Answer:
Step-by-step explanation:
Prove that 52n − 1 is divisible by 8 for all n ∈ N.
Solution
To prove by induction, we must
1. Show it is true for n = 1
2. Assume true for n and prove it is true for n + 1.
Let P(n) be the statement 52n − 1 is divisible by 8.
When n = 1, 52 − 1 = 24, which is divisible by 8.
This proves P(1).
Suppose that P(n) is true, i.e., 52n − 1 is divisible by 8.
Then 52(n+1) − 1 = 52
· 5
2n − 1 = 52
(52n − 1) + (52 − 1).
Note that 52n −1 is divisible by 8 using P(n) and also 52 −1 = 24 is divisible
by 8. Thus we have proved that P(n + 1) is true.
We conclude that P(n) is true for all n ∈ N.
About how many 8 3/4 - foot pieces g fencing can Justin get from a 100 foot roll
Answer:
11 but specifically it is 11.428571
Answer: 11
Step-by-step explanation: 100 divided by 8 3/4
If you want specific answer it's 11.4285714286
If 25% of $2000 is spent on food,how much money is spent on food?
Answer:
$500
Step-by-step explanation:
Simply change the 25% into a decimal which is 0.25 and multiply $2000.
Or you can change 25% into a a fraction which is 25/100 and simplify giving 1/4. Then simply multiply $2000 by the fraction: 2000/1×1/4. Cross multiply which is 2000×1/1×4=2000/4. Now simply divide 2000 by 4 and you get 500 as your answer.
h = -16t2 + 4t + 4
I don’t know how to approach this
Answer:
0.64 seconds
Step-by-step explanation:
Some extra unneeded information provided in this problem. Simply find t when h is equal to zero. (Factor out -4 if it makes it easier.)
0 = -16t^2 + 4t + 4
Solve using the quadratic equation:
t = ~0.64
how do i solve (4+6i)+(8-10i)?
Answer:
12- 4i
Step-by-step explanation:
(4+6i)+(8-10i)
4+6i+8-10i
4+8+6i-10i
12-4i
Ataxi service charges you $7.50 plus $0.60 per minute, m. for a trip to
the airport. The total charge is $13.50. Write an algebraic equation you
can use to determine the number of minutes it took to get to the airpor
take? (you do not need to solve)
Answer:
6
Step-by-step explanation:
13-7 =6
$6.00÷0.60¢ = 10
(I may be hella off, but it's worth a shot)
Simplify the expression, show all of your work:
18 : 2.3
5 - 2
Answer:
9
Step-by-step explanation:
Numerator:18 divided by 2=9 9 times 3= 27
Denominator:3
27/3=9
Please solve the math problem... I will mark you brainliest
Answer: XYZ = HGJ by the ASA postulate
Question Help Morgan saw 3x 10' cats in the park on Sunday. She saw three times as many cats on Monday as she saw on Sunday. How many cats did she see over the two days? Morgan saw cats over the two days.​
Answer:
60
Step-by-step explanation:
order .375, .27, .3, .83 (the 3 is repeating), .75 least to greatest pls
Answer:
0.27 , 0.3 , 0.375 , 0.75 , 0.83
Step-by-step explanation:
Hope this helps ^w^
Solve B=1/4m(s+z) for s
Answer:
[tex]s = \frac{-mz+4B}{m}[/tex]
Step-by-step explanation:
Step 1: Distribute.
[tex]B = \frac{1}{4}m * s + \frac{1}{4}m * z[/tex] [tex]B = \frac{1}{4}ms + \frac{1}{4}mz[/tex] [tex]\frac{1}{4}ms + \frac{1}{4}mz = B[/tex]Step 2: Subtract 1/4(mz) from both sides.
[tex]\frac{1}{4}ms + \frac{1}{4}mz - \frac{1}{4}mz = B - \frac{1}{4}mz[/tex] [tex]\frac{1}{4}ms = -\frac{1}{4}mz + B[/tex]Step 3: Divide both sides by m/4.
[tex]\frac{1}{4}ms/\frac{m}{4}=(\frac{-1}{4}mz + B)/\frac{m}{4}[/tex] [tex]s = \frac{-mz+4B}{m}[/tex]Find the LCD of the fractions and enter them
4/8 and 4/6
Answer:
The LCD IS 6
Step-by-step explanation:
Find two consecutive odd integers such that
4 times the smaller integer is 19 less than 5
times the larger integer.
Answer:
9 and 11
Step-by-step explanation:
let the consecutive odd integers be n and n + 2 , then
4n = 5(n + 2) - 19 , that is
4n = 5n + 10 - 19 ( subtract 5n from both sides )
- n = - 9 ( multiply both sides by - 1 )
n = 9 and n + 2 = 9 + 2 = 11
The 2 integers are 9 and 11
What is the rate of change for the equation y = 2x + 100?
The rate of change is 2.
good luck :)
Evaluate the expression when x = 6 and y = 2:
Answer:
[tex] \frac{3x + 4}{y} = \frac{3(6) + 4}{(2)} \\ = \frac{18 + 4}{2} = \frac{22}{2} \\ = 11[/tex]
Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. Angle N P O is 38 degrees. Angle P O N is 39 degrees. Exterior angle P N M is x degrees.
Which statement about the value of x is true?
x > 38
x < 39
x < 77
x > 103
Answer:
77 degrees
Step-by-step explanation:
<P + <O = 38 + 39 = 77 degrees
180 - 77 = <N = 103 degrees
180 - 103 = 77 degrees (<PNM)
In this picture, m
X?
A 52
B 20
C. 2.8
D 7
Which of the following is equivalent to this expression?-3x(-y+4)
-12x-3xy
-12x+3xy
12x+3xy
12x-3xy
-12x-3xy
-12x+3xy
12x+3xy
12x-3xy
Answer:
The answer is A
Step-by-step explanation:
Hope it helps!
Work out the area of this trapezium.
15cm
6cm
9cm
3cm
Answer:
33 cm
Step-by-step explanation:
my bad if im wrong havent done this in a while
Answer:
Step-by-step explanation:
area of trapeziumm=1/2(15+3)×6=9×6=54 cm²
George practises his guitar for 1 1/5 hours per day on school days. On Saturday he increases to 2 1/2 times his normal time. How many hours does he practice on Saturdays.
Answer: 231/10
Step-by-step explanation: 11/5 x 21/2
= (11 x 21) = 231
= 231/5 x 2
= 231/10
Answer:
3 hours
Step-by-step explanation
It would be easier to convert your fractions into decimals.
1/5 is the same as 2/10. Since the denominator was multiplied by 2 then the numerator must be multiplied by 2 also.
2/10 in decimal form is 0.2
He would practice 1.2 hours per day on school days
On Saturday his practice is 2 1/2 times longer than 1.2 hours.
Convert 1/2 into decimal form. 1/2 is the same as 0.5.
So 2 1/2 is the same as 2.5
If you multiply the original time (1.2 hours) by 2.5, you'll know how long he practices on Saturday.
1.2 x 2.5 = 3 hours.
1.2
x 2.5
-------
60
24
------------
300
since you have 1 decimal place in the top number and 1 decimal in the bottom number, you must move your decimal 2 places to the left on your answer. Instead of 300, your answer becomes 3.00
please gelp me with this question
Answer:
25
Step-by-step explanation:
75 ÷ 3 = 25
25 = 25
If f(x) = 52, what is the value of f(-6), to the nearest hundredth (if necessary)?
Answer:
the correct answer is 52
Given that D, E, and F are the midpoints of their respective sides, and AC = 24, what’s the length of line segment DE?
Question options:
2 units
12 units
4 units
6 units
The ratio of their corresponding sides will remain constant. Then the measure of the side length DE is 12 units.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
Given that D, E, and F are the midpoints of their respective sides of the triangle and AC = 24.
Then the length of line segment DE will be
We know that the triangle ΔABC is similar to the triangle ΔDBE. Then we have
BC = 2BE
Then the ratio of their corresponding sides will be
BE/BC = DE/AC
BE/2BE = DE/24
DE = 24/2
DE = 12
Then the correct option is B.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ1
m/_GFN = 4x+10, m/_NFE= 14x+3, and m/_ GFE=157°. Find m/_NFE. PLEASE EXPLAIN Thoroughly!!
Answer:
4x+10+14x+3=157
18x+13=157
18x=157-13
18x = 144
X = 144 /18
X= 8
NFE= 14x+3
= 14(8)+3
=112+3
=115
Step-by-step explanation:
The quotient of a number x and five
Answer: fun fact : by reading what i just right u just lost 5 sec of ut life
Step-by-step explanation:
0
help!!
which are the answers??
B, D, E.
Step-by-step explanation:
Answer:
to me this is extremely simple a stitscal Quinton is a question that needs math or science or has a logical answer not one that has assumptions
Step-by-step explanation:
the answer is A) D) F) G) GOOD LUCK
prove that 5^(2n - 1) is divisible by 8
Your teacher must have made a typo somewhere. The expression 5^(2n-1) is not divisible by 8.
The expression 5^(2n-1) is composed of 2n-1 copies of "5" multiplied together. The key here is that 5 is the only unique prime factor of this number.
On the other hand, 8 = 2*2*2 = 2^3 showing that 2 is the only prime factor for this number. At this point, we can see that there's no way that 5^(2n-1) is divisible by 8. It all comes down to the clash of the primes 5 and 2 not matching up, and having nothing in common.
Let's consider a few concrete examples:
If n = 1, then 5^(2n-1) = 5^(2*1-1) = 5^1 = 5 which is not divisible by 8. The number 5/8 = 0.625 isn't an integer.If n = 2, then 5^(2n-1) = 5^(2*2-1) = 5^3 = 125 which is also not a multiple of 8. The number 125/8 = 15.625 isn't an integer.I'll let you try other natural numbers for n, and you'll find that [tex]\frac{5^{2n-1}}{8}[/tex] isn't an integer.
Ryan borrowed $725 at an interest rate of 6.25%. How much interest will be pay if it takes 2 years to pay off his loan?
Answer:
$830 sana maka tulong po salamatThe ratio of hotdogs to hamburgers sold at the picnic was 3:4. If 98 dinners were sold, how many were hamburgers?
Answer:
56 Burgers
Step-by-step explanation:
First, add the 3 + 4 for a total of 7, because the total of the ratio will equal the total amount of "the dinners sold".
Then divide 98/7, which will give you 14.
Then in the ration 3:4, 4 represent burgers so multiply 14 x 4.
Which gives you 56 burgers.
Hope This Helps
What is 42 x 118 In a full equation?
Answer:
4956
Step-by-step explanation:
alternative forms
4.956×10³
simplify -1 1/2 divided by 1 2/3
Answer:
-5/2
Step-by-step explanation:
Or -2.5
If you divide a negative by a positive it becomes a negative.
Hope this helps any!
