Answer:
18 terms
Step-by-step explanation:
The first given sequence has first term a1=2 and common difference d=5. Its explicit formula is ...
an = 2 +5(n -1) = 5n -3
We want the n-th term of this sequence to be the same as the n-th term of the sequence defined by ...
an = 4n +15
We can find n that makes this true by setting the 'an' values equal:
an = an
5n -3 = 4n +15
n = 18 . . . . . . . . . . add 3-4n
The number of terms in each sequence is 18.
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<em>Additional comment</em>
The last term in each sequence is 87.
Since he bought more than one of each, he needs to find the total cost of the biscuits and sausage first.
The correct answer should be:
<span>B. Step 1: Calculate the price of 3 biscuits. Step 2: Calculate the price of 3 sausages. Step 3: Add the total amounts from Steps 1 and 2 to the amount of the tip. Step 4: Subtract that total amount from $25.</span>
Given profit,
p(t)=0.4t^2+5.3t-8
After the first year, t=1
p(1)=0.4*(1^2)+5.3*1-8=-2.3
Answer: the annual loss of the coffee shop after the first year (i.e. the second year) is $2,300.
In order to compare the amount of wax, you have to calculate the volume of both candles.
Candle of booth A = πr² h/3
A = π * 4² * 6/3
A = π * 16 * 2
A = 32π
Now, Candle of Booth B = π * 5² * 5/3
B = π * 25 * 5/3
B = 41.6π
In short, Booth B sells the candle with more wax.
Hope this helps!
F(x)=2x+4/3
Replace f(x) by y:
y=2x+4/3
Solving for x:
y-4/3=2x+4/3-4/3
Subtracting the two terms on the left side of the equation:
(3y-4)/3=2x
Dividing both sides of the equation by 2:
[(3y-4)/3]/2=2x/2
[(3y-4)/3]*(1/2)=x
[(3y-4)*1]/[(3)*(2)]=x
(3y-4)/6=x
x=(3y-4)/6
Replace "x" by "f^(-1) (x)" (inverse function) and "y" by "x":
f^(-1) (x) = (3x-4)/6 Inverse function
Then, for x=6
f^(-1) (6) = [ 3(6)-4]/6
f^(-1) (6) = (18-4)/6
f^(-1) (6)= 14/6
f^(-1) (6) = 7/3
Her hair will have grown 6 after 7/3 = 2.33 months
