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Sever21 [200]
1 year ago
10

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Mathematics
2 answers:
Arada [10]1 year ago
5 0
If y=3x^2+30x+71, then 
y=3(x^2+10x)+71=3(x^2+2\cdot5x+25-25)+71
y=3((x+5)^2-25)+71=3(x+5)^2-75+71=3(x+5)^2-4. So, in the first gap you can write 5 and in the second you can write -4.
Since (x+5)^2\ge 0, the minimum value of y is when (x+5)^2=0. The solution of the last equation is x=-5 and then y=-4 -- these are numbers, which you can write in the third and fourth gaps.

nexus9112 [7]1 year ago
4 0

Answer:

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

If a submarine dives 378 feet in 14 seconds, the average change in elevation is

27

feet per second.

Step-by-step explanation:

FOR PLATO TYPE "27"

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Two fish are put in a man-made lake with no other fish in it. Each month, the fish population triples. Which model and equation
aleksandr82 [10.1K]

Answer:

Step-by-step explanation:

The basic model for this growth is the exponential function:  y = a(b)^c, where a is the initial value, b is the growth rate and c is the time.

Here we have P = fish population = (2 fish)(3)^t

8 0
2 years ago
You plan to accumulate 100,000 at the end of 42 years by making the follow-
Mariana [72]

Answer:

  Y = 479.17

Step-by-step explanation:

At the end of year 14, the balance from the deposits of X can be found using the annuity due formula:

  A = P(1+r/n)((1 +r/n)^(nt) -1)/(r/n)

where P is the periodic payment, n is the number of payments and compoundings per year, t is the number of years, and r is the annual interest rate.

  A = X(1.07)(1.07^14 -1)/0.07 ≈ 24.129022X

This accumulated amount continues to earn interest for the next 28 years, so will further be multiplied by 1.07^28. Then the final balance due to deposits of X will be ...

  Ax = (24.129022X)(1.07^28) = 160.429967X

__

The same annuity due formula can be used for the deposits of Y for the last 10 years of the interval:

  Ay = Y(1.07)(1.07^10 -1)/.07 = 14.783599Y

__

Now we can write the two equations in the two unknowns:

  Ax +Ay = 100,000

  X - Y = 100

From the latter, we have ...

  X = Y +100

So the first equation becomes ...

  160.429967(Y +100) +14.783599Y = 100000

  175.213566Y +16,043.00 = 100,000

  Y = (100,000 -16,043)/175.213566 ≈ 479.17

Y is 479.17

7 0
1 year ago
Division of two quantities is expressed as the ____ of those two quantities.
andreev551 [17]


Division of two quantities is expressed as the  quotient of those two quantities.

The word quotient is derived from the Latin language. It is from the Latin word "quotiens" which means "how many times." A quotient  is the answer to a divisional problem. A divisional problem describes how many times a number will go into another. The first time that this word was known to have been used in mathematics was around 1400 - 1500 AD in England.

There are two different ways to find the quotient of two numbers.  One of them is through Fractions. The quotient of a fraction is the number obtained when the fraction is simplified. The other way to find a quotient is  by employing the long division method where the quotient  value is positioned above the divisor and dividend.
 


6 0
2 years ago
Adam is working two summer jobs, making $9 per hour washing cars and $8 per hour walking dogs. Last week Adam earned a total of
Phantasy [73]

Answer:

Washing cars= 4 hours

Walking dogs= 10 hours

Step-by-step explanation:

You want to start by creating equations. So one thing we know is that he makes $9 an hour washing cars(x) and $8 walking dogs(y).

$9x+$8y=$116

The second Equation is based off of the hours worked. We know that he worked 6 hours more walking the dogs than he did washing cars, so we can take x(being the washing hours) and add 6 to it to equal y (the number of dog hours).

y=x+6

Now You plug what y equals into the first equation to solve for x.

9x+8(x+6)=116     Next distribute the 8 to each term.

9x+8(x)+8(6)=116

9x+8x+48=116     Add the like terms together (9x+8x)

17x+48=116         Subtract the 48 from both sides

     -48  -48

17x=68             Now divide by 17 on both sides.

______

17    17

x=4                 Finally we can take x and plug it back in to one of the equations in order to solve for y. I'm going to choose the second equation.

y=(4)+6

y=10

8 0
2 years ago
Antonia is keeping track of the number of pages she reads. She started the school year having already read 95 pages her book, an
cupoosta [38]
F(x) means "function of" and x represents the day number, example: day 6 would be f(6)=(20×6)+95
4 0
2 years ago
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