Prove that the sum of the squares of two consecutive integers is odd
Answer:
Step-by-step explanation:
Start by breaking up the question into parts:'always an odd number' . An even number is any number divisible 2 e.g. 2n, an odd number is always 1 higher or lower than an even number e.g. 2n+1 or something similar. Getting an answer at the end of working of this form will prove the theory'any two consecutive integers' means two numbers that are next to each other on the number line.To prove this, we can do this in terms of n i.e. n and n+1'the squares' square the two terms we have just written down to give n2 and (n+1)2The 'sum of the squares' tells us to add these two parts together. We would then hope to work through this and get something similar to the idea of 2n+1 or something similarn2+(n+1)2=2n2+2n+1=2(n2+n) +1. The first part of this is even because it is divisible by 2. By adding 1 it must become odd.
Answer: Every even number can be expressed in the form (2n) where n is an integer. So we have an even number, 2n, and an odd number, 2m+r. Adding them together we get 2n + 2m + r, which can be expressed as 2 (n+m) + r.
Someone please help me out here
Answer:
Click the 'x' on the top of the tab
Step-by-step explanation:
Move your coursor to the 'x' and click.
Can someone help me solve this Y=5/2x-1
Answer:
m= 5/2
Step-by-step explanation:
Please help me it’s 7th grade regular math :)
Answer: 11 roses
11.75 + 3.50r = 52
r =
Step-by-step explanation:
11.75 + 3.50r = 52
- 11.75 -11.75
3.50r = 40.25
÷3.50 ÷3.50
r= 11.5
We round down to 11 since you cannot buy half of a rose.
Jackie has a recipe for banana bread. She uses 4 1/2 cups of flour to make 3 loaves of banana bread. Andre will follow the same recipe. He will make b loaves of banana bread using f cups of flour. Which of these equations represents the relationship between b and f? HELP
b=9/2f
b=3/2f
b=2/3f
b=2/9f
Answer:
b
Step-by-step explanation:
Write an
explicit formula for an, the nth term of the sequence 5, 15, 25, ....
Given:
The sequence is 5, 15, 25, ... .
To find:
The explicit formula for the nth term of the given sequence.
Solution:
We have,
5, 15, 25, ...
It is an AP because the difference between two consecutive terms are same.
Here,
First term : a = 5
Common difference : d = 15 - 5 = 10
Now, the explicit formula for the nth term of an AP is
[tex]a_n=a+(n-1)d[/tex]
Where, a is the first term and d is the common difference.
[tex]a_n=5+(n-1)10[/tex]
[tex]a_n=5+10n-10[/tex]
[tex]a_n=10n-5[/tex]
Therefore, the required explicit formula for the given sequence is [tex]a_n=10n-5[/tex].
Bananas sell for $0.98 per pound. How much will 4 pounds of bananas cost?
Answer:
$ 3.92
Step-by-step explanation:
help me fast smart people please haha lol
Answer:
1280 cubic
Step-by-step explanation:
length x width x height
Answer:
B
Step-by-step explanation: Volume=lwh
10*8*16=1280
Answer: B
Investors buy a studio apartment for $200,000 of this amount they have a down payment of $40,000 Their down payment is what percent of the purchase price? what percent of the purchase price would a $10,000 down payment be?
Answer:
20%
Step-by-step explanation:
HELP ASAP!!
-4y + 7 + 9y - 3
Answer:
5y+4
Step-by-step explanation:
Combine Like Terms:
=−4y+7+9y+−3
=(−4y+9y)+(7+−3)
=5y+4
Answer:
5y + 4
Step-by-step explanation:
-4y + 7 + 9y - 3
5y + 7 - 3
5y + 4
The bookstore has 4 women's magazines and 76 other magazines. What percentage of the magazines at the bookstore are women's magazines?
This question is dealing with fractions and percentages.
Fractions and percentages are just means of expressing a part of a whole portion.
percentage of magazines that belong to women is = 5%
Number of women magazines = 4
Number of other magazines = 76
Total number of magazines = 4 + 76 = 80
Therefore,
percentage of magazines that belong to women is; [tex]\frac{4}{80}[/tex] × 100
percentage of magazines that belong to women is = 5%
Read more at; brainly.com/question/13104179
6. If F(x) = -6(2x2 + 5x) - 9, what is the value of F(-4)?
Answer:
-81
Step-by-step explanation:
-6(2x² + 5x) - 9
substitute -4 for 'x'
-6[2(-4)² + 5(-4)] - 9
-6[2(16) + (-20) - 9]
-6(32 - 20) - 9
-6(12) - 9
-72 - 9 = -81
The graph shows the number of each type of sticker in a box.
Stickers
30
25
20
Number in Box
15
JU
10
5
0
bear
cat
frog
rabbit
dinosaur
Type
How many fewer frog stickers are there than cat stickers?
O A 10
O c. 2o
D. 25
B. 15
Answer:b?
Step-by-step explanation:
A rectangular parking lot is surrounded on its perimeter by a fence that is 1200 feet long. if the length of a rectangular parking lot is 5 times it’s width which equation can be used to find the width of the parking lot
Answer:
fah)',55%9+*_)64•%π\¥)--_f
Answer:
2w+2(w+5)=1200
Step-by-step explanation:
what did you do today? 3 things
Answer:
eat sleep play
Step-by-step explanation:
what is an equation of the line that passes through (0,8) and (4.0)?
A y= 2x+8
B y= 2x+4
C y=-2x+4
D y=-2 x+8
Answer:
Step-by-step explanation:
What is the area?
4 m
7 m
8 m
Answer:
224
Step-by-step explanation:
Multiply all the numbers
PLEASE HURRY WILL GIVE BRAINLIST
Answer:
87
Step-by-step explanation:
1.The electrical current, in amperes, in a circuit varies directly as the voltage.When 15 volts are applied, the current is amperes. what is the current when 18 volts are applied?
Step by Step Explanation:
R=V/I
R=12/4=3
so i =V/R
i=18/3
i=6 ans.
please answer fast im in a hurry and im panicking. (5×1,000)+(9×1)+(2×1/10)+(6×1/1,000).
please write it in decimal form. thank you
Answer:
5.1
Step-by-step explanation:
Answer:
54
Step-by-step explanation:
Don't Panic! pls mark brainliest
Can someone help me understand where the positive 2 came from?
Answer:
4(-2)-(0)-2(-1)
a negative number multiplied by a negative number will always equal a positive number as the two negatives cancel each other out.
-2 multiplied by -1 equals positive 2
this is why the 2 is positive.
PLEASE HELP?
let g be the function given by g (x) = 3x^4 - 8x^3. At what value of x on the closed interval [ -2,2 ] does g have an absolute maximum
Answer:
When we have a function g(x)
We will have a maximum at x when:
g'(x) = 0
g''(x) < 0.
Now we start with:
g(x) = 3*x^4 - 8*x^3
The first derivation is:
g'(x) = 4*3*x^3 - 3*8*x^2
g'(x) = 12*x^3 - 24*x^2
We can rewrite this as:
g'(x) = x^2*(12*x - 24)
Now we want to solve:
g'(x) = 0 = x^2*(12*x - 24)
We have one trivial solution, that is when x = 0.
The other solution will be when the term inside of the parentheses is equal to zero.
Then we need to solve:
12*x - 24 = 0
12*x = 24
x = 24/12 = 2
Then g'(x) is equal to zero for x = 0, and x = 2.
Notice that both of these points are included in the interval [ -2,2 ]
Now we need to look at the second derivative of g(x):
g''(x) = 3*12*x^2 - 2*24*x
g''(x) = 36*x^2 - 48*x
Ok, now we need to evaluate this in the two roots we found before:
if x = 0:
g''(0) = 36*0^2 - 48*0 = 0
g''(0) = 0
Then we do not have a maximum at x = 0, this is a point of inflection.
if x = 2:
g''(2) = 36*(2^2) - 48*2 = 48
then:
g''(2) > 0
This is an absolute minimum.
Now let's look only at the interval [ -2,2 ]
We know that:
g''(0) = 0
g''(2) > 0
Then at some point, we should have g''(x) < 0 in our interval.
We need to find the first point such that happens, so let's try with the lower limit of the interval but with the first derivation, if g'(x) < 0, this means that the function is decreasing from that point on, then that point will be a maximum in our interval.
x = -2
g'(-2) = (-2)^2*(12*-2 - 24) = -192
And if we look at the function:
g'(x) = x^2*(12*x - 24)
We can easily see that it is negative unitl x = 0, and then it keeps being negative until x = 2.
So in the interval [ -2,2 ], the function g'(x) is always negative or zero, this means that in the interval [ -2,2 ], the function g(x) is always decreasing or constant.
Then the absolute maximum of g(x) in the interval [ -2,2 ] will be x = -2
this means that:
g(-2) ≥ g(x) for all x ∈ [ -2,2 ]
Can someone help me with this question please
what is the volume of a cylinder if the radius is 3.2 centimeters and the height is 5 centimeters
Answer:
V ≈ 160.85 cm³ ≈ 0,161 lStep-by-step explanation:
Volume of cylinder: V = π×r² × h
r = 3.2 cm
h = 5 cm
Volume:
V = π×(3.2)²×5 = 51.2π cm³ = 160.8495.... cm³ ≈ 160.85 cm³
Val says there are at least 13, but less than 50, students on the bus. Write an
inequality to represent the situation. Use s to represent the number of
students on the bus.
Pls help
Solve for j 8 - 4j = -8j
Answer:
J = -2
Step-by-step explanation:
You must isolate the variable by dividing each side by factors that dont contain the variable.
So J would equal -2
What is the equation, in slope-intercept form, of the line parallel to -5x + y = 2 that passes through the point with coordinates (-2, 1)?
Answer:
y = 5x + 11
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
- 5x + y = 2 ( add 5x to both sides )
y = 5x + 2 ← in slope- intercept form
with slope m = 5
Parallel lines have equal slopes, then
y = 5x + c ← is the partial equation
To find c substitute (- 2, 1) into the partial equation
1 = - 10 + c ⇒ c = 1 + 10 = 11
y = 5x + 11 ← equation of parallel line
A crew has paved 3/4 of a mile of road. If they have completed 50% of the work, how long is the road they are paving?
1 1/2 miles
15/20 miles
3 miles
What is the graph of the function f(x) = the quantity of x squared minus 7 x plus 12, all over x minus 3? (1 point)
Answer:
Step-by-step explanation:
Hyhh
SMART PPL HELP LOL PLEASE