For the given expressions we will have:
y = exp(x - 4) →we have a shift of 4 units to the right.
y = exp (x +9) → we have a shift of 9 units to the left.
y = exp(x) + 7 → we have a shift of 7 units up.
y = exp(x) - 6 → we have a shift of 6 units down.
<h3>
How to work with vertical and horizontal shifts?</h3>
Remember that the shifts work as follows.
For a function f(x), we define a vertical shift of N units as:
g(x) = f(x) + N
- If N > 0, the shift is upwards.
- If N < 0, the shift is downwards.
For a function f(x), we define a horizontal shift of N units as:
g(x) = f(x + N)
- If N > 0, the shift is to the left.
- If N < 0, the shift is to the right.
Then, if we have:
exp(x - 4) we have a shift of 4 units to the right.
exp (x +9) we have a shift of 9 units to the left.
exp(x) + 7 we have a shift of 7 units up.
exp(x) - 6 we have a shift of 6 units down.
Learn more about translations
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three-dimensional graphs wouldn´t give you the right information but two-dimensional graphs would give you the actual size of the shape.
Answer:
w =< 70
(width is less or equal to 70 inches)
Step-by-step explanation:
Let l = length, w = width, h = height
Restrictions given in this question:
'sum of perimeter of the base and the height cannot exceed 130 inches'
perimeter of the base is 2 width and 2 length of the box
perimeter = 2w + 2l
Therefore, inequality involves here is
2w + 2l + h =< 130
(Note that =< here means less or equal)
Then a new condition given with
height, h = 60 in
and length is 2.5 times the width
l = 2.5w
Substitute this new condition into the equation will give us the following:
2w + 2(2.5w) + 60 =< 130
2w + 5w + 60 =< 130
7w + 60 =< 130
7w =< 130-60
7w =< 70
w =< 10
Answer:
200
Step-by-step explanation:
<u>Step 1: Add</u>
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
15 + 6 = 21
21 + 7 = 28
28 + 8 = 36
36 + 9 = 45
45 + 1 = 46
46 + 2 = 48
48 + 3 = 51
51 + 4 = 55
55 + 5 = 60
60 + 6 = 66
66 + 7 = 73
73 + 8 = 81
81 + 9 = 90
90 + 10 = 100
<em>100</em>
<u>Step 2: Multiply</u>
100 * 2
<em>200</em>
Answer: 200
3x+4=10
Subtract 4 from both sides
3x=6
Divide both sides by 3
X=2
Sides = 10,10,5
Problem 5. 4x+1=29
Subtract 1 from both sides
4x=28
X=7
