Solve 7x+6<3(x - 2).
1 answer:
You might be interested in
Option A : is the solution of the equation.
Explanation:
The equation is
To determine the value of x, let us simplify the equation.
Subtracting 5 from both sides of the equation, we have,
Simplifying, we get,
Now , dividing both sides of the equation by 8, we get,
Using the logarithmic definition that if then
Thus, rewriting the above expression using the logarithmic definition, we have,
⇒
Substituting the value of , we get,
Rounding off the answer to two decimal places, we get,
Hence, the solution of the equation is
Therefore, Option A is the correct answer.
Answer:
You can use either of the following to find "a":
- Pythagorean theorem
- Law of Cosines
Step-by-step explanation:
It looks like you have an isosceles trapezoid with one base 12.6 ft and a height of 15 ft.
I find it reasonably convenient to find the length of x using the sine of the 70° angle:
x = (15 ft)/sin(70°)
x ≈ 15.96 ft
That is not what you asked, but this value is sufficiently different from what is marked on your diagram, that I thought it might be helpful.
__
Consider the diagram below. The relation between DE and AE can be written as ...
DE/AE = tan(70°)
AE = DE/tan(70°) = DE·tan(20°)
AE = 15·tan(20°) ≈ 5.459554
Then the length EC is ...
EC = AC - AE
EC = 6.3 - DE·tan(20°) ≈ 0.840446
Now, we can find DC using the Pythagorean theorem:
DC² = DE² + EC²
DC = √(15² +0.840446²) ≈ 15.023527
a ≈ 15.02 ft
_____
You can also make use of the Law of Cosines and the lengths x=AD and AC to find "a". (Do not round intermediate values from calculations.)
DC² = AD² + AC² - 2·AD·AC·cos(A)
a² = x² +6.3² -2·6.3x·cos(70°) ≈ 225.70635
a = √225.70635 ≈ 15.0235 . . . feet
