Part (1)
n is some positive integer. Let's say for now that n is even. So n = 2k, for some integer k
This means n-1 = 2k-1 is odd since subtracting 1 from an even number leads to an odd number.
Now multiply n with n-1 to get
n(n-1) = 2k(2k-1) = 2m
where m = k(2k-1) is an integer
The result 2m is even showing that n(n-1) is even
------------
Let's say that n is odd this time. That means n = 2k+1 for some integer k
And also n-1 = 2k+1-1 = 2k showing n-1 is even
Now multiply n and n-1
n(n-1) = (2k+1)(2k) = 2k(2k+1) = 2m
where m = k(2k+1) is an integer
We've shown that n(n-1) is even here as well.
------------
So overall, n(n-1) is even regardless if n is even or if n is odd.
Either n or n-1 will be even. If you multiply an even number with any number, the result will be even.
=======================================================
Part (2)
n is some positive integer
2n is always even since 2 is a factor of 2n
2n+1 is always odd because we're adding 1 to an even number. The sequence of integers goes even,odd,even,odd, etc and it does this forever.
-----------
Another way to see how 2n+1 is odd is to divide 2n+1 over 2 and you'll find that we get (2n+1)/2 = 2n/2+1/2 = n+0.5
The 0.5 at the end is not an integer, so there's no way that (2n+1)/2 is an integer; therefore 2n+1 is odd.
Gas costs $2.07 a gallon.
Write an equation to model
this math situation.
How much will it cost for 15 gallons?
a
y=15x; $31.05
b
x=2.07y; $7.24
c
y=2.07x; $31.05
d
y=15x; $7.24
Challenger Elementary School has 800 students. Every Wednesday, 12% of the students stay after school for Chess Club. How many students attend on Wednesday’s?
Answer:
96 students attend chess club after school on Wednesday's.
Step-by-step explanation:
To solve this problem, simply multiply 800 x 0.12.
800 x 0.12 = 96
I hope this was helpful to you! If it was, please consider rating, pressing thanks, and marking my answer Brainliest. It would help a lot. Have a great day!
Answer:
[tex]\huge\boxed{\text{96 students}}[/tex]
Step-by-step explanation:
In order to find how many students stay back for Chess Club, we want to find 12% of 800.
To do this, we can set up a percentage proportion.
[tex]\frac{12}{100} = \frac{x}{800}[/tex]
We can now solve for x by cross multiplying.
[tex]800 \cdot 12 = 9600\\9600 \div 100 = 96[/tex]
So, 96 students attend Chess Club on Wednesdays.
Hope this helped!
What is the 10th term in the sequence -3, -8, -13, ..
Answer:
-48
Step-by-step explanation:
The full sequence until the tenth term is...
-3, -8, -13, -18, -23, -28, -33, -38, -43, -48,
Answer:
-48
Step-by-step explanation: You don't really care about the explanation. You already got the answer. What are you still doing here, reading this?
Stan, Greg, and Seth were cleaning the school gym in shifts. Stan
cleaned first, then Greg, then Seth. If they each cleaned the same
amount of time for a total of 11 hours, how many minutes did each one
clean?
Find the third side in simplest radical form:
1&3
Answer:
[tex]\sqrt{10}[/tex]
Step-by-step explanation:
[tex]1^{2} + 3^{2} =x^{2} \\1+9=x^{2} \\10=x^{2} \\\sqrt{10} =x\\[/tex]
help its mathnnnnnnnnnnnnnnnnnnnnnnn
Answer:
1
Step-by-step explanation:
6 ÷ 2(1 + 2) ; use "please excuse my dear aunt sally", please for parenthesis
6 ÷ 2(3); now do "my" for multiplication
6 ÷ 6 ; now do "dear" for division
1
Help please i need help
Answer:
The answer is c=8
3/6=4c
3(c)=4(6)
3c=24
To find the c divide 3 both side
3c÷3=24÷3
c=8
hope that helps you
Please answer correctly !!!!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!
A+22°=90° (SUM OF COMPLEMENTRY ANGLES )
A=90°-22°
A=68° ANSWER.
The angles of a triangle are x,2x,3x. Find the value of x in degrees
Answer:
x=30°
Step-by-step explanation:
x +2x+3x=6x
since triangles are 180° in total. 6/180=30
so 30° is your answer.
On Saturday morning 350 concert tickets went on a sale. Every 5 min 25 tickets were sold. Determine whether the number the number of remaining tickets is proportional to time in minutes.
Answer:
the number of tickets remaining is inversely proportional to the time in minutes:
number of tickets remaining = total amount of tickets - (25 tickets sold per minute x time in minutes) = 350 - 25T
Step-by-step explanation:
for example:
after 5 minutes, the number of tickets remaining = 350 - (25 x 5) = 225 tickets
after 10 minutes, the number of tickets remaining = 350 - (25 x 10) = 100 tickets
after 14 minutes, the number of tickets remaining = 350 - (25 x 145) = 0 tickets
please help me with this
Answer: C is no and the others are yes.
Step-by-step explanation:
George had $127 in his checking account on Thursday. He got paid on Friday and deposited $130.00 into his checking account. Then on Saturday, he wrote two checks: one for $167.00 and one for $42.00. What is his checking account balance after writing the checks
Answer:
The balance on George's checking account is $48.
Step-by-step explanation:
To find the balance on George's checking account after writing the checks, you have to take the initial balance and add the amount he got paid and subtract the amounts of the checks he wrote:
Checking account balance=$127+$130-$167-$42
Checking account balance=$48
According to this, the answer is that the balance on George's checking account is $48.
Alexa took a test and lost 3 points for each of the 7 questions she got wrong. She earned an additional 5 points for answering a bonus question correctly. How many points did Alexa receive or lose overall?
Answer:
Alexa lost 16 points overall
Step-by-step explanation:
To determine whether Alexa had a net receipt or loss of points, we will fine the total points received or lost, and find the difference:
points lost:
3 point for each of the 7 questions she answered wrong
lost point = 3 × 7 - 21 points
Points received:
5 points for answering a bonus question
point received = 5 point
The points lost (21) is greater than the points received (5), hence, there was a net loss. The net loss is calculated as follows:
points lost - points received
= 21 - 5 = 16
∴ Alexa lost 16 points overall
PLEASE HELP ME AND EXPLAIN.
Answer:
9*8=72 which would be more than enough to cover the wall
A serving of bagel chips contains 20 grams of carbohydrates, 3 grams of fat, and 3 grams of protein. How many calories would be in the serving of chips?
1 gram of protein= 4 calories, 1 gram of carbs= 4 calories, 1 gram of fat= 9 calories.
Answer:
119 calories in a serving
Step-by-step explanation:
>>1 gram of carbs=4 cal
20 g of carbs times 4 calories per gram of carbs= 80 calories
>>1 gram of fat=9 calories
3 g of fat times 9 calories per gram of fat= 27 calories
>>1 gram of protein=4 calories
3 g of protein times 4 calories per gram of protein= 12 calories
<80+27+12=119 calories total in a serving of chips>
can someone please answer the 2 questions in the photo, please let me know if you can or cannot see them.
Answer:
I have the same one! this isnt an answer but like i need help too-
Step-by-step explanation:
Find the zero of the function.
f(x) = 4x2 – 12x + 9
The zero of the function is x=
Answer:
x= 3/2
Step-by-step explanation:
I apologize if it is wrong!
I NEED HELP QUICK (20 points.)
"Here's a graph of linear function. Write the equation that describes that function. Express it in slope-intercept form."
Answer:
y = 1/2x - 6
Hope I helped!!!
Slope intercept form is:
y = mx + b
m is the slope
b is the x intercept
Which of the following is the graph of y==(x-2) 0 - 5?
12
1
2
3
4
15
X
-
3
4
5
-6
-7
-8
-9
-10
-5 -4 -3 -2 -1
1
2.
3
4
5
Which equation represents a line which is parallel to y=0
A) x= -5
B) y= -8
C) y= x
D) y= x+2
Jiro and Joey share a 30-ounce box of cereal. By the end of the week, Jiro has eaten 3/10 of the box, and Joey has eaten 3/5 of the box of cereal. How many ounces are left in the box?
Answer:
6 ounce of cerealStep-by-step explanation:
Step one:
given that the box is 30 ounce of cereal.
for Jiro----who ate 3/10 of the 30 ounce
=3/10*30
=9 ounce
Jiro ate 9 ounce
step two:
for Joey----who ate 5/10 of the 30 ounce
=5/10*30
=15 ounce
Joey ate 15ounce
the total ounces that both of them ate is
=9+15
=24
therefore the ounce left
=30-24
=6 ounce of cereal
The left over is 6 ounce of cereal
A car travels at a constant speed, as shown on the double number line. Double number line. Time, hours. Distance, kilometers. How far does the car travel in 14 hours? Explain or show your reasoning.
Answer:
980 km.
Step-by-step explanation:
The speed of the car is constant,
From the double number line:
When the time is 0 hour, the distance covered is 0 km.
When the time is 1 hour, the distance covered is 70 km.
When the time is 2 hours, the distance covered is 140 km,
which can be written as
when the time is 2 hours, the distance covered is 70 x 2 km.
Similarly,
When the time is 3 hours, the distance covered is 210= 70 x 3 km.
This can be generalized as,
When the time is n hours, the distance covered is 70 x n km, i.e
The distance traveled in n hours = 70 x n km.
So, for 14 hours, n= 14,
Hence, the distance traveled in 14 hours = 70 x 14= 980 km.
PLEASE help find measure of angle - TEst review today
Answer:
both measured would be 25 and 19
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
if x equals 4 then 21x+4 equals 88 and 23x-4 equals 88 too.
Make & the subject of the
Formula
6x ta=5(x+t)
What is the answer please
Answer:
x = 5t - a
Step-by-step explanation:
The problem deals with making a variable the subject of the formula in the expression.
Given expression:
6x + a = 5(x + t)
We are to make x the subject of the formula in the expression
Solution:
6x + a = 5(x+t)
On the right hand side, expand the parentheses and distribute the term outside;
6x + a = 5x + 5t
Bring the term desired to be the subject to one side by adding (-5x) to both sides;
6x + (-5x) + a = 5x + (-5x) + 5t
x + a = 5t
Now add (-a) to both sides
x + a + (-a) = 5t + (-a)
x = 5t - a
Select all that apply.
40 is what percent of 25. Hint: There are 2 correct answers.
А160%
B 62.5%
C 1600%
D625/1000
E 160/100
F1600/100
Answer:
B and D
Step-by-step explanation:
Hope this helps :3
if it did pls mark brainliest
Answer:
A & E
Step-by-step explanation:
First, multiply 40 by 100, giving you 4000. You then divide 4000 by 25, where you will get a quotient of 160. Now, this can be represented as 160% or 160/100 because a percentage is always out of 100.
use the line tool and select two points to graph the line
graph f (x) = - 1.5x +6
PLEASE HELP !!!
Answer:
Step-by-step explanation:
Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.
Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.
Let x = the number of packages of pasta and y = the number of jars of pasta sauce.
One package of pasta is the right amount to go with one jar of pasta sauce. What is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry?
How many packages of pasta?
How many jars of pasta sauce?
Explain your reasoning.
Answer:
8 packages of pasta and 8 jar of sauce which is $32 dollars and 20lbs in total
Step-by-step explanation:
8 pack of pasta is 8$ and 8lbs
8 jars of sauce is 24$ and 12lbs
8 plus 12 is 20 which is the max of lbs Tyler can carry.
Find 0.038 as a fraction in its lowest terms
Answer:
19 / 500
Pls mark as brainliest!!!
Answer:
19/5
Step-by-step explanation:
If you're using a scientific calculator you will be able to find this answer by just simply pressing 0.038 x 100 divided by 1
PLEASE HELP ME 16 POINTS PLEASE HELP
Answer:
the y-intercept is 0
Step-by-step explanation:
it goes straight through the origin
Solve for s.
4s + 6s - 4 = 6
Answer:
s = 1
Step-by-step explanation:
4s + 6s - 4 = 6
10s - 4 = 6
+ 4 +4
10s = 10
10s/10=
s = 1
Hope this helps! If you have any additional questions please don't hesitate to ask me or your teacher to be sure you master the subject. :) Stay safe and please mark brainliest!