Type the correct answer in the box. Write your answer as a fraction, using / for the fraction bar.
2 answers:
You might be interested in
We have to find the potential solutions to from least to greatest.
Using the properties of ln function.
Therefore, we get
taking antilog on both the sides, we get
So,
Therefore, the potential solutions to 2 ln x = 4 ln 2 from least to greatest is -4 and 4.
<h3>Complete Question:</h3>
Given:
(1) DC = 6x, and DA = 4x + 18, find the value of x. Then find AD, DC, and AC
(2) EB = 4y - 12, and ED = y + 17. Find y. Then find ED, DB and EB.
<h3>Answer:</h3>
x = 9, AD = 54, DC = 54, AC = 108
y = 23, ED = 40, DB = 40, EB = 80
<h3>Step-by-step explanation:</h3>The diagram for this question has been attached to this response.
(1) From the diagram, it can be observed that;
(a) DC and DA have equal lengths. i.e
=> DC = DA ---------------------(i)
(b) AC = DA + DC --------------------(ii)
<em>But;</em>
DC = 6x
DA = 4x + 18
<em>Substitute the values of DC and DA into equation (i) as follows;</em>
6x = 4x + 18 [<em>Solve for x</em>]
6x - 4x = 18
2x = 18
x = 9
Since x = 9, then
DC = 6x = 6(9) = 54
DA = 4x + 18 = 4(9) + 18 = 54
<u>Therefore</u>
DC = 54
AD = DA = 54
AC = 54 + 54 = 108 [using equation (ii)]
(2) Also, from the diagram, it can be observed that;
(a) ED and DB have equal lengths. i.e
=> ED = DB ---------------------(iii)
(b) EB = ED + DB --------------------(iv)
=>EB = ED + ED [since ED = DB]
=>EB = 2ED ------------------(v)
<em>But;</em>
EB = 4y - 12
ED = y + 17
<em>Substitute the values of EB and ED into equation (v) as follows;</em>
4y - 12 = 2(y + 17) [<em>Solve for y</em>]
4y - 12 = 2y + 34
4y - 2y = 34 + 12
2y = 46
y = 46 / 2
y = 23
Since y = 23, then
EB = 4y - 12 = 4(23) - 12 = 80
ED = y + 17 = 23 + 17 = 40
<u>Therefore</u>
EB = 80
ED = DB = 40