Look at the graph below carefully
Observe the results of shifting ={2}^{x}f(x)=2x
vertically:
The domain, (−∞,∞) remains unchanged.
When the function is shifted up 3 units to ={2}^{x}+3g(x)=2x +3:
The y-intercept shifts up 3 units to (0,4).
The asymptote shifts up 3 units to y=3y=3.
The range becomes (3,∞).
When the function is shifted down 3 units to ={2}^{x}-3h(x)=2 x −3:
The y-intercept shifts down 3 units to (0,−2).
The asymptote also shifts down 3 units to y=-3y=−3.
The range becomes (−3,∞).
Answer and Step-by-step explanation:
To simplify, distribute the negative number.
-(11 + 2b)
<u>-11 - 2b is the answer.</u>
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<em><u>#teamtrees #PAW (Plant And Water)</u></em>
<em><u></u></em>
<em><u>I hope this helps!</u></em>
Answer:
x ≥ 2
0 ≤ 20 (not quite sure if the question is right)
Step-by-step explanation:
x+18 ≥ 8x+4
x - 8x ≥ 4 - 18
-7x ≥ -14
x ≥ 
x ≥ 2
________________
15x-15 ≤ 15x+5
15x - 15x ≤ 5 + 15
0 ≤ 20
(I don't think this is the right question...cuz theres a 0)
Answer:
Step-by-step explanation:
(1). m∠5 = 40° → (a) Given
m∠2 = 140° → (b) Given
∠5 and ∠2 are supplementary angles → (c) Interior angles on the same side of the transversal.
∠5 and ∠2 are the same side interior angles → (d) Both angles are supplementary
a║b → (e) By interior angles theorem of the parallel lines.
(2). Statements Reasons
1. l║n 1. Given
2. ∠2 ≅ ∠6 2. Corresponding angles
3. ∠4 ≅ ∠2 3. Vertical angles
4. ∠6 ≅ ∠4 4. Transitive property of equality
(3). Statements Reasons
1. ∠1 ≅ ∠5 1. Given
2. ∠4 ≅ ∠1 2. Vertical angles
3. ∠4 ≅ ∠5 3. Alternate interior angles
4. p║r 4. Definition of parallel lines
<h2><u>Answer (d</u>) :</h2>
These triangles are congruent under the SAS congruence criterion. We can prove it using the following steps :
Given :
In triangle 1 and 2 :
- A side in triangle 1 and a side in triangle 2 are equal.
- Another side in triangle 1 and triangle 2 is equal.
- The angle between the equivalent sides is also equal.
Since the SAS congruence criterion says that two triangles are congruent if two of their sides and one included angle is equal and since these 2 triangles fulfill all of those rules, we can conclude that these triangles are congruent under the SAS congruence criterion.
