In both the cases when n is even and when n is odd, the expression is odd, we can conclude that if n ∈ Z, then [tex]5n^2 + 3n + 7[/tex]is odd.
To prove the proposition "if n ∈ Z, then[tex]5n^2 + 3n + 7[/tex]is odd" using a direct proof with cases, we consider two cases: when n is even and when n is odd.
Case 1: n is even.
Assume n = 2k, where k ∈ Z. Substituting this into the expression, we have [tex]5(2k)^2 + 3(2k) + 7 = 20k^2 + 6k + 7[/tex]. Notice that [tex]20k^2[/tex] and 6k are both even since they can be factored by 2. Adding an odd number (7) to an even number results in an odd number. Hence, the expression is odd when n is even.
Case 2: n is odd.
Assume n = 2k + 1, where k ∈ Z. Substituting this into the expression, we have [tex]5(2k + 1)^2 + 3(2k + 1) + 7 = 20k^2 + 16k + 15[/tex]. Again, notice that [tex]20k^2[/tex]and 16k are even. Adding an odd number (15) to an even number results in an odd number. Therefore, the expression is odd when n is odd.
Since we have covered all possible cases and in each case, the expression is odd, we can conclude that if n ∈ Z, then 5n^2 + 3n + 7 is odd.
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Find the volume of the figure.
10 cm
8 cm
10 cm
14 cm
10 cm
8 cm
cubic centimeters
Answer:
60 cm³
Step-by-step explanation:
Step-by-step explanation:
=896000 is the answer
method -10x8x10x14x10x8
️️
2
What is the system by which we can convert between
metric and customary units?
A None; it's different for every unit
B A base-6 algorithm
C A base-10 system
D A mix between multiplication and division
Answer:
i think that it's A.
Step-by-step explanation:
Metric units are the standard units of measurement while customary units are derived from the metric units. To convert between both units, you need a mix between multiplication and division.
Take distance as an instance.
The metric unit of distance is meters.
The customary units are: feet, inches, yards, miles, etc.
To convert from meters to feet, we multiply by 3.281
For instance:
[tex]2\ meters = 2 \times 3.281\ feet[/tex]
[tex]2\ meters = 6.562\ feet[/tex]
To convert from feet to meter, we divide by 3.281.
For instance:
[tex]6.562\ feet = \frac{6.562}{3.281}\ meters[/tex]
[tex]6.562\ feet = 2\ meters[/tex]
Hence, option (d) is true
Read more about metric and customary units at:
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Hi! PLS HELP ITS 30 POINTS!! Thanks!
A soda bottle holds 1.5 liters of soda. How many milliliters does the bottle hold?
15 millimeters
150 millimeters
1,500 millimeters
15,000 millimeters
Pls help!
Imma report u if its something off the topic!
Thanks again!
(its not b i tried it and got it wrong!! )
Answer:
1,500 millimeters
Step-by-step explanation:
1 litre = 1000 millilitre.
Try 1,500.
E = MV^2 ÷ 2 + mgh, Make V Subject of the formula
Answer:
[tex] \red{ \bold{ V = \sqrt{\frac{2(E - mgh)}{M}}}}[/tex]
Step-by-step explanation:
[tex]E = MV^2 ÷ 2 + mgh \\ \\ E - mgh = MV^2 ÷ 2 \\ \\ 2(E - mgh)= MV^2 \\ \\ \frac{2(E - mgh)}{M}=V^2 \\ \\ \sqrt{\frac{2(E - mgh)}{M}} = V \\ \\ \red{ \bold{ V = \sqrt{\frac{2(E - mgh)}{M}}}}[/tex]
If 95% of students are coming to school tomorrow, what is the complement?
Question 5 options:
A. 95%
B. 100%
C. 1%
D. 5%
Answer:
d
Step-by-step explanation:
can you help me with this question According to Frost in his poem "The Road Not Taken," what kind of difference did taking one road over another road make? A. It made a good difference, B. It made a bad diference, c. Frost does not say
Answer:
the answer is d
Step-by-step explanation:
it only takes 5% to get to 100%
pls help ty !
question is in the pic
Answer:
He is not correct
10.
Write a rule for the linear function in the graph.
A. y = 4/5x + 2
B. y = -5x - 2
C. y = 5/4x - 2
D. y = -4/5x + 2
Answer:
D. y = -4/5x + 2
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope:
−
4
5
y-intercept:
(
0
,
2
)
x
y
0
2
5
2
0
4. Six numbers are shown.
1.25, -1.5, -0.75,
34,
2 6/8,
5/4
Place each number in its correct location on the number line.
Step-by-step explanation:
sorry i couldn't solve the last and the last second one
Was it helpful?
comment down
If there is any kind of suspicious mistake
then sorry
heres a pic of my dog :) her name is tess
Answer:
She is so adorable
Step-by-step explanation:
Very adorable doggo
Answer:
She's adorable!! What type of dog is she?
Step-by-step explanation:
I have two rottweilers and I love them sooooo much <3
Smiths bike shop rents bikes for $10
plus $4 per hour. Anita paid $22 to
rent a bike. How many hours did
she rent the bike for? Write an
equation to represent this situation
and then solve.
Carlos got 5/6 of the test questions correct. This was 15 questions. How
many questions were on the test?
Answer:
5/6 is about a 84%, and 84% of 15 questions is 12.6. so the teacher just made the grading simplified
Step-by-step explanation:
Please help me 15 points it’s worth it please help me on this question
Answer:
last answer
Step-by-step explanation:
Due in 20 please help
The polygons are similar. Find the values of
the variables. Write an equation and solve,
showing ALL the work.
It tells you they are similar. This means the angles are the same, and the sides are proportionate.
Look at the 12 and 4 at the very bottom. This tells you the ratio of the sides. Since 12 / 4 = 3, you can find y with 2 * 3 which is 6.
From that, you also know that 3z = 3y - 2. Substitute the value of y in and you can find z.
Corresponding angles are exactly the same. which means, (3x)° = 100°
You should get x = 33 1/3, y = 6, z = 5 1/3
Christine has her own dog -walking business. She Charges her customers $20 per day to walk their day
Answer:
y= money made
x = amount of dogs walked
equation- y = 20x
for the table name # of dogs walked on the right and money earned on the left.
for the left put 1 2 3 4 5 6 7 and 8
1 goes with 20
2 goes with 40
3 with 60
4 with 80
5 with 100
6 with 120
7 with 140 and
8 with 160
Step-by-step explanation:
An account earns simple interest.
$600 at 5% for 2 years
a.Find the interest earned.
$___
b.Find the balance of the account.
$___
Please answer and give an explanation with your response. I will mark the correct and quickest answer BRAINLIEST!!!
Answer:
600×100/5×2=
6\10=3/5
Answer:
A is $60
B is $660
Step-by-step explanation:
For A, you move the decimal in 5% 2 over so it is 0.05. You then multiply 0.05 by 600, multiply that answer by 2, and you'll get $60.
Sorry I'm not sure how to do B, I looked up the answer to that one.
Well I need the help in this last question I will mark brain list if you got it right
Answer:
6x−11y+15
Step-by-step explanation:
Distribute the Negative Sign:
=5x−6y+7+−1(−x+5y−8)
=5x+−6y+7+−1(−x)+−1(5y)+(−1)(−8)
=5x+−6y+7+x+−5y+8
Combine Like Terms:
=5x+−6y+7+x+−5y+8
=(5x+x)+(−6y+−5y)+(7+8)
=6x+−11y+15
Answer:
6x−11y+15
I hope I helped!!
que volumen ocupará 600 g de agua?
Answer:
Step-by-step explanation:
600 ml
Triangles are similar Find the value of x.
Please help Thank you in advanced
Answer:
x=36
Step-by-step explanation:
14/42=12/x
14x=12(42)
14x=504
x=36
What is 631.051 as a fraction
sorry if that doesnt make sense.
Answer:
631 and 51/1000
Step-by-step explanation:
What is the scientific notation for .000472
Answer:
The scientific notation for 0.000472 is 4.72 * [tex]10^{-4}[/tex].
solve each system of eaquasions x+4y=4 -x+2y=8
Answer:
(-4, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsCoordinates (x, y)Solving systems of equations using systemsStep-by-step explanation:
Step 1: Define Systems
x + 4y = 4
-x + 2y = 8
Step 2: Rewrite Systems
x + 4y = 4
[Subtraction Property of Equality] Subtract 4y on both sides: x = 4 - 4yStep 3: Redefine Systems
x = 4 - 4y
-x + 2y = 8
Step 4: Solve for y
Substitution
Substitute in x: -(4 - 4y) + 2y = 8[Distributive Property] Distribute negative: -4 + 4y + 2y = 8Combine like terms: -4 + 6y = 8[Addition Property of Equality] Add 4 on both sides: 6y = 12[Division Property of Equality] Divide 6 on both sides: y = 2Step 5: Solve for x
Define original equation: x + 4y = 4Substitute in y: x + 4(2) = 4Multiply: x + 8 = 4[Subtraction Property of Equality] Subtract 8 on both sides: x = -4Which of these relations is a function?
X
y
9
10
-18
2
2
4
-12
2
20
3
y
17
19
-2
20
6
-10
X
1
-10
y
18
17
12
14
1
16
х
15
8
y
-8
5
17
0
-13
15
Answer:
I think the answer is 2 4
Step-by-step explanation:
Table {1} and table {2} represent the relations that are functions.
What is function? What is modulus function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
We can define the modulus function as -
|x| = - x {x < 0}
|x| = x {x > 0}
Given is to identify which of the relations are functions.
For a relation to be a function, it should have unique value of {y} for a unique value of {x}. One value of {x} cannot have more than one values at the same time. We can see in the image attached that only table 1 and 2 represent such relations. So, we can conclude that relation {1} and {2} represent the functions.
Therefore, table {1} and table {2} represent the relations that are functions.
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can someone please help me u can just do 5 and explain please
¿Puede alguien ayudarme? Puedes hacer 5 y explicar por favor.
Answer:
i only can explain until number 7
i am sorry
maybe that help you
Delia takes out a loan to buy a car for $18,000 with an interest rate of 6.5%. The amount of interest Delia will have to pay is $4,680. Write and solve an equation to determine the number of months her loan is for. Show all of your work and explain how you got your number of months.
Answer:
Delia pays $4,680 in 4 months
Step-by-step explanation:
Equation:
18,000 * 6.5% = 1170
4680 ÷ 4 = 1170
So, the answer is 4 months this is the equation.
Hope this helps! :)
How do you solve for x and y?
Answer:
x = 100, y = 50
Step-by-step explanation:
Make a system of equations:
First, you know that x + y degrees and 30 degrees are on a line together, they add up to 180 degrees:
x + y + 30 = 180
x + y = 150
Next, the interior angles of a triangle always add up to 180 degrees, and since 2y, x/2, and 30 are all the angles in a triangle, you have:
2y + x/2 + 30 = 180
x/2 + 2y = 150
Now, all you have to do is solve the system of equations.
To start, multiply the second equation by 2 to get rid of the fraction:
x + 4y = 300
Then, you can subtract the two equations:
x + 4y = 300
- (x + y = 150)
3y = 150
divide both sides by 3
y = 50
substitute y = 50 into the equation x + y = 150:
x + 50 = 150
x = 100
GIVING BRAINLIEST!!!
Answer:
i think its 78.5 but the answers not on there the closest one there to it is 76.5 so just put that one
Step-by-step explanation:
Can someone please tell me what is the solution
Answer:
[tex] \frac{1}{4} \tan {}^{4}(x) + c[/tex]
The altitude of an airplane is decreasing at a rate of 40 feet per second. What is the change in altitude of the airplane over a period of 20 seconds?
Answer:
Step-by-step explanation:
-40t
-40(20)
-800 ft
89+67
berapakah jawapan nya
Answer:
156
Step-by-step explanation
fgcfgvhvcfgvxxbbhhcx
Answer:
Jawapan kepada 89 + 67 = 156
Solve by elimination:
9x + 4y = 97
9x + 6y = 123
14
15'
B (5, 13)
(13,5)
D (1, 22)
Answer:
B (5, 13)
Step-by-step explanation:
9x + 4y = 97
9x + 6y = 123
To solve by elimination, we want to eliminate a variable. To do this, we must make one variable cancel out.
First, we can see that both equations have 9x. To cancel out x, we must make one of the 9x's negative. To do this, multiply each term in the equation by -1.
-1(9x + 6y = 123)
-9x - 6y = -123
This is one of your equations. Set it up with your other given equation.
9x + 4y = 97
-9x - 6y = -123
Imagine this is one equation. Since every term is negative, you will be subtracting each term.
9x + 4y = 97
-9x - 6y = -123
___________
0x -2y = -26
-2y = -26
To isolate y further, divide both sides by -2.
y = 13
Now, to find x, plug y back into one of the original equations.
9x + 4(13) = 97
Multiply.
9x + 52 = 97
Subtract.
9x = 45
Divide.
x = 5
Check your answer by plugging both variables into the equation you have not used yet.
-9(5) - 6(13) = -123
-45 - 78 = -123
-123 = -123
Your answer is correct!
(5, 13)
Hope this helps!