Prove that for any natural value of n the value of the expression (n+2)^2-(n-2)^2 is a multiple of 8.
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.
You run 6 miles in one hour and 24 miles in four hours.
a. 6 miles
per hour
c. 4 hours
b. 4 miles per hour
d. 6 miles
Answer:b
Step-by-step explanation:
Which statement best explains the relationship
between lines FG and HJ?
O They are perpendicular because their slopes are
equal.
O They are perpendicular because their slopes are
negative reciprocals.
They are not perpendicular because their slopes
are equal.
They are not perpendicular because their slopes
are not negative reciprocals.
Answer:
They are not perpendicular because their slopes are not negative reciprocals.
Step-by-step explanation:
Pls help a girl out :/ and show work pls
Answer:
it is B
Step-by-step explanation:
Kelly read 30 pages of her 300-page book in 6 hours. At this rate, how long will it take her to read the entire book? (5 points) 6 hours 5 hours 60 hours 30 hours
Answer:
It is 60 hours
Step-by-step explanation: 30 pages = 6 hours
30 × 10 = 300
6 × 10 = 60
Answer:
60
Step-by-step explanation:
trust me
These points are linear. Find the slope.
Answer:
Slope = 3/2
Step-by-step explanation:
The slope of an equation is rise/run, or y/x.
Since the graph indicates that y rises by 3 and x rises by 2, the slope would be 3/2
Answer:
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
To find the slope of a line, you need to find the [tex]\frac{rise}{run}[/tex] between two points. I will be calculating the slope using the two points (2, 3) and (4, 6).
Slope = [tex]\frac{rise}{run}[/tex]
= [tex]\frac{6-3}{4-2}[/tex]
= [tex]\frac{3}{2}[/tex]
a) Solve x² + 4x - 8 = 0 by completing the square
Answer:
x = 2 + 2i, x = 2 - 2i
Step-by-step explanation:
[tex] {x}^{2} - 4x + 8 = 0 \\ \\ {x}^{2} - 4x + 4 + 4= 0 \\ \\ {x}^{2} - 4x + {(2)}^{2} = - 4 \\ \\ {(x - 2)}^{2} = - 4 \\ \\ x - 2 = \pm \sqrt{ - 4} \\ \\ x - 2 = 2i \\ \\ x = 2 \pm 2i \\ \\ x = 2 + 2i, \: \: \: x = 2 - 2i[/tex]
A triangular flag has 2 sides with lengths 2 x and 1 side with length x.
A flag is the shape of an isosceles triangle, with two equal sides and a base. Sara has enough fabric to make a flag with a perimeter of 46.8 cm. She knows the flag needs a base that is half the distance of one of the sides.
What is the base of the largest triangular flag Sara can make?
cm.
Step-by-step explanation:
Perimeter = x + 2x + 2x = 5x
Since 5x <= 46.8cm, x <= 9.36cm.
The largest base is 9.36cm.
Answer:
9.36 is correct
Step-by-step explanation:
✨help✨
Madonna loves records. She has 338 of them. Her grand father gives her some for her birthday. She ends up with 456 after her birthday. At what percent did her grandfather give her. (I know it's a funky question. You have to divide the amount and then round it to the nearest hundred)
Answer:
34.9%Step-by-step explanation:
Ok, we need to express this number as a percent of increase. So, what we'll do is write this as a proportion.
456/338 = x/100
456 x 100 = 338x
45600 = 338x
x = 134.911242604
A 34.9% increase
Answer:
17.53%Step-by-step explanation:
Initial number = 388Final number = 456Increase in number:
456 - 388 = 68Increase in percent:
68/388*100% = 17.53% rounded to the nearest hundredsDarnelle has a $10,000, three-year loan with an APR of 5%. She uses the table on page 159 to compute information on the loan,
a. What is her monthly payment?
b. What is the total of all her monthly payments?
c. What is the total finance charge?
HELP
Her monthly payment would be $180.56, the total of all her monthly payments would be $13,000 and the total finance charge is $3000.
What is the expression of simple interest?The expression for the final amount for simple interest is
A = p(1+rt)
Given data
Principal = $10,000
Rate= 5 %= 0.05
Time = 6years (Assume)
A = p(1+rt)
A = 10,000(1+0.05×6)
A = 10,000(1+0.30)
A = 10,000(1.30)
A = 13,000
So the final amount for simple interest is $13,000
To determine her monthly payment
Given that it is spread over 6 years
There are 12×6 months= 72months
So monthly pay = 10000/72 = $180.56
The total of all her monthly payments would be $13,000 which is equal to the final amount.
The finance charge is equal to the interest.
⇒ $13,000 - $10,000 = $3000
So the finance charge would be $3000.
Therefore, her monthly payment would be $180.56, the total of all her monthly payments would be $13,000 and the total finance charge is $3000.
Learn more about the simple interest here:
brainly.com/question/22621039
#SPJ5
If the point (x, y) is in Quadrant IV, which of the following must be true?
Answer:
Any coordinate point with (positive x, negative y)
2.3a+3.5b-1.8a-2.7b simplify. Show work.
Answer:
a = -1.6b
Step-by-step explanation:
Simplifying
2.3a + -1.8a + 3.5b + -2.7b = 0
Combine like terms: 2.3a + -1.8a = 0.5a
0.5a + 3.5b + -2.7b = 0
Combine like terms: 3.5b + -2.7b = 0.8b
0.5a + 0.8b = 0
Solving
0.5a + 0.8b = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-0.8b' to each side of the equation.
0.5a + 0.8b + -0.8b = 0 + -0.8b
Combine like terms: 0.8b + -0.8b = 0.0
0.5a + 0.0 = 0 + -0.8b
0.5a = 0 + -0.8b
Remove the zero:
0.5a = -0.8b
Divide each side by '0.5'.
a = -1.6b
Value of 5.3x10 4.2x10 scientific notation
Write the linear equation in slope-intercept form, 5x − 2y = 10
Answer:
y=5x-2
Step-by-step explanation:
What is the product of 12 and 5 decreased by 17
Answer:
43
Step-by-step explanation:
Answer: 43
Step-by-step explanation:
12x5-17 would be the equation
60-17 multiplication due to PEMDAS
43 subtraction
In the game of rock, paper,scissors, two people play, and equally likely that you will win, lose or tie. Find the probability of having different outcomes in two tries.
A) 2/3
B) 1/2
C)1/3
D)5/9
someone sells a product for 10 cents and he sells 1000 products, how much money did he earn
Answer:
$100
Step-by-step explanation:
10¢ × 1,000 = 10,000¢To convert to dollars: Cents ÷ cents in 1 dollarTo convert to dollars: 10,000¢ ÷ 100¢ = $100I hope this helps!
What is the GCF of 88 and 66?
Answer:
the GCF would be 22 this is because that is 88 and 66 greatest common factor (gcf)
Step-by-step explanation:
have a good day!!
Jill would like an increase in the hourly wage she receives from the Mathematics Research Center, where she works in the mail room. Her boss gives her an equation to solve, telling her that her raise is the solution to the equation, but only if she can solve it. The equation is x 2- 6x + 9 = 0. What was the amount of her raise per hour? Answer:
Answer:
Jill will receive an increase of $3 per hour
Step-by-step explanation:
The Quadratic Equation
The quadratic equation can be represented in the standard form as:
[tex]ax^2+bx+c=0[/tex]
being a,b, and c are constants.
It can be solved by using the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Jill would like an increase in her hourly wage. The increase will come as the solution for a maths equation.
She must solve the equation:
[tex]x^2-6x+9=0[/tex]
The solution to the equation, or value of x, is the increase in her hourly wage.
Comparing with the general form, we have a=1, b=-6, c=9. Thus, the solutions are:
[tex]\displaystyle x=\frac{-(-6)\pm \sqrt{(-6)^2-4(1)(9)}}{2(1)}[/tex]
[tex]\displaystyle x=\frac{6\pm \sqrt{36-36}}{2}[/tex]
[tex]\displaystyle x=\frac{6\pm \sqrt{0}}{2}[/tex]
The square root is 0, therefore is only one solution:
[tex]\displaystyle x=\frac{6}{2}=3[/tex]
x = 3
Thus, her raise per hour is $3.
Free Brainliest
There are 7 red, 6 blue, 12 green and 9 yellow marbles in a bag. What is the probability of not selecting a red or yellow marble?
Answer:
there are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.
Step-by-step explanation:
Answer:
I believe its 52.94% (53 rounded)
Step-by-step explanation: First add all the numbers to see the total amount of marbles (34) Second is add the marbles that are NOT red or yellow (18).Then the final step is divide 18/34
Hope this helps and have a great day
monkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonkemonke
Answer:
monke
Step-by-step explanation:
delicious
Translate to a system of equations but do not solve
A nontoxic floor wax can be made from lemon juice and food grade linseed oil. The amount of oil should be twice the amount of lemon juice. How much of each ingredient is needed to make 42 ounces of floor wax?
Let x represent the number of ounces of lemon juice and y the number of ounces of linseed oil.
Complete the system of equations
x+y=
Answer:
The system of equations is:
x+y = 42
y = 2x
Step-by-step explanation:
Let x represent the number of ounces of lemon juice.
Let y represent the number of ounces of linseed oil.
A total of 42 ounces of floor wax is to be made, so:
x+y = 42
The amount of oil should be twice the amount of lemon juice. So:
y = 2x
so the system of equations is obtained.
Given the formula A = P(1 + )". compute A (rounded to two decimal places) if P = 10,000,7
= 0.08, k = 2, and n = 12.
A 124,800.00
B 16,010.32
C 25,181.70
D 129,600.00
30.32
Answer:
A = 16010.32
Step-by-step explanation:
Given that,
[tex]A=P(1+\dfrac{r}{k})^n[/tex]
Put P = 10,000, r = 0.08, k = 2 and n = 12 in the above formula to find A.
[tex]A=10,000(1+\dfrac{0.08}{2})^{12}\\\\=10,000\times (1.04)^{12}\\\\=16,010.32[/tex]
So, the value of A is 16010.32. Hence, the correct option is (B).
A boat traveled 54 km with the stream and 42 km against the stream spending a total of as much time as it would spend while travelling 96 km in a lake. Find the speed of boat while it is travelling in the lake, if the current of the river is 3 km/hour.
Answer:
18 miles / hour
the absolute value of 15.3 is the opposite of 15.3?
Answer:
No. The absolute value of 15.3 is 15.3, not the opposite.
Step-by-step explanation:
Absolute value makes any number its positive form. For example -2 in absolute form is 2. So 15.3 in absolute form is still positive 15.3.
Which of the following situations results in a sum of 1 1/2 ? Select all that apply .
1. I painted 5/8 of one room and 7/8 of another .
2. I gained 6 1/2 pounds and my wife lost 8 pounds .
3. I had 4 1/4 bottles of juice and drank 1 3/4 of them .
4. I cut 3 1/3 inches from my grass. The grass grew 1 5/6 inches over the next week .
5.I used up 1/4 of a pound of coffee and bought 1 1/4 of a Pound of coffee from the store .
6. I used 3/4 of a pound of ground beef to make burgers and purchased 2 1/4 of a pound of ground beef .
Answers ASAP!!!!
Answer:
A, E, And D
Step-by-step explanation:
i did the quiz :)
Find the reference angle for a rotation of 220°.
Answer:
ans is 40 degree
i hope this is correct
Write the statement as an equation Anumber decreased by six is five more than twice the number.
let the numbers be x
x-6-5=2x
Answer:
x - 6 = 2x + 5
Step-by-step explanation:
Let's break down the statement.
A number decreased by six means a number/variable subtracted by six. So, we have x - 6.
Five more than twice a number means five plus two times a number/variable. So, we have 2x + 5.
The 'is' in the middle of the statement signifies that they are equal to each other.
The equation would be x - 6 = 2x + 5.
Hope that helps.
Help I’ll thank you a lot :)
There is 10 inches of water in a bucket. The water is leaking out of the bucket at a rate of 1 inch per hour. How many hours will it take for the bucket
to fully empty?
Type your answer...