1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
KiRa [710]
3 years ago
8

Two integers, a and b, have a product of 36. What is the least possible sum of a and b?

Mathematics
1 answer:
Minchanka [31]3 years ago
8 0
<h3>Answer:  12</h3>

==============================================================

Explanation:

The two integers multiply to 36, so,

ab = 36

which solves to

a = 36/b

Then we want to add the numbers such that we get the smallest possible result.

a+b = (36/b)+b

So we want (36/b)+b to be as small as possible.

Let's say we replace b with x and we consider this function

f(x) = (36/x) + x

The goal is to find when f(x) is smallest, ie, we want to minimize the function.

If we were to graph out the function, we get the curve shown below.

To make things easier, we'll only focus on positive values of x.

The lowest part of the curve is what we're after. Using the "minimum" function/feature on the graphing calculator, we would then find the lowest point occurs at (6,12). This point is considered a local minimum because it's the lowest point in that given neighborhood of x values.

So the input x = 6 leads to the smallest output f(x) = 12.

This in turn means b = 6 is going to pair with a = 36/b = 36/6 = 6.

In short, a = 6 and b = 6.

----------------------

As a check,

a*b = 6*6 = 36

a+b = 6+6 = 12

We can make a table of various values to help confirm that 12 is the smallest sum.

Side note: If you're not allowed to use a graphing calculator, then you'll need to use calculus.

You might be interested in
.___________________.<br> .___________________.
astra-53 [7]

9514 1404 393

Answer:

  (x, y) = (0, -26)

Step-by-step explanation:

The y-intercept is the y-value that corresponds to x=0. Here, we have a table that has x-values that differ by 12 and 24. We want to find the y-value that corresponds to an x-value 24 less than the lowest one on the table:

  24 -24 = 0

We notice that when x-values differ by 24, the y-values differ by 10 -(-8) = 18. So, the y-value we want is 18 less than the lowest one in the table:

  y = -8 -18 = -26

The (x, y) coordinates of the y-intercept are (0, -26).

6 0
2 years ago
X to the third power = 125/27
nika2105 [10]
When raising a fraction to a power, we can raise the numerator and denominator to the power. To find x, we need to find the cube root of both 125 and  27. That is, the numbers that when multiplied by themseelves 3 times result in 125 and 27.

\sqrt[3]{125} = 5

\sqrt[3]{27} =3

So x = \frac{5}{3}
7 0
3 years ago
Write the equation of the line, given the y and x-intercepts:
kolezko [41]

Answer:

The answer to your question is:                161x + 17y - 391 = 0

Step-by-step explanation:

Data

y-intercept = 23         Get the points      (0, 23)

x- intercept = 4.75                                   (4.75, 0)

                      4.75 = 17/4                         (17/4, 0)

slope

              m = (y2 - y1) / (x2 - x1)

              m = (0 - 23) / (17/4 - 0)

              m = -23 / 17/4

             m = - 161 / 17

equation

              (y - y1) = m (x - x1)

              ( y - 23) = -161 / 17 (x - 0)

               y - 23 = -161/17 x

              17(y - 23) = -161x

              17y - 391 = -161x

              161x + 17y - 391 = 0

7 0
3 years ago
-6/13 - (-7/15)<br> pls solve it for me !!! :)
MAXImum [283]

Answer:

First, make the double negative a positive.

So, (-6/13) + (7/15)

Then multiply the numerator, 6×7=42

And denominator 13×15=195

42/195 simplify by dividing both by 3 so 14/65

8 0
2 years ago
Read 2 more answers
I theater sells tickets for a concert. Tickets for lower-level seats sell for $35 each and tickets for upper-level seats sell fo
lora16 [44]

Let X= the number of tickets sold at $35 each

Let 350 -X = the number of tickets sold at $25 each

The number of tickets sold for each type will be computed as follows:

X(35)+(350-X)25=10250

35X+8750-25X=10250

10X=10250-8750

X=1500/10

X=150 the number of tickets sold at $35 each

350-150 the number of tickets sold at $25 each

To recheck:

150(35)+200(25)

5250+5000

10250

7 0
3 years ago
Other questions:
  • Karen read 20 pages of her book in a half hour. If she reads for 3 hours at the same rate , about how many pages of her book can
    14·2 answers
  • If the length of the side PQ is 5 inches, what are the possible lengths of the other two sides?
    8·1 answer
  • The slope of the line 5x – y = 12 is
    12·1 answer
  • What is the distance between the points (−9,−2) and (50,54)?
    10·1 answer
  • Can you please help with rate please help filling in the missing box
    11·1 answer
  • Plz help with my math
    13·1 answer
  • Graph the function and label its intercepts. Round the intercepts to two decimal places.pt.2​
    12·1 answer
  • You are setting out snacks for some friends to come over. You have 18 crackers and 12 slices of cheese. If you want each plate t
    6·1 answer
  • Một ông 43 tuổi đến khám tổng quát. Phân tích nước tiểu thấy có đường niệu. Bạn vừa biết có một test T dung phát hiện bệnh tiểu
    5·1 answer
  • Brad bought a piece of industrial real estate for $192,345. The value of the real estate appreciated at a constant rate per year
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!