The ordered pairs (1, 4), (2, 16), (3, 64), (4, 256), and (5, 1,024) represent a function. what is a rule that represents this function?
Answers
As you can already notice, the y-values are increasing exponentially.
How would you get 4->16? 4^2
16->64? 4^3
I have attached a graph below that will help you visualize this.
Final answer:
The rule that represents the given function with ordered pairs (1, 4), (2, 16), (3, 64), (4, 256), (5, 1,024) is f(x) = 4^(x-1), which is determined by observing the pattern of the ordered pairs.
Explanation:
Identifying the Rule of a Function
The ordered pairs (1, 4), (2, 16), (3, 64), (4, 256), and (5, 1,024) represent a function where each input from the domain is mapped to a unique output in the range. Observing the pattern of the ordered pairs, we can infer a rule that corresponds to this function. Each second element in the pair appears to be an exponentiation of 4 to the power of the first element minus one.
The general rule for this function can be expressed as f(x) = 4^(x-1). We can verify this by plugging in the values from the domain (1 through 5) into the function:
For x = 1, f(1) = 4^(1-1) = 4^0 = 1
For x = 2, f(2) = 4^(2-1) = 4^1 = 4
For x = 3, f(3) = 4^(3-1) = 4^2 = 16
For x = 4, f(4) = 4^(4-1) = 4^3 = 64
For x = 5, f(5) = 4^(5-1) = 4^4 = 256
Therefore, the rule representing this function is f(x) = 4^(x-1).
Related Questions
The sum of four consecutive even integers is 180. what is the smallest integer?
Answers
let the smallest even number be x, than the four even numbers are x, x+2, x+4, x+6, their sum is 180
x+x+2+x+4+x+6=180
4x+12=180
4x=168
x=42
the smallest even number is 42.
The equation is 4x + 12 = 180. Then the value of the smallest integer will be 42.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The sum of four consecutive even integers is 180.
Let x be the smallest integer. Then the other three consecutive even integers will be x + 2, x + 4, and x + 6. Then the equation is given as,
x + x + 2 + x + 4 + x + 6 = 180
4x + 12 = 180
4x = 168
x = 42
The value of the smallest integer will be 42.
More about the Algebra link is given below.
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Evaluate.
12⋅(4^−2/4^−4)
a) 14
b) 34
c) 16
d) 192
Answers
Answer:
d) 192
Step-by-step explanation:
Your calculator can do this for you.
Or, you can simplify to
[tex]12\cdot\dfrac{4^{-2}}{4^{-4}}=12(4^{-2+4})=12(4^2)=192[/tex]
Answer:
d
Step-by-step explanation:192
What is the equation of the quadratic function with roots -3 and 1 and a vertex a (-1, -8)?
Answers
y-[-8] = a(x-[-1]), or y+8 = a(x+1)^2. The coefficient a is undetermined here. How do we find it?
At any root, y=0, as a "root" is a point at which the graph crosses the x-axis.
Thus, if we choose to work with the given root 1, the associated point is (1,0). Substitute these coordinates into the above equation y+8 = a(x+1)^2.
We get 0+8 = a(1+1)^2, or 8 = a(2)^2, or 8 = 4a, or a = 2.
Substituting this value for a into the above equation,
y+8 = 2(x+1)^2.
You should check this result by determining whether the other root (-3,0) satisfies this equation. If yes, then you'll know for certain that this equation correctly describes the parabola in question.
Nellie and her younger sister Debbie share expenses on a holiday. Nellie spends $122 more than Debbie. Their total expenses amount to $840.
Answers
A pair of vertical angles may also form a linear pair true or false
Answers
In a cross-country race with a 35 participants, the mean finish time was 21 minutes . Which statement must be true ?
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How does the graph of g(x)=⌈x⌉+7 differ from the graph of f(x)=⌈x⌉?
The graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted right 7 units.
The graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted up 7 units.
The graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted left 7 units.
The graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted down 7 units.
Answers
Hope I helped :)
Answer:
Step-by-step explanation:
Stretch pulling the graph up/down
The expression 2/+2w is used to find the perimeter of a rectangle with length / and width w.
What is the perimeter of a rectangle with length 14cm and width 4cm?
9cm
18cm
28cm
36cm
THANKS IN ADVANCE, I MARK BRAINLIEST!!!
Answers
Hope this helps! Good luck! :)
Answer: 36 cm
Step-by-step explanation:
Given : The expression 2l+2w is used to find the perimeter of a rectangle with length l and width w.
To find : The perimeter of a rectangle with length 14cm and width 4cm.
Substitute l=14 and w=4 in the given expression , we get
Perimeter= [tex]2(14)+2(4) =28+8=36\ cm[/tex]
Hence, the perimeter of a rectangle with length 14cm and width 4cm= 36 cm
If two angles are congruent and supplementary then each is a right angle true or false
Answers
90 + 90 = 180 - also supplementary.
Answer:
The statement is true. Supplementary angles have measures that add up to 180°. Each right angle has a measure of 90°. 90°+ 90° = 180°.
Step-by-step explanation:
A train leaves little rock, arkansas, and travels north at 70 kilometers per hour. another train leaves at the same time and travels south at 55 kilometers per hour. how long will it take before they are 375 kilometers apart?
Answers
To find (t) or time, you will want to start by combining like terms, so that the equation is: 125(t) = 375
Dividing the equation by 125 so that (t) will be separated from all other factors
125(t) = 375
------------------ ==> (t) = 3 hours
125
Which are perfect squares? Check all that apply. 49 17 g 143 225
(need answer NOW plssss)
(90 points)
Answers
9,
and
225
are all perfect squares.
I hope this helps you!
Brainliest if satisfied :D
Would mean a lot
We have that the 49 and 225 are the Perfect squares
Perfect squares
Question Parameters:
49 17 143 225Generally, Perfect Square are gotten by multiplying two equal numbers
Therefore
49 and 225 are square rooted to attain 7 and 15
Hence, The are the Perfect squares
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What is the value of x when f(x) 25?
Answers
I hope this right if not let me know hope I helped and didn't srew u up good luck
The question wants to find the value of x when f(x) equals 25. The exact value cannot be determined without the clearly defined function f(x). The value of x can vary depending on the definition of the function.
Explanation:
This is a function notation question where you want to find the value of x when f(x) equals 25. The information provided is not sufficient to determine the exact value of x since the function f(x) is not clearly defined. Depending on the function definition, the value of x when f(x) = 25 can vary. For example, if the function is f(x) = 0.25e(-0.25x), then the value of x would be calculated differently than if the function was f(x)=5x or f(x)=x^2. I'd recommend checking your question again and confirming the function's correct formula or equation for an accurate solution.
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On the average, actively managed mutual funds have an expense ratio of about __________ .
a. 5 percent
b. 3 percent
c. 2.5 percent
d. 1.5 percent
Answers
And here's a quizlet link to help you
https://quizlet.com/81564997/finn-3003-ch-17-flash-cards/
HELP!!!!!!!! PLZ!!!!!!!!WILL GIVE BRAINLIEST!!!!!!!! :)
Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Lia’s parents allow her to work a maximum of 15 hours per week overall. Lia’s goal is to earn at least $120 per week.
1.)Write a system of inequalities to represent this situation. Let r be the number of hours worked at the restaurant, and let y be the number of hours of yard work.
2.)Graph the inequalities.
3.)What is the maximum number of hours Lia can work at the restaurant and still meet her earnings goal? Explain.
4.)What is the maximum amount of money Lia can earn in 1 week? Explain.
Answers
r>=5
8r+12y>=120
(3) assuming she will work 15 hours, y = 15-r
so
8r + 12(15-r) >= 120
8r+180-12r>=120
-4r+180>=120
-4r >= -60
r <= 15
looks like she could work all 15 hours and still make 120 dollars
(4) r= 5 required hours in the restaurant then
8r + 12(15-r)= 160
What type of endorsement is illustrated by the following example: Tom Ash 7609-25-26-3 A) Restrictive endorsement B) Full endorsement C) Blank endorsement D) Signature endorsement
Answers
The answer is letter c which is blank endorsement. It is a sign by the maker of an instrument, for instance a check, which allows any holder of the instrument to declare a claim for payment. Since no payee is stated, such an endorsement fundamentally turns the instrument into a bearer security.
The example given 'Tom Ash 7609-25-26-3' indicates a blank endorsement, which is when the original holder of a negotiable instrument signs their name without naming a new payee or providing other instructions, making the instrument payable to the bearer.
Explanation:The type of endorsement illustrated by 'Tom Ash 7609-25-26-3' is a blank endorsement. In a blank endorsement, the holder of a negotiable instrument, such as a check, simply signs their name on the back of the instrument without specifying the new payee or any other instructions. This means that the instrument becomes payable to the bearer and can be transferred merely by delivery. The other types of endorsements include restrictive, full, and signature endorsements, but since there are no additional instructions or named endorsee next to the signature, it does not qualify as any of those.
The perimeter of a rectangular concrete patio is 34 meters. the area is 70 square meters. what are the dimensions of the patio?
Answers
To find the dimensions of the rectangular patio, use the equations for perimeter and area and solve for length and width.
Explanation:To find the dimensions of the rectangular patio, we can use the given information about its perimeter and area. Let's assume the length of the patio is L and the width is W.
The perimeter is given as 34 meters, which is equal to 2L + 2W. So, we have the equation 2L + 2W = 34.
The area is given as 70 square meters, which is equal to L * W. So, we have the equation L * W = 70.
We can use these equations to solve for L and W using substitution or elimination method.
Write an equation to represent: four-fifths of z added to six equals eight
A) 4/5 z + 6 = 8
B) 4/5 + 6z = 8
C) 4/5 (6)(z) = 8
D) 4/5 (6) + z = 8
Answers
4/5z + 6 = 8...its A
Answer:
Option A - [tex]\frac{4}{5}z+6=8[/tex]
Step-by-step explanation:
To find : Write an equation to represent : four-fifths of z added to six equals eight ?
Solution :
The expression is 'four-fifths of z added to six equals eight',
Write in number term by term,
four-fifths of z is [tex]\frac{4}{5}z[/tex]
four-fifths of z added to six is [tex]\frac{4}{5}z+6[/tex]
four-fifths of z added to six equals eight is [tex]\frac{4}{5}z+6=8[/tex]
Therefore, The representation is [tex]\frac{4}{5}z+6=8[/tex]
So, Option A is correct.
A box of cookies can hold 24 cookies, and a container can hold 75 boxes of cookies. write a program that prompts the user to enter the total number of cookies, the number of cookies in a box, and the number of cookie boxes in a container. the program then outputs the number of boxes and the number of containers to ship the cookies. note that each box must contain the specified number of cookies, and each container must contain the specified number of boxes. if the last box of cookies contains less than the number of specified cookies, you can discard it and output the number of leftover cookies. similarly, if the last container contains less than the number of specified boxes, you can discard it and output the number of leftover boxes.
Answers
The provided math problem involves writing a program that helps to calculate the number of cookie boxes and containers required to ship a specific number of cookies considering the capacity of each item. If there are leftover cookies that do not fill a box or if there are leftover boxes that do not fill a container, these are also calculated.
Explanation:This is a programming problem which requires logic to calculate the number of boxes and containers needed to ship a given number of cookies. Assume that 'total_cookies', 'cookies_per_box', and 'boxes_per_container' are user inputs. Initially, you should calculate the total boxes by 'total_boxes = total_cookies / cookies_per_box'. The floored division operator is applied to discard the last box if it contains less than the specified number of cookies. Then, calculate the total containers with 'total_containers = total_boxes / boxes_per_container'. Again, you use the floored division operator to discard the last container if it contains less than the specified number of boxes. Lastly, calculate the leftover cookies and boxes, which is done by applying the modulus operator. 'leftover_cookies = total_cookies % cookies_per_box' and 'leftover_boxes = total_boxes % boxes_per_container'.
The logic of the given program focuses on the calculation of boxes and containers needed to ship the given number of cookies keeping in consideration the capacity of each box and container. Also, the algorithm calculates the leftover cookies and boxes, if not enough to fill a box or container fully.
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Out of 100 lottery tickets, each having 50% chance of winning, 2 tickets are bought at random. what is the probability that at least one ticket will win?
Answers
Simplify using long division
Answers
the answer is above the division.
hope this helps , give brainliest
----------------
x+2
Answer:
28
x+8- _____
x+2
5. The dimensions, in inches, of a shipping box at We Ship 4 You can be expressed as width x, length x + 5, and height 3x - 1. The volume is about 7.6 f3. Find the dimensions of the box in inches. Round to the nearest inch. (Hint: 1 f 1,728 in.3)
Answers
To find the dimensions of the shipping box, calculate the volume in cubic inches, then set up and solve the volume equation x(x + 5)(3x - 1), substituting the given volume after conversion from cubic feet. Solve for x, then use it to find and round the box's dimensions.
Explanation:To find the dimensions of the shipping box, we need to calculate the volume using the given dimensions in inches and compare it to the provided volume in cubic feet. Recall that the conversion factor between cubic feet and cubic inches is 1 cubic foot equals 1,728 cubic inches. Firstly, convert the volume of the box from cubic feet to cubic inches: 7.6 cubic feet are 7.6 x 1,728 cubic inches.
Next, we can set up the volume equation for the box using the given dimensional expressions: volume = width x length x height, which for this box is x x (x + 5) x (3x - 1). Now we solve the equation for x given that the volume in cubic inches is equal to 7.6 x 1,728 inches.
Once x is found, we can determine the width, length, and height by plugging x back into the expressions x, x + 5, and 3x - 1, respectively, and rounding each to the nearest inch.
Determine the growth defined by the equation y=3(3.4)x
Answers
Answer:
Exponential growth.
Round 977.259856871 to 3 decimal places
Answers
look at the number to the right of 9, it is 8, and 8 > 5. IF the number is 5 or greater, round up.
so your answer is 977.260
hope this helps
The third decimal place is 9.
The number after that is above 5, so round up.
Your answer should be 977.260
Can someone help me with 7?
Answers
Solving the equation for y puts it in slope-intercept form.
[tex]3x-5y=5\qquad\text{given equation}\\3x-5=5y\qquad\text{add 5y-5}\\y=\dfrac{3}{5}x-1\qquad\text{divide by 5}[/tex]
This tells you one point can be plotted on the y-axis at y=-1. Another point can be plotted 3 units up and 5 units to the right of that one, at (5, 2). The graph is the line through those points.
Since you're asked to plot at least 3 points, your third point could be 5 units left and 3 units down from the first one, at (-5, -4).
True or false a positive slope goes up as you move from left to right along the x-axis.
Answers
whats the answer to the problem
Answers
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Work Shown:
Flip the second fraction and multiply. Reduce the fraction as much as possile.
[tex]\frac{11}{12} \div \frac{1}{3} = \frac{11}{12} \times \frac{3}{1}[/tex]
[tex]\frac{11}{12} \div \frac{1}{3} = \frac{11*3}{12*1}[/tex]
[tex]\frac{11}{12} \div \frac{1}{3} = \frac{11*3}{4*3}[/tex]
[tex]\frac{11}{12} \div \frac{1}{3} = \frac{11}{4}[/tex]
I only need number 30 answered
Answers
-(2a)^3+2a+1 = -8a^3+2a+1
Multiplying that polynomial by 5, we get:
-40a^3+10a+5
Which of the binomials below is a factor of this trinomial?
x2 + 13x + 42
A. x - 7
B. x + 7
C. x + 84
D. x2 + 12
Answers
x² + 6x + 7x + 42
x(x + 6) + 7(x + 6)
The factors are : (x + 7)(x + 6)
Solution: B. x + 7
The trinomial x^2 + 13x + 42 factors into (x + 7)(x + 6), making x + 7, which is option B, the correct binomial factor of the trinomial.
To determine which binomial is a factor of the trinomial x2 + 13x + 42, we need to factor the trinomial. To factor the trinomial, we are looking for two numbers that multiply to give us the constant term (42) and add to give us the linear coefficient (13). These two numbers are 7 and 6 because 7 * 6 = 42 and 7 + 6 = 13.
So, we can factor the trinomial as (x + 7)(x + 6). Thus, the binomial that is a factor of x2 + 13x + 42 is x + 7, which is option B.
Find the resultant of these two vectors: 2.00 x 102 units due east and 4.00 x 102 units 30.0° north of west.
Answers
If two vectors are represented both in magnitude and direction by the two adjacent sides of a triangle taken in an order, then their resultant is given by the third side taken in the reverse order.
Resultant vector :
R = sqrt of A^2 + B^2 + 2ABcosθ
given :
A = 200 units
B = 300 units
θ = 30 degrees
∴ R = sqrt of 200^2 + 300^2 + 2(200)(300)cos35
the answer is 477.805656
If two vectors are represented both in magnitude and direction by the two adjacent sides of a triangle taken in an order, then their resultant is given by the third side taken in the reverse order.
Resultant vector :
R = sqrt of A^2 + B^2 + 2ABcosθ
given :
A = 200 units
B = 300 units
θ = 30 degrees
∴ R = sqrt of 200^2 + 300^2 + 2(200)(300)cos35
the answer is 477.805656
The formula for the area a of a triangle is a equals 1 half b where is the base and h is the height. solve the formula for h and then find the height of a triangle whose area is 1768 square inches and whose base is 52 inches. round to the nearest tenth if necessary. height = inches
Answers
Area of triangle is given as:
A = (1/2) b * h
where b is base and h is height
So given that:
A = 1768 inches^2
b = 52 inches
Rearranging the equation to find for h:
h = 2 A / b
h = 2 * 1768 inches^2 / 52 inches
h = 68 inches