Answer:
The three options are;
1) If p = a number is negative and q = the additive inverse is positive, the original statement is p → q
2) If p = a number is negative and q = the additive inverse is positive, the original statement the inverse of the original statement is ~p → ~q
3) If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q
Step-by-step explanation:
Given a statement if p then q, we have, p → q. The converse of the original statement is then, if q, then p while the inverse of the original statement is then if not p then not q, and the contrapositive statement is then if not q then not p
Mathematically, we have;
The given conditional statement;
If a number is negative, the additive inverse is positive which can be expressed as follows;
The conditional statement is p → q
The converse statement is q → p
The inverse statement is ~p → ~q
The contrapositive statement is ~q → ~p
Therefore, we have;
1) The conditional statement, if p = a number is negative and q = the additive inverse is positive, the original statement which is a conditional statement is therefore p → q
2) If p = a number is negative and q = the additive inverse is positive, the original statement, which is a conditional statement is p → q, the inverse of the original conditional statement is therefore, ~p → ~q
3) If q = a number is negative and p = the additive inverse is positive, the original statement, which is a conditional statement is therefore, q → p, the contrapositive of the original conditional statement is therefore ~p → ~q.
The three options are;
1) If p = a number is negative and q = the additive inverse is positive, the original statement is p → q
2) If p = a number is negative and q = the additive inverse is positive, the original statement the inverse of the original statement is ~p → ~q
3) If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q
What is additive inverse?The additive inverse of any number is defined as when it is added to the number it gives zero as a result.
Given a statement if p then q, we have, p → q. The converse of the original statement is then, if q, then p while the inverse of the original statement is then if not p then not q, and the contrapositive statement is then if not q then not p
Mathematically, we have;
The given conditional statement;
If a number is negative, the additive inverse is positive which can be expressed as follows;
The conditional statement is p → q
The converse statement is q → p
The inverse statement is ~p → ~q
The contrapositive statement is ~q → ~p
Therefore, we have;
1) In The conditional statement, if p = a number is negative and q = the additive inverse is positive, the original statement which is a conditional statement is, therefore, p → q
2) If p = a number is negative and q = the additive inverse is positive, the original statement, which is a conditional statement is p → q, the inverse of the original conditional statement is, therefore, ~p → ~q
3) If q = a number is negative and p = the additive inverse is positive, the original statement, which is a conditional statement is, therefore, q → p, the contrapositive of the original conditional statement is, therefore, ~p → ~q
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Find the value of x that makes m
m
n
(2x + 20)
(32°
Answer: x= 20
Step-by-step explanation:
If m and n are parallel then the 3x and 2x+20 has to have the same measures which means they have to equal each other . So set them equal each other and solve for x.
2x + 20 = 3x
-2x -2x
20 = 1x
x= 20
INTERPRETING EXPRESSIONS:
ln the expression 9x - 9, the variable is ___
What is the mean of 25, 27, 32, 29, 42?
Step-by-step explanation:
To find the mean, or average, you add all of the numbers and divide the sum by how many there are.
In this case, you add 25,27,32,29, and 42 and then divide the sum by 5.
25+27=52+32=84+29=113+42=155.
Then divide.
155/5=31.
hope it helps!
determine which of the following pairs of triangles are similar.
Triangles given in Options (b) and (c) are similar.
Theorems of similar triangles: If two angles of a pair of triangles are equal in measure, then the triangles will be similar by A-A property. If corresponding sides of two triangles are proportional, both the triangles will be similar.
From the picture attached,
a). In triangle ABC,
∠A + ∠B + ∠C = 180° [By triangle sum theorem]
60° + ∠B + 40° = 180°
∠B = 80°
Similarly, in ΔDEF,
∠D + ∠E + ∠F = 180°
60° + 85° + ∠F = 180°
∠F = 35°
Since, measure of angles of both the triangles are different in measures, triangles will not be similar.
b). In ΔABC,
∠A + ∠B + ∠C = 180°
45° + 50° + ∠B = 180°
∠B = 85°
In ΔDEF,
∠D + ∠E + ∠F = 180°
50° + 85° + ∠F = 180°
∠F = 45°
Hence, ∠C ≅ ∠D, ∠A≅ ∠F and ∠B ≅ ∠E
Since, measure of corresponding angles are equal, both the
triangles (ΔABC ~ ΔFED) will be similar.
c). Here, corresponding sides of both the triangles are proportional,
[tex]\frac{AB}{DE}= \frac{CA}{FD}= \frac{BC}{EF}[/tex]
[tex]\frac{14}{7}= \frac{12}{6}= \frac{16}{8}[/tex]
[tex]\frac{2}{1}= \frac{2}{1}= \frac{2}{1}[/tex]
Both the triangles ΔABC and ΔDEF will be similar.
Therefore, Option B and Option C are the correct options.
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simplify the expression -4(x - 5)
Answer:
-4x+20
Step-by-step explanation:
[tex]-4(x - 5)\\\\=-4x-4(-5)\\\\=-4x+20[/tex]
Can anyone help me with this
Answer:
2700[tex]ft^{3}[/tex]
Step-by-step explanation:
First you find the volume of the bigger cuboid:
Volume= Length * width * height
Volume= 22 * 10 * 11
Volume= 2420[tex]ft^{3}[/tex]
Then the volume of the smaller cuboid:
Volume= Length * width * height
Volume= 7 * 10 * 4
Volume= 280[tex]ft^{3}[/tex]
Then add the volumes of the two shapes:
2420 + 280= 2700[tex]ft^{3}[/tex]
HOPE THIS HELPED
what number is 10 times less than 20?
Answer:
180
Mathematically, 10 times less than 20 would be: Take 20, subtract (10 x 20). Answer: -180.
Help please!!! Thank you!
Choose the equation that represents this situation. Use t to represent the
number of tickets sold, and use m to represent the total money raised.
The junior class sells tickets to a talent show to raise money. Each ticket sells
for $8. How much money do they raise?
A.m=t divided by 8
B.m=8+t
C.m=8t
D.t=8m
Answer:
m=8t
Step-by-step explanation:
money raised will equal 8 dollars per ticket sold
QR has endpoints at Q(2,6) and R(0,2). Find the midpoint M of QR
Answer:
Step-by-step explanation:
Well, the midpoint formula is M=((x↓1 +x↓2)/2,(y↓1 +y↓2)/2 ). (not exponents, they tell you which x or y value).
If you plug in your 2 points, it becomes m=((2+0)/2,(6+2)/2).
When you add, it is m=(2/2, 8/2)
When simplified, it is m=(1,4)
BINGO
7 26 35 51 73
14 23 44 5563
6 19 FREE 48 64
12 22 32 54 70
11 16 33 47 69
What output corresponds with 12?
Answer:
23
Step-by-step explanation:
The United States Tennis Association is researching the effect of what color the professional tennis players wear and
the number of foot faults called on them in one match. They collect data from every televised event of the year, noting
the color of the player's clothes and how many foot faults were called on the player. Which is this an example of?
-experiment
-simple random sample
-observational study
-convenience sample
Answer:
the answer is observation study
Step-by-step explanation:
show that (x+1)(x+3)(x+5) can be written in the form ax^3 + bx^2 + cx+ d where a,b,c and d are all positive integers.
Answer:
x³ + 9x² + 23x + 15
Step-by-step explanation:
Given
(x + 1)(x + 3)(x + 5) ← expand the first pair of factors using FOIL
= (x² + 4x + 3)(x + 5)
Each of the terms in the second factor is multiplied by each of the terms in the first factor, that is
x²(x + 5) + 4x(x + 5) + 3(x + 5) ← distribute the 3 parenthesis
= x³ + 5x² + 4x² + 20x + 3x + 15 ← collect like terms
= x³ + 9x² + 23x + 15 ← in the form ax³ + bx² + cx + d
Twice the sum of a number and 3 is equal to three times the difference of the number and 7. Find the number
Answer:
The number is 27
Step-by-step explanation:
Let us change the word statement to an algebraic equation
→ Assume that the number is x
→ Twice the sum of a number and 3, means add x by 3, then multiply the sum by 2
→ The algebraic expression is 2(x + 3)
→ Three times the difference of the number and 7, means subtract x and 7, then multiply the difference by 3
→ The algebraic expression is 3(x - 7)
→ Equate the two expressions
∴ 2(x + 3) = 3(x - 7)
→ Simplify each side
∵ 2(x + 3) = 2(x) + 2(3) = 2x + 6
∵ 3(x - 7) = 3(x) - 3(7) = 3x - 21
∴ 2x + 6 = 3x - 21
Let us solve the equation to find x
→ Subtract 6 from both sides
∴ 2x + 6 - 6 = 3x -21 - 6
∴ 2x = 3x - 21
→ Subtract 3x from both sides
∴ 2x - 3x = 3x - 3x - 27
∴ -x = -27
→ Divide both sides by -1
∴ x = 27
The number is 27
what is the inverse of f={(1,3),(4,2),(5,1)}
Answer:
f={(3,1),(2,4),(1,5)}
Iola has $75. She buys a pair of shoes on sale for one-half off and a pair of socks for $6. She has $32 left. Which equation can be used to find x, the regular price of the shoes?
Answer:
To solve for the problem above, let x be the regular price of the shoe.
1/2x is the one-half price of the shoe then we add 6 for the pair of socks,
1/2x + 6, then lola has 32 left so we add that too, 1/2x + 6 + 32 = 75. The total amount of lola spent is 75 - 32, which is 1/2x + 6.
Step-by-step explanation:
HELP ME PLEASE i need this right now
Answer:
jimragarant 1
Step-by-step explanation:
pls can u help me with the questions i have posted i will give u anything u want
pls help its urgent
Answer:
108.8 yd²
Step-by-step explanation:
The area (A) of the triangle can be calculated as
A = [tex]\frac{1}{2}[/tex] absinC
where a, b are 2 sides and C the angle between them
Here a = 23, b = 9.5 and C = 85° , thus
A = 0.5 × 23 × 9.5 × sin85° ≈ 108.8 yd² ( to the nearest tenth )
6x+2y=12 how do I show my work solve for y :) please help me
Answer:
x=2
Step-by-step explanation:
6x+2y=12
6x+2x0=12
6x+0=12
6x=12
x=2
3m - 12 =18
Step by step
Answer:
3m=18+12
3m=30
divide both sides by 3
m=10
Answer:
m = 10
Step-by-step explanation:
3m - 12 =18
Add 12 to each side
3m - 12+12 =18+12
3m = 30
Divide by 3
3m/3 = 30/3
m = 10
PLEASE HELP ASAP!!!!!
Answer:
D
Step-by-step explanation:
Compare the process of solving
|x - 1 + 1 < 15 to that of solving
1x – 1| + 1 > 15.
Answer:
x-1+1<15; this gonna be x<15 and 1x-1+1>15 this is gonna be the same
Step-by-step explanation:
Solve using the order of Operations:
- 5- (- 4 + 2)2
O -1
0-9
O 9
O 1
Math
Hey there! I'm happy to help!
Order of operations is PEMDAS. Parentheses comes first.
(-4+2)=-2
So, now we have -5-(-2)2
The next available option is multiplication.
-5-(-4)
Now we do addition and subtraction.
-5+4
-1.
Have a wonderful day! :D
HELP ME ASAP WILL GIVE 5 STARS AND A THANKS
Answer:
The mayor will lose by a large percentage.
Answer:
D??
Step-by-step explanation:
It may be D or A I’m not sure!!
52 regular playing cards are randomly dealt to four players with each players receiving 13 cards. What is the probability that each player will have exactly one ace
Answer:
The probability is 1/28,561
Step-by-step explanation:
Here, we want to find the probability that each of the players will receive exactly one ace.
In a deck of cards, we have 4 suites of 13 cards each, with each of the suites consisting of 1 ace.
So, the probability of getting an ace for each of the four players will be 4/52 = 1/13
Now, the probability of each of the players getting exactly one ace will be; first got one ace , second got one , third got one and fourth got one.
mathematically, this probability will be 1/13 * 1/13 * 1/13 * 1/13 = (1/13)^4 = 1/28,561
What is the slope of a line passing through points (-7,5) and (5,-3)?
Answer:
- 2/3
Step-by-step explanation:
A colored chip is yellow on one side and red on the other. The chip was flipped 50 times and landed on the yellow side 29 times. what is the relative frequency of the chip landing with the yellow side facing up?
38%
42%
56%
58%
Answer:
58 %
Step-by-step explanation:
A file that is 242 megabytes is being downloaded. If the download is 17.1% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Answer:
4.1 megabytes
Step-by-step explanation:
well we use the rule of three
242 megabytes ------- 100%
x megabytes -------- 17.1%
(x megabytes)(100%)=(242 megabytes)(17.1%)
[tex]x=\frac{242*17.1}{100} \\\\x=\frac{4138.2}{100} \\\\x=4.1382\\\\x=4.1[/tex]
so there have been downloaded 4.1 megabytes
2.)Solve for Y
3.)Solve for G
5.)Solve for B
6.)Solve for D
Answer:
See below
Step-by-step explanation:
2) x =5y Solve for y
Divide both sides by y
x/5 = y
3) f/g = h Solve for G
Multiply both sides by g
(g/1) f/g =h(g)
f =hg
Divide by h
f/h = g
5) bf = m Solve for b
divide both sides by f
bf/f = m/f
b = m/f
6) 8 = b/d solve for d
Multiply both sides by d
8 ( d) = b
Divide by 8
d = b/8
When 19,346 is divided by a number,the quotient is 841 and the remainder is 3.What is the number?
Answer
Hi mate,
Divided=divisor*quotient+remainder
19346=x*841+3
19346-3=841x
19343/841=x
x=23
Hope this helps u
Mark me as brainliest
Step-by-step explanation:
4(n+9)-3(2+n)
Help now plz
Answer:
n + 30
Step-by-step explanation:
[tex]4(n+9)-3(2+n)\\\\\mathrm{Expand}\:4\left(n+9\right):\quad 4n+36\\=4n+36-3\left(2+n\right)\\\\\mathrm{Expand}\:-3\left(2+n\right):\quad -6-3n\\=4n+36-6-3n\\\\\mathrm{Simplify}\:4n+36-6-3n:\\\quad n+30[/tex]
Answer:
4n + 36 - 6 -3n
n + 30
Step-by-step explanation:
Work out 5
5-² x 3√8
Give your answer as a decimal.
Answer:
I got -11.97056 as the answer