y = log ( 7x + 3) - 2
To find the y intercept, let x = 0
y = log (3) - 2 ≈ -1.52
To find the x intercept, let y = 0
0 = log ( x + 3) - 2 add 2 to both sides
2 = log (x + 3) this says that
10^2 = x + 3
100 = x + 3 subtract 3 from both sides
97 = x
This is the "natural log"
ln (121) ≈ 4.796
17.
√[2x + 13 ] - 5 = x add 5 to both sides
√[ 2x + 13 ] = x + 5 square both sides
2x + 13 = x^2 + 10x + 25 subtract 2x, 13 from both sides
x^2 + 8x + 12 = 0 factor
(x + 6) ( x + 2) = 0
Set each factor to 0 and solve for x and we have that
x = -6 or x = - 2
The first solution does not solve the original equation
Only the second is good
16.
35√ [(x + 2)3 ] + 3 = 27 subtract 3 from both sides
35√ [(x + 2)3 ] = 24 divide both sides by 3
5√ [(x + 2)3 ] = 8 take each side to the 5/3 power
(x + 2) = 85/3 and we can write
(x + 2) = ( 81/3)5
(x + 2) = 25
x + 2 = 32 subtract 2 from both sides
x = 30
Here's the graph of 8
It's the cube root function shifted 5 units to the right and 1 unit down
https://www.desmos.com/calculator/8neckfvbrw
Very nice, RainbowPanda !!!
11.
The input value is put into one function and evaluated. Then, this result is put into a second function and the result of this is the output.
12. To give a simplistic answer, if the prime factors and variables under the radicand have individual powers on them that are less than the index of the root, it is fully simplified.
Avg rate of change =
[ f(14 ) - f(8) ] / [ 14 - 8 ] =
[ ( √ [14 - 4] ) - (√ [8 - 4]) ] / 6 =
[ √10 - √4 ] / 6 =
0.19
If we have a regular polygon, we can just add the areas of the individual triangles to find the total area....actually....we only need the area of one of these triangles....all the rest will have the same area
Here's the way lynx got the second answer
√2 - √6
______ multiply top/bottom by the conjugate of the denominator ⇒ √2 - √6
√2 + √6
√2 -√6 √2 - √6 2 - 2√12 + 6 8 - 2*2√3
______ _____ = ___________ = __________ =
√2 + √6 √2 - √6 2 - 6 -4
8/-4 + -4√3 / - 4
-2 + √3
