Answer:4x+30
Step-by-step explanation:
Distribute 4(5+x) to get 20+4x
So then 10+20+4x
Which is 4x+30
Suppose that P(n) is a propositional function. Determine for which nonnegative integers n the statement P(n) must be true if a) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n 2) is true. b) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n 3) is true. c) P(0) and P(1) are true; for all nonnegative integers n, if P(n) and P(n 1) are true, then P(n 2) is true. d) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n 2) and P(n 3) are true
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].
Roy made 7 identical sundaes using 5 pints of ice cream. How much ice cream did Roy use for each sundae?
A back account pays an interest rate of 6% every 1 year. You deposit $5000 into the account. How much money will you have in 5 years?
A. $7092
B. $3449
C. $3670
D. $6691
Answer:
C: $6691
Step-by-step explanation:
This problem is one in compound interest. The general formula is shown below. The principal, P, is $5000, the annual interest rate, r, is 0.06 (expressed as a decimal fraction), and the number of years, t, is 5 years: A represents the Amount after 5 years:
A = P(1 + r)^t becomes A = ($5000)(1 + 0.06)^5, or
A = (5000)(1.06)^5 = $6691.12 (Answer D)
Please help me please help ASAP this is really really important
Answer:
3rd. 1
Step-by-step explanation:
A TV station executive is planning the new lineup for next season's shows. On Monday nights, there will be 6 sitcoms and 6 dramas, for a total of 372 minutes of programming, not counting commercials. On Tuesday nights, he has scheduled 2 sitcoms and 6 dramas, for a total of 288 minutes of non-commercial programming. All sitcoms have the same length and all dramas have the same length. How long is each type of show?
Answer:
x = length of sitcoms = 21 minutes
y = length of dramas = 42 minutes
Step-by-step explanation:
Let
x = length of sitcoms
y = length of dramas
6x + 6y = 372 (1)
2x + 6y = 288 (2)
Subtract (2) from (1) to eliminate y
6x - 2x = 372 - 288
4x = 84
x = 84/4
x = 21
Substitute x = 21 into (1)
6x + 6y = 372
6(21) + 6y = 372
126 + 6y = 372
6y = 372 - 126
6y = 246
y = 246/6
y = 41
x = length of sitcoms = 21 minutes
y = length of dramas = 42 minutes
Please helpppppp!!!!!!!!
Answer:
a, cube
Step-by-step explanation:
the scale factor is 1 : 87. If the diameter of a wheel on a model train is 0.3 inch, what is the diameter of the actual wheel?
Answer:
26.1
Step-by-step explanation:
Consider 0.3 as 1. Now multiply 0.3 by 87.
Needed ASAP for tonight, 10 quick homework questions
30 points and a brainly (see attached picture)
Hester sells televisions. She earns a fixed amount for each television and an additional $15 if the buyer gets an extended warranty. If Hester sells 15 televisions with extended warranties, she earns $1,275. How much is the fixed amount Hester earns for each television?
Answer: [tex]\$ 70[/tex]
Step-by-step explanation:
Given
Hester get a fixed amount and an additional $15 for an extended warranty
Suppose x is the amount of fixed amount
for 15 television sale, the price is $1275
Thus, we can write
[tex]\Rightarrow 15(x+15)=1275\\\Rightarrow x+15=85\\\Rightarrow x=\$70[/tex]
Therefore, the fixed amount of television is [tex]\$70[/tex]
5x – 9 > 8 + 5x Find the solution set:
Answer:
Here you go, it's In the attachment
Which solid has two faces, zero lateral faces, two bases, zero vertices, and zero edges?
cube
cone
sphere
cylinder
Answer:
cylinder
isn't this eighth grade geometry? i thought u were in high school
thank you lol i’m not smart sorry
Answer: 65
Step-by-step explanation: Sum of angles in triangles is always 180, we know one angle is 25 and another is 90, so 25 + 90 = 115, then 180 - 115 = 65.
can someone help me with the picture I put above please
Answer:
9
Step-by-step explanation:
3x+8=35
3x=27
x=9
Hello, this isn't really a question, but a tip!
So if your trying to find a perfect square and you given 225 you would just find the square root and if its a whole number then its a perfect square. If your asked to find the number that would make the perfect square that is asked for, you would take each number and multiply it by it self and then you can find your perfect square!!
Answertank cu
Step-by-step explanation:
Answer:
Ok, thanks for the tip you give keep safe.pls help ill give brainliest. the red isnt part of it was just how it was screenshot.
Find the area of a circle with 7cm radius .
Use the value 3.14 for π, and do not round your answer.
Be sure to include the correct unit in your answer.
Answer:
153.9
Step-by-step explanation:
hope it helps
Can y’all guys give me a list websites to wach anime on that are not bloked by the school cause please thank u
Answer:
it depends on what your school district restricts
Step-by-step explanation:
Are the ratios 15:12 and 6:4 equivalent?
Answer:
No
Step-by-step explanation:
To get to 12 from 4 you'd have to multiply by 3 but, if you multiply 6 by 3 you get 18, not 15.
Which rules define the function graphed below?
Please help. I’ll give extra points and brainliest for a real answer
Answer:
y=x+2; y=5
Step-by-step explanation:
Answer:
y=x+2; y=5
Step-by-step explanation:
got it right on the quiz
Each side of a square sandbox is 36 inches long. What is the area of the sandbox
The area of the square sandbox is 1,296 square inches
What is area of square?The area of a square is the measure of the space or surface occupied by it. It is equal to the product of the length of its two sides. Since the area of a square is the product of its two sides, the unit of the area is given in square units.
Area of a square = Side × Side
= [tex]Side ^{2}[/tex]
According to the question
Side of a square sandbox = 36 inches
Therefore,
The area of the square sandbox = [tex]Side ^{2}[/tex]
= [tex](36)^{2}[/tex]
= 1,296 square inches
Hence, the area of the square sandbox is 1,296 square inches
To know more about area of square here:
https://brainly.com/question/1658516
#SPJ2
multiply:- 4a^2 - 6a + 5 by 3a + 2.
Ans it fast plz.
i will mark u as brainliest.
Answer:
4a^2 + 9a + 10
Step-by-step explanation:
First we distribute
-4a^2 + (−6a) + (5)(3a) + (5)(2)
-4a^2 - 6a + 15a + 10
Then we combine like terms
4a^2 has no like terms, so it cannot be added onto anything else.
We add -6a to 15a
15a - 6a = 9a
4a^2 + 9a + 10
Answer:
Simplifying
(6a + -8)(4a2) = 0
Reorder the terms:
(-8 + 6a)(4a2) = 0
Remove parenthesis around (4a2)
(-8 + 6a) * 4a2 = 0
Reorder the terms for easier multiplication:
4a2(-8 + 6a) = 0
(-8 * 4a2 + 6a * 4a2) = 0
(-32a2 + 24a3) = 0
Solving
-32a2 + 24a3 = 0
Solving for variable 'a'.
Factor out the Greatest Common Factor (GCF), '8a2'.
8a2(-4 + 3a) = 0
Ignore the factor 8.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:
Simplifying
a2 = 0
Solving
a2 = 0
Move all terms containing a to the left, all other terms to the right.
Simplifying
a2 = 0
Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(-4 + 3a)' equal to zero and attempt to solve:
Simplifying
-4 + 3a = 0
Solving
-4 + 3a = 0
Move all terms containing a to the left, all other terms to the right.
Add '4' to each side of the equation.
-4 + 4 + 3a = 0 + 4
Combine like terms: -4 + 4 = 0
0 + 3a = 0 + 4
3a = 0 + 4
Combine like terms: 0 + 4 = 4
3a = 4
Divide each side by '3'.
a = 1.333333333
Simplifying
a = 1.333333333
Solution
a = {0, 1.333333333}
Step-by-step explanation:
For each sentence, write an equation.
Solve the equation to find the number.
a) A number divided by 6 is 9.
b) A number divided by -4 is -3.
c) A number divided by -5 is 7.
From 99° to 70°f what is the percent decrease
Answer:
should be -29.29 %
Step-by-step explanation:
Answer:
29.(29)%
Step-by-step explanation:
Solve the system of linear equations by substitution for x and y
1. X+y=7
Y=-3
2. 3x+4y=-10
X=-3y
Answer:
(10,5)
Step-by-step explanation:
●x+(-3)=7
x=7+3
x=10
●3x+4y=-10
3(-3y)+4y=-10
-6y+4y=-10
-2y=-10
y=5
Help me fast I have 30 min to finish the testtt!!!!!!!!!
please help me ! thank you
Answer:
57
Step-by-step explanation:
3 * 3 * 3 = 27 + 5*6 =30 27+30=57
Hope this helps!
Answer:
c.57
Step-by-step explanation:
.3^3= 27
.and 5 (6)=30
27+30=57
remember to use pemdas!! (parenthesis, exponents, multiplication/division, addition/subtraction)
find the value of given expression
[tex] \sqrt{300 \times 3} [/tex]
Answer:
√(300×3)=√900=√30²=±30 is your answer
Suppose a fair coin is tossed and the spinner below is spun one time. What is the probability of flipping heads and spinning a number greater than 2?
Answer:
3
Step-by-step explanation:
Answer:
3/10
Step-by-step explanation:
The weather forecast was calling for 8 inches of snow. It actually only snowed 2 1/4 inches. How far off was the forecast’s prediction?
Yolonda withdrew 60 dollars from her checking account.Write a signed number to represent this change in her account.
Answer:
$ 60.00
Step-by-step explanation:
.
To prepare for a party, Jada poured 0.45 liter of juice into each of several cups. Altogether she poured 9 liters of juice into the cups. How many cups did Jada fill? H e l p please :)
Answer:
20 cups
Step-by-step explanation:
Jada poured 0.45 liters of juice into several cups
9 liters was poured into each cup
Therefore the number of cups that Jada will fill up in the party can be calculated as follows
= 9/0.45
= 20
Hence Jada will fill up 20 cups