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lys-0071 [83]
2 years ago
7

2x + 5x = -14 What is the answer

Mathematics
1 answer:
Mekhanik [1.2K]2 years ago
6 0

Answer:

x= -2

Step-by-step explanation:

2(-2)+5(-2)= -4+-10= -14

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Suppose a ball is thrown upward to a height of h 0 meters. After each​ bounce, the ball rebounds to a fraction r of its previous
gladu [14]

Answer:

A)1st term:45

2nd term:48.75

3rd term:49.6875

4th term:49.921875

B) Sₙ = h₀ + 2h₀((∞, n=1) Σrⁿ)

Step-by-step explanation:

We are given;

h₀ = Initial height of the ball = 30

r = Rebound fraction = 0.25

a) The arithmetic sequence of bouncing balls is given by the following;

Sₙ=h₀+2h₀(r¹+r²+r³+r⁴.........rⁿ)

The first term of the sequence is;

S₁ = h₀ + 2h₀r¹

S₁ = 30 + (2 × 30 × 0.25)

S₁ = 45

The second term of the sequence is;

S₂ = h₀ + 2h₀(r¹+r²)

S₂ = 30 + (2 × 30 × (0.25 + 0.25²)) = 48.75

The third term of the sequence is;

S₃ = h₀ + 2h₀(r¹ + r² + r³) = 30 + (2 × 30 × (0.25 + 0.25² + 0.25³)) = 49.6875

S₄ = h₀ + 2h₀(r¹ + r² + r³ + r⁴)

S₄ = 30 + (2 × 30 × (0.25 + 0.25² + 0.25³ + 0.25⁴)) = 49.921875

B) The general expression for the nth term of the sequence is;

Sₙ = h₀ + 2h₀((∞, n=1) Σrⁿ)

4 0
3 years ago
I know you want to answer this question.
Alik [6]

Answer:

D. x = 3

Step-by-step explanation:

\frac{1}{2} ^{x-4} - 3 = 4^{x-3} - 2

First, convert 4^{x-3} to base 2:

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

\frac{1}{2} ^{x-4} - 3 = (2^{2})^{x-3} - 2

Next, convert \frac{1}{2} ^{x-4} to base 2:

\frac{1}{2} ^{x-4} = (2^{-1})^{x-4}

(2^{-1})^{x-4} - 3 =  (2^{2})^{x-3} - 2

Apply exponent rule: (a^{b})^{c} = a^{bc}:

(2^{-1})^{x-4} = 2^{-1*(x-4)}

2^{-1*(x-4)} - 3 = (2^{2})^{x-3} - 2

Apply exponent rule: (a^{b})^{c} = a^{bc}:

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

2^{-1*(x-4)} - 3 = 2^{2(x-3)} - 2

Apply exponent rule: a^{b+c} = a^{b}a^{c}:

2^{-1(x-4)} = 2^{-1x} * 2^{4}, 2^{2(x-3)} = 2^{2x} * 2^{-6}

2^{-1 * x} * 2^{4} - 3 = 2^{2x} * 2^{-6} - 2

Apply exponent rule: (a^{b})^{c} = a^{bc}:

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

(2^{x})^{-1} * 2^{4} - 3 = (2^{x})^{2} * 2^{-6} - 2

Rewrite the equation with 2^{x} = u:

(u)^{-1} * 2^{4} - 3 = (u)^{2} * 2^{-6} - 2

Solve u^{-1} * 2^{4} - 3 = u^{2} * 2^{-6} - 2:

u^{-1} * 2^{4} - 3 = u^{2} * 2^{-6} - 2

Refine:

\frac{16}{u} - 3 = \frac{1}{64}u^{2} - 2

Add 3 to both sides:

\frac{16}{u} - 3 + 3 = \frac{1}{64}u^{2} - 2 + 3

Simplify:

\frac{16}{u} = \frac{1}{64}u^{2} + 1

Multiply by the Least Common Multiplier (64u):

\frac{16}{u} * 64u = \frac{1}{64}u^{2} + 1 * 64u

Simplify:

\frac{16}{u} * 64u = \frac{1}{64}u^{2} + 1 * 64u

Simplify \frac{16}{u} * 64u:

1024

Simplify \frac{1}{64}u^{2} * 64u:

u^{3}

Substitute:

1024 = u^{3} + 64u

Solve for u:

u = 8

Substitute back u = 2^{x}:

8 = 2^{x}

Solve for x:

x = 3

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B) f(x) = 3 |x – 41| + 5<br> Domain:<br> Range:
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The domain is (-infinity, +infinity)
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