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What is the solution of the equation 9^2x=6? Round your answer to the nearest ten-thousandth.

sammy [17]

Answer:

0.4077

Step-by-step explanation:

It's important to use parenthesis to avoid confusion.

9^(2x) = 6

Use exponent properties:

(9^2)^x = 6

81^x = 6

Take log of both sides

ln(81^x) = ln(6)

Use log properties:

x ln(81) = ln(6)

Solve for x:

x = ln(6) / ln(81)

x ≈ 0.4077

4 0

2 years ago

Abraham is installing carpet in his bedroom. On the blueprints, Abraham's bedroom is 6 inches wide and 10 inches long. If the sc

erma4kov [3.2K]

Answer:

240 square feet

Step-by-step explanation:

Hello, I can help you with this

Step one

find the real scale

According to the data

scale is 1 in : 2 ft

also remember 1ft=12 inches

so

scale is 1in: 2(12 inches)

scale is 1 in :24 in

the purpose of use inches a unit in both sides is to eliminate the, the scale must be adimensional

so escales is

1:24 , this means, that a measure on the blueprint must be multiplied by 24 to know its real value

Step 2

with the escale find the real dimensions, you can use a rule of three

Abraham's bedroom is 6 inches wide

blueprint ⇔ bedroom

1 in ⇔ 24 in

6 in ⇔x

x=(6*24)/1

x=144 inches=12 ft

Abraham's bedroom is 10 inches long

1 in ⇔ 24 in

10 in ⇔y

y=(10*24)/1

x=240 inches=20 ft

Step 3

find the area

the area is wide *long

area=x*y

area=12ft*20ft

area=240 square feet.

Have a good day

5 0

3 years ago

There are 3 feet in a yard. How many yards, as a mixed number, will you drive until you reach this exit?

Ratling [72]

The number of yards, as a mixed number, will you drive until you reach this exit is 333 1/3 yards

<h3>How to determine the number of yards to drive?</h3>

The complete question is added as an attachment

From the attached figure, we have:

Exit = 1000 feet

From the question, we have

3 feet = 1 yard

So, the number of yards is

Number of yard =Exit/3 yards

This gives

Number of yard = 1000/3 yards

Evaluate the quotient

Number of yard = 333 1/3 yards

Hence, the number of yards, as a mixed number, will you drive until you reach this exit is 333 1/3 yards

Read more about mixed numbers at:

brainly.com/question/1746829

#SPJ1

6 0

1 year ago

A total of 480 were sold for the school play. They were either adult tickets or students tickets. The number of student tickets

Talja [164]

Ok so basically, the number of student tickets is 3x, where x=the number of adult tickets sold. And we know that s(for student tickets)+x=480 total tickets sold. So if we replace s with 3x we have 3x+x=480, or 4x=480. We divide by 4 and get x=120, which is the amount of adult tickets sold.

5 0

3 years ago

Bradley made a house for his dog, Bowser, out of wood with a cube base and a triangular prism top. The dimensions of the dog hou

Luda [366]

The complete question is
<span>Bradley made a house for his dog, Bowser, out of wood with a cube base and a triangular prism top. The dimensions of the dog house are a = 2 feet, b = 1 foot, and c = 1.4 feet.
</span><span>If Bradley plans to paint the outside of the dog house blue, not including the bottom, how many square feet of paint will he use?

the picture in the attached figure
</span>
we know that

surface area of the figure=surface area of cube+surface area of triangular prism

surface area of cube=4*a²----> 4*2²-----> 16 ft²

surface area of triangular prism=2*[a*c]+2*[a*b/2]---> 2*[2*1.4]+[2*1]
surface area of triangular prism=5.6+2----> 7.6 ft²

surface area of the figure=16 ft²+7.6 ft²----> 23.6 ft²

the answer is
23.6 ft²

7 0

3 years ago

Read 2 more answers