other problems, look at f(x): if it has the top, where y is the biggest, then it is the maximum value (so if y = 4.5 is the biggest y, first statement is correct); if it has the bottom, where y is the smallest, then it is minimum value (factually, statement 3 will be correct if statement 1 is correct because 9/4.5 = 2). Finally, if f(x) has the top, then statement 4 is correct because f(x) and g(x) would be both constantly decreasing functions.
Hope this helps.
Answer:
The conditional statement "∀x, If x is an insect, then x has six legs" is derived from the statement "All insects have six legs" using "a. existential" generalization
Step-by-step explanation:
In predicate logic, existential generalization is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition. In first-order logic, it is often used as a rule for the existential quantifier in formal proofs.
Answer:
Step-by-step explanation:
We'll just work on solving both so you can see what's involved in solving an absolute value equation. Because an absolute value is a distance, we can have that distance being both to the right on the number line of the number in question or to the left. For example, from 2 on the number line, the numbers that are 5 units away are 7 and -3. Using that logic, we will simplify the equation down so we can set up the 2 basic equations needed to solve for x.
If 
then
What you need to remember here is that you cannot distribute into a set of absolute values like you would a set of parenthesis. The -2 needs to be divided away:
Now we can set up the 2 main equations for this which are
.5x + 1.5 = .5 and .5x + 1.5 = -.5
Knowing that an absolute value will never equal a negative number (because absolute values are distances and distances will NEVER be negative), once we remove the absolute value signs we can in fact state that the expression on the left can be equal to a negative number on the right, like in the second equation above.
Solving the first one:
.5x = -1 so
x = -2
Solving the second one:
.5x = -2 so
x = -4
