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Iteru [2.4K]
3 years ago
15

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2^−x and y = 8^x+4 intersect are the s

olutions of the equation 2^−x = 8^x+4.
Part B: Make tables to find the solution to 2^−x = 8^x+4. Take the integer values of x between −3 and 3.

Part C: How can you solve the equation 2^−x = 8^x+4 graphically?
Mathematics
1 answer:
joja [24]3 years ago
5 0

Answer:

See explanation

Step-by-step explanation:

A) the x-intercept is the solution because there are only x's in the equation when they are set equal to each other.

B) (-3, 8), (-3, 4)

   (-2, 4), (-2, 4)***** this is the solution

   (-1, 2), (-1, 4 1/8)

   (0, 1), (0, 5)

   (1, 1/2), (1, 12)

   (2, 1/4), (2, 68)

   (3, 1/8), (3, 516)

C) Graph them and show the intersection

See Attachment

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If 18√8 - 8 √18 = √n, what is n?
Yuliya22 [10]

Answer:

n=288

Step-by-step explanation:

Rewrite the equation as  

√

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−

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√

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To remove the radical on the left side of the equation, square both sides of the equation.

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(

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2

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Simplify  

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Multiply the exponents in  

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Apply the power rule and multiply exponents,  

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a

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n

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⋅

2

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(

18

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√

18

)

2

Cancel the common factor of  2  

Cancel the common factor.

n

1

2

⋅

2

=

(

18

√

8

−

8

√

18

)

2

Rewrite the expression.

n

1

=

(

18

√

8

−

8

√

18

)

2

Simplify.

n

=

(

18

√

8

−

8

√

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2

Simplify  

(

18

√

8

−

8

√

18

)

2

Simplify each term.

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2

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Factor  

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(

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(

2

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−

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)

2

Rewrite  

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n

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−

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2

Pull terms out from under the radical.

n

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18

(

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−

8

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18

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2

Multiply  

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2

Rewrite  

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n

=

(

36

√

2

−

8

√

9

(

2

)

)

2

Rewrite  

9

as  

3

2

.

n

=

(

36

√

2

−

8

√

3

2

⋅

2

)

2

Pull terms out from under the radical.

n

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(

36

√

2

−

8

(

3

√

2

)

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2

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24

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2

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12

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2

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2

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2

2

as  

2

.

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a

x

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a

x

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2

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2

1

2

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n

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144

(

2

1

2

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2

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a

m

)

n

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a

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n

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n

=

144

⋅

2

1

2

⋅

2

Combine  

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2

and  

2

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n

=

144

⋅

2

2

2

Cancel the common factor of  

2

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Cancel the common factor.

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=

144

⋅

2

2

2

Rewrite the expression.

n

=

144

⋅

2

1

Evaluate the exponent.

n

=

144

⋅

2

Multiply  

144

by  

2

.

n

=

288

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