Answer:
a. ∀ a, b ∈ Z, if a < 0 ∧ b < 0 ⇒ a + b < 0
b. ∀ a, b ∈ Z, if a > 0 ∧ b > 0 ⇒ a - b < 0 ∨ a - b > 0
c. ∀ a, b ∈ Z, a² + b² ≥ (a + b)
d. ∀ a, b ∈ Z, |ab| = |a||b|
Step-by-step explanation:
a. The sum of two negative integers is negative.
First, we take the quantifier ∀ and write the two integers a and b as a element of the set of integers Z as ∀ a, b ∈ Z. Now, if a and b are negative, we write if a < 0 ∧ b < 0 where the logical operator ∧ represents "and". So, we have the statements ∀ a, b ∈ Z, if a < 0 ∧ b < 0. Then finally, we use the logical operator ⇒ to imply the summation of the two integers as ⇒ a + b. And since we are to show that their sum is less than zero, we write ⇒ a + b < 0.
Combining this statement with the previous expressions, we have
∀ a, b ∈ Z, if a < 0 ∧ b < 0 ⇒ a + b < 0
b. The difference of two positive integers is not necessarily positive.
First, we take the quantifier ∀ and write the two integers a and b as a element of the set of integers Z as ∀ a, b ∈ Z. Now, if there exists a and b that are positive, we write if a > 0 ∧ b > 0 where the logical operator ∧ represents "and". So, we have the statements ∀ a, b ∈ Z, a > 0 ∧ b > 0. Then finally, we use the logical operator ⇒ to imply the difference of the two integers as ⇒ a - b. And since we are to show that their difference is either less than zero or greater than zero, we write ⇒ a - b < 0 ∨ a - b > 0 where ∨ implies the logical operator "or".
Combining this statement with the previous expressions, we have
∀ a, b ∈ Z, if a > 0 ∧ b > 0 ⇒ a - b < 0 ∨ a - b > 0
c. The sum of the squares of two integers is greater than or equal to the square of their sum.
First, we take the quantifier ∀ and write the two integers a and b as a element of the set of integers Z as ∀ a, b ∈ Z. Now, since we are dealing with the sum of the squares of each integer, we write a² + b². And, we are to show that this sum is greater than the sum of the individual integers, we write their sum as a + b, and we show the previous sum to be greater than or equal to this as a² + b² ≥ (a + b).
Combining this statement with the previous expressions, we have
∀ a, b ∈ Z, a² + b² ≥ (a + b)
d. The absolute value of the product of two integers is the product of their absolute values.
First, we take the quantifier ∀ and write the two integers a and b as a element of the set of integers Z as ∀ a, b ∈ Z. Now, since we are to show that absolute value of the product of the integers equals the product of the absolute value of the individual integers, we write the that absolute value of the product of the integers as |ab| and the product of the absolute value of the individual integers as |a||b|.
Since we are to show that this expression and the previous expression are equal, we write |ab| = |a||b|.
Combining this statement with the previous expressions, we have
∀ a, b ∈ Z, |ab| = |a||b|
f(x) = -22 + x + 14
Find f(2)
Answer:
sln
f(x) =-22+x+14 put 2 in x
f(2)=-22+2+14
f(2) =38
Which scatterplot demonstrates the strongest relationship between two quantitative variables?
A graph has x on the x-axis, and y on the y-axis. Points are scattered throughout the graph.
A graph has x on the x-axis, and y on the y-axis. Points curve up and then down in a line.
A graph has x on the x-axis, and y on the y-axis. Points increase loosely together.
A graph has x on the x-axis, and y on the y-axis. Points decrease loosely together.
The scatterplot demonstrates the strongest relationship is, a graph has x on the x-axis, and y on the y-axis. Points increase loosely together.
What is Correlation coefficient of scatterplot?The correlation coefficient of scatterplot is used to demonstrate the relationship between variables.
When two variables increases together, they are said to have positive correlation.
When one is increasing and another is decreasing, they are said to have negative correlation.
When most of data points form a straight line or lies close to the straight line, it indicates strong linear correlation.
From the given options;
Option A, zero correlation
Option B, less than 1
Option C, 1 or greater than 1
Option D, -1 or less than 1
Thus, the scatterplot demonstrates the strongest relationship between two quantitative variables is option C, "a graph has x on the x-axis, and y on the y-axis. Points increase loosely together".
Learn more about scatterplot here: brainly.com/question/6592115
#SPJ2
1651.43 rounded to the nearest hundred
Answer:
1600
Step-by-step explanation:
The number of that grow sugar beet =12
Answer:
I think question is not proper
you should check it again
hope your day will fine
Answer:
Whatttt
Step-by-step explanation:
Can someone do this real quick plz
Answer:
(3.5, 2)
Step-by-step explanation:
From the attachment, we have:
[tex]H = (1,1)[/tex]
[tex]J= (2,3)[/tex]
[tex]K=(6,3)[/tex]
[tex]L = (5,1)[/tex]
Required
Determine the point of intersection
To do this, we simply calculate the midpoints of the diagonals; which are:
HK and JL
Midpoint is calculated as:
[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]
For HK:
[tex]M = \frac{1}{2}(1+6,1+3)[/tex]
[tex]M = \frac{1}{2}(7,4)[/tex]
[tex]M = (3.5,2)[/tex]
For JL:
[tex]M = \frac{1}{2}(2+5,3+1)[/tex]
[tex]M = \frac{1}{2}(7,4)[/tex]
[tex]M = (3.5,2)[/tex]
For both diagonals, the coordinate of the midpoint is (3.5, 2).
Hence, the point of intersection is: (3.5, 2)
What is the answer for this?
Answer:
Proved
Step-by-step explanation:
Given
[tex](2 * 10^2) * (3 * 10^5) = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Required
Prove
On the right hand side, we have:
[tex]2 * 10^2 * 3 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Rewrite:
[tex]2 * 3* 10^2 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
[tex]6* 10^2 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Apply law of indices
[tex]6* 10^{2+5} = 3.5 * 10^7 + 2.5 * 10^7[/tex]
[tex]6* 10^7 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Express 6 as 3.5 + 2.5
[tex](3.5 + 2.5)* 10^7 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Open bracket
[tex]3.5 *10^7+ 2.5*10^7 = 3.5 * 10^7 + 2.5 * 10^7[/tex]
Proved
A group of 28 people bought tickets to a show. The tickets cost $23.98 each.
What was the total cost of the tickets?
Enter your answer in the box.
Answer:
$671.44
Step-by-step explanation:
$23.98 * 28 (people) = $671.44
Answer:
$671.44
Step-by-step explanation:
Lucy is standing on a balcony looking down at her friend Grace, as shown in the diagram.
20 feet
Lucy<-] 0
1
14 feet
Grace
To the nearest degree, what is the measure of the angle of depression?
Answer:
35
Step-by-step explanation:
The answer is 35 degrees
can you please help me with this question?
Answer: 32, 25, and 13 are possible side lengths.
Step-by-step explanation:
The lengths of any two sides of a triangle must sum up to more than the length of the third side.
15 + 27 = 42
42 = 42
The sum has to be MORE than the third side.
15 + 27 = 42
42 > 11
15 + 11 = 26
26 < 27
The sum of two sides can't be LESS than the third side.
15 + 27 = 42
42 > 32
15 + 32 = 47
47 > 27
27 + 32 = 59
59 > 15
Possible Side Length!
15 + 27 = 42
42 < 45
Can't be less
15 + 27 = 42
42 > 25
15 + 25 = 40
40 > 27
27 + 25 = 52
52 > 15
Possible Side Length!
15 + 27 = 42
42 > 13
15 + 13 = 28
28 > 27
27 + 13 = 40
40 > 15
Possible Side Length!
Which graph represents the function?
f(x)=−x2+x+6
What Is The Answer
k3 - 4j +12, when k=8, j=2
Answer:
The answer would be 28
Step-by-step explanation:
You would plug 8 in where k is and 2 where j is
so (8)3 - 4(2) +12
answer is 28
A new parking lot is being built for a medical office. The expression representing the number of parking spots in the new lot is StartFraction 15 x over 4 EndFraction minus 9, where x represents the number of parking spots in the first row. How many spots are in the parking lot if there are 32 parking spots in the first row?
79
88
111
129
Answer:
111
Step-by-step explanation:
A variable is a letter, for example x, y or z, that represents an unspecified number. To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12.
Answer:
C
Step-by-step explanation:
A square pyramid and a cube have the same total surface area. The width of the cube is 8 centimeters. The base of the pyramid is equal to base of the cube. What is the slant height of the square pyramid?
Answer:
Step-by-step explanation:
surface area of cube = 6×8² = 384 cm²
lateral area of pyramid = surface area of pyramid - base area
= 384 - 8²
= 320 cm²
area of triangular face = 320/4 = 80 = ½(base)(slant height) = ½(8)(slant height)
slant height = 20 cm
__________________________
Answer:
1.57
Step-by-step explanation:
Answer:
1.57
Step-by-step explanation:
Circumference = 2pi(r) = 2(3.14)1 = 6.28
1/4x6.28=1.57
Find three consecutive numbers whose sum equals
999.
Answer:
332, 333, 334
Step-by-step explanation:
First, we acknowledge that the equation that we need to solve will be "x+(x+1)+(x+2)=999" This is because x represents the smallest of three consecutive numbers whose sum is 999. Simplifying this equation will leave us with 3x+3=999 which is simplified further to 3x=996 and again simplified to x=332. X is the smallest number of the three.
4) find the first five terms of the recursively defined sequence.
a1=5, an+1=-3an+1
Answer:
566556565*7*7/*7+666364
what happened to tansen when he sang the deepak raga with great vigour
[tex]7x5[/tex]
-6y+11x=-34
-4y+7x=-24
Answer:
no idea but mabye someone whose NOT in 3rd grade will know?
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 mm
Answer:
[tex]\dfrac{dV}{dt}=502.65\ mm^3/s[/tex]
Step-by-step explanation:
The volume of a sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
The rate of change of volume means,
[tex]\dfrac{dV}{dt}=\dfrac{d}{dt}(\dfrac{4}{3}\pi r^3)\\\\\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r\times \dfrac{dr}{dt}[/tex]
We have, [tex]\dfrac{dr}{dt}=2\ mm/s\ and\ r=40\ mm[/tex]
So,
[tex]\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3\times 20\times 2\\\\=502.65\ mm^3/s[/tex]
So, the volume is increasing at the rate of [tex]502.65\ mm^3/s[/tex].
Zach bought a video game that was 30% off. He paid $40 for the video game. How much was the game ORIGINALLY? (40 is the AMOUNT PAID so what Percent was me use to match that PART?)
Answer:
57.14$
Step-by-step explanation:
70/100 ( Remember 30% off so only paid 70% of original price) = 40/x ( 40$ is the price paid, x is the unknown original price)
70 = 40
100 X
40×100 = 4,000
4,000÷ 70X = 57.14
PLEASE HELP IF POSSIBLE, ASAP!!!!!!!! :)
The Sum of all 3 needs to equal 1
A. 1/9 + 1/2 + 1/3 = 17/18
B. 1/9 + 2/9 + 1/3 = 6/9 = 2/3
C. 1/6 + 3/9 + 1/3 = 3/18 + 6/18 + 6/18 = 15/18
D. 2/9 + 8/18 + 1/3 = 4/18 + 8/18 + 6/18 = 18/18 = 1
The answer is D
Assignment
os
Calculate the volunce the solid.
een
Answer:
2000ffdtsyjeauets esy siy eut aiteais6i6 es i6sei6 s3
ABCD is a rhombus with diagonals intersecting at E. If mABC is three times mBAD, find mABC.
And the answer is : 4m+m=180.
Do hope you will find it helpful!
Step-by-step explanation:
What is the slope of the line?
Answer:
Slope: -1
Step-by-step explanation:
(0, -2) and (1, -3)
m= (y2-y1)/(x2-x1)
m= (-3+2)/(1-0)
m= (-1)/(1)
m = -1
77006
75863
Subtract
Answer:
1143
Step-by-step explanation:
5 in = ___________ ft
Answer:
0.416667 foot
Step-by-step explanation:
Answer: 0.41666667
Step-by-step explanation:
From the internet
A bicyclist ride 1/4 miles 1/60 hours
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answer: C
Step-by-step explanation: The layers of rocks implies superposition and changes in species implies evolution
Please anyone see if I did this correct let me know the missing number for the bottom part. I upload it
Answer:
you got it!
Step-by-step explanation:
Answer:
You did do it correct!
For questions 21 and 22 is their a certain way you have to fill in the missing numbers?
I would do...
21. 2 and 5
22. 10 and 10
I am not sure though if there is a correct way to answer those two questions.
Step-by-step explanation:
If x = -8, then which of the following equations makes a true statement?
A. 3x - 5 = -23
B. 2x - 2 = -18
C. 2x - 1 = -10
D. 3x - 1 = -16