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Inessa05 [86]
3 years ago
8

Translate this problem to an equation and solve. The product of 2 positive consecutive even integers is 48. What is the smaller

number?
Mathematics
1 answer:
bonufazy [111]3 years ago
8 0
Let x represent the first even integer: x = 2(k) → y = 2k
Let y represent the second even integer: y = 2(k + 1)  → y = 2k + 2

   x  ·     y        = 48
(2k) · (2k + 2) = 48
 4k² + 4k - 48  = 0
 4(k² + k - 12)  = 0
4 (k + 3)(k - 2) = 0
k = -3, k = 2  (Note: POSITIVE integers so k = -3 is ruled out)

x = 2k → x = 2(2) → x = 4
y = 2(k + 1) → y = 2(2 + 1) → y = 2(3) → y = 6

The smaller number (x) is 4
        


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logs are stacked in a pile on the bottom row and 15 on the top row . there are 10 rows in all with each row having one more log
WITCHER [35]
Since there is a common difference of one, this is an arithmetic sequence of the form a(n)=a+d(n-1) which in this case is:

a(n)=15+1(n-1)

All arithmetic sequences have a sum which is equal to the average of the first and last terms time the number of terms, mathematically:

s(n)=(2an+dn^2-dn)/2  (that is just the result of ((a+a+d(n-1))(n/2)) )

Since a=15 and d=1 this becomes:

s(n)=(30n+n^2-n)/2

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8 0
3 years ago
Read 2 more answers
Question 1b.
Ainat [17]

Answer:  i) Reasonably symmetric

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

Explanation:

The data set is

35,40,45,49,51,54,57,58,58,64,68,68,75,77

Erase the outer pair of values (35 and 77) to end up with this smaller set

40,45,49,51,54,57,58,58,64,68,68,75

Repeat and erase off the outer values (40 and 75) to end up with

45,49,51,54,57,58,58,64,68,68

Keep going until we have either one or two elements left

  • 49,51,54,57,58,58,64,68
  • 51,54,57,58,58,64
  • 54,57,58,58
  • 57,58

At this point, we see that the center is between these two last values. So the median is (57+58)/2 = 57.5

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

The center is at 57.5

Let L = {35,40,45,49,51,54,57} consist of the set of numbers lower than the median

Let U = {58,58,64,68,68,75,77} be the upper set of values larger than the median.

The middle of set L is 49 and the middle of set U is 68. So Q1 and Q3 are 49 and 68 respectively.

From that, we see the IQR = Q3 - Q1 = 68-49 = 19

Let A and B be the lower and upper fence

We would then say

A = Q1 - 1.5*IQR = 49-1.5*19 = 20.5

B = Q3 + 1.5*IQR = 68 + 1.5*19 = 96.5

Notice how all of the given data values are between A = 20.5 and B = 96.5, which means we don't have any outliers.

Furthermore, if we plotted a box-and-whisker plot (see below), we can see that the two whiskers are fairly the same length. It's not perfect but they're reasonably symmetric. Similarly, the median is somewhat in the middle of the box itself. So this gives a rough idea that the data set we're dealing with is fairly symmetric.

More confirmation can be in the form of a histogram which is also part of the image below. This histogram is fairly symmetric as the left half is nearly (not perfectly) a mirror image of the right half, and vice versa. No one side pulls too far out to create a highly skewed distribution.

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Answer:

The answer is "bulb, expands, and glass ".

Step-by-step explanation:

The bulb thermometer is the common glass temperature sensor for which you might be grown up. This thermometer is filled with a liquid, typically mercury. Bulb thermometers work on the simple premise that it volume of the liquid varies in proportion to its volume.

It is a glass tube that is pre full with a fluid such as a hydrogen or liquor and is sealed at both sides. The fluid in the glass tube rises as the mercury inside the thermometer's bulb increases. When the temperature gauge is warm, the liquid inside flows up in the tube.

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Jane wants to share her pizza with two friends. She wants to make sure they all get the same amount. How should she cut the pizz
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Answer:

Into 1/3 pieces

Step-by-step explanation:

1/3 + 1/3 + 1/3 = 1 the whole pizza pie, yum

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If j = 10 cm and k = 12.5 cm what is the length of l
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