f(x) = 2([tex]2^{x}[/tex])
Step-by-step explanation:
Step 1 :
Given
When x =0, f(x) = 2
x =1, f(x) = 4
x =2, f(x) = 8
x =3, f(x) = 16
Step 2 :
Substituting for x in the function f(x) = 2([tex]2^{x}[/tex]) we get,
When x =0, f(x) = 2
x =1, f(x) = 4
x =2, f(x) = 8
x =3, f(x) = 16
This matches the given sequence and this shows that the function represents the given sequence .
Final answer:
The function rule for the given sequence 2, 4, 8, 16, ... is [tex]f(x) = 2^x[/tex], representing the sequence's exponential growth pattern where each term is double the previous term.
Explanation:
The given sequence is 2, 4, 8, 16, ..., which is a geometric sequence where each term is multiplied by 2 to get the next term. This pattern corresponds to an exponential function where the base is 2 and the exponent is the position of the term, which can also be thought of as the function's input, x. Therefore, the function that represents this sequence is f(x) = 2x.
The other function choices given, such as f(x) = 2x + 2 or f(x) = 2, do not correctly represent the pattern observed in the sequence. The correct function rule for the given sequence is f(x) = 2x which fits the pattern where when x is substituted for each term's position (starting from 0), the function provides the corresponding term of the sequence.
What is the answer to the question ?
Answer:
si amuigos hasta luego to es bien cien nueve
Step-by-step explanation:
3/4 divided by w equals what
Answer:
3/4w
Step-by-step explanation:
3/4 ÷w = 3/4 × 1/w = 3/4w
Jackson is building a double desk.The tops need to be 120 in long.Each board is 66 inches.How much will he need to cut if he buys 2 ?
He will need to cut altogether 12 inches to fit on the top if h buys 2 to adjust on the double desk.
Step-by-step explanation:
Jackson building a double desk requires 120 in long.When each board is 66 inches Therefore, if he buys 2 Boards, 2 x 66 = 132He needs to cut . subtracting 132 - 120 to adjust on the desk.132-120 = 12 if he cuts the board to adjust on each desk.Calculate the area of the regular pentagon below:
Answer:
1064.8 in^2
Step-by-step explanation:
12.1 x 17. 6 / 2 to find one half of a triangle will equal 106.48
there are 10 triangle therefore 106.48 x 10 = 1064.8
Answer:
532.4 in²
Step-by-step explanation:
The area (A) of the regular pentagon is calculated as
A = 0.5 × perimeter × apothem
Perimeter = 5 × 17.6 = 88 in
The apothem is the segment from the centre to the midpoint of one of the sides.
Here the apothem = 12.1 in, thus
A = 0.5 × 88 × 12.1 = 44 × 12.1 = 532.4 in²
UREGENT HELP please quick
Answer:
A
Step-by-step explanation:
Write a number of your choice, using the following clues:
a two digit number
greater than 40
divisible by both 2 and 3
Answer:
42
Step-by-step explanation:
42/2 = 21
42/3 = 14
Answer:
54 is what I thought of.
2. a. How could you distinguish between traveling west at 5 miles per hour and
traveling east at 5 miles per hour without using the words "east" and "west"
b. Four people are cycling. They each start at the same point. (0 represents their
starting point.) Plot their finish points after five seconds of cycling on a number line!
• Lin cycles at 5 meters per second
• Diego cycles at -4 meters per second
• Elena cycles at 3 meters per second
Answer:
Traveling east 5miles/hour can be represented as; traveling 45 degrees from south at 5 miles per hour .
Traveling west 5miles/hour can be represented as;
Traveling 45 degrees from south towards the north
The second part is on the attached file
Step-by-step explanation:
You will declare variables before you start solving the questions
Answer:
Step-by Traveling east 5miles/hour can be represented as; traveling 45 degrees from south at 5 miles per hour .
Traveling west 5miles/hour can be represented as;
Traveling 45 degrees from south towards the north
The second part is on the attached filey-step explanation:
Hi! Can somebody help me with this question? I am quite confused. Thanks!
Answer:
what is your problem in the figure
Answer:
Here are a couple questions I came up with myself! Feel free to use one!
Step-by-step explanation:
This chart is asking “ Well, we have data and we want you to make a question out of it”
So,
“How much was the population in Suwanee?”
“How much more is the population in Cartersville than Lilburn?”
“If you add the population of Cartersville, Suwanee, Lilburn, and Norcross, how much would the population be then?”
Hope this helped! ~Oreo
HELP ME!!! I've been stuck!
Answer:
You have to fill the blank squares to complete the table.See the figure attached and the explantion below.Explanation:
The figure attached shows the three squares that you have to fill to complete the table to summarize the different theorems to prove triangles are congruent.
1. SAS
SAS stands for Side Angle Side. That means that whenever two sides and the included angle on one triangle are congruent to two sides and the included angle of another triangle, then those two triangles are congruent.
Thick marks are used to mark the corrsponding parts, sides or angles that are congruent. That is why the two triangles to the first triangles on the image (on the upper square to the right) are marked:
One thick straight mark for two sides that are congruentTwo thick straight marks for the other two sides that are congruentOn thick curved mark for the two angles that are congruentIn that way, the figures show two triangles, with two congruent sides and the included angle congruent, to prove that the two triangles are congruent by the SAS theorem.
2. ASA
ASA stands for Angle Side Angle.
The ASA congruency theorem states that if two angles of a triangle and the included side are congruent, then the two triangles are congruent.
Thus you have to add the legend "Two congruent angles with and included side", which means that if the two angles and the included side on one triangle are congruent to two angles and the included side of other triangles, then both triangles are congruent.
The rule to mark the sides and angles that are congruent is with the use of thick marks. This is how it was done in the drawing of the two triangles in the lower right square:
One thick straight mark for two sides that are congruentOne thick curved mark for two angles that are congruentTwo thick curved marks for the other two angles that are congruentWh
at is 15,000:00 in ratio of 5:3
Answer:
9375 : 5625
Step-by-step explanation:
The total of the ratio units is 5+3=8, so each ratio unit stands for ...
15000/8 = 1875
Multiply each number of ratio units by this value to get your division:
5(1875) : 3(1875) = 9375 : 5625
What is X +2/5 equals 3 1/3
Answer:
Exact Form: X = 44/15
Decimal Form: X = 2.93¯
Mixed Number Form: X = 2 14/15
Step-by-step explanation:
Leila‘s coffee shop makes a blend that is a mixture of two types of coffee type a coffee cost Layla $4.85 per pound and type B coffee cost $5.90 per pound this month leather made it 142 pounds of the blend for the total cost of $781.10 how many pounds of type B coffee did she use
Answer:
Therefore she used (142-54)=88 pounds of type B coffee.
Step-by-step explanation:
Given, Leila's coffee shop makes a blend that is a mixture of two types of coffee.Type A coffee $4.85 per pound and type B coffee cost $5.90 per pound. She made 142 pounds of the blend for the total cost of $781.10.
The cost price of the blend per pound is = $(781.10÷142)
=$5.5
Let , the amount type A in the blend be x
Then the amount of type B in the blend is (142-x)
The cost price of x pound of type A coffee is = $(4.85×x) =$4.85x
The cost price of(142- x) pound of type B coffee is =$(142-x)×5.90
According to the problem,
4.85x+(142-x)×5.90 = 781.10
⇔4.85x +837.8-5.90x=781.10
⇔1.05x=56.7
⇔x=(56.7÷1.05)
⇔x=54
Therefore she used (142-54)=88 pounds of type B coffee.
the cruise ship is traveling at a uniform speed. after 11 hours, the cruise ship will be____nautical miles from light house.
Hence, After 11 hours, the cruise ship will be 244.25 nautical miles from the lighthouse. Hence, At the start of the journey, the cruise ship was 10.5 nautical miles from the lighthouse.
Answer:
the answer is the ship is traveling at 21.25 MPH, started 10.5 miles from lighthouse and after 11 hours will be 244.25 miles from the lighthouse.
Step-by-step explanation:
A building in a city has a rectangle base. The length of the base measures 70 feet less than three times the width. The perimeter of this base is 900 feet. What are the dimensions of the base?
Answer:
Width 130 ft and
Length 320 ft
Step-by-step explanation:
We are given;
Length of the rectangular base is 70 ft less than three times the width;Perimeter of the rectangular base is 900 ftWe are required to determine the dimensions of the rectangular base;
Assuming the width of the rectangular base is x ft
Then length will be (3x - 70) ft
But;
Perimeter = 2L + 2W
Thus;
900 ft = 2(3x-70) + 2(x)
900 ft = 6x -140 +2x
1040 = 8x
x = 130
Thus;
Width = 130 ft
Length = 3x -70 = 320 ft
Hence the dimensions of the rectangular base are width 130 ft and length 320 ft
In the basketball game, you made 12 baskets and scored 19 points. How many 2-point shots did you make? How many free throws did you make?
Answer:
0.5
Step-by-step explanation:
Answer:12 baskets - 19pts
2×7= 14pts
1×5= 5pts
Therefore: (7+5) baskets= (14+5)pts
> 12 baskets = 19pts
Step-by-step explanation:
For a 2-point shots to make 14pts, there will be 7 baskets/throws.
A free throw shot is 1pts, so there has to be about five (5) free throws which will make 5pts.
Therefore, there will be (7+5 baskets) 12 shots in total.
2-point shots = 7
1-free throws = 5
{(-2, 6), (-5, -1), (3, 7), (-5, 0)}
Domain:
Range:
Function?
{(-2, 6), (-5, -1), (3, 7), (-5, 0)}
Domain: The domain is all the x-values (-2, -5, 3, -5)
Range: The range is all the y-values (6, -1, 7, 0)
Function: It's not a function because of the x-value -5 is repeating.
Answer:
Step-by-step explanation:
domain (ur x values) = [ -5,-2,3 ]...only write repeating values once
range (ur y values) = [ -1,0,6,7]
a function will not have any repeating x values....it can have repeating y values, just not the x ones...all x's have to be different
therefore, this is not a function because u have repeating x values of -5
(0, 3) and (-2,5);
(5,-2) and (0, 3)
Answer:
Step-by-step explanation:
Select all equations that have no solution.
A. 12x – 3 – 6x = 6x – 3
B. 3 + 16x = 3 + 24x – 8x
C. 2 + 12x - 4x = 2 + 8x
D. 12x – (6x + 8) = 6x + 4
Answer:
D
Step-by-step explanation:
A.
12x – 3 – 6x = 6x – 3
12x - 3 = 12x -3
-3 = -3 infinite solution
B.
3 + 16x = 3 + 24x – 8x
3 + 16x = 3 + 16x
3 = 3 infinite solution
C.
2 + 12x - 4x = 2 + 8x
2 + 8x = 2 + 8x
2 = 2 infinite solution
D.
12x – (6x + 8) = 6x + 4
6x - 8 = 6x + 4
-8 = 4 no solution
Please help, I’m really stuck on this question!
How can you make different triangles with the same angle measures?
Form different triangles with angle measures 90°, 60°, and 30°
How can you make different triangles with the same angle measures?
OA. Make triangles with the same side lengths but different angle measures
OB. It is not possible to make different triangles with the same angle measures.
OC. Make triangles with the same angle measures and the same side lengths
OD. Make triangles with the same angle measures but different side lengths
Click to select your answer and then click Check Answer.
Answer:
D. Make triangles with the same angle measures and different side length.
Step-by-step explanation:
Since the values of the angles of the triangle are constant, varying the length of the sides would give series of triangles. Note that the length of the three sides must not be equal at any stage of the varying process.
Choose the correct simplification of (2x)(4y).
8xy
6xy
2xy
8y
Answer:
8xy
Step-by-step explanation:
(2x)(4y)
By expansion we have
2x x 4y
8xy
In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.
Somebody help, I don't get this!
Answer:
1. False
2. True
3. True
Step-by-step explanation:
1. ∠AHB and ∠AHG are vertical angle False
2.∠EHF and ∠DHE are adjacent angle True
3. The measure of ∠FHG is equal to the measure ∠DHF True
How much larger is the volume of a cylinder with a height of 8.5 inches and a radius of 4 inches compared to a cylinder with a volume of 390 cm^3?
______cm^3 larger
The first cylinder is larger by 6607.9 cm³.
Step-by-step explanation:
Step 1: Calculate volume of cylinder 1 using formula V(1) = πr²h, where r = 4 in = 10.16 cm and h = 8.5 in = 21.59 cm⇒ V(1) = 3.14 × 10.16² × 21.59 = 6997.9 cm³
Step 2: Find the difference between the volumes of the 2 cylinders.V(2) = 390 cm³
⇒ Difference = 6997.9 - 390 = 6607.9 cm³
Answer:
37.04
Step-by-step explanation:
HELP I AM DYEING STUCK ON THIS QUESTION
Q: v-14≤-18
I'm gonna assume you want us to simplify it.
v-14≤-18. Add 14 to both sides:
v ≤ -4
Answer:
v ≤ -4
Step-by-step explanation:
v - 14 ≤ -18
v -14 + 14 ≤ -18 + 14
v ≤ -4
what is the imaginary part of the number 9?
Answer:
0iStep-by-step explanation:
The imaginary number has form:
a + bi
a - real part
bi - imaginary part
i - imaginary unit (i = √-1)
We have the number 9.
9 is a real part
An imaginary part is equal 0.
Therefore the imaginary part of number 9 is 0i.
max spends three times as long on his math homework than he does on his science homework
3m=s
Where m= math homework and s= science homework.
nannie
HELP ME PLEASE :( <3 Which expression is equivalent to 4147−−−√ a - 37√ . b - 283√ . c - 127√
The simplified expression equivalent to 4147−−−√ a - 37√ . b - 283√ . c - 127√ is 64 - 6√ * b - 283√ * c - 127√.
To simplify the expression 4147−−−√ a - 37√ . b - 283√ . c - 127√, we can first try to identify any common factors among the terms.
However, since each term involves a different square root, it's not possible to simplify the expression further using common factors.
To proceed, we can try to simplify each term individually. For instance, we can simplify 4147−−−√ by identifying that 4147 is a perfect square. Since 4147 = 64 * 64, we can rewrite the expression as:
4147−−−√ = √(64 * 64) = 64
Similarly, we can simplify 37√ . b by identifying that 37 is a perfect square. Since 37 = 6 * 6, we can rewrite the expression as:
37√ . b = √(6 * 6) * b = 6√ * b
Applying the same logic to the remaining terms, we get the simplified expression:
64 - 6√ * b - 283√ * c - 127√
Therefore, the simplified expression equivalent to 4147−−−√ a - 37√ . b - 283√ . c - 127√ is:
64 - 6√ * b - 283√ * c - 127√
Terrance buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, which function represents the car’s value?
A portrait without its frame has a height 1.5 times its width w, in inches. Its frame is 2 in. wide all along its perimeter. What is an expression for the area of
the framed portrait in terms of w?
A. 1.5W2 + 5W + 4
B. 1.5w2 + 8w + 8
C. 1.5w2 + 8.5w + 16
D. 1.5w2 + 10w + 16
Answer:
The correct answer is A. 1.5w² + 5w + 4
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Height of the portrait = 1.5 times its width in inches
Frame = 2 inches all along its perimeter
2. What is an expression for the area of the framed portrait in terms of w?
Let's recall that the area of a rectangle is length or height * width.
A = height * width
Now, we can replace in terms of w:
A = 1.5w * w
But we need to add the 2 inches of the frame, this way:
A = (1.5w + 2) * (w + 2)
A = 1.5w² + 2w + 3w + 4
A = 1.5w² + 5w + 4
The correct answer is A. 1.5w² + 5w + 4
Final answer:
The expression for the area of the framed portrait in terms of w is 1.5w^2 + 8w + 8.
Explanation:
To find the expression for the area of the framed portrait, we need to consider the dimensions of both the portrait and the frame. Let's assume the width of the portrait is w inches. According to the given information, the height of the portrait without the frame is 1.5 times the width, so the height is 1.5w inches.
To calculate the dimensions of the framed portrait, we need to add 2 inches to the width and height for the frame. The width of the framed portrait is w + 2 inches, and the height is 1.5w + 2 inches.
The area of the framed portrait is equal to the product of its width and height. Therefore, the expression for the area, in terms of w, is (w + 2) * (1.5w + 2). When we simplify this expression, we get 1.5w2 + 8w + 8.
adam sells medical magazine and books. the table shows price for both Magazine £8
books £15
each week Adam earns £ 200 basic pay 10% of the magazine price for each sold
15% of the books price for each sold
last week Adam sold 42 magazines and 14 books
work out the total amount Adam earned last week
Adam earned a total of £265.10 last week.
Step-by-step explanation:
Step 1; Adam earns a basic pay of £200 each week. He earns 10% of the magazine price for each sold and 15% of the book price for each sold. Each magazine costs £8 and each book costs £15. He sells 42 magazines and 14 books.
Money earned for selling a magazine = 10% × £8 = 0.10 × £8 = £0.80,
Money earned for selling a book = 15% × £15 = 0.15 × £15 = £2.25,
Money earned for selling 42 magazines = 42 × £0.80 = £33.60,
Money earned for selling 14 books = 14 × £2.25 = £31.50,
Money earned for selling 42 magazines and 14 books = £33.60 + £31.50 = £65.10.
Step 2; Now we have to calculate his last week's salary which is his weekly pay and his earnings from selling magazines and books. We found that he earned £31.50 from selling books and magazines. His weekly salary is £200.
Last week's salary = £200 + £65.10 = £265.10.
Answer: £265.10
Step-by-step explanation:
Adam gets £200 each week.
10% of 42 magazines
Magazines opcost £8
10% × £8 = 0.10 × £8 = £0.80
42 × £0.80 = £33.60
15% of 14 books
Each book cost £15
15% × £15 = 0.15 × £15 = £2.25,
14 × £2.25 = £31.50
Last Week's Salary:
£31.50 + £33.60 = £65.10
£200 + £65.10 = £265.10 (last weeks salary)
Solve the following equation: 3x^3+5x^2-4x-4=0
Answer:
1
Step-by-step explanation:
Simplifying
3x + 2(4x + -4) = 3
Reorder the terms:
3x + 2(-4 + 4x) = 3
3x + (-4 * 2 + 4x * 2) = 3
3x + (-8 + 8x) = 3
Reorder the terms:
-8 + 3x + 8x = 3
Combine like terms: 3x + 8x = 11x
-8 + 11x = 3
Solving
-8 + 11x = 3
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '8' to each side of the equation.
-8 + 8 + 11x = 3 + 8
Combine like terms: -8 + 8 = 0
0 + 11x = 3 + 8
11x = 3 + 8
Combine like terms: 3 + 8 = 11
11x = 11
Divide each side by '11'.
x = 1
Simplifying
x = 1