Answer:
Option 4 is correct.
Step-by-step explanation:
Consider a function g, it has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18. It is given that g(-1) = 2 and g(2) = 8.
The statement g(5) = 12 is not true because the value of x is 5 which is not in its domain.
The statement g(1) = -2 is not true because the value of function g(x) is -2 which is not in its range.
The statement g(2) = 4 is not true because g is a function and each function has unique output for each input value.
If g(2)=8 and g(2)=4, then the value of g(x) is 8 and 4 at x=2. It means g(x) is not a function, which is contradiction of given statement.
The statement g(3) = 18 is true because the value of x is 3 which is in the domain and the value of function g(x) is 18 which is in its range.
Therefore, the correct option is 4.
<span>Simplifying
-15x2 + -2x + 8 = 0
Reorder the terms:
8 + -2x + -15x2 = 0
Solving
8 + -2x + -15x2 = 0
Solving for variable 'x'.
Factor a trinomial.
(2 + -3x)(4 + 5x) = 0
Subproblem 1Set the factor '(2 + -3x)' equal to zero and attempt to solve:
Simplifying
2 + -3x = 0
Solving
2 + -3x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2
Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2
Combine like terms: 0 + -2 = -2
-3x = -2
Divide each side by '-3'.
x = 0.6666666667
Simplifying
x = 0.6666666667
Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve:
Simplifying
4 + 5x = 0
Solving
4 + 5x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 5x = 0 + -4
Combine like terms: 4 + -4 = 0
0 + 5x = 0 + -4
5x = 0 + -4
Combine like terms: 0 + -4 = -4
5x = -4
Divide each side by '5'.
x = -0.8
Simplifying
x = -0.8
Solutionx = {0.6666666667, -0.8}</span>
Answers:
- Domain is (-4, 3]
- Range is (-5, 5]
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Explanation:
The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that 
. It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).
The interval then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.
It says: x is between -4 and 3. It can't equal -4 but it can equal 3.
So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.
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The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.
The range as a compound inequality is 
. This condenses into the shorthand of (-5, 5] which is the range in interval notation.
Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.
Answer:
Which statement best explains how enzymes speed up a chemical reaction?
Enzymes add heat to a chemical reaction.
Enzymes lower the activation energy of a chemical reaction.
Enzymes remove heat from a chemical reaction.
Enzymes are not changed as a result of a chemical reaction.
Step-by-step explanation:
Answer:
A) Associative Property of Addition
Step-by-step explanation:
<u><em>Associative Property of Addition</em></u>
Let A, B and C be any three real numbers
A+(B+C) = (A+B) + C
Given data
(20.4 + 3.75) + 4.25 = 20.4 + (3.75 + 4.25)
= 20.4 + 8.0
= 28.4
