Prove that for any natural value of n the value of the expression (n+2)^2-(n-2)^2 is a multiple of 8.
Answers
Answer:
We have the expression:
(n + 2)^2 - (n - 2)^2
Let´s break the parentheses:
(n + 2)^2 = n^2 + 4*n + 4
(n - 2)^2 = n^2 - 4n + 4
Then:
(n + 2)^2 - (n - 2)^2 = (n^2 + 4*n + 4) - (n^2 - 4n + 4) =
= (n^2 - n^2) + (4 - 4) + (4n - (-4n)) = 4n - (-4n) = 8*n
Then for any natural value of n, 8*n will be a multiple of 8.
Related Questions
Rachel is pouring a concrete patio. Her patio will be 6 inches deep, 6 feet long and 8 feet wide. If she rounds up to the nearest hundredth, how many cubic yards of concrete will she need? (Remember, yd3=in3÷46,656 )
Answers
Answer:
2.6667yd^3
Step-by-step explanation
Volume of the concrete = Length * width * height
Given
height = 6 inches
To yards;
1 in = 0.0277778yd
6 in = 6 * 0.0277778
6in = 0.1666668 yards
Width = 8 feet
Length = 6ft
LW = 48ft²
To yards;
1 ft = 0.333333yd
48 ft = 48(0.333333)
48 ft^ 2 = 15.999984yd^2
Volume = 15.999984 * 0.1666668
Volume = 2.6667 yd^3
Hence she will need 2.6667yd^3 concrete
HELP!!! ASAP MARKING BRAINLIEST!!!!
Answers
Answer:
A. y=1/2x-4
Step-by-step explanation:
maths
Quamain is selling chocolate bars for a fundraiser. In his box, he had 12 milk chocolate bars, 8 caramel bars, 9 almond chocolate bars, and 6 dark chocolate bars. What is the ratio of milk chocolate to almond chocolate bars in his box?
4:3
Answers
Answer: 12:9
Step-by-step explanation:
He had 12 milk chocolate bars and 9 almond chocolate bars so the answer is 12:9
And it is also 12:9 is because they ask milk chocolate TO almond chocolate .
!!HELP!! What is q times 10?
Answers
Answer:
Q10. You just put them together because it's multiplying of a letter and a number
**I thought I answered this question yesterday, is this a deja vu or something**
If you rotate figure GTR 270° clockwise about the origin. What will be the coordinates of G’T’R’ (Please Help I need this done in five minutes.)
Answers
Answer:
C. G' (4,-7), R' (2,-3), T'(6,-4)
Step-by-step explanation:
Get a piece of paper and draw 2 intersecting lines, like how a graph looks like. Then get another paper that's transparent enough, and place a dot roughly where R would be. Rotate it 270* clockwise (3 times around 90 degrees), and R would be in the bottom right area. That means the figure would be around that area and you can base the coordinates from that.
TRUE OR FALSE
The unit rate is when the ratio has a denominator 1
True
False
Answers
Answer:
that would be true
Step-by-step explanation:
Answer:FALSE
Step-by-step explanation:
If a = -9 and b = -4, what is the value of a + b ?
-5
5
-13
13
Answers
16. Adam uses a microscope to observe insects in science class. The
microscope enlarges objects to 100 times their actual size. Find the length of
each insect as seen in the microscope.
A=
cm
(Type a whole number or a decimal.)
Answers
Answer:
A= 0.5, B=2.2, C=0.12, D=.0.9.
Step-by-step explanation:
The demand on a power plant changes over time. cause or effect
Answers
Answer:
effect
Step-by-step explanation:
What is the solution set for 2x – (x + 5) < 3x – 9 ?
Answers
Answer:
x > 2
Step-by-step explanation:
x - 5 < 3x - 9
x - 5 + 5 < 3x - 9 + 5
x < 3x - 4
x - 3x < 3x - 4 - 3x
-2x < -4
(-2x)(-1) > (-4)(-1)
2x > 4
2x/2 > 4/2
x > 2
Answer:
x > 2.
The solution in interval notation is (2, ∞).
Step-by-step explanation:
2x - (x + 5) < 3x - 9
2x - x - 5 < 3x - 9
2x - x - 3x < -9 + 5
-2x < -4
Divide both sides by -2
x > 2 (Note that the sign flips because we are dividing by a negative)
Please help me answer this question will give Brainlst!:) I
Answers
Answer:
B, E, and F
Step-by-step explanation:
Functions that are linear form a straight line when graphed.
Answer:
B,E,F
Step-by-step explanation:
A linear function follows the formula of...
y = mx + b
So don't get tripped up by exponents (letter c and d)
C is a quadratic and D is an exponential function
and...
A is a parabola
E, might trip some people up but communitive property is "at hand", the equation does (a + x) is the same as (x + a) ( <--- for example)
*communitive property is only seen in multiplication and addition
F is where you have to use the distributive property, distribute the 5 to the x and the 0.6
Formulas:
Linear: y = mx + b
Quadratic: y = x^2
Exponential: y = b^x
Parabola: y = 1/x
Suppose that the test score of a student taking the final of a probability course is a random variable with mean 76.
Required:
a. Give an upper bound for the probability that a student's test score will exceed 86. Suppose, in addition, that the professor knows that the variance of a student’s test score is equal to 25.
(b) What can be said about the probability that a student will score between 65 and 85?
c. How many students would have to take the examination to ensure, with probability at least .9, that the class average would be within 5 of 75? Do not use the central limit theorem.
Answers
Answer:
a. 0.8837
b. 0.6914
c. 10 student
Step-by-step explanation:
a. using markov's inequality; P(u >= X)<= E(u) / X
mean u = 76
X, test score = 86
= 76 / 86 = 0.8837
b. variance v = 25
The test is between 65 and 85 P(65 <= X <= 85);
P(|65 - X|<= |X - u| <= |85 - X|) = P(65 - 76 <= |X - u| <= 85 -76)
= P(-11 <= |X - u| <= 9)
= P(|X - u| <= 9)
using the chebyshev's inequality;
P(|X - u| <= 9) = 1 - variance / (standard deviation of individual test score)^2
= 1 - 25/ 9^2
= 1 - 25/81 = 1 - 0.3086 = 0.6914
c. P(|X - 76| <= 5) = 0.9
still using chebyshev's inequality;
= 1 - variance / lower limit^2 (E)
where E = 1 - 0.9 = 0.1
lower limit = 5
= 1 - 25/ 5^2 (0.1) = 10
A person invests 4000 dollars in a bank. The bank pays 6.25% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 9600 dollars?
Answers
Answer:
14.4
Step-by-step explanation:
Given that :
Principal = 4000
Interest (r) = 6.25% compounded annually
Calculate time, t, if final amount A = 9600
Using the compound interest formula :
A = P(1 + r/n)^n*t
A = final amount
n = number of times interest is applied per period
9600 = 4000(1 + 0.0625)^t
9600 = 4000(1.0625)^t
9600/4000 = 1.0625^t
2.4 = 1.0625^t
Take the log of both sides
0.3802112 = 0.0263289t
t = 0.3802112/0.0263289
t = 14.440811
t = 14.4 ( nearest tenth)
Please help, I really need help, will mark brainliest
Answers
ANSWER
have it right it is -4
Stella predicted that she would sell 56 sculptures. She actually sold 30 sculptures. What are the values of a and b in the table below? Round to the nearest tenth if necessary.
Answers
Answer:
a=26 / 56 and b = 46.4 percent
Step-by-step explanation:
From the question, the Approximate value is given as = 56
While the Exact value is given as 30
Error
Absolute error= 56-30=26
Where Ratio= a= error/Approximate value=26/56
Percent error = b= 26/56×100%=46.4
it's a
have an nice day day
If a number is doubled the result is sixty
Answers
Answer:
30
Step-by-step explanation:
30x2=60
This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint.
f(x, y) = xy; 4x2 + y2 = 8
Answers
Answer: minimum value of f = -2 and maximum value of f = 2
Step-by-step explanation:
Given that;
f(x, y) = xy; 4x² + y² = 8
S(x,y) = xy + λ(4x² + y² - 8)
dS/dλ = 4x² + y² - 8 = 0
dS/dx = y + 8λx = 0 -> y = -8λx
dS/dy = x + 2yλ = 0 -> x + 2λ(-8λx) = x(1 - 16λ²) = x(1-4λ)(1+4λ) = 0
-> x = 0 , λ = 1/4 , λ = -1/4
x = 0 -> y = 0 -> it doesn't satisfy 4x² + y² = 8
λ = 1/4 -> y = -8λx = -2x -> 4x² + y² = 8x² = 8 -> x = -1 , 1 -> y = 2 , -2
λ = -1/4 -> y = -8λx = 2x -> 4x² + y² = 8x² = 8 -> x = -1 , 1 -> y = -2 , 2
we have 4 critical points:
(-1, 2) -> f = -2
(1, 2) -> f = 2
(-1, -2) -> f = 2
(1 , -2) -> f = -2
Therefore; minimum value of f = -2 and maximum value of f = 2
What are the solutions?
y=k^2-16k-4
Answers
Answer:
y−k
2
+16k+4=0
2 Use the Quadratic Formula.
k=\frac{-16+2\sqrt{y+68}}{-2},\frac{-16-2\sqrt{y+68}}{-2}k=
−2
−16+2√
y+68
,
−2
−16−2√
y+68
3 Simplify solutions.
k=8-\sqrt{y+68},8+\sqrt{y+68}k=8−√
y+68
,8+√
y+68
Step-by-step explanation:
1) What is the constant of proportionality that relates y to x
х
Y
8
6
20
15
28
21
a. 1.33
6,48
0.0.75
b. 14
f
Answers
Answer: The Answer Is A Because if u just add the numbers then divide them
Find the distance between the two points in simplest radical form.
(-2,-1) and (-8,7)
Answers
Answer:
The distance in radical form is √100 (which is equal to 10units
Step-by-step explanation:
Distance=√(-8--2)²+(7--1)²
D=√(-6)²+(8)²
D=√36+64
D=√100
D=10units
At the first game of the Major League Baseball season, a statistician keeps track of every pitch that a player throws during the game. The statistician reported that the mean pitch speed was 80 miles per hour (mph) and the standard deviation of the serve speeds was 10 mph. Assume that the statistician also gave us the information that the distribution of pitch speeds was mound- shaped and symmetric. What percentage of the player's serves were between 80 mph and 100 mph
Answers
Answer:
47.725%
Step-by-step explanation:
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 80 mph
σ is the population standard deviation = 10 mph
For x = 80 mph
z = 80 - 80/10
z =0
Probability value from Z-Table:
P(x = 80) = 0.5
For x = 100 mph
z = 100 - 80/10
z = 2
Probability value from Z-Table:
P(x = 100) = 0.97725
Probability of the player's serves thay were between 80 mph and 100 mph is calculated as:
P(x = 100mph) - P(x = 80 mph)
= 0.97725 - 0.5
= 0.47725
The percentage of the player's serves that were between 80 mph and 100 mph is calculated as:
Converting to percentage:
0.47725 × 100 = 47.725%
what is the answer for this
Answers
Answer:
4
Step-by-step explanation:
I CAN GIVE BRAINLIEST!!!!!!
Answers
Answer: 2/1
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Line is passing through the points (2, 3) & (5, 9)
Slope = (9 - 3)/ (5 - 2) = 6/3 = 2
Slope of the line is 2.
What is most reasonably measured in miles?
Answers
Answer:
Length of a Road
Step-by-step explanation: No man that has ever lived (Well unless they're a nephilim or smth) is over a mile tall. Swimming pools and buildings aren't usually big enough to be measured in miles unless they're either a skyscraper or a Wisconsin water park attraction.
HELPP QUICKKK its timedd
Answers
Answer:
10
Step-by-step explanation:
i put my age as 98 years old
Answers
Answer:
grandpa
Step-by-step explanation:
love u grandpa
Find all the real square roots of -49
Answers
Answer:
-7
Step-by-step explanation:
Answer:
7i
Step-by-step explanation:
the square root of 49 is 7
i equals -1
7 squared times -1 equals -49
xoxo,your highness...help meeeeeeeeeeeeeeeeeee
Answers
Answer:
18
Step-by-step explanation:
the other right triangle is 3-4-5. so, 3*4/2=6
4*6/2=12
6+12=18
give brainliest pls
On Monday, Byron spent $8.00 on lunch to purchase two tacos and one burrito. On Wednesday, he purchased one enchilada, one taco, and one burrito and spent $8.50. On Friday, it cost Byron $10.00 for two enchiladas and two tacos. If t represents the cost of a taco, b represents the cost of a burrito, and e represents the cost of an enchilada, which system of equations can be used to find the cost of each?
Answers
Answer:
2t+b=8.00
e+t+b=8.50
2e+2t=10.00
Step-by-step explanation:
for a new neighbor, 100 acres of land will be split into 10 lots. How many acres will each lot have?
Answers
Answer:
Your answer is 10 cause 100 divided by 10 is 10
Step-by-step explanation: