Answer:
60 degrees
Step-by-step explanation:
Restructured question:
The measure of two opposite interior angles of a triangle are x−14 and x+4. The exterior angle of the triangle measures 3x-45 . Solve for the measure of the exterior angle.
First you must know that the sum of interior angle of a triangle is equal to the exterior angle
Interior angles = x−14 and x+4
Sum of interior angles = x-14 + x + 4
Sum of interior angles = 2x - 10
Exterior angle = 3x - 45
Equating both:
2x - 10 = 3x - 45
Collect like terms;
2x - 3x = -45 + 10
-x = -35
x = 35
Get the exterior angle:
Exterior angle = 3x - 45
Exterior angle = 3(35) - 45
Exterior angle = 105 - 45
Exterior angle = 60
Hence the measure of the exterior angle is 60 degrees
<em>Note that the functions of the interior and exterior angles are assumed. Same calculation can be employed for any function given</em>
Answer:
<u>1,216 cm³</u>
Step-by-step explanation:
Volume (composite space figure) = Volume (pyramid) + volume (prism)
- ⇒ [16 x 6 x 14 / 3] + [16 x 6 x 8]
- ⇒ 96 [14/3 + 8]
- ⇒ 96 [14/3 + 24/3]
- ⇒ 96 x 38/3
- ⇒ 32 x 38
- ⇒ <u>1,216 cm³</u>
Answer:
log[3(x+4)] is equal to log(3) + log(x + 4), which corresponds to choice number three.
Step-by-step explanation:
By the logarithm product rule, for two nonzero numbers 
and 
,
.
Keep in mind that a logarithm can be split into two only if the logarithm contains the product or quotient of two numbers.
For example, 
is the number in the logarithm ![\log{[3(x + 4)]}](https://tex.z-dn.net/?f=%5Clog%7B%5B3%28x%20%2B%204%29%5D%7D)
. Since is a product of the two numbers 
and 
, the logarithm can be split into two. By the logarithm product rule,
![\log{[3(x + 4)]} = \log{(3)} + \log{(x + 4)}](https://tex.z-dn.net/?f=%5Clog%7B%5B3%28x%20%2B%204%29%5D%7D%20%3D%20%5Clog%7B%283%29%7D%20%2B%20%5Clog%7B%28x%20%2B%204%29%7D)
.
However, 
cannot be split into two since the number inside of it is a sum rather than a product. Hence choice number three is the answer to this question.
The answer is (3x^2 - x +2 )= to AC
Area = 1/2 |BD| |AC|
(9x^3 - 3x^2 + 6x) = 1/2 (AC) 6x
3x ( 3x^2 - x +2 )= 1/2 (AC) 2(3x)
3^2 - x +2 = AC
