It's kind of self-evident. Any power of 21 will have a 1 in the units place, and adding 9 to it makes it 0 and hence the number is divisible by 5.
To prove the claim by induction, first establish the base case. I assume [tex]n\in\Bbb N[/tex], so for [tex]n=1[/tex] we have
[tex]21^1 + 9 = 21 + 9 = 30[/tex]
and of course 30 = 5×6 is divisible by 5.
Assume the claim is true for [tex]n=k[/tex], that [tex]5 \mid 21^k + 9[/tex]. This means that for some integer [tex]\ell[/tex], we can write
[tex]21^k + 9 = 5\ell[/tex]
Now the induction step: when [tex]n=k+1[/tex], we have
[tex]21^{k+1} + 9 = \bigg(21\times(21^k + 9) - 9\times21\bigg) + 9 \\\\ ~~~~~~~~~~~~~~ = 21\times5\ell - 9\times20 \\\\ ~~~~~~~~~~~~~~= 5\times(21\ell - 9\times4)[/tex]
which is divisible by 5. QED
4 Mr. Von's 5th-grade class is going on a field trip. Each
student is given a name card to wear that is 1/4 foot wide 1/3 foot long
1/4foot x 1/3 foot = square foot
Answer:
the answer is 1/12 square foot
Step-by-step explanation:
.
Need help with math question 8th grade math
Answer:
Step-by-step explanation:
I am also in 8th grade, anyways
x reprsents = 30 nickles
y represents = $1.02.
I am very sorry i do not know EQ1 and EQ2, but hopefully this is helpful!
Answer:
Step-by-step explanation:
x reprsents = 30 nickles
y represents = $1.02.
If 9 x 7 = 3545 and 4 x 3 = 1520 then 6 x 8 = ?
Answer:
4030 or 3040 I think 4030 though
Step-by-step explanation:
I think this is it but 6*8 is 48....I used a little logic so hopefully this is right
Answer:
4030
Step-by-step explanation:
if 9× 7 = 3545 then it 7 × 5, 9× 5 which gives 3545
4x3 = 3× 5, 4×5 which gives 1520
so 6× 8 will give 8×5, 6×5 = 4030
9° TERMINO DE 7.10.13
Answer:
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Answer:
Evaluate
18 ER TM×2,130
The square root of y^3 simplified
Answer:
(√y)3
Step-by-step explanation:
[tex] {n}^{6} \times \frac{4}{25} {n}^{2} \times \frac{5}{4} {n}^{3} \times n[/tex]
Step-by-step explanation:
reduce the numbers by solving and add the powers
Please I need help.
Find the measure of the angle DCB in the rhombus ABCD.
Answer:
53
Step-by-step explanation:
its the same to DAB because it is in the opposite side to the DAB
Answer:
Step-by-step explanation:
In Rhombus, diagonals are angle bisectors.
So, ∠DAC = ∠CAB
∠A = ∠DAC+∠CAB
= 53 + 53
∠A = 106
In Rhombus, opposite angles are equal.
∠DCB = ∠A
∠DCB = 106°
Find the area of the triangle.
Answer:
86.1yd
Step-by-step explanation:
area of a triangle= base*height/2
21*8.2=172.2
172.2/2=86.1
Answer:
86.1yd2
Step-by-step explanation:
area=1/2×b×h
a=1/2×21×8.2
a=86.1yd2
Dora buys some T-shirts for $8.75 each and pairs of shoes for $27.50 each. If she buys 4 T-shirts, how much money would she have to spend in all
8.75*4=35 so $35 for shirts
and depending on how many shoes she buys but lets just say one pair
35+27.50= 62.50 so it would be a total of $62.50
Step-by-step explanation:
4 shirts with each price $8.75 = 4 × $ 8.75= $ 351 pair of shoes with price = $ 27.50so total price = $ 35 + $ 27.50 = $ 62.50MARK ME AS BRAINLISTPLZ FOLLOW METhe ratio of the length to the width the official german flag is 5:3.Sanda is making 12 german flags for a cuiture show.Each flag she makes has a length of 20 centimeters . It takes her 4 hours to make all the flag. What is the width of each flag and the average amount of time it takes sandra to make each flag?
Answer: The width of each flag = 12 cm
The average amount of time it takes Sandra to make each flag = 20 minutes.
Step-by-step explanation:
Given: The ratio of the length to the width the official german flag is 5:3.
Let length = 5x, width = 3x
Length of each flag = 20 cm
i.e. [tex]5x=20\Rightarrow\ x=\dfrac{20}{5}=4\text{ cm}[/tex]
Then width of each flag = 3 x 4 = 12 cm
i.e. width of each flag = 12 cm
Total time to make 12 flags = 4 hours
Time taken to make 1 flag = [tex]\dfrac{4}{12}[/tex] hour
Time taken to make 1 flag = [tex]\dfrac{1}{3}[/tex] hour
1 hour = 60 minutes
Time taken to make 1 flag = [tex]\dfrac{1}{3}\times60[/tex] minutes = 20 minutes.
Hence, the average amount of time it takes Sandra to make each flag = 20 minutes.
13
Calculate a, b and m so that the
polynomials P and Q defined by :
P(x) = (m - 2)x2 + (2a + 3)x +b +6 and
Q(x) = 3x2 - (m - 2)x + 2a - 3 , are equal.
Answer:
m = 5
a = -3
b = -15
Step-by-step explanation:
(m - 2) = 3 for x^2
(2a + 3) = - (m - 2) = (2 - m) for x^1
(b + 6) = (2a - 3) for x^0
Help me please and thank you
True for one value: -1
True for no values: 0
True for all values: 5
Determine the value of y, if x is-9.
Answer:
[tex]y=82[/tex]
Step-by-step explanation:
We know the value of x is -9 so we can plug it in as -9.
[tex]y=x^2+1\\y=(-9)^2+1\\y=81+1\\y=82[/tex]
Answer:
82=y
Step-by-step explanation:
-9 x -9 = 81
81 + 1 = 82
please help! give the answer in simplified form
Answer:
5a. 8:21
6a. 26:1
Please help me solve this
Answer:
Q. 11 x=29
Q. 12 x=24
Step-by-step explanation:
Q.11
sum of all sides of triangle = 180°
(2x+20)+(x+10)+(2x+5)=180°
5x+35=180°
5x=180°-35
5x=145°
x=145/5
x=29°
Q.12
sum of all sides of triangle=180°
96+(2x)+(x+12)=180°
3x+108=180°
3x=180-108
3x=72
x=72/3
x=24
it’s sad when I help people because they don’t do the same for so pls... answer me once:((((((((((((((((((((((((((((((((((((((
16 model airplanes on his shelf
4 times as many model airplanes as model trains
let's denote the number of model trains as m
So,
m=16×4
m=64
Therefore,there are 64 model trains.
pleasemark me as brainliest answer
Calculate the area of a kite that has diagonals that measure 6 centimeters and 8 centimeters.
9514 1404 393
Answer:
24 cm²
Step-by-step explanation:
When the diagonals of a quadrilateral cross at right angles, the area of it is half their product.
A = (1/2)(d1)(d2)
A = (1/2)(6 cm)(8 cm) = 24 cm²
The area of the kite is 24 square centimeters.
A car travels at an average speed of 68 miles per hour. How many miles does it travel in 5 hours and 45 minutes?
Answer:
391.
Step-by-step explanation:
There is 60 minutes every hour, so you divide by 60. 68 / 60 = 1.1333333333.
Now, we have to find out how many minutes there are in 5 hours and 45 minutes. Since there is 60 minutes every hour, 6 x 5 + 45 = 300 + 45 = 345. 1.1333333333 x 345 = 390.9999999885, rounded = 391.
Question:
A soccer ball has a radius of 11 cm. What is the volume of the soccer ball in cubic centimeters? Use 3.14 for pi. Round your
answer to the nearest hundredth.
Answer:
V = 4/3 * pi * radius^3
= 4/3 * 22/7 * 11*11*11 = 117128/21 = 5577.5238092.....
Step-by-step explanation:
There was an activity planned outdoors, but it started to rain. They took a vote and 45 people of the 60 people wanted to stay inside. The other 15 people voted to go outside in the rain. What percent of the class wants to go outside? Round to the nearest percent if needed.
Answer:
15/60×100=25%
Step-by-step explanation:
the number of students wanted to go outside/the whole number of students×100
15/60×100=25%
Rodeny rented a machine for $70.00 to make popcorn at a school event.In addition to the machine rental cost, the popcorn supplies cost him $0.15 per bag sold.Rodeny sold the popcorn for $1.00 per bag. How much profit did Rodeny make If he sold 200 bags of popcorn.
Answer:
100$
Step-by-step explanation:
he profit from 1 popcorn=0.85$
from 200=170$
170$-70$=100
HELP.................................................................
Answer:
A. [tex]\frac{1}{6^{2} }[/tex]
Step-by-step explanation:
A. [tex]\frac{1}{6^{2} } = \frac{1}{36} = 0.02777[/tex]
B. [tex]6^{-3} = 0.004629[/tex]
C. [tex]\frac{1}{216} = 0.004629[/tex]
D. [tex]\frac{1}{6^{3} } = \frac{1}{216} = 0.004629[/tex]
Answer:
I think it is A because B or D is not it so I was left with A and C. So I am pretty sure that is A.
In triangle ABC, point D is the centroid, and BD = 6. Find BE.
Given:
In triangle ABC, point D is the centroid, and BD = 6.
To find:
The measure of side BE.
Solution:
We know that the centroid divides each median in 2:1.
In the given figure BE is a median and point D is the centroid. It means point D divides the segment BE in 2:1.
Let BD and DE are 2x and x respectively.
We have, BD = 6 units.
[tex]2x=6[/tex]
[tex]x=\dfrac{6}{2}[/tex]
[tex]x=3[/tex]
Now,
[tex]BE=BD+DE[/tex]
[tex]BE=6+x[/tex]
[tex]BE=6+3[/tex]
[tex]BE=9[/tex]
Therefore, the measure of side BE is 9 units.
EXERCISE 6.1
1. What will be the unit digit of the squares of the following numbers?
(i)81 -
(ii) 272 -
(iii) 799 -
(iv) 3853 -
(v) 1234 -
(vi) 26387-
(vii) 52698
(vii) 99880
(ix) 12796
(x) 55555-
Rhea earned P9,876.88 a month while Jane earned P10,675.50. How much more did Jane earn month than Rhea?
1. What is asked in the problem?
2. What are the given facts?
3. What is the operation to be used?
4. What is the number sentence?
5. What is the correct answer
3 1183 long division
Factorise fully
X^2 - 25
Answer:
(x+5)(x-5)
Step-by-step explanation:
x^2-25 = x^2 - 5^2 = (x+5)(x-5)
rule: a^2 - b^2 = (a+b)(a-b)
PLEASE HELP ASAP
Jonathan has a rectangular rug with whose length is 5 inches less than its width. The area of the rug is 36 square inches
Help plsss!!!! Thnk you!!!!
Step-by-step explanation:
General quadratic equation: y = ax² + bx + c.
When x = 0, y = -3.
=> (-3) = a(0)² + b(0) + c, c = -3.
We now have y = ax² + bx - 3.
When x = 2, y = -4.
=> (-4) = a(2)² + b(2) - 3, 4a + 2b - 3 = -4,
4a + 2b = -1.
Our 1st system of equations is 4a + 2b = -1.
When x = 4, y = -3.
=> (-3) = a(4)² + b(4) - 3, 16a + 4b - 3 = -3,
16a + 4b = 0, 4a + b = 0.
Our 2nd system of equations is 4a + b = 0.
Now we solve the system of equations:
4a + 2b = -1
- (4a + b = 0)
=> b = -1
Hence 4a + (-1) = 0, 4a = 1, a = 1/4. (B)
its a screen shot do do do doooo
Depends on what pi is.
It could be
50.24 yards (pi is rounded)
OR
16π yards