Answer:
a) 3, 6, 9, 12, 15,...,[tex]3\cdot n[/tex], b) 4, 7, 10, 13, 16,...,[tex]3\cdot n +1[/tex], c) Both sequences are arithmetic.
Step-by-step explanation:
a) The sequence of natural numbers which are multiplied by 3 are represented by the function [tex]f(n) = 3\cdot n[/tex], [tex]n\in \mathbb{N}[/tex]. Let see the first five elements of the sequence: 3, 6, 9, 12, 15,...
b) The sequence of natural numbers which are multiplied by 3 and added to 1 is represented by the function [tex]f(n) = 3\cdot n + 1[/tex], [tex]n\in \mathbb{N}[/tex]. Let see the first five elements of the sequence: 4, 7, 10, 13, 16,...
c) Both sequences since differences between consecutive elements is constant. Let prove this statement:
(i) [tex]f(n) = 3\cdot n[/tex]
[tex]\Delta f = f(n+1) -f(n)[/tex]
[tex]\Delta f = 3\cdot (n+1) -3\cdot n[/tex]
[tex]\Delta f = 3[/tex]
(ii) [tex]f(n) = 3\cdot n +1[/tex]
[tex]\Delta f = f(n+1)-f(n)[/tex]
[tex]\Delta f = [3\cdot (n+1)+1]-(3\cdot n+1)[/tex]
[tex]\Delta f = 3[/tex]
Both sequences are arithmetic.
p(x)=x^3 -2x^2 -5x+6;3
Answer:
P(0)=2
Step-by-step explanation:
List three different possible three letter combination the phone could show on the screen after Sam presses 364
Answer: DOG, FNH, and EMI.
Step-by-step explanation: Each number on a phone corresponds to letters.
please help me please will give brainliest to anyone who is right
show your work
Answer:
N = st
Step-by-step explanation:
N/s = t
so st = N
I would appreciate Brainliest
Answer:
The correct answer is B. N = st
Step-by-step explanation:
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
t = number of toothpicks received by each student
s = number of students
N = total number of students
2. Which equation can be used to find the total number of toothpicks, N, given out by the teacher for the project?
Total number of toothpicks for the project = number of toothpicks received by each student * number of students, replacing with the variables:
N = t * s = s * t
The correct answer is B. N = st
Suppose the postal service charge is $10.30 per pound on a package shipped to England what is this rate in dollars per ounce
Answer: The required rate = 0.64 per pounce.
Step-by-step explanation:
We are given that,
Postal service charge = $10.30 per pound.
As we know, 1 pound = 16 ounces.
So, Postal service charge = $10.30 per 16 ounces.
Postal service charge[tex]=\$\dfrac{10.30}{16}\ \text{ per ounce}[/tex]
[tex]\approx 0.64\text{ per ounce}[/tex]
Hence, the required rate = 0.64 per pounce.
Solve 0=x^2 +6x+13 by completing the square
Answer:
No real solutions
Step-by-step explanation:
0=x^2+6x+13
Step 1: Subtract x^2 from both sides.
0−x^2=x^2+6x+13−x^2
−x^2=6x+13
Step 2: Subtract 6x from both sides.
−x^2−6x=6x+13−6x
−x^2−6x=13
Step 3: Since the coefficient of -x^2 is -1, divide both sides by -1.
−x^2−6x/−1 = 13/−1
x^2+6x=−13
Step 4: The coefficient of 6x is 6. Let b=6.
Then we need to add (b/2)^2=9 to both sides to complete the square.
Add 9 to both sides.
x^2+6x+9=−13+9
x^2+6x+9=−4
Step 5: Factor left side.
(x+3^)2=−4
Step 6: Take square root.
x+3=±√−4
Step 7: Add -3 to both sides.
x+3+−3=−3±√−4
x=−3±√−4
Help me with this pls
Without computing, decide whether the value of each expression is much smaller than
1, close to 1, or much greater than 1.
a. 100 - 1000
b. 504 + 50-
C. 4.7-5.2
d. 2= 7335
product in simplest form.
-blank y^2-{5y-y(-7-9)]-[-y(15y+4)]=0
Answer:
hope this helps
Step-by-step explanation:
PLZZZ MARK BRAINLIEST
Maddison hid 12 of her sister's birthday gifts around the house. If this was 15% of the gifts, how many total gifts did her sister have?
Answer:
80 gifts
Step-by-step explanation:
Maddison hid 12 of her sister's birthday gifts around the house. If this was 15% of the gifts, how many total gifts did her sister have?
Let the Total gifts that her sister has be represented by x
Hence:
15% of x = 12
15/100 × x = 12
15x /100 = 12
Cross Multiply
15x = 100 × 12
15x = 1200
x = 1200/15
x = 80 gifts
Hence, the total gifts her sister has is 80 gifts
Answer:
80 total gifts
Step-by-step explanation:
Step one:
given data
Maddison hid 12 of her sister's birthday gifts
we are told that 12 gift is 15% of the total gifts
let the total gifts be x
so
=15/100*x= 12
=0.15x= 12
divide both sides by 0.15
x= 12/0.15
x=80 total gifts
Find last year's salary if, after a 6% pay raise, thisyear's salary is 40810
A cafeteria worker is cutting apple wedges for student lunches.Each student lunch requires two apple wedges
The number of apple wedges that the cateteria worker needs to prepare is a linear function of the number of student lunches. Which statement correctly describes the domain of this function?
A numbers
B all real numbers
C all whole numbers
D all even whole numbers
Which expression is equivalent to 5 to the 3rd power
Answer:125
Step-by-step explanation: 5x5x5=125
How to solve step by step the following polynomial factoring problem:
(x + 3) - x(x^{2} + 6x+9)
Answer:
(x + 3) - x(x² + 6x + 9)
= (x + 3) - x(x + 3)²
= (x + 3)[1 - x(x + 3)]
= (x + 3)(1 - x² - 3x)
Step-by-step explanation:
Answer:
[tex](x+3)(1-x^2-3x)[/tex]
Step-by-step explanation:
First, let's factor that quadratic on the right:
[tex]x^2+6x+9[/tex] happens to factor nicely into [tex](x+3)^2[/tex], and putting that into our expression gets us
[tex](x+3)-x(x+3)^2[/tex]
Factoring out an (x + 3) from each term, we get
[tex](x+3)[1-x(x+3)][/tex]
Simplifying that expression on the right:
[tex](x+3)(1-x^2-3x)[/tex]
We can't factor that right-side expression any more, so we can just leave it like that!
4. Nick wants to buy a bike that cost $195. If he waits one more month, the bike will be discounted by 40%. How much money will Nick save if he waits for the discount to purchase the bike? *
7 points
$78
$55
$83
$91
5. One way to convert .9 to a percent would be to...
5 points
divide .9 by 100
multiply .9 by 100
add 100 to .9
subtract .9 by 100
6. Shawn is 22 years old. His cousin Marvin is 35% older than him. How old is Marvin?
7 points
27 years old
32 years old
25 years old
29 years old
7. Brianna went to diner for breakfast. The total bill was $38.50. The sales tax is 7%, and she decides to tip the waiter 25% of the original bill. What will be the total cost of the bill?
10 points
$50.83
$42.95
$48.72
$55.29
8. This year Monica scored a 70 on the FSA math test. Last year Monica scored a 45 on the FSA. What is the percent change in Monicas' FSA score?
7 points
62%
48%
56%
36%
-6 (x+3)umm helppp again I’m really bad at math
Answer:
-6(x + 3)
= -6x - 18
hope it helps you
Please help I don’t understand it’s like angles and stuff picture above. 20 POINTS WILK MARK BRAINLEST FOR RIGHT ANSWERS ONLY
Since 6x - 44 and 88 degrees are the same (exterior angles), we can start off with the first equation, 6x - 44 = 88
6x - 44 = 88
+44 +44
6x = 132
÷6 ÷6
x = 22
same with the second problem (exterior angles are equal):
equation:
15x + 6 = 9x + 54
-6 -6
15x = 9x + 48
-9x -9x
6x = 48
÷6 ÷6
x = 8
Hope this helped! :D
Answer:
1. x=22
2. x=8
Step-by-step explanation:
1. Opposite exterior angles are congruent, so 6x-44=88. You would add 44 to both sides, making the equation 6x=132, and then divide both sides by 6 to get your answer of x=22.
2. Again, opposite exterior angles are congruent, so 15x+6=9x+54. You would subtract 9x from both sides, making the equation 6x+6=54, then subtract 6 from both sides, making the equation 6x=48, and then divide both sides by 6 to get your answer of x=8.
(hope this helps!)
need help fast not sure how to get the answer
9514 1404 393
Answer:
x = 5y = 52Step-by-step explanation:
In any isosceles triangle, the base angles have the same measure:
y° = 52°
In any triangle the sum of angles is 180°.
52° +(14x +6)° +52° = 180°
14x = 70 . . . . . . . . subtract 110°, divide by °
x = 70/14 = 5 . . . . divide by the coefficient of x
The values of x and y are 5 and 52, respectively.
Helloooo please give the right answer :)
Answer:
9 feet
Step-by-step explanation:
3X3=9 feet therefore 3 yards is equal to 9 feet
The marked price of fan is Rs.1250, and the shopkeeper allows a discount of 6% on it . Find the selling price of the fan .
Given:;
Marked price of a fan = Rs. 1250.
Discount percent = 6%.
To find:
The selling price of the fan.
Solution:
We have,
Marked price of a fan = Rs. 1250.
Discount percent= 6%.
So,
Selling price = Marked price - Discount
[tex]S.P.=1250-\dfrac{6}{100}\times 1250[/tex]
[tex]S.P.=1250-75[/tex]
[tex]S.P.=1175[/tex]
Therefore, the selling price of the fan is Rs. 1175.
Suppose y varies directly with x, and y = 60 when x = 12. What is y when x is 20?
Step-by-step explanation:
y = kx, where k is a real constant.
When x = 12, y = 60.
=> (60) = (12)k, k = 5.
Therefore when x = 20,
y = kx = (5)(20) = 100.
The ratio of the surface area of two cubes is 49:81. Find the ratio of there volumes.
Answer:
343 : 729
Step-by-step explanation:
A cube is made up of 6 square faces. If each face has a side length of a, we can find the surface area of that cube with the formula [tex]A=6a^2[/tex], since we'll have 6 faces with area a². Let's call the edge length of the first cube a and the edge length of the second cube b. The ratio between their surface areas is then 6a² : 6b², or simply a² : b². If we compare this to our given ratio 49 : 81, we can see that a² = 49 and b² = 81, or, square rooting both equations, a = 7 and b = 9.
The volume of a cube with a side length a is a³, so the ratio between our cubes here must be a³ : b³. Using the values for a and b we just found, this ratio becomes 7³ : 9³, which we can simplify to 343 : 729.
Answer:
343 : 729
Step-by-step explanation:
If the ratio of the sides of a cube = a : b , then
ratio of areas = a² : b² and
ratio of volumes = a³ : b³
Given ratio of areas = 49 : 81, then
ratio of sides = [tex]\sqrt{49}[/tex] : [tex]\sqrt{81}[/tex] = 7 : 9 , so
ratio of volumes = 7³ : 9³ = 343 : 729
a box of dried fruit has 51 calories in 3 servings. how many calories are in 1 serving?
Answer:
17 calories
Step-by-step explanation:
What is the slope (1,-2), (0,1)
Answer:
m=-3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
1--2=3/(0-1)
3/-1=-3
Help me with this pls
Answer:
The answer should be C) 4x + 5x = 180
Step-by-step explanation:
Answer:
4x+5x=180
Step-by-step explanation:
to find x they must both add up to 180
What is the slope of the line that passes through (-5, 0) and (-5, 5)
Answer:
The entered points belong to a vertical line. There is no slope.
Equation: x = -5.
Step-by-step explanation:
Answer:
slope = infinite
Step-by-step explanation:
if a line passes through (-5, 0) and (-5, 5), then it's running straight up and down – the dead giveaway is that fact that the x-coordinates are the same.
by definition, the slope of a vertical line is infinite.
The original cost of a comic book was $3.95. The store markup on the comic book was 20%. What is the store's price for the comic book?
Answer:
$3.16
Step-by-step explanation:
Put the sentence in equation form Thirty-five more than a number is three hundred.
Answer:
35+x=300
Step-by-step explanation:
35 more would be 35 +, and then I added x in as the "number", and since it all adds up to 300, there would be the =300.
(hope this helps :P)
Elkan played 9 songs from his playlist. Ryan played 3 more songs than Elkan. How many songs did Ryan play?
Answer:
12
Step-by-step explanation: Ryan played 12 songs because 9+3=12
Brianna took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.30 plus $1.25 per mile. The total fare was $35.55, not including the tip. How many miles was the taxi ride?
Answer:
35.55-4.30=31.25
31.25/1.25= 25
total miles 25
Answer:
25
Step-by-step explanation:
sub 4.30 35.55 - 4.30 = 31.25
Divide 1.25 31.25/1.25 = 25
Final answer is 25
After dividing what you subtracted, you will successfully get your answer.
what is an equivalent expression to −56z+28
Answer:
(
2
z
−
1
)
Step-by-step explanation:
-56z:28
z equal to 28/56
