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Katarina [22]
3 years ago
5

Shelf A had 40 books and Shelf B had 16 books. After Abigail borrowed an equal number of books from Shelf A and Shelf B, there w

ere 3 times as many books on Shelf A than on Shelf B. How many books did Abigail borrow altogether?
Mathematics
1 answer:
FinnZ [79.3K]3 years ago
8 0

Answer:

120

Step-by-step explanation:

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Beth is painting a picture. She usually buys acrylic paints at Michaels for $5.25 a tube. She runs out of black paint so she goe
andre [41]

Answer:

5.25

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
After the mill in a small town closed down in 1970, the population of that town started decreasing according to the law of expon
wlad13 [49]

Answer:

P_o = \frac{143000}{e^{-20*0.01303024661}}=110193.69

And we can round this to the nearest up integer and we got 110194.  

Step-by-step explanation:

The natural growth and decay model is given by:

\frac{dP}{dt}=kP   (1)

Where P represent the population and t the time in years since 1970.

If we integrate both sides from equation (1) we got:

\int \frac{dP}{P} =\int kdt

ln|P| =kt +c

And if we apply exponentials on both sides we got:

P= e^{kt} e^k

And we can assume e^k = P_o

And we have this model:

P(t) = P_o e^{kt}

And for this case we want to find P_o

By 1990 we have t=20 years since 1970 and we have this equation:

143000 = P_o e^{20k}

And we can solve for P_o like this:

P_o = \frac{143000}{e^{20k}}   (1)

By 2019 we have 49 years since 1970 the equation is given by:

98000 = P_o e^{49k}   (2)

And replacing P_o from equation (1) we got:

98000=\frac{143000}{e^{20k}} e^{49k} =143000 e^{29k}  

We can divide both sides by 143000 we got:

\frac{98000}{143000} =0.685 = e^{29k}

And if we apply ln on both sides we got:

ln(0.685) = 29k

And then k =-0.01303024661[/tex]

And replacing into equation (1) we got:

P_o = \frac{143000}{e^{-20*0.01303024661}}=110193.69

And we can round this to the nearest up integer and we got 110194.  

7 0
3 years ago
Find the values of p and q such that 4x-5-x^2=q-(x+p)^2
Solnce55 [7]

Answer:

p = - 2 , q = - 1

Step-by-step explanation:

Rearrange the left side into standard form

- x² + 4x - 5

Factor out - 1 from - x² + 4x

= - (x² - 4x) - 5

Using the method of completing the square

add/subtract ( half the coefficient of the x- term)² tp x² - 4x

= - (x² + 2(- 2)x + 4 - 4) - 5

= - (x - 2)² - (- 4) - 5

= - (x - 2)² + 4 - 5

= - 1 - (x - 2)²

Comparing to q - (x + p)²

with p = - 2 and q = - 1

4 0
2 years ago
Find csc if tan= 3/4
barxatty [35]

Answer:

5/3

Step-by-step explanation:

Tangent is defined as the length of the opposite side of the triangle divided by the length of the adjacent side of the triangle. Since you know that two of the legs are 3 and 4, using the pythagorean theorem you know that the last side is 5. Sin is defined as the length of the opposite side divided by the length of the hypotenuse, which in this case is 3/5. Cosecant is just the reciprocal of that, or 5/3. Hope this helps!

6 0
3 years ago
Simplify fully 50y3/ 8xy2​
Mashutka [201]

Answer:

\frac{25y}{4x}

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
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