Solution :
a). [tex]$P(0)$[/tex] is true
Then ,[tex]$P(0+2)=P(2)$[/tex] is true.
[tex]$P(2+2)=P(4)$[/tex] is true
[tex]$P(4+2)=P(6)$[/tex] is true.
Therefore, we see that [tex]$P(n)$[/tex] is true for all the even integers : [tex]$\{0, 2,4,6,...\}$[/tex]
b). [tex]$P(0)$[/tex] is true
Then ,[tex]$P(0+3)=P(3)$[/tex] is true.
[tex]$P(3+3)=P(6)$[/tex] is true
[tex]$P(6+3)=P(9)$[/tex] is true.
Therefore, we see that [tex]$P(n)$[/tex] is true for all the multiples of 3 : [tex]$\{0, 3,6,9,12,...\}$[/tex]
c). [tex]$P(0)$[/tex] and [tex]$P(1)$[/tex] is true, then [tex]$P(0+2)=P(2)$[/tex] is true
[tex]$P(1)$[/tex] and [tex]$P(2)$[/tex] is true, then [tex]$P(1+2)=P(3)$[/tex] is true.
[tex]$P(2)$[/tex] and [tex]$P(3)$[/tex] is true, then [tex]$P(2+2)=P(4)$[/tex] is true.
So, we observe that [tex]$P(n)$[/tex] is true for all the non- negative integers : [tex]$\{0, 1,2,3,4,5,6,...\}$[/tex].
d). [tex]$P(0)$[/tex] is true,
So, [tex]$P(0+2)$[/tex] and [tex]$P(0+3)$[/tex] is true or [tex]$P(2)$[/tex] and [tex]$P(3)$[/tex] is true.
Now, [tex]$P(2)$[/tex] is true.
Again, [tex]$P(2+2)$[/tex] and [tex]$P(2+3)$[/tex] is true or [tex]$P(4)$[/tex] and [tex]$P(5)$[/tex] is true.
Now, [tex]$P(3)$[/tex] is true.
Again, [tex]$P(3+2)$[/tex] and [tex]$P(3+3)$[/tex] is true or [tex]$P(5)$[/tex] and [tex]$P(6)$[/tex] is true.
Thus,
[tex]$P(n)$[/tex] is true for all the non- negative integers except 1 : [tex]$\{0, 2,3,4,5,6,...\}$[/tex].
HELP!!! Will give brainliest:) What shapes have all sides that are congruent?
Answer:
A square has all sides congruent. SIDE A, B, C and D would be congruent in size to one another, and the angles would also be equal to one another. However, most any polygon can be drawn with all sides and angles equal. For instance, an equilateral triangle has all sides and all angles equal, and that is the definition of a polygon. Polygons with more sides are described as "regular" e.g., a stop sign or an equilateral octagon is also a shape that has all sides congruent. A rectangle, however, would not, since only two sides would be congruent to one another.
( I hope this was helpful) >;D
You are making lemonade. The amount of sugar you need depends on the amount of lemonade mix you use. Cups of sugar \dfrac13 3 1 start fraction, 1, divided by, 3, end fraction 111 333 Packets of lemonade mix 111 333 999 Is the amount of sugar you need proportional to the amount of lemonade mix you use?
Answer:
Yes, the amount of sugar you need proportional to the amount of lemonade mix you use.
Step-by-step explanation:
You are making lemonade. The amount of sugar you need depends on the amount of lemonade mix you use. Cups of sugar
1/3
1
3
Packets of lemonade mix
1
3
9
Is the amount of sugar you need proportional to the amount of lemonade mix you use?
Cups of sugar ∝ Number of packets
C ∝ N
C = k/N
k = C/N
a) For
1/3 cups of sugar and 1 packet of Lemonade mix
1/3 ∝ 1
1/3 = 1k
k = 1/3/1
k = 1/3
b) For
1 cups of sugar and 3 packets of Lemonade mix
1 ∝ 3
1 = 3k
k = 1/3
k = 1/3
c) For
3 cups of sugar and 9 packets of Lemonade mix
3 ∝ 9
3= 9k
k = 3/9
k = 1/3
Therefore, Yes, the amount of sugar you need proportional to the amount of lemonade mix you use. This is because the value is k is the same
Answer:
yes
Step-by-step explanation:
Help me please !!!!!!!!
Step-by-step explanation:
[tex] \tan(45) = \frac{x}{13} \\ 1 = \frac{x}{13} \\ x = 13[/tex]
[tex] \cos(45) = \frac{13}{y} \\ 2 \sqrt{2} = \frac{13}{y} \\ 2y \sqrt{2} = 13 \\ y = \frac{13}{2 \sqrt{2} } [/tex]
Write the following expression using symbolic language.
1) Five less than the product of seven and a number x
2) The difference of nine times a number y and eighteen
3) Half a number n increased by four times the number
4) Twice the sum of a number w cubed and twenty-three
Answer:
1) 7x - 5 2) 9y - 18 3) 0.5n + 4n 4) 2(w³+23) Step-by-step explanation:1)
The product of seven and a number x: 7·x = 7x
Five less than the product of seven and a number x:
7x - 52)
nine times a number y: 9·y = 9y
The difference of nine times a number y and eighteen:
9y - 183)
half a number n: 0.5n
four times the number: 4·n = 4n
Half a number n increased by four times the number:
0.5n + 4n4)
a number w cubed: w³
the sum of a number w cubed and twenty-three: w³+23
Twice the sum of a number w cubed and twenty-three:
2(w³+23)
hiii please help i’ll give brainliest thanks
Answer:
0
Step-by-step explanation:
Welcome To Brainly!
Evaluate using PEMDAS
Parenthesis - None
Exponents 2^3
2x2 = 4
4x2 =8
now we have
72/9 - 1 x 8
Multiplication and Division
Going left to right
72/9=8
-1x8=-8
now we have 8 - 8
our last step is to subtract
8 - 8 = 0
the answer is 0
what would happen to a mounthly payment if the interest rate decreased
What is the payment you start with?
R = 21 ft. find the radius or diameter
Answer:
Radius = 21 ft
Diameter = 42 ft
Step-by-step explanation:
Answer:
radius is 10.5 ft.
Step-by-step explanation:
bc I said so
HELP PLS!!
If the sequence 4, 8, 12, 16 continues, what will be the 7th
term?
Answer:
28
Step-by-step explanation:
In order to find the seventh term in this arithmetic function, you need to find its function; in order to do this, you must first identify the common difference by finding the difference between two consecutive terms:
16 - 12 = 4; the common difference is 4
Now, you need to find the 0th term, which is the 1st term minus the common difference:
4 - 4 = 0
At this point, you can write out the function (where f(n) = [0th term] + [common difference]n:
f(n) = 4n
Finally, you can plug 7 into this function:
f(n) = 4(7)
f(n) = 28, so the 7th term is 28
Determine if the two triangles are congruent. If yes, which theorem proves their congruence?
Answer:
Not congruent.
The Angle-Side-Side Postulate does not exist because an angle and two sides does not guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non included angle, then triangles are NOT NECESSARILLY congruent.
Step-by-step explanation:
need help ASAP !!!
[tex] \sqrt{18 \times 18 \times 4} [/tex]
Answer:
36
Step-by-step explanation:
The first step to solving this equation is multiplying. Multiply the numbers on the inside of the square root.
18 × 18 × 4 = 1296
Now, you are going to find the square root of 1296.
[tex]\sqrt{1296}[/tex] = 36
You now have your final answer.
I hope this makes sense and is easy to understand. Please let me know if you need any more help. Have a great day! :]
Answer:
Step-by-step explanation:
[tex]\sqrt{18(18)(4)}\\ \\ \sqrt{2(3^2)2(3^2)2^2}\\ \\ \sqrt{2^4(3^4)}\\ \\ 2^2(3^2)\\ \\ 4(9)\\ \\ 36[/tex]
Josiah had 128 toy cars. If he organizes them into groups of 7 , how many cars will be in the final group?
Answer:
2
Step-by-step explanation:
128divided by 7 = 126
A grocer wants to mix two kinds of coffee. One kind sells for $1.00 per pound, and the other sells for $2.55 per pound. He wants to mix a total of 28 pounds and sell it for $1.35 per pound. How many pounds of each kind should he use in the new mix? (Round off the answers to the nearest hundredth.)
The measure of an angle is 39°. What is the measure of its complementary angle?
Answer:
51 degrees
Step-by-step explanation:
Complementary angles are two angles whose sum is (90degrees). If one is given an angle measure and needs to find its complementary angle, then all one has to do is subtract the given angle measure from (90degrees).
90 - 39 = 51
Answer:
51°Step-by-step explanation:
Complementary angles add to 90°.If one of them is 39°, then the other is:
90° - 39° = 51°Avery is going to invest $270 and leave it in an account for 20 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Avery to end up with $600?
Answer:
50
Step-by-step explanation:
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Answer:
3.99%
Step-by-step explanation:
2 EASY QUESTIONS HELP
Answer:
what are the questions
Step-by-step explanation:
what is the question
I need help in the answer it’s math
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Step-by-step explanation:
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Jamil has $62.67 in his saving account. His grandma gave him $5.00 for mowing the lawn and $.75 for taking out the garbage. How much money does Jamil have altogether?
You deposit $400 in an account . The account earns $ 16 simple interest in years . What is the annual interest rate? year
Answer:
The correct answer is 25.
Step-by-step explanation:
deposit- 400
interest- 16
Rate= deposit divided by interest
400 divided by 16 = 25
Which numbers are solutions of the inequality?
x > –5; –7, –5, –1
–7 and –5
–1
–5 and –1
–5
Answer:
—1 ...........................
If a printer can print 68 lines in per minute how many lines can it print in an hour? (hint: 1 hour=60 minutes)
Answer:
4080
Step-by-step explanation:
You are just multiplying 68 x 60= 4080
PLEASE HELP I WILL GIVE BRAINLIEST PLEASE 20 POINTS
9514 1404 393
Answer:
[tex]\begin{cases}3x+12&\text{if }x>-4\\0&\text{if }x=-4\\-3x-12&\text{if }x<-4\end{cases}[/tex]
Step-by-step explanation:
The absolute value function negates its argument when its argument is negative. The expression 3x+12 will be negative when ...
3x +12 < 0
x +4 < 0
x < -4 . . . . . makes the absolute value function change its argument's sign
Using this fact, we can divide the domain into intervals below -4, at -4, and above -4. The above answer shows the function value in each domain interval.
The three interior angle measures of this triangle are x= ___, y= ___, and z= ___.
Answer:
∡x = 30°
∡y = 70°
∡z = 80°
Step-by-step explanation:
The Bower family and the Jones family went to a restaurant and ordered food.
• Each burger cost the same, and each drink cost the same.
• The Bowers ordered 3 burgers and 2 drinks for a total of $13.50.
• The Joneses ordered 5 burgers and 4 drinks for a total of $23.50.
Which system of equations can be used to determine the cost of each burger, m, and each drink, p?
Answer:
right now in Bonny
Step-by-step explanation:
am so sorry for your prayers
hope it helps
A triangle has side lengths of 16 cm and 7 cm. Which could be the value of the third side, 28 cm or 19 cm?
The Value _______ cm is the value of the third side.
Drop down options:
28
19
Answer:
19Step-by-step explanation:
by pythagoras theorm
11. What is the value of x?
X
X-
2
x + 5
x + 1
da - x+5
Explicación
cualquier expresión multiplicada por 1 es igual a si mismo
x-2x+s
agrupe los términos semejantes
-x+5
help this is due today ;::
Answer: C- 17
Step-by-step explanation:
The graph of an equation is shown below:
Answer:
D, or (-3,2)
Step-by-step explanation:
Because the point (-3,2) is on the line of the equation shown, it is a solution. You can also notice that none of the other options are on the line and use the process of elimination.
Simplifying Radicals
in simplest radical form
Ra...
a.
v-117
b. V12 - 27 + 2 V3
c.
V3 * 142
Answer:
Step-by-step explanation:
2t-3=9-4t
Anyone know it.??
Answer:
Step-by-step explanation:
2t−3=9−4
2−3=−4+9
=2
solve for x
4x=30
give your answer as an improper fraction in its simplest form
Answer:
x=15/2Step-by-step explanation:
given:-4x=304x/4=30/4x=7.5 when we convert to improper fraction=75/10=15/2