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.
20) Find the length of a side of a square with a
diagonal length of 100 cm.
Answer:
about 7.0710678cm
Step-by-step explanation:
it's a square so the sides are equal.
the diagonal is 100cm
This makes a right triangle with two sides
since the sides are equal, they both are equal to the square root of 50, which is half of 100
the square root of 50 is about 7.0710678cm
help me pls!! thank you!!
Answer:
J) y=4/3x+2
Step-by-step explanation:
The initial value is 2 so the y-intercept should be at (0, 2)
The slope is 2/1.5=1.3333
4/3=1.3333 so 2/1.5=4/3
y=mX+b
m= slope
b= Initial Value
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
wooba wooba wooba wooba wooba wooba wooba wooba wooba wooba wooba wooba
Answer:
wooowooowowowowowowowowow
Step-by-step explanation:
Answer:
epic ninja
Step-by-step explanation:
ninja
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
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).
ABCE is a parallelogram . determine the meaSure of
Answer:
D. 78°
Step-by-step explanation:
ABCD is a parallelogram.
Measures of the opposite angles of a parallelogram are equal.
Therefore,
[tex]3x = x + 52 \\ \\ 3x - x = 52 \\ \\ 2x = 52 \\ \\ x = \frac{52}{2} \\ \\ x = 26 \\ \\ m\angle B = (3x) \degree \\ \\ m\angle B = (3 \times 26) \degree \\ \\ m\angle B = 78\degree[/tex]
What is 3/4 divided by 12?
Answer: 0.0625
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
How many gallons of pure water must be added to 10 gal of 30% salt water to make a solution that is 25% salt water?
Answer:
2 gallons must be added Hope this helps!
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:
Find the area of the triangle.
7 yd
24 yd
The area is
square yards.
Answer:
84 yd^2
Step-by-step explanation:
Answer:
½ × 7yd × 24yd = 84yd² <<<<< the answer
A toy marks down every toy by 25% in January. Use p for the price in December to write an expression of the price in January?
Answer: since the toy is marked down 15%,
you do p*.85
to find the remaining cost
Step-by-step explanation: I got this from a friend. But I hope this helps! <3
x+4=6 find out the value of x
Answer:
Step-by-step explanation:
x=2
X+4= 6
Move + 4 to the other side to get X by itself
Sign changes from +4 to -4
X+4-4=6-4
X=6-4
X= 2
Answer: X= 2
5(a +3)= 40 *
What is the answer
Answer:
sorry i had too
Step-by-step explanation:
someone passed this to me) 90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you
Answer: a = 5
Step-by-step explanation:
5(a + 3) = 40
5a + 15 = 40
5a -15 = -15
5a = 25
5a/5a = 25/5a
a = 5
Hope this helps :)
A line has a slope of -1/8 passed through the point 5,10
Answer:
what i do not know what i am on
Step-by-step explanation:
Write the linear equation in slope-intercept form, 5x − 2y = 10
Answer:
y=5x-2
Step-by-step explanation:
Darnelle 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)
Pls help pls help pls help 20 points yall pls help pls help
Help I’ll thank you a lot :)
Which set of ordered pairs are solutions to this linear equation?
-4x+y=6
O(-5, -34), (2, 8), (6, 32)
o(-1, 2), (0, -4), (1, -2)
0 (-1, 2), (0, 6), (1, 10)
O(-3, -22), (-1, -2), (1, 2)
PLEASE
Answer:
0(-1,2),(0,6),(1,10)
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.
pls pls pls pls help
Answer:
im guessing it says they give $5 to the father
if that is the case then the answer is c
Step-by-step explanation:
3/2x+5=-3x-3 what is the value of x?
Select Yes or No to indicate whether each of the ordered pairs is most likely a solution to the equation represented by the graph.
If RX = 2y + 2x, XT = 3y - 1, and US = 28 find the values of x and y.
Answer:
Step-by-step explanation:
The question is in this image.
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!!