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|
What is the value of x in the following equation? 4(x-1) = 2(x +1)
The two figures shown are congruent. Which statement is true?
One figure is a translation image of the other.
One figure is a rotation image of the other.
Neither figure is a translation or rotation image of the other.
9514 1404 393
Answer:
(b) One figure is a rotation image of the other
Step-by-step explanation:
The axis of symmetry is horizontal for the left figure, and vertical for the right figure. The right figure has been rotated 90° CW from the left figure.
difference quotient for f (x) = 2x + 3 /5x
Answer:
1 and -0.6
Step-by-step explanation:
A car la 160 inches long
A truck is 7percentage longer thanks they car
Answer:
171.2
Step-by-step explanation:
7% x 160 = 11.2
11.2 + 160 = 171.2
pls answer I'll mark u brainliest urgent
Answer:
a = 110
Please mark as brainliest if answer right
Have a great day, be safe and healthy
Thank u
XD
Answer:
A=110
that is what I think
Please Help, what is the answer
Answer:
The correct option is (2).
Step-by-step explanation:
We need to find the value of the given expression i.e.
[tex]\dfrac{(8x^6)^2}{(4x^2)^3}[/tex]
We can calculate it as follows :
[tex]\dfrac{(8x^6)^2}{(4x^2)^3}=\dfrac{8^2\times (x^6)^2}{(4)^3\times (x^2)^3}\\\\=\dfrac{x^{12}}{x^6}\\\\=x^6[/tex]
So, the final answer is x⁶. The correct option is (2).
A commuter airline makes lattes in the galley and sells them to passengers. A regular latte contains a shot of espresso, 1 cup of 2% milk, steamed, and 0.5 cup of whipped cream. The low-fat latte contains a shot of espresso, 1.25 cups of skim milk, frothed, and no whipped cream. The plane begins its journey with 100 shots of espresso, 60 cups of skim milk, 60 cups of 2% milk, and 30 cups of whipped cream. The airline makes a profit of $1.58 on each regular latte and $1.65 on each low-fat latte. Assuming that all lattes that are made can be sold, what would be the ideal mix of regular and low-fat lattes to maximize the profit for the airline?
Answer:
To maximize profit, the amount of each type of coffees made are;
The number of regular latte made = 52 cups
The number of low-fat latte made = 48 cups
Step-by-step explanation:
The given parameters are;
The number of espresso in a regular latte = 1 shot
The number of cups of 2% milk in regular latte = 1 cup
The amount of whipped cream in a regular latte = 0.5 cup
The number of cups of skim milk in the low-fat latte = 1.25 cup
The number of espresso in a low-fat latte = 1 shot
The amount of whipped cream in a low-fat latte = 0 cup
The number of cups of espresso in the journey = 100 shots
The number of cups of skim milk in the journey = 60 cups
The number of cups of 2% milk in the journey = 60 cups
The amount of profit the airline makes on each regular latte = $1.58
The amount of profit the airline makes on each low-fat latte = $1.65
Let 'x' represent the number regular lattes made and let 'y' represent the number low-fat lattes made, we have;
x ≤ 30/0.5 = 60
x ≤ 60
y ≤ 60
y ≤ 60/1.25 = 48
∴ y ≤ 48
x + y ≤ 100
Therefore, the given that more profit is made from the sale of low-fat latte than for regular latte, the maximum number of low-fat latte should be made
Therefore, the number of low-fat latte made, y = 48
Therefore, the number of regular latte made, x ≤ 100 - 48 = 52
For maximum profit, the maximum number of low-fat latte, 'x', should be made
Therefore, x = 52
The ideal mix of regular and low-fat lattes to maximize profit is 52 cups of regular latte and 48 cups of low-fat latte
Find the distance between the points (-3, 4) and (-3, -5).
Answer:
[tex]\displaystyle d = 9[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (-3, 4)
Point (-3, -5)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(-3+3)^2+(-5 - 4)^2}[/tex][Distance] [√Radical] (Parenthesis) Add/Subtract: [tex]\displaystyle d = \sqrt{(0)^2+(-9)^2}[/tex][Distance] [√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{81}[/tex][Distance] [√Radical] Evaluate: [tex]\displaystyle d = 9[/tex]If Robert buys a candy bar for 78 cents, how much
change does he get back from a one-dollar bill?
32 cents
23 cents
22 cents
33 cents
Marta can pick 10 baskets of peaches in one hour. How long will it take her to pick 60 baskets of peaches?
Answer:
It will take her 6 hours for her to pick 60 baskets of peaches.
Step-by-step explanation:
Solve the simultaneous equation
4x-y=9
2x-3y= -23
Answer:
x = 5
y = 11
Step-by-step explanation:
y = 4x - 9
2x -3(4x - 9) = -23
2x - 12x + 27 = -23
-10x = -23 -27
-10x = -50
minus cancels out
x = 5
y = 4(5) -9
y = 20 - 9
y = 11
13 in = ___________ ft
Answer:
1.0833333 Feet
Hope this helps! If I could have brainliest im trying to level up.
Step-by-step explanation:
13 Inches =
1.0833333 Feet
(rounded to 8 digits)
What does it mean to evaluate?
Answer:
Evaluate means to assess or determine something.
Step-by-step explanation:
Answer:
Means to simply solve, sometimes you may need to show your thinking, depending on the question.
Step-by-step explanation:
PLEASE HELP 20 POINTS
SHOW ALL WORK
Answer:
Steps below
Step-by-step explanation:
8) x = y²/2 2rcosΘ = r²sin²Θ 2cosΘ = rsin²Θ
r = 2cosΘ/sin²Θ = 2cotΘcscΘ
9) (x+2)²+y²=4 y= rsinΘ x=rcosΘ
(rcosΘ+2)²+y²sin²Θ = 4
r²cos²Θ+4rcosΘ+4+y²sin²Θ=4
r²(sin²Θ+cos²Θ)+4rcosΘ=0
r²+4rcosΘ=0 r+4cosΘ=0
r = - 4cosΘ
10) r = 2sinΘ r=2* y/r r²=2y x²+y²=2y
x² + (y²-2y+4) = 4 x²+(y-2)² = 4
11) r = 3tanΘsecΘ = 3* (y/x) * (r/x)
1 =3y/x²
x² = 3y 3y = x²
In the parallelogram below,
y = [?]
5y-20
2y+25
PLEASE HELP
natasha has a sales job and receieves $60,440 as her annual pay plus commission. her company pays her a commision of 12% on her total sales if she makes sales of $70,000 in the first 3 months how much will she be paid for those 3 months?
Answer:
$68,840
Step-by-step explanation:
70,000*12%=8,400
8440+64,440=$68,840
Can someone help meee
Answer:
69
the measure of angle will
111 + AXB = 180
AXB = 180 - 111
AXB = 69
hope it helps
Answer:
angle AXB= 180-111=69°
Step-by-step explanation:
you want your markup to be 35% of the final selling price. Your cost is $200. For what price should you sell the product
a. $235.00
b. $270.00
c. $279.00
d. $307.69
Joel had a coin collection. He had two hundred coins,
which were dimes and quarters. The total value of his
collection was worth $32.
Remember to define your variables.
Create 2 equations
(Each equation should have a "common theme" for
example in this problem one equation will be the the
total number of coins and the other will be the total
value of the coins)
The next step is to solve the problem. Remember to
think of the best method for problem solving
Answer:
Joel's coin collection had 120 dimes and 80 quarters.
Step-by-step explanation:
Given that Joel had a coin collection of two hundred coins, which were dimes and quarters, and the total value was worth $32, to determine how many coins of each type he had, the following equations must be performed:
0.25 - 0.10 = 0.15
200 x 0.10 = 20
32 - 20 = 12
12 / 0.15 = 80
200 - 80 = 120
(80 x 0.25) + (120 x 0.1) = X
20 + 12 = X
32 = X
Therefore, Joel's coin collection had 120 dimes and 80 quarters.
Target buys pants for $6.42 and marks up the price for customers by 70%. How much do they sell pants for?
0.7\left(6.42\right)=\$4.490.7(6.42)=$4.49
$4.49 is not the correct answer. What is the mistake? Explain.
I don’t understand I need help
Answer:
3/29
Step-by-step explanation:
area of total rectangle is 12x8 or 96 sq cm
area of shaded square is 9
96 - 9 = 87 sq cm, which is area of unshaded region
9 out of 87 is the probability of selecting a point in the shaded region, which simplifies to 3/29
Answer:
lol i see r o b l o x
Step-by-step explanation:
Rectangle = bxh
thats is 96
the we know that the square in the middle is 3x3x3x3 or 81
then subtract the two which is 15
there are 60 minutes in a hour.how many minutes are there in 24 hours
There are 1440 minutes in 1 hour
Step-by-step explanation:
Since there are 60 minutes in 1 hour multiply 60 by 24, you get 1440.
How many fluid ounces are in 4 quarts?
A. 16 fl. oz
B. 32 fl. oz
C. 64 fl. oz
D. 128 fl. oz
Answer:
D: 128 fl. oz
Step-by-step explanation:
1 quart is 32, to multiply by 4. :D
Answer:
hi your ans is d hope it helps please give brainliest
Step-by-step explanation:
Can y’all please help me out?
Answer:
19.5 degrees
Step-by-step explanation:
180 - (33.5 + 127) =
180 - 160.5 =
19.5
Hope that helps!
what's the domain and range
Please help me if you can 10 points if you help
Answer:
C) 0%
Step-by-step explanation:
Let’s give the square sides equaling 4. The area would equal 16.
Decreasing the top by 75% would make it 1. Increasing the bottom by 75% makes it 7.
(1+7)/2=4
The height is still four so 4x4=16
No change in area.
The sum of two numbers is 15 and their difference is 11.
What are the two numbers
Answer:
13 and 2
Step-by-step explanation:
x+y=15
x-y=11
2x=26
x=13
13+y=15
y=2
USE SYSTEMS OF EQUATIONS
HEY can You help me with this work pls i need help don't put random. if u don't know it pls guys.
1️⃣Remove parentheses
6a+6+3x-2+2a+4
2️⃣Collect like terms
(6a+2a)+(6-2+4)+3x
3️⃣Simplify
8a+8+3x
Answer: 8a+8+3x
QUESTION 21️⃣Remove parentheses.
-2z-3+4c+6y+y+3c
2️⃣Collect like terms.
-2z-3+(4c+3c)+(6y+y)
3️⃣Simplify
-2z-3+7c+7y
Answer: -2z-3+7c+7y
QUESTION 31️⃣Subtracting (7.8 - 5.1t) from (2.8 - 3.2t)
(2.8 - 3.2t) - (7.8 - 5.1t)
2️⃣Remove the parentheses.
2.8 - 3.2t - 7.8 + 5.1t
= 5.1t - 3.2t + 2.8 - 7.8 (we have now shown the difference in another way)
3️⃣Subtracting the like terms, will give:
1.9t - 5
4️⃣Recall
(2.8 - 3.2t) - (7.8 - 5.1t).
(-3.2t + 2.8) - (-5.1t + 7.8)
Answer:
a. (-3.2t + 2.8) - (-5.1t + 7.8)
b. 1.9t - 5
c. (-3.2t + 2.8) - (-5.1t + 7.8)
QUESTION 41️⃣Simplify
1/2p-(1/4p-4)
2️⃣Simplify
p2-(p/4-4)
3️⃣Simplify
p2-p/4+4
4️⃣Combine Terms
(p/2-p/4)+4
5️⃣Combine Terms
p/4+4
Answer: p/4+4
Done ✔
What divides a design so that every point on one side of the line coincides
with a point on the other side of it?
A. Equator of symmetry
B. Point of symmetry
C. Line of symmetry
D. Symmetrical half life
The design that every point on one side of the line coincides with a point on the other side of it is Line of symmetry
What is Symmetry?Symmetry in mathematics means that when one shape is moved, rotated, or flipped, it looks exactly like the other shape.
A circle or band that divides a body's surface into two typically equal and symmetrical portions.
When a shape or item has a central point, point symmetry occurs when all points on the opposing sides are at the same distance from the centre.
The term "line of symmetry" refers to the fictitious axis or line that can be used to fold a figure into symmetrical halves.
It denotes that one half is the other half's mirror image.
Thus, the required design is Line of Symmetry.
Learn more about Symmetry here:
https://brainly.com/question/15970176
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find the term to term rules for the following sequences. 28 25 22 19 16 .
Answer:
a) next one is previous one -3
b) next one is 3 times previous one