Kamila buys a dress for £30 in a sale. It was advertised "25%off". Kamila says"25% of £30 is £7.50 so i saved £7.50". Explain wh
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Answer:
Shifted left by 2 units
Step-by-step explanation:
When you have a function (say f(x)), you can translate it left or right by replacing what's inside the function. In this case it is shown that the x in f(x) is replaced with x+2 in g(x). Therefore:
Rewriting g(x) like this shows that there is a +2 in the f(x). Whenever there is a number being added inside the function, then the graph is shifted left that many units (and vice versa for subtraction). So in this case since 2 is being added inside the function the graph will be translated left 2
Angles formed when two parallel are intersected by a common transversal include, corresponding, alternate interior and exterior, same-side interior, and vertically opposite angles
The correct option is Same–Side Int. ∠s Thm. m∠1 = 30°, m∠5 = 150°
The reason the selection is correct is as follows:
The given angles are;
m∠1 = (30·x - 30)°. m∠5 = (40·x + 70)°
∠1, and ∠5, are located on the same side of the transversal and are both formed on the interior side of the parallel lines
Therefore, they are same–side interior angles
Same side interior angles theorem states that same side interior angles formed between parallel lines are supplementary
Therefore, we have;
m∠1 + m∠5 = 180°
Which gives;
(30·x - 30)° + (40·x + 70)° = 180°
(70·x + 40)° = 180°
70·x = 180° - 40° = 140°
m∠1 = (30·x - 30)° = (30 × 2 - 30)° = 30°
m∠1 = 30°
m∠5 = (40·x + 70)° = (40 × 2 + 70)° = 150°
m∠5 = 150°
The correct option is therefore;
Same-Side Int. ∠s Thm. m∠1 = 30°, m∠5 = 150°
Learn more about parallel lines cut by a transversal here:
The graph of the function f(x) = -(x+1)^2 shows that the domain of the function f(x) = -(x+1)² is: -∞ < x < ∞. The range of the function is f(x) ≤ 0.
<h3>What is the graph of a function?</h3>The graph of a function is the arrangement of all ordered pairs of the function. Typically, they are expressed as points in a cartesian coordinate system. The graph of f is the collection of all ordered pairings (x, f(x)) such that x lies inside the domain of f.
The graph of a function might similarly be defined as the graph of the equation y = f(x). As a result, the graph of a function is a subset of the graph of an equation.
From the given information: the graph of the function f(x) = -(x+1)² can be determined if the domain, the range, and the vertex of the function are known.
- The domain of the function f(x) = -(x+1)² is: -∞ < x < ∞
- The range of the function is f(x) ≤ 0
- The x-intercepts and the y-intercepts are (-1,0) and (0, -1) respectively
- The vertex is maximum at (-1,0)
Since the parabola curve from the graph shows that the graph is facing down, then the function is negative and decreasing.
Learn more about the graph of a function here:
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