Answers
The sum of the algebraic expressions, (1/2)·n·(n + 1) and (1/2)·(n + 1)·(n + 2) is the quadratic expression; n² + 2·n + 1 = (n + 1)², which is a square number
What is a quadratic expression?A quadratic expression is an expression of the form; a·x² + b·x + c, where; a ≠ 0, and a, b, and c are the coefficients.
The specified algebraic expressions can be presented as follows;
(1/2)·n·(n + 1) and (1/2)·(n + 1)·(n + 2)
Algebraically, we get;
(1/2)·n·(n + 1) = (n² + n)/2 = n²/2 + n/2
(1/2)·(n + 1)·(n + 2) = n²/2 + 3·n/2 + 1
Therefore;
(1/2)·n·(n + 1) + (1/2)·(n + 1)·(n + 2) = n²/2 + n/2 + n²/2 + 3·n/2 + 1
The addition of like terms indicates that we get;
n²/2 + n²/2 + n/2 + 3·n/2 + 1 = n² + 2·n + 1
Factoring the quadratic equation., we get;
n² + 2·n + 1 = (n + 1)²
Therefore;
(1/2)·n·(n + 1) and (1/2)·(n + 1)·(n + 2) = (n + 1)², which is always a square number
Learn more on the factoring quadratic expressions here: https://brainly.com/question/29120255
#SPJ1
Related Questions
Find the value of x:
A. X = 41.0
B. X = 122.0
C. X = 61.0
D. X = 120.5
Answers
Step-by-step explanation:
hope this will help you..
What is the slope-intercept equation of the line below?
Answers
Answer:
D. y = 2x -3
Step-by-step explanation:
The equation of a line in slope-intercept form is
y = mx + b
We need to find m, the slope, and b, the y-intercept.
We can find those two numbers from the graph.
We look in the graph and see that the y-intercept, b, is -3.
Now we have y = mx - 3.
Now we look for the slope. Start at (0, -2). We need to go vertically and horizontally to the next point that is easy to read. We see that point (1, -1) is on a grid intersection making it easy to read, so we will use that point.
Go up 2 units. That is a rise of positive 2. Now go right 1 unit. That is a run of positive 1.
slope = rise/run = 2/1 = 2
m = 2, so now we have
y = 2x - 3
Answer: D. y = 2x -3
URGENT PLEASE HELP ASAP
Answers
AHAHAHAHAHAHA SO JM IS EQUAL TO 29⁰ AND YOU NEED TO FIND ANGLE L BUT I DON'T KNOW WHAT IT EQUALS TO
A ring-shaped region is shown below. Its inner radius is 8m, and its outer radius is 11m. 8m 11m Find the area of the shaded region. Use 3.14 for π. Do not round your answer.
Answers
Answer:
329.91 cm^2
Step-by-step explanation:
A ring-shaped region is shown below. Its inner radius is 8m, and its outer radius is 11m. 8m 11m Find the area of the shaded region. Use 3.14 for π. Do not round your answer.
Your answer
Given data
inner radius= 8cm
area= πr^2
area= 3.142*8^2
area= 3.142*16
area= 50.272 cm^2
outer radius= 11cm
area= πr^2
area= 3.142*11^2
area= 3.142*121
area= 380.182 cm^2
Hence the area of the shaded part is
=380.182-50.272
=329.91 cm^2
Daryl jumped off of a diving board, and dove into a pool. The graph below shows his height relative to the surface of the water over time, where Daryl’s height (y) is measured in meters and time (x) is measured in seconds. Which of the following statements are true? (Please select all options which are true.)
Answers
Answer:
B,D,E
Step-by-step explanation:
Not entirely sure
A 15-ft by 15-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 304 ft^2, how wide is the walkway?
Answers
Answer:
4 ft = width of walkway
Step-by-step explanation:
It helps if you can draw a figure.
Let x = width of walkway
Length of pool + walkway = (2x + 15)
Width of pool + walkway = (2x + 15)
area of pool and walkway together = (2x + 15)(2x + 15) = [tex]4x^{2} = 60x + 225[/tex]
Area of the pool = 15(15) = 225
Now,
The area of the walkway = area of pool and walkway together - area of pool
304 = 4[tex]x^{2}[/tex] + 60x + 225 - 225
304 = [tex]4x^{2}[/tex] + 60x
4[tex]x^{2}[/tex] + 60x - 304 = 0
4([tex]x^{2}[/tex] +15x - 76) = 0
4(x - 4)(x + 19) = 0
x = 4 x = -19
-19 must be discarded because a length cannot be negative
Therefore x = 4 ft = width of walkway
133=7(1+2x) solve
Answer ASAP please
Answers
Answer:
x=9
Step-by-step explanation:
Step-by-step explanation:
133=7+14x
133-7=14x
14x=133-4
14x=129
14x=129
14 14
x=129
14
Give me the slope for the following points (9, 10)
and (7,2)
Answers
The answer is
m = 4
Have a great day!!!
Answer:
4 is the slope
Step-by-step explanation:
We know this by using the slop formula, which is y2-y1/x2-x1
We just plug in the points that we know and solve from there,
Give brainliest please :3
anyone knows the answer?
Answers
Answer:
20 miles
Step-by-step explanation:
x = break even miles
$10 + x($1.50 = x($2.00)
10 + 1.5x = 2x
0.5x=10
x = 20 miles
A chemical solution contains 4% alcohol. If there is 24 ml of alcohol, what is the volume of the solution?
Answers
Answer: 600 ml
Step-by-step explanation:
Let the volume of the solution be represented by x.
Therefore, we can form an equation based on the information given which will be:
= 4% × x = 24.
4/100 × x = 24.
0.04 × x = 24
0.04x = 24
x = 24/0.04
x = 600
The volume of the solution is 600ml
The Sum Of A Number And Six
Answers
Answer:
x+6
Hope this helps! :)
Answer:
The sum of a # and 6 is...
Step-by-step explanation:
It’s at 15??
Un cable de 42 pies se corta en 3 tramos. Si cada tramo tiene 2 pies de longitud más que el anterior; calcular la longitud del tramo mayor.
Answers
Answer:
dividimos los 42 dejando 12 para cada 1 sobran 6 pies para el primero le aumentamos 4 al segundo 2 y el ultimo se quedaria asi y asi tendria 2 pies de longitud mas que el anterios y el mas largo tendria 16 pies el mediano 14 y el mas pequeño 12
-30-0.6k
what does k equal?
Answers
Answer:
K would equal to:
K= 50
Hope that helps! :)
Step-by-step explanation:
Jessica and her friends have gone to dinner. When they finished eating their bill came to $82. Jessica decided that she wanted to give a 19% tip
Answers
Answer:
97.58
Step-by-step explanation:
Answer: D $15
Step-by-step explanation:
how to do Pythagorean Theorem
Answers
Answer:
pythagorean theorem is a^2 +b^2=c^2
Step-by-step explanation:
basically the two shorter sides added together squared is equal to the longest side squared. if trying to find the length of the longest sidee you just have to do the square root of a^2+b^2
please help me find the slope and y intercept! i’m the worst at math, i’d really appreciate it <333 (click on photo)
Answers
Answer:
3.) y-int = 0
4.) y-int = -1
5.) slope = 2
y-int = 4
6.) slope = -1
y-int = -6
7.) slope = 5
y-int = 8
8.) slope = 7
y-int = 1/2
Step-by-step explanation:
basically, you want to get each of your functions in terms of (y = mx + b)
for each of these:
m will be your slope
b will be your y-intercept
what is the answer to 2 - (-5)
Answers
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
learn the table of how these symbols work.
in this case its two minuses which make plus so 2+5=7
simplify: 4 (3y +x) please show your work
Answers
Answer:
12y+4x
Step-by-step explanation:
Multiply 4*3y and 4*x
Distributive property
Olivia has at most 90$ to spend on clothes she wants to buy a pair of jeans for 22$ and spend the rest on shirts that cost 8$ each what is the greatest number of shirts she can buy
Answers
Answer:the greatest number of shirts she can buy = 8
Step-by-step explanation:
Amount of money Olivia has =$90
cost of pair of jeans =$22
such that if she buys the pair of jean, Money left to buy shirts = $90-$22= $68
If 1 Shirt= $8
Number of shirts she can buy with $68 = $68/$8= 8.5= 8 1/2
Therefore the greatest number she can buy = 8 shirts.
choices
3/4
3/5
5/4
4/5
Answers
Answer:
4/5
Step-by-step explanation:
sine is opposite over hypotenuse,
so it's 40/50=4/5
Hope this helps
Which of these rational numbers is also an integer?
1. 2/4
2. 0.24
3. 4/2
4. 2.4
Answers
Answer:
Ce clasă ești sa văd daca te pot ajuta
Answer:
3. 4/2
Step-by-step explanation:
Easier way to explain it is the numerator or the top number is higher then the denominator or the bottom number.
Solve for x
x^2 - 7x + 10 = 0
Answers
Answer:
Step-by-step explanation:
x²-7x+10=0
(x-2)(x-5)=0
x=2 or x=5
Answer:
Step-by-step explanation:
x2−7x+10=0
Step 1: Factor left side of equation.
(x−2)(x−5)=0
Step 2: Set factors equal to 0.
x−2=0 or x−5=0
x=2 or x=5
(You can confirm this by plugging in the numbers yourself)
What time is it in Vietnam right now?
Answers
Answer:
it's
3:26 pm to be exact!
Step-by-step explanation:
15:26
Friday,19February 2021
I hope it's helpful!
Graph the image of △JKL after a reflection over the line y=x
Answers
Answer:
K (2,-4)
L (4,-6)
J (2,-9)
Step-by-step explanation:
The required graph of the image of △JKL after a reflection over the line y=x has been attached below.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The triangle △JKL is given in the represented graph, which vertices are as follows :
J (-9, 2)
K (-4, 2)
L (-6, 4)
The image of △JKL after a reflection over the line y = x will be triangle △J'K'L' that vertices are as follows :
K' (2,-4)
L' (4,-6)
J' (2,-9)
Hence, the required graph of the image of △JKL after a reflection over the line y=x has been attached below.
To learn more about the transformations click here :
https://brainly.com/question/28029674
#SPJ2
A man is cycling in a place where wind is blowing. He travels 12 km against the direction of the blowing wind. In doing so, he took the same time while going 28 km in the direction of the wind. Find the speed of the wind. ( Hint - When the man is cycling in the direction of the wind, wind speed is added to his speed; otherwise it is subtracted.)
Answers
Answer:
The speed of the wind is 4.8 km/hr
Step-by-step explanation:
The parameters of the motion of the man are;
The distance the man travels in the given time while moving against the wind = 12 km
The distance the man travels in the giving time while going with the wind = 28 km
From search online for of a similar question, we have;
The speed with which the man is cycling = 12 km/hr
Let. 't', represent the time the travels each distance, let 'w', represent the speed of the wind and let 'v' represent the speed of the man, we have;
Time, t = Distance, d/(Velocity, v)
The resultant speed of the man when he travels against the wing = v - w
The resultant speed of the man when he goes in the the wing = v + w
Therefore, we have;
12/(v - w) = 28/(v + w)
12·v + 12·w = 28·v - 28·w
12·w + 28·w = 28·v - 12·v = 16·v
40·w = 16·v
∴ w = (16/40) × v = (2/5) × v
The speed with which the man is cycling = 12 km/hr
∴ The speed of the wind, w = (2/5) × v = (2/5) × 12 km/hr = 4.8 km/hr
The speed of the wind = 4.8 km/hr.
10 - 20 - 20 - 20 -20 2- + 1000
Answers
Answer:
928
Step-by-step explanation:
Answer: It would be 1252
Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.
5
A. (x + 1)(x - 7)
B. (x + 1)(x + 7)
C. (x - 1)(x - 7)
D. (x - 1)(x + 7)
Answers
Answer:
The answer is
(x-1) (x-9)
The factored form of the related polynomial function is [tex](x-1)(x+7).[/tex]
What is polynomial function ?Polynomial function is a function that involves non-negative integer powers or positive integer exponents of a variable in an equation like the quadratic equation, cubic equation.
We have,
In the graph given in question, we can see that [tex]x-[/tex]intercepts the axis twice.
And graphs behave differently at various [tex]x-[/tex]intercepts. Sometimes the graph will cross over the [tex]x-[/tex]axis at an intercept and other times the graph will touch the [tex]x-[/tex]axis and bounce off.
Now, in graph;
The [tex]x-[/tex]intercept at [tex]x=1[/tex], i.e. the solution of the [tex]x-1=0[/tex] and passes through the axis.
Now,
The [tex]x-[/tex]intercept at [tex]x=7[/tex] is the solution of [tex]x-7=0[/tex] and again passes through the axis.
So, from the above statements we can say that the factored form of the related polynomial is [tex](x-1)(x+7).[/tex]
Hence, we can say that the factored form of the related polynomial function is [tex](x-1)(x+7).[/tex]
To know more about polynomial function click here
https://brainly.com/question/14711679
#SPJ2
Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them up to $400 by paying them $25 when one of them mows the lawn and $10 for each hour that one of them babysits their younger brother. They will have to do a combination of both chores in order to earn the money.
Select the equation that represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
Answers
Step-by-step explanation:
25m + 10b = 400
not enough info to solve for m or b. but that's the equation you would use.
Necesito ayuda con el punto 4
Answers
Henry drove 567 miles in 9 hours. At the same rate, how long would it take him to drive 315 miles?
Answers
Answer:
in one hour = 567÷9
= 63
hence, to drive 315 miles he would need = 315×63 hours
divide yourself my dear friend.
Was it helpful?
comment down
If there is any kind of suspicious mistake
then sorry
Answer:
5 hours.
Step-by-step explanation:
567/9 = 63mph
315/63 = 5