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.
Please help me with this homework please from 1 to 4 and the check
Answer:
1. x=1
2. y=5
3. m=-6
4. z=3
Step-by-step explanation:
Answer:
I don't know because i am doing math along the way to solve answer.
Step-by-step explanation:
4x+8=2x+10
4x-2x+8=10
2x=10-8
2x=2
x=1 ANSWER FOR 1
2.)
Same thing as 1.
9y-3=6y+12
3y=15
Divide both by 3 and you get
y=5 Answer For 2
________________________
3.)
8m+4=4m-20
4m=-24
m=-6 Answer For 3
_________________________
4.)
11z-14=5z+4
6z=18
z=3 Answer for 4
Evaluate the following expression. Be sure to show your work.
Answer:
12
Step-by-step explanation:
[tex] \frac{ {6}^{2} }{3} = \frac{36}{3} [/tex]
[tex] \frac{36}{3} = 12[/tex]
Answer:
Step-by-step explanation:
Here you go mate
Step 1
[tex]\frac{6^2}{3}[/tex] Equation
Step 2
[tex]\frac{6^2}{3}[/tex] Simplify the fraction
[tex]\frac{36}{3}[/tex]
Step 3
[tex]\frac{36}{3}[/tex] Divide both sides by 3
12
answer
12
Hope this helps
Which point is on the graph of the function y = 3x + 2?
A. (1,5)
B. (2,3)
C. (3,2)
D. (5,1)
Answer:
a 1,5
Step-by-step explanation:
if the yintercept is 2, and the y increases 3 per every x value, then when the x would be one the y would be 5
Please help due ASAP
Show workings
Answer:
CD=66
Step-by-step explanation:
12x-30=6x+18
6x=48
x=8
12(8)-30=66
CD=66
4 5/2 - 4 3/2
ANSWER WITH EXPLANATION. BRAINLIST!!!!!
Answer:
1
Step-by-step explanation:
First, we have to make the fractions improper.
To this we would need to multiply the denominator by the whole number and add it to the numerator. 2*4 is 8. 8 + 5 is 13. So for the first fraction, it will be 13/5. Let’s do the second fraction. 2*4 is 8. 8 + 3 is 11. So for the second fraction, it will be 11/2. Since the fractions have the same denominator, we will not have to do anything to them. Now, all you have to do is simple subtraction. 13 - 11 is 2. Since the denominators are the same, it will equal to 2. So the final answer is 2/2 or 1.
Casey's grandmother sent her an $85 gift card for her birthday last year. This year, she sent her a $125 gift card. Which proportion can be used to find what percent of last year's gift this year's gift is, if n represents the unknown percent?
This better? If u seen my last one
Find the volume of a rectangular prism that has a height of 5 meters and the area of the base is 8cm squared
Answer:
Volume of prism = 4000 cm cubed
Step-by-step explanation:
Given that:
Height of rectangular prism = 5 meters
Converting into centimeters as the area of base is in centimeters.
1 meter = 100 centimeter
5 meters = 500 cm
Area of the base = 8 cm squared
Volume of prism = Area of base * Height
Volume of prism = 8 * 500
Volume of prism = 4000 cm cubed
Hence,
Volume of prism = 4000 cm cubed
When you are born, your parents deposited $500 into a simple interest account that
earns 2.5% annually. How much money would be in the account, for you, when you
turn 30 years old?
9514 1404 393
Answer:
$875
Step-by-step explanation:
The account pays simple interest, so the formula for the balance is ...
A = P(1 +rt)
A = $500(1 +0.025×30) = $500(1.75) = $875
There will be $875 in the account at age 30.
can someone help me find the area
Answer:
64a^2c^4
Step-by-step explanation:
What PERCENT is equivalent to 3 4/5?
3.6
36%
360%
Answer:
380%
Step-by-step explanation:
Turn into an improper fraction:
3x5=15 15+4= 19/5
You can do two ways
multiply by 20
19 x20 380
------ = ----------
5 x20 100
Other way: put into calculator
3,8
Turn into percent by multiplying by 100
=380
In the given right triangle, find the miss length.
A. 25 m
B. 27 m
C. 26 m
D. 28 m
Answer:
26
Step-by-step explanation:
Answer:
C. 26 m
Step-by-step explanation:
home / math / pythagorean theorem calculator
Pythagorean Theorem Calculator
Please provide any 2 values below to solve the Pythagorean equation: a2 + b2 = c2.
Result
abc
Given a=24 and b=10,
c = 26
∠α = 67.38° = 67°22'48" = 1.17601 rad
∠β = 22.62° = 22°37'12" = 0.39479 rad
area = 120
perimeter = 60
h =
120
13
= 9.2307692307692
+ Show Calculation Steps
a =
24
√
b =
10
√
c =
√
Calculate
Related
Triangle Calculator | Right Triangle Calculator
Pythagorean Theorem
The Pythagorean Theorem, also known as Pythagoras' theorem, is a fundamental relation between the three sides of a right triangle. Given a right triangle, which is a triangle in which one of the angles is 90°, the Pythagorean theorem states that the area of the square formed by the longest side of the right triangle (the hypotenuse) is equal to the sum of the area of the squares formed by the other two sides of the right triangle:
In other words, given that the longest side c = the hypotenuse, and a and b = the other sides of the triangle:
a2 + b2 = c2
This is known as the Pythagorean equation, named after the ancient Greek thinker Pythagoras. This relationship is useful because if two sides of a right triangle are known, the Pythagorean theorem can be used to determine the length of the third side. Referencing the above diagram, if
a = 3 and b = 4
the length of c can be determined as:
c = √a2 + b2 = √32+42 = √25 = 5
It follows that the length of a and b can also be determined if the lengths of the other two sides are known using the following relationships:
a = √c2 - b2
b = √c2 - a2
The law of cosines is a generalization of the Pythagorean theorem that can be used to determine the length of any side of a triangle if the lengths and angles of the other two sides of the triangle are known. If the angle between the other sides is a right angle, the law of cosines reduces to the Pythagorean equation.
There are a multitude of proofs for the Pythagorean theorem, possibly even the greatest number of any mathematical theorem.
Algebraic proof:
In the figure above, there are two orientations of copies of right triangles used to form a smaller and larger square, labeled i and ii, that depict two algebraic proofs of the Pythagorean theorem.
In the first one, i, the four copies of the same triangle are arranged around a square with sides c. This results in the formation of a larger square with sides of length b + a, and area of (b + a)2. The sum of the area of these four triangles and the smaller square must equal the area of the larger square such that:
(b + a)2 = c2 + 4
ab
2
= c2 + 2ab
which yields:
c2 = (b + a)2 - 2ab
= b2 + 2ab + a2 - 2ab
= a2 + b2
which is the Pythagorean equation.
In the second orientation shown in the figure, ii, the four copies of the same triangle are arranged such that they form an enclosed square with sides of length b - a, and area (b - a)2. The four triangles with area ab 2 also form a larger square with sides of length c. The area of the larger square must then equal the sum of the areas of the four triangles and the smaller square such that:
(b - a)2 + 4
ab
2
=
(b - a)2 + 2ab
= b2 - 2ab + a2 + 2ab
= a2 + b2
Since the larger square has sides c and area c2, the above can be rewritten as:
c2 = a2 + b2
which is again, the Pythagorean equation.
There are numerous other proofs ranging from algebraic and geometric proofs to proofs using differentials, but the above are two of the simplest versions.
The Change in your pocket weighs 23.42 grams. You remove a quarter that weighs 8.74 grams. How much weight is in your pocket?
Answer:
14.68
Step-by-step explanation:
it simple 23.42 minus 8.74
a store owner sells a mix that is 45% cashew nuts how many pounds of cashews should be add to 36 lb to make it 60% cashews
Answer:
13.5 lbs
Step-by-step explanation:
The number of pounds to be added with 36 lb to make cashews nut 60% is 12 pounds.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
45% cashew nuts = 36 lb
Multiply 60/45 on both sides.
60% = 60/45 x 36 lb
60% = 48 lb
The number of pounds to be added.
= 48 - 36
= 12 lb
Thus,
12 pounds of cashew should be added to 36 lb to make it 60% cashews.
Learn more about percentages here:
https://brainly.com/question/11403063
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In quadrilateral PQRS, the exterior angle at Q measures 155 and PS = QR. What measure of ∠PSR would confirm that PQRS is a parallelogram? I will mark brainliest :)
Answer: 25
Step-by-step explanation:
the exterior angle at q is 155, and the exterior and interior angle add up to 180. so, the interior angle at q is 180-155, which equals 25. angle PSR is across from interior angle q, and in parallelograms, angles across from one another must equal each other. this means that for PQRS to be a parallelogram, angle PSR must be 25 degrees.
3(b+1) +1 = 4b
please hurry i need it now
Answer:
4=b
Step-by-step explanation:
3b+3+1=4b
3b+4=4b
-3b -3b
4=b
please help me please will give brainliest to anyone who is good
Answer:
D
As temperature increases, so does mpg meaning better milage in warmer temperatures
In a sale, the original price of a bag was reduced to
80% its original value. The sale price of the bag is £56.
Work out the original price.
Answer =:70
Step-by-step explanation:
Question 5
1 pts
5) If a person runs 1/3 mile in 1/9 of an hour, what is
the unit rate per hour?
A. 1/9 mi/hr
B. 1/3 mi/hr
C. 3 mi/hr
D. 9 mi/hr
Gwen's blog post about camping has 70 comments. 30% of the comments were questions for Gwen about camping gear. How many of the comments were questions about camping gear? Pick the model that represents the problem.
To figure out how many of the 70 comments were those about questions for Gwen about camping gear, you need to first find the decimal of 30%, which is 0.3. Then the equation should be:
70 x 0.3
Answer: 21
Answer:21 comments about camping gear
Step-by-step explanation: Because percentages are just fractions out of 100, we know that 30% is 30/100. If you multiply 30/100 by 70, you get 21.
Pythagorean theory m3/9=3
Answer:
Step-by-step explanation:
m3/9=3
We move all terms to the left:
m3/9-(3)=0
We multiply all the terms by the denominator
m3-3*9=0
We add all the numbers together, and all the variables
m^3-27=0
#learnwithbrainly
What is the equation of this trend line? Please help ASAP!
Answer:8+2x
Step-by-step explanation:
“The quotient of two integers is always
an integer"
This statement:
A
is true.
B
is false.
С
does not provide
enough information.
Answer:
“The quotient of two integers is always an integer"
B. FalseStep-by-step explanation:
Suppose, 3 and 7 are integers but it's quotient 3/7 is not a integer.
If you can choose one scoop of ice cream and one topping, how many different sundaes can you make?
ice cream
vanilla
chocolate
toppings
fudge
cherry
marshmallow
find the value of x
A) 3
B) 14
C) 5
D) 2
Answer:
C) 5
Step-by-step explanation:
The measure of angle TSU is 75°. (180° - 105° because it is a flat angle)
The sum of all the angles of a triangle is 180° as well.
You can write an equation to solve for x.
12x + 9x + 75 = 180
Isolate x.
12x + 9x = 180 - 75
12x + 9x = 105
Add the 12 and the 9.
21x = 105
Find what x is.
x = 105 ÷ 21
x = 5
Write your answer in the form of (Yes or No because it has ___ml more or less) *
plz answer my question
Answer:
65
Step-by-step explanation:
15*3+15=60
30*2+15=75
20*4+15=85
10*5+15=65
Karrem says that the ratio 4:1 is eqivilent to the ratio of 12:9 because 4+8=12 and 1+8 =9 is karreem correct
Answer:
No, Kareem is incorrect.
Step-by-step explanation:
Kareem says that the ratio of [tex]\frac{4}{1}=\frac{12}{9}[/tex] because 4 + 8 = 12 and 1 + 8 = 9
But the correct way to rewrite the ratio 4 : 1 is,
[tex]\frac{4}{1}=\frac{4\times 3}{1\times 3}[/tex]
Which becomes as,
[tex]\frac{4}{1}=\frac{12}{3}[/tex]
Therefore, Kareem is not correct.
Correct ratio equivalent to 4 : 1 is 12 : 3.
Find fg(x)
[tex]f(x) = {x}^{2} + 2[/tex]
[tex]g(x) = {x}^{2} + 6x + 11[/tex]
Answer:
f(g(x)) = x^4 + 12x^3 + 14x^2 -132x + 123
Step-by-step explanation:
Here, we simply will place g(x) into f(x)
So every x in f(x) is replaced by g(x)
Thus, we have;
(x^2 + 6x + 11)^2 + 2
= (x^2+6x-11)(x^2 + 6x -11) + 2
= x^4 + 6x^3 -11x^2 + 6x^3 + 36x^2 - 66x -11x^2 -66x + 121 + 2
= x^4 + 12x^3 + 14x^2 -132x + 123
A rectangle has a length of 80 cm and a width of 50 cm. The rectangle is dilated by a scale factor of 3.5 to create a new rectangle. What is the area in square centimeters of the dilated rectangle?
Answer:it’s 4,000
Step-by-step explanation:
The area in square centimeters of the dilated rectangle will be A[d] = 49000 square centimeters.
What is scale factor? How it is used in Dilating sides?
Scale factor tells us by how much one quantity is greater than the other. It is denoted by [K]. Mathematically -
K = a/b.
Rewriting, we get -
a = Kb
If a side length [a] of any 2 - D figure is dilated by a scale factor of [k], then the length of new side will be [Ka]
Given is a rectangle has a length of 80 cm and a width of 50 cm. The rectangle is dilated by a scale factor of 3.5 to create a new rectangle.
Now, after dilation the new dimensions will be -
Length = 3.5 x 80 = 280 cm
Width = 3.5 x 50 = 175 cm
The area in square centimeters of the dilated rectangle will be -
A[d] = 280 x 175 = 49000 square centimeters
Therefore, the area in square centimeters of the dilated rectangle will be A[d] = 49000 square centimeters
To solve more questions on dilation, visit the link below-
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