Reproduce the proof. When n = 1, we have
n³ + 2n = 1³ + 2 = 3
which is clearly divisible by 3.
Assume n³ + 2n is divisible by 3. Then for the next natural number n + 1, we have
(n + 1)³ + 2 (n + 1) = n³ + 3n² + 3n + 1 + 2n + 2
= n³ + 2n + 3 (n² + n + 1)
The first two terms n³ + 2n are divisible by 3 according to our assumption, and 3 (n² + n + 1) is clearly a multiple of, and therefore divisible by, 3 as well.
So the claim that 3 divides n³ + 2n is true for all natural numbers n.
Dev ordered 10 ink cartridges and 1 box of copy paper for his office. The box of copy paper cost $45. He had a coupon for $2 off each ink cartridge. He spent a total of $175.
Based on the cost of the copy paper and the discount on ink cartridges, the cost of the ink cartridge is $15 each.
First find the amount paid for the ink cartridges:
= Total spent - cost of copy paper
= 175 - 45
= $130
He got a discount of $2 per cartridge. For 10 cartridges he got a discount of:
= 2 x 10
= $20
The cost of each ink cartridge is:
= (Amount spent on ink cartridges + Discount) / Number of cartridges
= (130 + 20) / 10
= $15 each
In conclusion, each cartridge cost $15.
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I don’t understand this :(
Answer:
3 < S < 17
Step-by-step explanation:
picture the 10 side as the bottom
the 7 side pivoting on the right end of the 10 leg
when it swings toward the left the shortest the third side can be is >3
when it swings to the right the longest the third side can be is <17
Write an expression for the operation described below.
the product of r and s
Answer:
r + s
Step-by-step explanation:
the product of r and s
\/
Addition
\/
the product of r and s
\/
r + s
Have a nice day!
If this is not what you are looking for - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
can you please fin x and y
So we know that x = 90º because it is a right angle. And angle B also has to be 47º because it is a reflection of angle C. And all the angles of any triangle are equal to 180º, so if we do 180-(90+47)=43. So now we know that y=43º and x=90º Your welcome, please give me brainlest.
work out
a) 4 1/3 x 6
b) 2 3/5 x 3 1/3
Answer:
a) 26
b) 26/3
Step-by-step explanation:
a) 4 and 1/3 = 13/3
13/3 x 6/1 = 13/1 x 2/1
b) 2 and 3/5 = 13/5, 3 and 1/3 = 10/3
13/5 x 10/3 = 13/1 x 2/3
Convert the following measurements into the indicated units:
Step-by-step explanation:
1) 2.057 kg
2)1.25× 10^-1 um
3)65.8km
4)2.78 × 10^2 mg
5)9.44 yards
6) 5.91ft
7)200000cm^3
8)1287.48km
Please help me! I will mark brainliest if correct! (Question is in the image shown)
2nd one the combining with y one
Factor. Check by multiplying.
x²- 6x
- BRAINLIEST answerer
1) Solve 3x+2= 5.
A. Model 3 2 x+ = 5.
B. Perform the step to have the variables (circles) alone on one side.
C. Write the resulting step.
D. Divide the variables (circles) and numbers (squares) into equal groups.
E. Show the value of one group.
DO EVERY SINGLE ONE
Answer:
x = 1
Step-by-step explanation:
3x + 2 = 5
→ Minus 2 from both sides
3x = 3
→ Divide both sides by 3
x = 1
please can i have help
Answer:
1:6ab
2: c^6x
3: 10y^7x
4:3g^4 h^5 x^4
Which of these inequalities is graphed below
Y>2x-6
Y<2x-6
Y<2x-6
Y>2x-6
Answer:
D
Step-by-step explanation:
The line looks dotted (image quality isn't the best) so we can already exclude the inequalities with [tex]\le[/tex] or [tex]\ge[/tex]. At this point let's check an "easy" point, 0.0.
[tex](0)>2(0)-6 \rightarrow 0>-6[/tex] Which is indeed true. The correct answer is D
A tree that is 15 feet tall casts a 10 foot shadow. What is the length of the shadow of a nearby 21 foot tall tree?
Answer:
16 ft is the 21ft tall tree.
Step-by-step explanation:
15:10
21 - 5 is 16
Percent of 51,300-45,800
Answer: the percent is 112.01. please mark brainliest
Step-by-step explanation:
Plzzzzzx help meeeeee
Step-by-step explanation:
first find out the area of sector ECF
π(10)² × 40°/360°
=100π×1/9
=100π/9 m²
now find the area of sector DCG
π(2)² × 40°/360°
=4π/9 m²*
so the area of the shaded region would be the big sector minus the small sector
so
100π/9 - 4π/9
=96π/9
=33.5 m² (3sig.fig.)
*Note that 4π/9 DOES NOT equal to 2π/3
4/9 DOES NOT EQUAL TO 2/3
A group of students is going on an overnight camping trip. The cost of the campsite is $19 and the cost of food is $12 per person.
pls help me
Answer:
Step-by-step explanation:
12 times 19 equals 228 final answer 228
The graphs of the equations 2x - By = 7 and Ax + 3y = 10 are both the same line. Find A and B.
Answer:
[tex]\bold{A = \frac{20}{7}}[/tex]
[tex]\bold{B = -\frac{21}{10}}[/tex]
Step-by-step explanation:
[tex]\underline{\mathrm{Same \:lines:}}\\\\y = \frac{2x}{\mathrm{B}} - \frac{7}{\mathrm{B}}\\\\ y = \frac{\mathrm{-A}x}{3} +\frac{10}{3}[/tex]
[tex]\mathrm{If\:they\:are\:in\:the\:same\:line,\:then\:the\:Slopes\:and\:Intercepts\:are\: Equal.}[/tex]
Help me! Quick! Please. 25 points
Answer:
A. would be correct
Step-by-step explanation:
if 1 package is $8 and 2 packages cost $16
the ratio would be $8:1 so the unit rate would be $8 per package
help plzz 78 % of R340 ,00
Answer:
R26,520
Step-by-step explanation:
78÷100×34000. This is the explanation
Use the graph below to fill in the blank with the correct number:
F(0)=
Answer:
f(0) = 1.
Step-by-step explanation:
f(0) means the value of f when x = 0.
From the graph this is 1.
A helicopter floats 120m above a helipad, a dog is 85m from the helipad, if the dog could fly, how far would it have to fly to get to helicopter?
Answer: 35m
Step-by-step explanation:
A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (2, 4).
The graph of the function is negative on (4, infinity).
The graph of the function is positive on (negative infinity, –7).
The graph of the function is negative on (–7, –1).
Answer:
C. The graph of the function is positive on (negative infinity, –7).Step-by-step explanation:
With given conditions we can state:
The graph is positive between (-∞, -7)∪(-7, -1)∪(4, +∞), since it touches -7 and is positive either side of it.The graph is negative between (-1, 2) and (2, 4), since it touches 2 and is negative either side of it.Overall shape is U as leading coefficient is positive and is of even degree.Comparing with the answer choices, correct choice is C.
at noon a contained 20 in of water after several hours it contained 16 in of water what is the percent decrease of water the tank
Answer:
20%
Step-by-step explanation:
20 x .2 =4
0.2 because its 20%
20-4=16
convert to 75 km/ into m/s
Answer:
1(kilometer/hour) = 1000(meters) / 3600(seconds) can also be expressed as 1(kilometer/hour) = 5/18 (meters/second), which is its simplified form. To convert km/h to m/s, directly multiply the given value of speed by the fraction 5/18
Step-by-step explanation:
so the answer wil be 20.8333 m/s
I= $50
P= $500
r= ?
t= 5 years
Answer:
2%
Step-by-step explanation:
Interest Rate = (Simple Interest × 100)/(Principal × Time).
50= 500(5)(r)
50= 2500r
50/2500= .02 or 2%
Find all missing angles
Answer:
10
Step-by-step explanation:
best guess ever
find the measure of KH
Answer:
i dont know
Step-by-step explanation:
NEED ASAP
What are the coordinates of the midpoint of AB if A (4, 6) and B(-8, 2)?
o (6, 4)
O (-6, 4)
O (-2, 4)
o (2, 4)
Answer:
(- 2, 4 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) , then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Here (x₁, y₁ ) = A (4, 6 ) and (x₂, y₂ ) = B (- 8, 2 )
midpoint = ( [tex]\frac{4-8}{2}[/tex] , [tex]\frac{6+2}{2}[/tex] ) = ( [tex]\frac{-4}{2}[/tex] , [tex]\frac{8}{2}[/tex] ) = (- 2, 4 )
Midpoint be p(x,y)
P(x,y)=
[tex]\\ \sf\longmapsto \left(\dfrac{4-8}{2},\dfrac{6+2}{2}\right)[/tex]
[tex]\\ \sf\longmapsto \left(\dfrac{-4}{2},\dfrac{8}{2}\right)[/tex]
[tex]\\ \sf\longmapsto (-2,4)[/tex]
Find the equation of the linear function represented by the table below in slope-intercept form. x y -1 -4 3 -8 7 -12 11 -16
If you had half a dollar, three quarters, eight dimes, six nickels, and nine pennies, how much money would you have altogether?
Answer:
$1.69
Step-by-step explanation:
Half a dollar = $0.50
Eight dimes = $0.80
Six nickels = $0.30
Nine pennies = $0.09
Total = $0.50 + $0.80 + $0.30 + $0.09 = $1.69
Answer:
1.69
Step-by-step explanation:
evaluate the following using identity ( part 2 )
4. (0.4a + 1/4 b) (0.4a - 1/4b)
5. (x + 1/y) ( x-1/y)
6. (2/3x + 3/11y) (2/3x - 3/11y)
Answer:
refer the attachment pls
