Answer:
x = 60
Step-by-step explanation:
Add up all the angles, they make 360 since it forms a full circle
(2x-10) + (2x+40) +90 = 360 Combine like terms
4x + 120 = 360 solve for x
4x = 240
x = 60
Answer:
(a) ln(x) = 0
Then 0 < x < 1
(b) e^x > 2
Then ln2 < x < ∞
(a) ln(3x - 17) = 5
x = 55.1377197
ln(a + b) + ln(a - b) - 5ln(c)
= ln[(a² - b²)/c^5]
Step-by-step explanation:
First Part.
(a) ln(x) < 0
=> x < e^(0)
x < 1 ....................................(1)
But the logarithm of 0 is 1, and the logarithm of negative numbers are undefined, we can exclude the values of x ≤ 0.
In fact the values of x that satisfy this inequalities are between 0 and 1.
Therefore, we write:
0 < x < 1
(b) e^x > 2
This means x > ln2
and must be finite.
We write as:
ln2 < x < ∞
Second Part.
(a) ln(3x - 17) = 5
3x - 17 = e^5
3x = 17 + e^5
x = (1/3)(17 + e^5)
= 55.1377197
Third Part.
We need to write
ln(a + b) + ln(a - b) - 5ln(c)
as a single logarithm.
ln(a + b) + ln(a - b) - 5ln(c)
= ln(a + b) + ln(a - b) - ln(c^5)
= ln[(a + b)(a - b)/(c^5)]
= ln[(a² - b²)/c^5]
Answer:
The three-dimensional figure is an octagonal prism
Step-by-step explanation:
<u><em>Verify each case</em></u>
<em>case a)</em> square prism
The net is made of 2 squares and 4 (rectangles or squares)
<em>case b)</em> square pyramid
The net is made of 1 square and 4 triangles
<em>case c)</em> octagonal prism
The net is made of 2 octagons and 8 (squares or rectangles)
<em>case d)</em> octagonal pyramid
The net is made of 1 octagon and 8 triangles
therefore
The three-dimensional figure is an octagonal prism
Answer:
x = -19
Step-by-step explanation:
-10x - 19 = 19 - 8x
-10x + 8x = 19 + 19
-2x = 38
x = -19
