Answer:
1/3
Step-by-step explanation:
1/2 of 2/3 = 1/2·2/3 = (1·2)/(2·3) = 1/3
A community is building a square garden with a walkway around the perimeter with the design shown at the right. Find the side length of the inner square that would make the area of the inner square equal to 75% of the total area of the garden. Round to the nearest tenth of a foot.
1. What is an expression for the area of the inner square?
2. What is the area of the entire garden?
3. What is 75% of the area of the entire garden?
4. Write an equation for the area of the inner square using the expressions from Steps 1 and 3.
5. Solve the quadratic equation. Round to the nearest tenth of a foot.
6. Which solution to the quadratic equation best describes the side length of the inner square? Explain.
Answer: The side length of the inner square is 17.3 ft.
Step-by-step explanation: Given that a community is building a square garden with a walkway around the perimeter with the design shown at the right.
We are to find the area of the inner square equal to 75% of the total area of the garden.
The step-wise solutions area s follows:
(1) From the figure, we note that
The side length of the inner square is x ft.
We know that the area of a square is equal to (side)².
So, the area of the inner square will be
[tex]A_i=x\times x\\\\\Rightarrow A_i=x^2~\textup{sq. ft}.[/tex]
(2) The whole garden is in the form of a square with side length 20 ft.
Therefore, the area of the entire garden is given by
[tex]A_g=20\times 320\\\\\Rightarrow A_g=400~\textup{sq. ft}.[/tex]
(3) The area of the entire garden is 400 sq. ft.
So, 75% of the area of the entire garden will be
[tex]75\%\times 400\\\\=\dfrac{75}{100}\times 400\\\\=\dfrac{3}{4}\times 400\\\\=3\times 100\\\\=300~\textup{sq. ft}.[/tex]
(4) Since the area of the inner square is equal to 75% of the area of the entire garden, so we must have
[tex]x^2=300.[/tex]
(5) The solution of the quadratic equation is as follows:
[tex]x^2=300\\\\\Rightarrow x=\pm\sqrt{300}\\\\\Rightarrow x=\pm10\sqrt{3}.\\\\\Rightarrow x=\pm10\times 1.732\\\\\Rightarrow x=\pm17.32\\\\\Rightarrow x=17.32,~-17.32.[/tex]
So, the required solution is x = 17.32, - 17.32.
Rounding to nearest tenth, we get
x=17.3, - 17.3.
(6) Since the length of the side of a square cannot be negative, so the solution that best describes the side length of the inner square will be
x = 17.3.
Thus, all the questions are answered.
And, the side length of the inner square is 17.3 ft.
i need help on 2, 3 and 4 plz thank u ( :
Answer:
2. x = √3
3. y = 3√2
4. a = (2/3)√2
Step-by-step explanation:
In an isosceles right triangle, the length of the hypotenuse is √2 times the length of one side. Said another way, the length of the side is 1/√2 times the length of the hypotenuse.
___
2. x = √6/√2 = √(6/2) = √3 . . . . . divide the hypotenuse by √2 to find x
___
3. (12 -√2y) = √2y . . . . . equate the hypotenuse to √2 times the leg and solve
12 = 2√2y
12/(2√2) = y = 6/√2 = 3√2
___
4. 3a = 2√2 . . . . . . equate the hypotenuse to √2 times the leg and solve
a = 2√2/3 = (2/3)√2
_____
Comment on "rationalizing the denominator"
"Simplest radical form" usually means the radical is in the numerator. To eliminate it from the denominator, multiply by the radical:
1/√n = (√n)/(√n) · 1/√n = (√n)/(√n)^2 = (√n)/n
That is, ...
1/√2 = (√2)/2 . . . . for example.
Find the missing length. Round to the nearest tenth, if necessary.
A. 441
B. 22.5
C. 64
D. 19.4
Using the Pythagorean theorem:
21^2 = √(8^2 + x^2)
441 = √( 64 + x)
441 - 64 = √x
377 = √x
x = √377
x = 19.4
The answer is D.
given a=-3 and b=4 and c=-5, evaluate a+b/c
Answer:
1/5 = 0.2
Step-by-step explanation:
First
[a + b] / c is an algebraic expression
Then
[(-3) + (4)] / 5
[1] / 5
1/5
Best regards
Answer:
-3 4/5
Step-by-step explanation:
a+b/c
Substitute the values in
-3 + 4/-5
-3 + -4/5
-3 4/5
If the expression was (a+b)/c
then (-3 +4)/-5
We would do the parentheses first
1/-5
-1/5
Mikey worked 8 hours on Wednesday, 6 hours on Thursday, and 7 hours on Friday. His gross pay for all three days was $187.95
A. $8.95
B. $8.98
C. $28.13
D. 65.63
Answer:
Step-by-step explanation:
Mikey worked 8 hours on Wednesday, 6 hours on Thursday and 7 hours on Friday.
Total Work = 8+6+7 = 21 hours.
Gross Pay = 187.95 dollars.
Hourly Rate = (Gross pay)/(Total work) = (187.95)/21 = 8.95 dollars per hour.
Hence, option A is correct i.e. 8.95 dollars per hour.
I'll give brainliest if you show your work. Plz answer quickly.
Nolan used the following procedure to find an estimate for the square root of 18.
Step 1: Since 4^2=16 and 5^2= 25 and 16 < 18 < 25, the square root of 18 is between 4 and 5.
4.1^2=16.81
4.2^2=17.64
4.3^2=18.49
4.4^2=19.36
Step 3: Since 18.49 rounds to 18, 4.3 is the best approximation for the square root of 18.
In which step, if any, did Nolan make an error?
A) In step 1, the square root of 18.
is between 4 and 5 because the square root of 18 equals about 20 and 4 times 5= 20.
B) In step 2, he made a calculation error when squaring.
C) In step 3, he should have determined which square is closest to 18.
D) Nolan did not make an error.
Answer:
C) In step 3, he should have determined which square is closest to 18.
Step-by-step explanation:
17.64 also rounds to 18. 17.64 differs from 18 by ...
18 -17.64 = 0.36
whereas 18.49 differs from 18 by ...
18.49 -18 = 0.49
Hence 17.64 is closer to 18 and we might expect 4.2 to be closer to √18 than is 4.3.
___
The actual root of 18 is about 4.243, so 4.2 is a better approximation.
C) In step 3, he should have determined which square is closest to 18.
A group of people were given a personality test to determine if they were Type A or Type B. The results are shown in the table below:
Answer:
Option A: P(Male or Type B) > P(Male | Type B)
Step-by-step explanation:
Total Female = 85 type A, 12 type B ⇒ 97 Female.
Total Male = 65 type A, 38 type B ⇒ 103 Male
Total type A = 65 + 85 = 150
Total type B = 12 + 38 = 50
total number of people = 97 + 103 = 200
Then the probability would be:
P(Male | Type B) = [tex]\frac{number of male in B}{total number of male}[/tex]
= [tex]\frac{38}{103}[/tex]
= 0.368
P(Male or Type B) = [tex]\frac{total number of male + (total number of people in B - total number of male in B)}{total number of male}[/tex]
= [tex]\frac{103 + (50 - 38)}{200}[/tex]
= [tex]\frac{103 + 12}{200}[/tex]
= [tex]\frac{115}{200}[/tex]
= 0.575
Hence, P(Male or Type B) > P(Male | Type B)
What is the measure of the inscribed angle ABC if the measure of the arc, which this angle intercepts is: 48, 57, 90, 124, 180.
➷ The rule is:
The inscribed angle would be half the measure of the intercepted arc
If the arc was 48, the inscribed angle = 48/2 = 24 degrees
If the arc was 57, the inscribed angle = 57/2 = 28.5 degrees
If the arc was 90, the inscribed angle = 90/2 = 45 degrees
If the arc was 124, the inscribed angle = 124/2 = 62 degrees
If the arc was 180, the inscribed angle = 180/2 = 90 degrees
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
I hope you understand it well :)
The measure of an inscribed angle is half the measure intercepted arc.
With that rule
If the arc is 48 the inscribed angle would be [tex]\frac{48}{2}=24[/tex]If the arc is 57 the inscribed angle would be [tex]\frac{57}{2}=28.5[/tex]If the arc is 90 the inscribed angle would be [tex]\frac{90}{2}=45[/tex] If the arc is 124 the inscribed angle would be [tex]\frac{124}{2}=62[/tex]If the arc is 180 the inscribed angle would be [tex]\frac{180}{2}=90[/tex]Hope this helps :)
If you have a doubt just reply over here, I would be happy to help you further :)
i need help with this problem please
Answer:
(a) reduction
(b) 1/2
Step-by-step explanation:
The image figure A'B'C'D' is smaller than the original figure ABCD, so the dilation is a reduction.
Each of the points A'B'C'D' is half as far from the origin as the original points ABCD, so the scale factor is 1/2.
_____
Draw lines C'C and D'D. You will see they meet at the origin, which is the center of dilation. Then look at how far the points are along those lines. C' is one grid square diagonal along the line; C is 2 grid square diagonals along that line, so is twice as far from the origin. That is, C' is 1/2 the distance of C, so represents a reduction by a scale factor of 1/2.
The same distance considerations are observed along the line D'D. The point D' is the diagonal of a 2x1 rectangle from the origin (A distance of √5.) The point D is the diagonal of a 4x2 rectangle from the origin, so is twice as far. Once again D' is 1/2 the distance of D, so represents a reduction by a factor of 1/2.
A power line extends from a light pole 43 meters to the ground and makes an angle of 60 degrees with the ground. To the nearest tenth of a meter, how tall is the light pole?
Answer: 37.2 meters
Step-by-step explanation:
The triangle shown in the image attached is a right triangle.
Therefore, to calculate the height of the light pole (x), you can apply the proccedure shown below:
-Apply [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
-Substitute values.
-Solve for the height of the light pole (x).
Then you obtain the following result:
[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\sin(60\°)=\frac{x}{43}\\\\x=43*sin(60)\\x=37.2[/tex]
Answer:
37.2 meters
Step-by-step explanation:
Since this is the right triangle, the side that is 43 m is the hypotenuse.
Note: the side opposite of 90 degree angle is hypotenuse.
Also, we want the height of the pole, which is the side that is "opposite" to the angle 60 degree given.
Now, which trigonometric ratio relates "opposite" and "hypotenuse"??
It is SINE. Now we can write and solve (let the height of the pole be h):
[tex]Sin(\theta)=\frac{Opposite}{Hypotenuse}\\Sin(60)=\frac{h}{43}\\h=Sin(60)*43\\h = 37.24[/tex]
The light pole is 37.24 meters tall, to the nearest tenth, it is 37.2 meters
Analyze the data set below. Which of the following statements are true? Select all that apply.
In analyzing the data set and the corresponding box plot, we can determine the accuracy of several statements. It is true that 25 percent of the data are at most five. However, it is false to say that there is the same amount of data from 4-5 as there is from 5-7. Additionally, there are data values of three, but it is false to say that 50 percent of the data are four.
Explanation:A. True – the first quartile (Q1) is equal to the 25th percentile, which means that 25 percent of the data fall at or below Q1. If Q1 is at most five, then at least 25 percent of the data is at most five.
B. False – the second quartile (Q2) is equal to the median, which separates the data into two halves. If there is the same amount of data from 4-5 as there is from 5-7, then the median would not be in the middle of the data.
C. False – there are data values of three, as shown by the lower whisker in the box plot.
D. False – the second quartile (Q2) is equal to the median, which is the value that separates the data into two halves. If 50 percent of the data are four or less, then the median would be four or less.
Learn more about Analyzing box plots here:https://brainly.com/question/16709010
#SPJ12
One month Yoko rented 3 movies and 5 video games for a total of $40. The next month she rented 9 movies and 7 video games for a total of $74. Find the rental cost for each movie and each video game.
Answer:
movie: $3.75video game: $5.75Step-by-step explanation:
Two equations in two unknowns can be written:
3m +5v = 40
9m +7v = 74
These can be solved a variety of ways. One of them is using Cramer's rule. It tells you the solution to
ax +by = cdx +ey = fis given by ...
∆ = bd -eax = (bf -ec)/∆y = (cd -fa)/∆For the numbers above,
∆ = 5·9 -7·3 = 24m = (5·74 -7·40)/24 = 90/24 = 3.75v = (40·9 -74·3)/24 = 138/24 = 5.75The rental cost for each movie is $3.75; for each video game, it is $5.75.
___
The attached graph shows a graphing calculator solution to these equations.
How many possible hands are in the card game euchre with a deck including 24 cards.
Cards are kings, queens, jacks, aces. 10s, and 9s
Each of these cars come in the four different types: hearts, spades, clubs, and diamonds
Answer:
42,504
Step-by-step explanation:
(24 x 23 x 22 x 21 x 20) / 5!
The reason for this is because there are 24 cards and each player would get 5
I hope this helps
There are 42,504 different possible hands in the game of Euchre when using a 24-card deck.
The student is asking about the number of possible hands in the card game Euchre when using a deck with 24 cards, which includes the kings, queens, jacks, aces, 10s, and 9s of the four suits: hearts, spades, clubs, and diamonds. In Euchre, each player is dealt a hand of five cards. To calculate the number of possible hands, we use the combination formula, which is C(n, k) = n! / (k!(n - k)!), where n is the total number of cards and k is the number of cards in a hand.
The calculation would go as follows: C(24, 5) = 24! / (5!(24 - 5)!) = 24! / (5!19!) = 42,504. So, there are 42,504 different possible hands in Euchre when using a 24-card deck.
At a gas station the price of gas is $2.40 a gallon. Draw a graph to represent the relationship between the cost of gas and the volume purchase. Also write an equation using Y= MX + B form.
Answer:
Part A) The graph in the attached figure
Part B) [tex]y=2.40x[/tex]
Step-by-step explanation:
Let
y------> the price of gas
x-----> the volume of gas purchase
we know that
The relationship between the cost of gas and the volume purchase represent a direct variation and remember that a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem the constant of proportionality k is equal to
[tex]m=k=2.40\frac{\$}{gallon}[/tex]
and the y-intercept b is equal to zero because the line passes through the origin
[tex]b=0[/tex]
therefore
the linear equation is
[tex]y=2.40x+0\\y=2.40x[/tex]
using a graphing tool
see the attached figure
A survey was done of 902 students. The mean of their results was 26 and the standard deviation was 4. How many students responded above 35?
Answer:
11 students out of 902 responded above 35
Step-by-step explanation:
Using z-score we can find what percentage of student will be above 35. Using this percentage we can calculate how many students out of 902 scored above 35.
Mean = u = 26
Standard deviation = s = 4
Target Value = x = 35
Formula for the z score is:
[tex]\frac{x-u}{s}[/tex]
Using the values in this formula, we get:
[tex]\frac{35-26}{4} =2.25[/tex]
Using the z table we can find the percentage of values that would be 2.25 standard deviations above the mean in a normal distribution. Using the z-table we get this value to be 0.0122 or 1.22%
Thus 1.22% of the values will be above 35.
1.22% of 902 is 11 (rounded to nearest whole number)
Thus 11 students out of 902 responded above 35
Answer:
the answer is 11
Step-by-step explanation:
Twelve friends share 4 bread loaves equally. What fraction of bread loaf does each friend get
Answer:
1/3.
Step-by-step explanation:
Since there are 12 friends and 4 bread loaves, you would divide 4/12 by 4 which is 1/3.
In the expression (x+y)^8, if x=0.3 and y=0.7 , what is the numerical value of the third term?
Answer:
0.01000188
Step-by-step explanation:
The third term is ...
8C2·x^6·y^2 = 28 x^6 y^2
Putting in the given values for x and y, we get ...
28·3^6·7^2·10^-8 = 1000188×10^-8 = 0.01000188
_____
8C2 = 8!/(2!·(8-2)!) = 8·7/(2·1) = 28
Two students use different methods to solve this multiplication problem: 2/5 x -15 5/8
Answer:
see attachment for answers and correction
Step-by-step explanation:
Your answer is correct for Wyatt.
The missing blanks for Abigail are filled with the integer part and the fractional part of the mixed number Abigail started with.
___
Beware signs. In this problem -6 + 1/4 is not the same as -6 1/4.
How to solve:
In(x+3) - In(x-1) = 3
Answer:
x = (e^3 +3)/(e^3 -1) ≈ 1.20958
Step-by-step explanation:
Take the antilog and solve in the usual way.
ln(x+3) -ln(x -1) = 3
ln((x +3)/(x -1)) = 3 . . . . rearrange to a single log
(x +3)/(x -1) = e^3 . . . . take the antilog
x +3 = e^3·(x -1)
3 +e^3 = x(e^3 -1)
x = (e^3 +3)/(e^3 -1) ≈ 1.20958
___
Check
This answer checks OK in the original equation:
ln(4.20958) -ln(0.20958) = 3
Explain how to estimate the lateral area of a right cone with radius 5 cm and slant height 6 cm. Is your estimate an underestimate or overestimate? Explain.
Answer:
The answer in the procedure
Step-by-step explanation:
we know that
The lateral area of a cone is equal to
[tex]LA=\pi rl[/tex]
where
r is the radius of the base
l is the slant height
we have
[tex]r=5\ cm[/tex]
[tex]l=6\ cm[/tex]
assume [tex]\pi =3.14[/tex]
substitute the values
[tex]LA=(3.14)(5)(6)=94.2\ cm^{2}[/tex]
This value is an underestimate, because the assumed pi value is less than the real value
assumed value [tex]\pi =3.14[/tex]
real value [tex]\pi =3.1415926536...[/tex]
Hong's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Hong $5.75 per pound, and type B coffee costs $4.10 per pound. This month, Hong made 170 pounds of the blend, for a total cost of $858.70. How many pounds of type A coffee did he use?
Answer:
98 pounds
Step-by-step explanation:
Let A be pounds of A-type coffee and B be pounds of B-type coffee.
We can set-up two equations and solve simultaneously.
"This month, Hong made 170 pounds of the blend":
[tex]A+B=170[/tex]
"Type A coffee costs Hong $5.75 per pound, and type B coffee costs $4.10 per pound ... a total cost of $858.70":
[tex]5.75A+4.10B=858.70[/tex]
Now we can multiply first equation by -5.75 and then ADD UP this new equation and equation 2 to get B. We have:
[tex](-5.75)*(A+B=170)\\-5.75A-5.75B=-977.5[/tex]
Now solving for B:
[tex]-5.75A-5.75B=-977.5\\5.75A+4.10B=858.70\\-------------\\-1.65B=-118.8\\B=72[/tex]
B = 72
Now plugging in this value into B of original first equation and solving for A gives us:
[tex]A+B=170\\A+72=170\\A=170-72\\A=98[/tex]
Thus, he used 98 pounds of Coffee A.
Which of the following are examples of exponential decay?
A: The population of a Florida is increasing by 43% every year.
B: The pesticide DDT has a half-life of 15 years.
C: March Madness has 64 teams in the bracket. Each round, half the teams are eliminated.
D: After an antibiotic is added to a culture of bacteria, the number of bacteria is reduced by half every three hours.
E: A tree frog population doubles every three weeks.
Answer:
B: The pesticide DDT has a half-life of 15 years.C: March Madness has 64 teams in the bracket. Each round, half the teams are eliminated.D: After an antibiotic is added to a culture of bacteria, the number of bacteria is reduced by half every three hours.Step-by-step explanation:
Exponential decay describes a situation in which the dependent variable is reduced by the same factor when the independent variable is increased by the same amount.
A — the population is increasing, not being reduced
B — the amount is cut in half when time increases by 15 years (exp. decay)
C — the number of teams is cut in half when the number of rounds increases by 1 (exp. decay)
D — the amount is cut in half when time increases by 3 hours (exp. decay)
E — the population is increasing, not being reduced
someone please help me !!
Answer: Y=-13/4 + 4
Hope this helps! :)
table Given the graph of a linear function, identify the steps used to find the initial value. Check all that apply. Find the rate of change using rise over run. Find corresponding y values when x = 6, x = 7, and x = 8. Then plot the points to finish the line. Find corresponding y values when x = 2, x = 1, and x = 0. Then plot the points to finish the line. The initial value corresponds to the y value when x = 1. The initial value corresponds to the y value when x = 0.
To find the initial value of a linear function from its graph, examine the y-intercept where x=0, and use the slope to verify the linearity. The initial value is the y value at x=0.
Explanation:Identifying the initial value of a linear function from its graph involves examining the y-intercept, where x=0. The steps to find it include:
Finding the rate of change using rise over run. This step helps to confirm the linearity and slope of the function.Finding corresponding y values when x = 0. Since the initial value, also known as the y-intercept, corresponds to the value of y when x = 0, this is the most direct way to ascertain the initial value.The notion that the initial value corresponds to the y value when x = 1 is incorrect for linear functions. The initial value or y-intercept is always found where x = 0. Adjustments or predictions for other values of x, such as x = 1, 2, 6, 7, or 8, involve using the line's slope or rate of change but do not directly determine the initial value.
Answer:
its a, c, e
hope this helps!!
What is 7(2n+3) simplified without parenthesis
14n+21
(distribute the 7 to the values in the parenthesis)
please help ... .. .....
Answer:
a. P
b. C
c. C
d. C
e. P
Step-by-step explanation:
When order matters, the count is of permutations. When order doesn't matter, then you count combinations.
_____
a. Order matters: It makes a difference to the three people chosen which one gets what color ribbon. (permutations)
__
b. Order doesn't matter. Bob and Charlie and Alice are effectively the same as Alice and Bob and Charlie. (combinations)
__
c. Order doesn't matter. (combinations)
__
d. Assuming the representative positions all have the same duties, order doesn't matter. (combinations)
__
e. The order of sprinters on a relay team matters. (permutations)
a triangle has a base of 15 inches and an area of 82.5 square inches. What is the height of the triangle
Area of a triangle = 1/2 x base x height.
Replace are and base to get:
82.5 = 1/2 x 15 x height
Multiply both sides by 2:
165 = 15 x height
Divide both sides by 15:
Height = 165 / 15
Height = 11 inches.
What is the sum of the first 27 terms of the arithmetic sequence?
-15,-11,-7,-3,..
[tex]\bf -15~~,~~\stackrel{-15+4}{-11}~~,~~\stackrel{-11+4}{-7}~~,~~\stackrel{-7+4}{-3}~~~~,...\qquad \qquad \boxed{d=4} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ d=4\\ a_1=-15\\ n=27 \end{cases} \\\\\\ a_{27}=-15+(27-1)4\implies a_{27}=-15+(26)4 \\\\\\ a_{27}=-15+104 \implies a_{27}=89[/tex]
[tex]\bf \rule{34em}{0.25pt}\\\\ \textit{ sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\[-0.5em] \hrulefill\\ n=27\\ a_1=-15\\ a_{27}=89 \end{cases} \\\\\\ S_{27}=\cfrac{27(a_1+a_{27})}{2}\implies S_{27}=\cfrac{27(-15+89)}{2}\implies S_{27}=\cfrac{27(74)}{2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill S_{27}=999~\hfill[/tex]
I have no clue how to do 2.3
Answer:
A D and E are the answers
Step-by-step explanation:
The general formula is n * CD so all you do is multiply n times the original length.
A is true. 3/2 * 12 = 36/2 = 18 True.
============
B is not true 4*12 = 48 not 3
B would be true if n = 1/4
1/4 * 12 = 3
============
C is not true 8*12 = 96 not 20
============
D is true 2 * 12 = 24
============
E is true 3/4 * 12 = 36/4 = 9
A D and E are the answers
-3m < 15
PLEASE HELP
Answer:
m > -5
Step-by-step explanation:
Divide your inequality by the coefficient of m, which is -3. Doing that requires you reverse the comparison symbol:
(-3m)/(-3) > (15)/(-3)
m > -5
_____
The comparison symbol is reversed whenever an inequality is multiplie or divided by a negative number. You might be able to see why when you look at the relation between a couple of integers:
-2 < -1
2 > 1 . . . . . . multiply the above by -1
Multiplying by a negative number effectively reflects the comparison across the center of the number line. As we know from looking in a mirror; reflection reverses left and right, so numbers that were farther to the right (more positive) are now farther to the left (more negative).