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djverab [1.8K]
3 years ago
6

See the attachment below for the question.

Mathematics
2 answers:
kicyunya [14]3 years ago
6 0

Answer: Third option.

Step-by-step explanation:

We need to remember that:

a^m=a^n\\\\m=n

In this case, given this expression:

4^x=8^{( x- 1)}

We need to descompose 4 and 8 into their prime factors:

4=2*2=2^2

8=2*2*2=2^3

Rewriting the expression:

2^{2x}=2^{3(x - 1) }

Then:

2x = 3(x - 1)

Finally, applying Distributive property on the right side and solving for "x", we get:

2x=3x-3\\\\3=3x-2x\\\\x=3

tangare [24]3 years ago
5 0

Answer:

The correct answer is third option

x = 3

Step-by-step explanation:

It is given that,

4ˣ = 8⁽ˣ ⁻ ¹⁾

<u>To find the value of x</u>

4ˣ  = (2²)ˣ

8⁽ˣ ⁻ ¹⁾ = (2³)⁽ˣ ⁻ ¹⁾

4ˣ = 8⁽ˣ ⁻ ¹⁾

(2²)ˣ =  (2³)⁽ˣ ⁻ ¹⁾

2²ˣ = 2⁽³ˣ ⁻ ³⁾

2x = 3x - 3

3x - 2x = 3

x = 3

The correct answer is third option

x = 3

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Answer:

Step-by-step explanation:

Yes

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3 years ago
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The function f(x)=70n -400 models the profit of the instructor of a guitar class per month, where n is the number of students en
suter [353]
Given:
f(x) = 70n - 400   : equation for monthly profit.
n = number of students enrolled in the guitar class.

70 refers to the amount charged per student.
400 is the fixed expense made by the instructor.

For the instructor to have a profit, the product of 70n must be more than 400.

400/70 = 5.7 or 6

There must be at least 6 students enrolled in class for the instructor to generate profit.

f(x) = 70(6) - 400 = 420 - 400 = 20

1000 = 70n - 400
1000 + 400 = 70n
1400 = 70n
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There must be 20 students enrolled in class for the instructor to earn 1000 in profit.

1000 = 70(20) - 400
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3 0
3 years ago
Sara has opened her own bakery, where customers can buy three chocolate chip cookies for $2.49. a. What is the unit price? b. Wh
inysia [295]

Answer:

a) $0.83

b) k = 1.205

c) In the context of this problem, k means

The number of chocolate chip cookies increases as the price increases because number of chocolate chip cookie is directly proportional to its price

Step-by-step explanation:

Sara has opened her own bakery, where customers can buy three chocolate chip cookies for $2.49.

a. What is the unit price?

The unit price means the cost of 1 cookie

Hence:

3 chocolate chip cookies = $2.49

1 chocolate chip cookies = x

3x = $2.49 × 1

x = $2.49 × 1/3

x = $0.83

Hence, the unit price = $0.83

b. What is the constant of proportionality, or k?

Chocolate chip cookie ∝ Price

Chocolate chip cookie is directly proportional to the Price

C = kP

Where k is constant of proportionality

k = Chocolate chip cookie/Price

k = C/P

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k = 3/2.49

k = 1.2048192771

k = 1.205

c. In a complete sentence, explain what k means in the context of this problem.

In the context of this problem, k means

The number of chocolate chip cookies increases as the price increases because number of chocolate chip cookie is directly proportional to its price

6 0
3 years ago
A 24 foot flagpole casts a 20 foot shadow of the building next to it is an 85 foot shadow find the height of the building
Zigmanuir [339]

Answer: 102 foot / feet tall

Step-by-step explanation:

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Second, multiply . . . what is 1.2 x 85 ? 102

( sorry if this is wrong - I forgot how to do the second part for a sec )

6 0
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Find the measure of the angle. <br> I need to show my work, please, thank you!!!
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Answer:

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Step-by-step explanation

A you may have studies,

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x=132

Angle S = 132

but to find ? you have to add U and T

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6 0
3 years ago
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