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liubo4ka [24]
3 years ago
6

-3^(-x)-6=-3^x+10Solve the equation below for x by graphing plz

Mathematics
2 answers:
vitfil [10]3 years ago
8 0
To graph it, just graph y=-3^{-x}-6 and y=-3^x+10 and see where they intersect

I would like to solve it by using math and not graphing
if you don't want to see the math, just don't scroll down
the graphical meathod is above, first line, just read it

hmm
multiply both sides by -1
3^{-x}+6=3^x-10
multiply both sides by 3^x
3^0+6(3^x)=3^{2x}-10(3^x)
1+6(3^x)=3^{2x}-10(3^x)
minus 1 from both sides and minus 6(3^x) from both sides
0=3^{2x}-16(3^x)-1
use u subsitution
u=3^x
we can rewrite it as
0=u^2-16u-1
now factor
I mean use quadratic formula
for ax^2+bx+c=0 x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}
so for 0=u^2-16u-1, a=1, b=-16, c=-1
u=\frac{-(-16)+/-\sqrt{(-16)^2-4(1)(-1)}{2(1)}
u=8+/-\sqrt{65}
remember that u=3^x so u>0
if we have u=8+√65, it's fine, but u=8-√65 is negative and not allowed
so therfor
u=8+\sqrt{65}=3^x
8+\sqrt{65}=3^x
if you take the log base 3 of both sides you get
log_3(8+\sqrt{65})=x
if you use ln then
ln(8+\sqrt{65})=xln(3)
then
\frac{ln(8+\sqrt{65})}{ln(3)}=x

nordsb [41]3 years ago
5 0

Answer:

x = 2.527

Step-by-step explanation:

We have to solve the equation -3^{-x}-6=-3^x+10 by graphing method.

In order to solve this equation from graphing method, we graph the below two equations in the same coordinate axes.

y=-3^{-x}-6...(i)\\\\y=-3^x+10...(ii)

The x -coordinate of the intersection point of these two graphs would be the solution of the equation.

Please see the attached graph.

The x-coordinate of the intersection point is 2.527.

Hence, the solution to the given equation is x = 2.527

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which metod is most efficent in solving a system of linear equations when the two equations have x-values with opposite coeffici
telo118 [61]

Answer:

See below

Step-by-step explanation:

Just add the two equations together....this will eliminate 'x' and you can then solve for 'y'

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3 0
2 years ago
A rancher has 2 comma 200 feet of fencing to enclose a rectangular pig pen.​ However, one side of the pen lies along a river and
DiKsa [7]

Answer:

A = 2200x - 2x^2

Step-by-step explanation:

Let's x be the length of the side that is NOT the same as the side along the river (or in opposite). From the fencing perimeter of 2200ft we can calculate the other side y of the rectangular:

y = 2200 - 2x

The area A of the pen would be the product of the 2 sides

A = xy = x(2200 - 2x) = 2200x - 2x^2

7 0
3 years ago
Could 1.5, 2.5, 3.5 and 6, 10, 12 be the corresponding sides of two similar triangles
boyakko [2]

Answer:

No

Step-by-step explanation:

If the ratios of the corresponding sides are equal then they would be the sides of 2 similar triangles.

Calculate the ratio of corresponding sides.

\frac{6}{1.5} = 4

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\frac{12}{3.5} ≠ 4

Thus the sides are not the corresponding sides of similar triangles.

4 0
3 years ago
Please help this is important<br> -1.5x+12=2.5x-12
Anna35 [415]

Answer:

x = 6

Step-by-step explanation:

move all terms to the left:

-1.5x+12-(2.5x-12)=0

get rid of parentheses

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add all the numbers together, and all the variable.

-4x+24=0

move all terms containing x to the left, all other terms to the right

-4x=-24

x=-24/-4 - divide

x=+6

7 0
3 years ago
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