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Kitty [74]
3 years ago
6

Lana is the oldest of four sisters. Her youngest sister is half her age. The other two sisters are twins $2$ years younger than

Lana. When the four sisters' ages are added together, the result is $45$. If the youngest sister is $n$ years old, what is $n$?
Mathematics
1 answer:
ivanzaharov [21]3 years ago
6 0
N= 7
2n+n+2n-2+2n-2=45
7n-4=45
7n=49
n=7
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2a + b = 3 and a - 3b = 5
vfiekz [6]

Answer:

a= 2 b=-1

Step-by-step explanation:

a-3b=5

or, a= 5+3b_(i)

substituting value of a in 2a+b=3,

2×(5+3b)+b=3

or, 10+6b+b=3

or, 7b=3-10

or, 7b=-7

b= -1

substituting value of b in(i),

a=5+3b

=5+3×(-1)

=5-3

=2

6 0
3 years ago
A sample of tritium-3 decayed to 94.5% of its original amount after a year.
Zolol [24]
(a) If y(t) is the mass after t days and y(0) = A then y(t) = Ae^{kt}.

y(1) = Ae^k = 0.945A \implies e^k = 0.945 \implies k = \ln 0.945

\text{Then } Ae^{(\ln 0.945)t} = \frac{1}{2}A\ \Leftrightarrow\ \ln e^{(\ln 0.945)t} = \ln \frac{1}{2}\ \Leftrightarrow\  ( \ln 0.945) t = \ln \frac{1}{2} \Leftrightarrow \\ \\
t = - \frac{\ln 5}{\ln 0.945} \approx 12.25 \text{ years}

(b)
Ae^{(\ln 0.945) t} = 0.20 A \ \Leftrightarrow\ (\ln 0.945) t \ln \frac{1}{5}\ \implies \\ \\
t = - \frac{\ln 5}{\ln 0.945} \approx 28.45\text{ years}
3 0
4 years ago
I need help on this it’s about trig identities
Cerrena [4.2K]

Answer:

The answer to your question is:

Step-by-step explanation:

1.-

\frac{1 + sin\alpha }{cos\alpha } + \frac{cos\alpha }{1 + sin\alpha } = 2 sec\alpha

\frac{(1 + sin\alpha)^{2} + cos^{2} \alpha  }{cos\alpha (1 + sin\alpha) }

\frac{1  + 2sin\alpha + sin^{2} \alpha+ cos^{2} \alpha  }{cos\alpha + sin\alphacos\alpha  }

\frac{2 + 2sin\alpha }{cos\alpha+ sin\alpha cos\alpha  }

\frac{2(1 + sin\alpha) }{cos\alpha(1 + sin\alpha ) }

\frac{2}{cos\alpha }

2sec\alpha

2.-

   sec²x - tanxsecx

\frac{1}{cos^{2}x } - \frac{sinx}{cosx} \frac{1}{cosx}

\frac{1}{cos^{2} x} - \frac{sinx}{cos^{2}x}

\frac{1 - sinx}{cos^{2}x }

\frac{1 - sinx}{1 - sin^{2}x }

\frac{1 - sinx}{(1 - sinx)(1 + sinx)}

\frac{1}{1 + sinx}

3 0
3 years ago
Given the equation 7(x + 2) = 2x − 1, solve for the variable. Explain each step and justify your process. Jeff solved a similar
Galina-37 [17]
You have to distribute the 7 to x and 2 so :
7x+14=2x-1
Add one to both sides (inverse operations)
7x+14=2x-1
+1 +1
7x+15=2x
Cross Cancel by subtracting 7x from both sides
7x+15=2x
-7x -7x
15=-5x
Divide by -5
15/-5= -5/-5
X= -3

6 0
3 years ago
What is the measure of angle 2? ​
Anit [1.1K]

Answer:

137

Step-by-step explanation:

38 + 48 = 86

86/2 = 43

180 - 43 = 137

5 0
3 years ago
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