Answer:
a. Explicit: f(x) = 2x² +3. Recursive: f(-3) = 21; f(x) = f(x -1) +4x -2
b. Explicit: g(x) = 3x² -2x. Recursive: g(5) = 65; g(x) = g(x -1) +6x -5
Step-by-step explanation:
Given two tables of values, you want to find the explicit and recursive formulas for those values.
General approachWhen the x-values are consecutive integers, as they are in these tables, it is usually useful to look at the first difference of the y-values. If those are constant, the table represents a linear function.
When the first differences are not constant, the exercise can be repeated. If the second differences are constant (as here), then the explicit formula will be a second-degree polynomial. The coefficients of the polynomial can be found different ways. We will describe one way here.
2nd degree explicit formulaThe constant second differences are double the leading coefficient of the quadratic that describes the relation between x and y. Knowing this, we can see how well the 2nd degree term by itself represents the relation. To that end, we have added to the table columns for the difference between the y-value and the 2nd degree term (y1 -ax^2), and the difference of those differences (diff).
Explicit formula, Table AThe attachment shows the first second difference of the values of Table A is 4. That means our first approximation of the sequence will be (4/2)x². The next column shows us this is always 3 less than the value of y, so our explicit formula can be ...
f(x) = 2x² +3
Explicit formula, Table BThe attachment shows the first second difference of the values of Table B is 6. That means our first approximation of the sequence will be (6/2)x². Subtracting this from the value of y, we find an arithmetic sequence that has a common difference of -2, and a value of -10 when x=5.
The explicit formula for an arithmetic sequence with a first term a1 and a common difference d is ...
an = a1 +d(n -1) . . . . . . where 1 is the x-value of the first term
Our sequence of differences doesn't start with x=1, but with x=5. This means our explicit formula will be ...
g(x) = 3x² +(-10 +(-2)(x -5))
g(x) = 3x² -2x
2nd degree recursive formulaA recursive formula is one that expresses a given term as a function of previous terms of the sequence. When the sequence is 2nd degree, as here, we know the difference from one term to the next is an arithmetic sequence. Thus we can write the formula for a term as the sum of the previous term and a value that depends on the term number.
The explicit formula for the arithmetic sequence of differences has the form shown above. For the purpose here, the difference from the previous term is shown on the line above the x-value.
Recursive formula, Table AThe applicable sequence of first differences has first term -10 and common difference 4. The first of the differences of consequence corresponds to x=-2, so can be written ...
d(x) = -10 +4(x -(-2)) = 4x -2
Then the recursion relation is
f(x) = f(x -1) +d(x) = f(x -1) +4x -2
And the recursive formula is ...
f(-3) = 21; f(x) = f(x -1) +4x -2
Recursive formula, Table BThe applicable sequence of first differences has first term 31 and common difference 6. The first of the differences of consequence corresponds to x=6, so can be written ...
d(x) = 31 +6(x -6) = 6x -5
Then the recursive formula is ...
g(5) = 65; g(x) = g(x -1) +6x -5
-I’ll mark brainliest-
Is 3 a factor?
Answer:
yes it can be depending on the question.
Step-by-step explanation:
say you are trying to find the factors of 24, the factors are just the numbers you can multiply to get 24 so it would be 1,2,3,4,6,8,12 and 24
A grid that represents 1 whole , what would you shade for 0.4 and 0.04? 100 squares in rows of 10.
Tanner brings donuts to school and for his friends. He brings six chocolates frosted donuts, eight glazed donuts, and four sprinkles donuts, In home room, his friends eat 1/3 of the donuts, How many donuts, did his friends eat
Answer:
6 donuts
Step-by-step explanation:
total donut = 6 + 8 + 4
= 18
\( \frac{1}{3} \times 18 = 6\)
Ryan and Mark had the same number of marbles at first . Ryan lost 87 marbles and mark received another 125 marbles. Then Mark had 5 times as many marbles as Ryan. How many marbles did Mark have in the end?
Please without algebra
Which number is bigger: 0.135 or 0.14?
The number 0.14 is bigger than 0.135.
To compare the two numbers, you can look at their digits after the decimal point. In both numbers, the digit in the tenths place is 1. The next digit in 0.14 is 4, which is greater than the corresponding digit in 0.135, which is 3.
Since the digit in the hundredths place (4) is greater than the digit in the hundredths place (3), the number 0.14 is bigger than 0.135.
In summary, the order of the numbers from smallest to largest is:
0.135 < 0.14.
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. An arch has the shape of a semi-ellipse. The arch
has a height of 12 feet and a span of 40 feet. Find
an equation for the ellipse, and use that to find the
distance from the center to a point at which the
height is 6 feet. Round to the nearest hundredth.
The height of the arch at a distance of 5 feet from the center is approximately 10. 93 feet
Equation of an eclipse
It is important to note that the standard equation of an eclipse centered at origin behind the shape of arch is given as;
\(\frac{x^2}{a^2} + \frac{y^2}{b^2}\)
Where;
x - Horizontal distance, in feety - Vertical distance, in feeta - Horizontal semi - axis length (half-width), in feetb - Vertical semi - axis length (height), in feetIf we know that x = 6feet , a = 20 feet and b = 12feet, then the height of the arch at this location is;
\(y = b . \sqrt{1 + \frac{x^2}{a^2} }\)
\(y = 12. \sqrt{1 - \frac{6^2}{20^2} }\)
\(y = 10. 92\) feet
Thus, the height of the arch at a distance of 5 feet from the center is approximately 10. 93 feet
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Jenny bought 5 pounds of carrots for $2.50. What is the unit rate for
Jenny's purchase? Identify the true statement that corresponds to this
situation.
A. 2 pounds of carrots per $1
B. $5 per pound
Answer:
A. 2 pounds of carrots per $1
Step-by-step explanation:
\(\frac{5 pounds }{2.5 dollars}=\frac{2pounds }{1 dollars}\)
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
help with this please
Two parallel lines are crossed by a transversal.
What is the value of d?
The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.
What is a Transversal?In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.
The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.
Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°
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A delivery driver makes $78 each day that he works and makes approximately $10 in tips for each delivery that he makes. If he wants to make at least $238 in one day, at least how many deliveries does he need to make?
Answer:
16 deliveries
Step-by-step explanation:
We can model the situation using a linear inequality. Since we're told that the driver makes $10 in tips for each delivery.Thus, this is the slope.Since he makes $78 each day, this number is a constant and he makes it even when no deliveries are made. Thus, this is the y-interceptSince he wants to make at least #238, we want to find a value of d (number of deliveries) which would cause his wages to equal #238. Thus, we can use the following equation to find:238 ≤ 10d + 78
160 ≤ 10d
16 ≤ d
Thus, he needs to make at least 16 deliveries to make at least $238 in one day. Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.
1.) Solve the following equation for w: 3w-4(w-3) = 6
Answer: w=6
Step-by-step explanation: 1. Simplify. Distribute the -4 to the w and the -3. -4*w is -4w and -4*-3 is +12, so your left with 3w-4w+12=6.
2. simplify again. 3w-4w is -w.
3. -w+12=6. Subtract w to both sides, so its -w=-6. The negatives cancel out, so w just equals 6.
on 5 of 10
A student performed the following steps to find the solution to the equation
2² +4x120. Where did the student go wrong?
Step 1. Factor the polynomial into (x+6) and (x-2)
Step 2. x-6= 0 and x + 2 = 0
Step 3. x= 6 and x = -2
OA. The student did not make any mistakes, the solution is correct
OB. in Step 1
OC. in Step 2
D. in Step 3
Based on the equation given ,the student made a mistake in Step 1. Let's analyze the steps and identify the error:
How to identify the errorStep 1: Factor the polynomial into (x+6) and (x-2)
The student factored the polynomial 2² + 4x120 incorrectly. The correct factorization should be 4x² + 120, which can be further simplified as 4(x² + 30). However, the student mistakenly factored it as (x+6)(x-2).
Therefore, the correct answer is B. The student made the mistake in Step 1.
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The standard error of is the _____. Group of answer choices variance of variance of the sampling distribution of standard deviation of the sampling distribution of difference between the two means
Answer:
standard deviation of the sample distribution of the difference between these two sample means
Step-by-step explanation:
when a number was divide by 12 the quotient was 52 and the reminder was 5 what was the number
Answer:
???
Step-by-step explanation:
1. 52 + 5 = 57
2. 57 × 12 = 684
3. Test it out
684 ÷ 12 = 57
which is wrong because of the remainder.
BUT the remainder is not possible because 12 was the number it was divided by and 12 can not go into 5
so either your question is wrong or my solution is wrong
Please help me. Please dont answer if you dont know. i will give brainliest. thankyou, have a great day! :)
Answer:
1. 3,077.2 cm³
2. 1,808.6 ft³
3. 602.9 in.³
4. 230.8 yd³
5. 191.8 m³
6. 70.3 in.³
Step-by-step explanation:
Recall: Volume of cylinder = πr²h
1. r = 7 cm
h = 20 cm
π = 3.14
Volume = 3.14*7²*20 = 3,077.2 cm³
2. r = 8 ft
h = 9 ft
π = 3.14
Volume = 3.14*8²*9 ≈ 1,808.6 ft³
3. r = ½(8) = 4 in.
h = 12 in.
π = 3.14
Volume = 3.14*4²*12 ≈ 602.9 in.³
4. r = 3½ yd = 3.5 yd
h = 6 yd
π = 3.14
Volume = 3.14*3.5²*6 ≈ 230.8 yd³
5. r = ½(5.3) = 2.65 m
h = 8.7 m
π = 3.14
Volume = 3.14*2.65²*8.7 ≈ 191.8 m³
6. r = 1.9 in.
h = 6.2 in.
π = 3.14
Volume = 3.14*1.9²*6.2 ≈ 70.3 in.³
Rewrite 4(30+5) using the Distributive Property of Multiplication over Addition.
Answer:
Step-by-step explanation:
4(30+5)
4(30)+4(5)
120+20
140
Find the area of the pentagon
Answer:
A=1
45(5+25)a2
Step-by-step explanation:
This is a picture of a cube and the net for the cube.
What is the surface area of the cube?
Responses
30 cm²
30 cm²
70 cm²
70 cm²
125 cm²
125 cm²
150 cm²
150 cm²
A cube and a net of the cube are shown. The edge length of the cube is labeled 5 centimeters. The net consists of 4 squares connected vertically, and 1 square is attached to the left of the third square and 1 square is attached to the right of the third square. One square in the net is labeled with a side labeled 5 centimeters.
The surface area of the cube is 1536 ft².
We have,
The cube can be seen as 6 square areas in the net.
So,
The surface area of the cube.
= 6 x area of one square surface.
Now,
Side = 16 ft
Area of one square surface.
= side²
= 16²
= 256 ft²
Now,
The surface area of the cube.
= 6 x area of one square surface.
= 6 x 256
= 1536 ft²
Thus,
The surface area of the cube is 1536 ft².
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An image of lines p and q parallel to each other. Lines m and n are not parallel to each other. Line m, p form an angle of one hundred two degrees and an angle marked y. Lines n, q form an angle marked x and an angle of one hundred fifteen degrees.Parallel lines p and q are cut by two non-parallel lines, m and n, as shown in the figure. The value of x is degrees, and the value of y is degrees.
Answer:
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Find the mean, median, mode 1. 40, 38,29,34,37, 22, 15, 38 2. 26, 32, 12, 18, 11, 14, 21, 12,27 3. 3,3,4,7,5,7,6,7,8,8,8. 9,8, 10, 12, 9, 15, 15
NEED THE ANSWER ASAP
NONSENSE, REPORT
i will (brainliest) if it's correct!!!
Mean: 34.125, Median: 31.5, Mode: 38
Mean: 19.222, Median: 18, No mode
Mean: 8.611, Median: 8, Mode: 8
Let's find the mean, median, and mode for each set of numbers:
Set: 40, 38, 29, 34, 37, 22, 15, 38
Mean: To find the mean, we sum up all the numbers and divide by the total count:
Mean = (40 + 38 + 29 + 34 + 37 + 22 + 15 + 38) / 8 = 273 / 8 = 34.125
Median: To find the median, we arrange the numbers in ascending order and find the middle value:
Arranged set: 15, 22, 29, 34, 37, 38, 38, 40
Median = (29 + 34) / 2 = 63 / 2 = 31.5
Mode: The mode is the number(s) that appear(s) most frequently in the set:
Mode = 38 (appears twice)
Set: 26, 32, 12, 18, 11, 14, 21, 12, 27
Mean: Mean = (26 + 32 + 12 + 18 + 11 + 14 + 21 + 12 + 27) / 9 = 173 / 9 ≈ 19.222
Median: Arranged set: 11, 12, 12, 14, 18, 21, 26, 27, 32
Median = 18
Mode: No mode (all numbers appear only once)
Set: 3, 3, 4, 7, 5, 7, 6, 7, 8, 8, 8, 9, 8, 10, 12, 9, 15, 15
Mean: Mean = (3 + 3 + 4 + 7 + 5 + 7 + 6 + 7 + 8 + 8 + 8 + 9 + 8 + 10 + 12 + 9 + 15 + 15) / 18 ≈ 8.611
Median: Arranged set: 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 12, 15, 15
Median = 8
Mode: Mode = 8 (appears 4 times)
Mean: 34.125, Median: 31.5, Mode: 38
Mean: 19.222, Median: 18, No mode
Mean: 8.611, Median: 8, Mode: 8
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I need to know this answer
The equation of the line is y = (3/2)x - 1/2.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Let's say you need to know the answer about the equation of a line that passes through points (3, 4) and (5, 7).
Now,
The equation of a line.
y = mx + c
The line passes through points (3, 4) and (5, 7).
m = (7 - 4) / (5 - 3)
m = 3/2
Slope = 3/2 _____(1)
Now,
(3, 4) = (x, y)
4 = 3/2 x 3 + c
4 = 9/2 + c
c = 4 - 9/2
c = (8 - 9) / 2
c = -1/2
y-intercept = -1/2 ____(2)
Now,
y = mx + c
From (1) and (2),
y = (3/2)x - 1/2
Thus,
The equation of the line is y = (3/2)x - 1/2.
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The complete question.
Find the equation of a line that [passes through the point (2, 4), and (5, 7).
SOMEONE PLEASE HELPP MEE
The end-points of the line segment will be negative 1.25 and 0.25.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
The length of the line segment is 1.50 units and the midpoint of the line segment is negative 0.50. Then the end-points of the line segment are given as,
⇒ - 0.50 ± (1.50) / 2
Simplify the expression, then we have
⇒ - 0.50 ± (1.50) / 2
⇒ - 0.50 - (1.50) / 2, - 0.50 + (1.50) / 2
⇒ - 0.50 - 0.75, - 0.50 + 0.75
⇒ - 1.25, 0.25
The end-points of the line fragment will be negative 1.25 and 0.25.
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m=-4/5,(-7, - 2) Find the equation of the line that has the given slope
Answer: \(y=-\frac{4}{5}x-\frac{38}{5}\)
Step-by-step explanation:
To find the equation, you plug in the slope and given point. Then, you can solve and find the y-intercept.
\(-2=-\frac{4}{5}(-7)+b\) [multiply]
\(-2=\frac{28}{5}+b\) [subtract both sides by \(\frac{28}{5}\)]
\(b=-\frac{38}{5}\)
Now that we have the y-intercept, the equation is \(y=-\frac{4}{5}x-\frac{38}{5}\).
16.*
X.
Solve for
3x + 12 = -12
1.x = -8
2.x=-4
3.x=0
4.x=8
Answer:
1.x=-8
Step-by-step explanation:
3x+12=-12
-12 -12
3x=-24
/3 /3
x=-8
An artist's canvas has sides measuring 3x + 5 and 2x + 1 inches.
What is the area of the canvas? Show all work.
The artist laid the canvas flat on the floor and poured some paint in the center. The paint flows at a rate of r(t) = 2t where t represents time in minutes and r represents how far the paint is spreading on the canvas. The area of the paint can be expressed as A[r(t)]= rur?. What is the area of the circle created by the paint?
If the artist wants the circle to be at least 300 in?, will it be that large in 5 minutes? Support your answer with your work.
The area of the circle created by the paint is given by the expression 4πt².
The area of the circle is 100π, which is approximately 314.16 in².
The circle will be at least 300 in² in 5 minutes. Yes.
To find the area of the canvas, we multiply the lengths of its sides:
Area = (3x + 5) × (2x + 1)
Expanding the expression:
Area = 6x² + 3x + 10x + 5
Combining like terms:
Area = 6x² + 13x + 5
The area of the canvas is given by the expression 6x² + 13x + 5.
Now, let's find the area of the circle created by the paint.
The area of a circle is given by the formula A = πr², where r represents the radius.
The radius is given by the spreading of paint, which is r(t) = 2t.
Substituting the value of r(t) into the formula, we have:
A[r(t)] = π(2t)²
Simplifying:
A[r(t)] = π(4t²)
A[r(t)] = 4πt²
Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.
Substitute t = 5 into the area formula:
A[r(5)] = 4π(5)²
A[r(5)] = 4π(25)
A[r(5)] = 100π
Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.
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a. One week, Park Street's revenues were $7500, which was the 15th highest revenue recorded for that restaurant. In the same wook, Bridge Road's
revenue was $7100, the 12th highest for that restaurant Use percentiles and 7-scores to compare how successful each restaurant was that wook,
relative to their typical weekly revenue
Answer:
The percentile rank for Park Street's revenues this week is 60th.
The percentile rank for Bridge Road's revenues this week is 73rd.
Step-by-step explanation:
The missing information are as follows:
Variable N Mean SD
Park 36 6611 3580
Bridge 40 5989 1794
A z-score (aka, a standard score) specifies the number of standard deviations an observation is from the mean.
The formula to compute the z-score is, \(Z = \frac{(X - \mu)}{\sigma}\), where X = observation, µ = mean, σ = standard deviation.
Compute the z-score for Park Street's revenues, $7500 as follows:
\(Z_{p} = \frac{(X - \mu)}{\sigma}=\frac{7500-6611}{3580}=0.25\)
The z-score for Park Street's revenues this week is 0.25.
Compute the percentile rank for Park Street's revenues this week as follows:
\(P(Z<Z_{p})=P(Z<0.25)=0.5987\approx 0.60\ \text{or}\ 60\%\)
The percentile rank for Park Street's revenues this week is 60th.
This implies that the Park Street's performed better than 60% of the revenue recorded for the restaurant.
Compute the z-score for Bridge Road's revenues, $7100 as follows:
\(Z_{p} = \frac{(X - \mu)}{\sigma}=\frac{7100-5989}{1794}=0.62\)
The z-score for Bridge Road's revenues this week is 0.62.
Compute the percentile rank for Bridge Road's revenues this week as follows:
\(P(Z<Z_{b})=P(Z<0.62)=0.7324\approx 0.73\ \text{or}\ 73\%\)
The percentile rank for Bridge Road's revenues this week is 73rd.
This implies that the Bridge Road's performed better than 73% of the revenue recorded for the restaurant.
Find the 75th term of the following arithmetic sequence 16,25,34,43
Answer:
\(\boxed {\boxed {\sf 682}}\)
Step-by-step explanation:
The nth term of an arithmetic sequence can be found using the following formula.
\(a_n=a+d(n-1)\)
where a is the first term, d is the common difference, and n is the term.
First, we should find the common difference.
We can do this by subtracting each term from the term following it. Basically, subtract the first term from the second term, the second from the third, and so on.
\(d= a_2-a_1\)
The second term is 25 and the first is 16.
\(d= 25-16\)
\(d=9\)
Now we know the common difference is 9. We also know the first term is 16 and we are looking for the 75th term.
\(d=9 \\a=16 \\n= 75\)
Substitute the values into the formula.
\(a_{75}=16+9(75-1)\)
Solve according the PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).
Solve the parentheses first.
\(a_{75}=16+9(74)\)
Multiply next.
\(a_{75}=16+666\)
Finally, add.
\(a_{75}=682\)
The 75th term in the sequence is 682.
A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total admission revenue, not including sales tax, and had a total of 450 guests.
The system of equations below can be used to model the number of guests that were children, x, and the number of guests that were adults, y.
First, place a point on the graph representing the solution to the system of equations. Notice that one of the equations in the system has already been graphed.
Then, determine the approximate number of guests that were children and the approximate number of guests that were adults for that day.
The approximate number of guests that were children are 172 and adults are 278
How to determine the approximate number of guests that were children and adults for that day?From the complete question, we have the following system of equations
25x + 12y = 9014
x + y = 450
Make y the subject in x + y = 450
y = 450 -x
Substitute y = 450 - x in 25x + 12y = 9014
25x + 12(450 - x) = 9014
Expand the expression
25x + 5400 - 12x = 9014
Evaluate the like terms
13x = 3614
Divide both sides by 12
x = 278
Substitute x = 278 in y = 450 -x
y = 450 - 278
Evaluate
y = 172
Hence, the approximate number of guests that were children are 172 and adults are 278
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|3y - 7| - 10 = -5 solve for y:
Answer: y=1.25
Step-by-step explanation:
First things first you have to find what is in the bracket things (i don’t know what it’s called) So 3 - 7 is -4y but since it’s absolute it’s going to be 4y.
So now you’ve got 4y - 10 = -5. Your going to want to eliminate 10 so, subtract 10 to both sides giving you 4y = -5
Lastly to get y by itself you need to divide it by its self so, 4y divided by 4. Do it to both sides. This gives you…
Y = 1.25
The camera cost $540 if the sales tax is 7.2% what is the tax change and the total cost?
Answer:
$75 ?
Step-by-step explanation:
If this is wrong super sorry :)