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coldgirl [10]
3 years ago
5

Solve the system of equations below by graphing them with a pencil and paper. Choose the correct ordered pair (b, u).

Mathematics
1 answer:
Cloud [144]3 years ago
4 0
U = -b + 21 . . . (1)
u = -2b + 30 . . . (2)
Equating (1) and (2),
-b + 21 = -2b + 30
-b + 2b = 30 - 21
b = 9
u = -9 + 21 = 12

Therefore, (b, u) = (9, 12).
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For the equation ae^ct=d, solve for the variable t in terms of a,c, and d. Express your answer in terms of the natural logarithm
saveliy_v [14]

We have been given an equation ae^{ct}=d. We are asked to solve the equation for t.

First of all, we will divide both sides of equation by a.

\frac{ae^{ct}}{a}=\frac{d}{a}

e^{ct}=\frac{d}{a}

Now we will take natural log on both sides.

\text{ln}(e^{ct})=\text{ln}(\frac{d}{a})

Using natural log property \text{ln}(a^b)=b\cdot \text{ln}(a), we will get:

ct\cdot \text{ln}(e)=\text{ln}(\frac{d}{a})

We know that \text{ln}(e)=1, so we will get:

ct\cdot 1=\text{ln}(\frac{d}{a})

ct=\text{ln}(\frac{d}{a})

Now we will divide both sides by c as:

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t=\frac{\text{ln}(\frac{d}{a})}{c}

Therefore, our solution would be t=\frac{\text{ln}(\frac{d}{a})}{c}.

5 0
3 years ago
What would be the shortened fraction of 9/120
ale4655 [162]

Answer:

3/40

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 9 and 120 is 3

Divide both the numerator and denominator by the GCD

9 ÷ 3

120 ÷ 3

Reduced fraction:

3/40

5 0
3 years ago
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