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Paul [167]
3 years ago
13

3 to the x power - 1 = 9 to the x power+2

Mathematics
1 answer:
Tom [10]3 years ago
8 0

So we need to solve:

3ˣ⁻¹ = 9ˣ⁺²

To do this, we need to have the same base for both sides of the equation.

So let's go with the base of 3.

3² = 9

3ˣ⁻¹ = (3²)ˣ⁺²

3ˣ⁻¹ = 3²ˣ⁺⁴

Since the bases are the same now, we need to get rid of them and we would get:

x - 1 = 2x + 4

Subtract both sides by 2x:

-x - 1 = 4

Add 1 to both sides:

-x = 5

Divide both sides by -1:

x = -5

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Answer:

On what?

Step-by-step explanation:

6 0
3 years ago
Whoever responds first will get marked best!!!!!The Garcia family is driving from 3,272 miles from San Diego, CA ot Bar Harbor,
mojhsa [17]

Answer:

8

Step-by-step explanation:

We know that in 5 days they have travelled 2045 miles. This means that their per day average for travel is 2045/5=409 miles per day.

Now the distance left is 3272-2045=1227 miles.

And if we divide the average miles with the miles left, it gives us= 1227/409

=3

So, the total time taken for travel will be= 5+3=8 days

I guess this is the way to do it.

8 0
2 years ago
Read 2 more answers
A 12-meter ladder leans against a building forming a 30° angle with the building.
KatRina [158]

Answer:

will show you two (2) ways to solve this problem.

A diagram is needed to see what is going on....

 

Without loss of generality (WLOG)

The wall is on the right. The ladder leans against the wall

with a POSITIVE slope, from SW to NE (quadrant 3 to quadrant 1).

The measure from the bottom of the ladder to the wall is 6.

 

 

Option 1:

 

The ladder, ground and wall form a right triangle.

 

The hypotenuse (ladder) is 14 feet.

 

 The bottom of the ladder is 6 feet from the wall,

  so the base of this right triangle is 6 feet.

 

The top of the ladder to the ground represents

the missing leg of the right triangle.

 

The pythagorean theorem applies, which says

 6^2 + h^2 = 14^2   where h is the height

                                 of the top of the ladder to the ground

 

36 + h^2 = 196

 

 h^2 = 196 - 36

 

h^2  = 160

 

h = sqrt(160)

 

   = sqrt(16 * 10)

 

    = sqrt(16)* sqrt(10)

 

    = 4*sqrt(10) <--- exact answer

 

    = 4 * 3.16227766016838....

 

     = 12.64911....

 

    12.65 <--- rounded to 2 digits as directed

 

----------------------------------------------

Option #2: using trig

 

With respect to the angle formed by the bottom of the

ladder with the ground

  cos T = 6/14 = 3/7  

 T = inverse-cosine(3/7) = 64.623006647 degrees

 

 sin(64.623006647) = h/14

 

 h = 14*sin(64.62300647) = 12.6491106 <--- same answer                        

hope this helps

Step-by-step explanation:

5 0
2 years ago
A parabola has a vertex of (5,4) and goes through the point (6,-10)
natali 33 [55]
Y = -2(x-5)^2 + 4

Note: vertex form is 0, f(x), y, or nothing= a(x-h)^2 + k
The opposite of the x value of the vertex is h
The y value value of the vertex is k.


Find a. Plug in (6,-10)

-10 = a(6-5)^2 + 4
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a = -2
5 0
3 years ago
Answer and explanation?
bazaltina [42]
C!
One dollar = $1
And in a math equation is usually a decimal
56 cents is .56 because it’s not a whole new If you add them together you get $1.56 :) hope it helps
8 0
2 years ago
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