Which recursive sequence would produce the sequence 4,-17,46,…?
Answers
The recursive formula will be
\(a_n = (-1)^{n+1\) [3 times difference + previous term]
What is Recursive formula?When objects are defined in terms of other objects of the same type, the process is said to be recursive. The full class of objects can then be constructed from a few beginning values and a handful of rules using some kind of recurrence relation.
Given:
4,-17,46,…
Now, as the difference is
s= -17- 4= -21
and, d= 46 - (-17)= 63
Then, the recursive formula will be
\(a_n = (-1)^{n+1\) [3 times difference + previous term]
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Related Questions
$20 haircut; 10% tip
Answers
Answer:
I think the answer is $22.00
Give your answer in scientific notation using only WHOLE numbers.
Answers
The number of pennies weighing as much s earth is 193 × 10²⁴
What are index forms?Index forms are described as described as those forms that are used to represent numbers that are too large or small in more proper ways.
Other names for index forms are scientific notation and standard forms.
What is ratio?Ratio is described as the comparison of numbers or variables on the basis of their size.
It shows how many times one number contains another.
From the information given, we have that;
The earth weighs = 5. 972 × 10 ²⁴ kilograms
The penny weighs = 3.1 × 10 ⁻³ kilograms
Divide the values
= 5. 972 × 10 ²⁴/3.1 × 10 ⁻³
= 1.93 × 10 ²⁶
= 193 × 10²⁴
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Let A be a 7×5 matrix with rank equal to 4 and let b be a vector in R8. The four fundamental sub- spaces associated with A are R(A), N(AT ), R(AT ), and N (A).
Answers
The value of R(A) = 4, N(AT ) = 3, R(AT ) = 4, and N (A) = 3.
Given that
Dimension of matrix = 7×5
Rank of matrix = 4
The range space of A,
Which is a subspace of R, is known as R(A).
It is made up of all conceivable linear combinations of A's columns.
The dimension of R(A) = rank of A,
Which is 4 in this case.
The null space of the transpose of A,
Which is also a subspace of R, is designated as N(AT).
All potential answers to the equation ATx = 0,
Where x is a R column vector, are included in it.
N(AT) has a dimension = nullity of A,
which in this case is 3 in this example.
The range space of the transposition of A, is designated as R(AT).
The rows of A are arranged in all conceivable linear configurations.
The rank of A = 4
Thus it equal to dimension of R(AT).
N(A) is the null space of A.
Axe = 0, where x is a column vector in R, are included in it.
The nullity of AT, which is three, is likewise equivalent to the dimension of N(A).
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Brianna made 9 1/4 bags of popcorn for a movie night with some friends. Together they ate 4 bags of it. How much popcorn was left?
Answers
There were 5 1/4 bags of popcorn left after eating 4 bags.
To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.
Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:
9 1/4 = (4 * 9 + 1) / 4 = 37/4
Now, let's subtract the 4 bags eaten from the total:
37/4 - 4
To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:
37/4 - 4/1
Now, let's find a common denominator and subtract the fractions:
37/4 - 16/4 = (37 - 16) / 4 = 21/4
The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:
21/4 = 5 1/4
Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.
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Erin has 5 cans of juice and drinks 1/3 of a can daily. in how many days will she empty all the cans she has? I think it's 1/15 I'm not sure though.
Answers
What is the meaning of "all free variables of a formula ϕ(u1, . . . , un) are among u1, . . . , un"?
Answers
The phrase "all free variables of a formula ϕ(u1, . . . , un) are among u1, . . . , un" refers to a property of a logical formula ϕ with variables u1, u2, ..., un. In logic and formal systems, variables are used to represent unspecified elements or objects.
What does the phrase imply?When a variable is considered "free" in a formula, it means that it is not bound by any quantifiers or other logical operators in the formula. In other words, it is a variable that is not restricted in any way within the formula.
The given statement implies that all the free variables in the formula ϕ(u1, . . . , un) are explicitly listed among the variables u1, u2, ..., un. In other words, the formula ϕ does not contain any additional free variables beyond the ones explicitly mentioned.
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Magan went shopping for a new camera because of a sale. The price on the tag was $21, but Magan paid $12.60 before tax. Find the percent discount.
Answers
Answer:
40%
Step-by-step explanation:
To find the percent discount, take the original price and subtract the discounted price.
21 - 12.60=8.4
Divide this by the original price.
8.4/21 = .4
Change this to percent form.
.4 = 40%
Answer:
8.4
Step-by-step explanation:
The price of a bag = 21
Magan paid 12.60
00. 21
12.00
- - - - - - - - -
8.4
Last year, Ron underestimated the number of notebooks he would need. So this year. Ron bought 310 notebooks, and had 60 more than he needed. Fill in the table for this year's values.
Options for A:250 310 330
Options for B:250 310 330
Options for C:40 60 330
Options for E:19% 24% 81%
i did D already
someone please help!
Answers
Answer:
a =
✔ 310
b =
✔ 250
c =
✔ 60
d =
✔ 60/250
e =
✔ 24%
Step-by-step explanation:
(02.06)If a piece of ribbon is 6 and 1 over 4. feet long, how long is it in inches? 25 inches 72 inches 75 inches 84 inches
Answers
Answer:
C
Step-by-step explanation:
1 foot = 12 inches Find 1/4 foot in inches
1/4 a foot = 1/4 * 12 = 3 inches
6 1/4 feet = (6 + 1/4) * 12
=72 + 3
75 inches
plz SOLVE it CORRECTLY step by step asap
Answers
Answer:
Step-by-step explanation:
area of circle=π\(r^{2}\)
=22/7*\(21^{2}\)
=22/7*441
=9702/7
=1386 cm^2
A store pay $120 for a bicycle. The store has a 60% markup policy. What is the selling price of the bicycle? (answer $192)
Use your answer from the above question to help answer this question!! The store is now going out of business and is selling all of the bicycles at a 30% discount. What is the sale price of the bicycle?
Answers
Work: 192 x .7
Given that <2=<6.
Which theorem proves that line d is parallel to line e.
A. Alternate interior angle theorem
B.Converse of the alternate exterior angle
theorem
C.Converse of the alternate interior angle
theorem
D.Alternate Exterior angle theorem
Answers
Answer: B . Converse of the alternate exterior angle theorem.
The converse of the alternate exterior angle proves that line d is parallel to line e which is the correct answer would be an option (C).
What are Alternate Interior Angles?Alternate Interior Angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles.
According to the alternate exterior angles theorem, if two parallel lines are intersected by a transversal, the alternate exterior angles are congruent. In light of this, the converse of the alternate exterior angle theorem would state that if the two outside angles are congruent, the lines that the transversal cuts must be parallel.
The graph indicates that the outer angles are congruent (both equal x) shows that the lines are parallel.
Therefore, the converse of the alternate exterior angle proves that line d is parallel to line e.
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g(x)= x^2-6/3x+10
Algebra 2
Answers
Answer:
g(2) = 13
Step-by-step explanation:
The given expression is :
\(g(x)=x^2-\dfrac{6}{3x}+10\) ...(1)
We need to find the value of g(2).
Put x = 2 in equation (1).
\(g(2)=2^2-\dfrac{6}{3\times 2}+10\\\\=4-1+10\\\\=13\)
So, the answer is 13.
which of the following are solutions to the quadratic equation check all that apply x ^ 2 + 10x + 25 = 2
Answers
Answer:
to solve the equation you first need to bring it to factors and by doing that you first need to let the equation equal 0 hence you need to minus 2 on both sides of the equation therefore
x^2 + 10x + 25 - 2 =2 - 2
therefore
x^2 + 10x +23 = 0
now since the equation cannot be factored, we use the formula.
x= \(\frac{-b +- \sqrt{b^{2}-4ac } }{2a}\)
where
a=1
b=10
c=23
note we use the coefficients only.
therefore x = \(\frac{-10 -+ \sqrt{10^{2}-4(1)(23) } }{2(1)}\)
=\(\frac{-10-+\sqrt{100-92} }{2}\)
=\(\frac{-10-+\sqrt{8} }{2}\)
then we form two equations according to negative and positive symbols
x=\(\frac{-10+\sqrt{8} }{2} or x =\frac{-10-\sqrt{8} }{2}\)
therefore x = \(-5+\sqrt{2}\) or x=\(-5-\sqrt{2}\)
What is the simplified form of x minus 5 over x squared minus 3x minus 10⋅ x plus 2 over x squared plus x minus 12 ? (6 points) Select one: a. 1 over the quantity x minus 3 times the quantity x plus 4 b. 1 over the quantity x minus 3 times the quantity x plus 2 c. 1 over the quantity x plus 4 times the quantity x minus 5 d. 1 over the quantity x plus 2 times the quantity x minus 5
Answers
Answer:
\(\ \text{a. }\quad\dfrac{1}{(x-3)(x+4)}\)
Step-by-step explanation:
Maybe you want the product ...
\(\dfrac{x-5}{x^2-3x-10}\cdot\dfrac{x+2}{x^2+x-12}=\dfrac{x-5}{(x-5)(x+2)}\cdot\dfrac{x+2}{(x-3)(x+4)}\\\\=\boxed{\dfrac{1}{(x-3)(x+4)}}\)
__
Numerator factors of (x-5) and (x+2) cancel those in the denominator.
If you on a motorcycle trip of 30 miles in the and 5\19 of the trip is downhill, how many miles of the trip are not downhill? Reduce to the lowest term.
Answers
Answer:
1/4 of the trip is not down hill
Todd Lyle worked Monday through Friday from 8:00 A.M. to 5:00 P,M. with an hour off for lunch. He is paid $10,50 an hour. Find his earnings for the week.
Answers
Answer:
$315
Step-by-step explanation:
He earns $63 everyday, and then you just have to multiply that by 5 since he works 5 days in a week.
A right circular cone is intersected by a plane that passes through the cone's
vertex and is parallel to its base, as in the picture below. What is produced
from this intersection?
OA. A pair of intersecting lines
OB. A point
OC. A pair of parallel lines
OD. A parabola
Answers
Answer:
B. A point
Step-by-step explanation:
You want a description of the intersection between a plane and a cone given that the plane is parallel to the base and passes through the vertex of the cone.
VertexThe vertex of a cone is a single point. If a plane passes through that, but does not intersect the base of the cone, it will not intersect anywhere else.
The intersection is one point.
__
Additional comment
Figure f in the attachment illustrates this case.
17. Find the circumference given
KL 4.6 in. Round to the nearest
tenth.
Answers
The circumference of the given circle is approximately 47.3 inches.
Since the length of the arc KL and the measure of the central angle ∠KOL are known, we can use the formula for arc length to find the circumference of the circle:
arc length = (central angle / 360°) x circumference
Plugging in the known values, we have:
4.6 in = (35° / 360°) x circumference
Solving for the circumference, we get:
circumference = 4.6 in / (35° / 360°)
circumference = 4.6 in x (360° / 35°)
circumference ≈ 47.3 in (rounded to the nearest tenth)
Therefore, the circumference of the circle is approximately 47.3 inches.
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Is (49,13),(61,36),(10,27),(76,52),(23,52) a function
Answers
Answer:
No
Step-by-step explanation:
To determine whether the given set of ordered pairs {(49,13),(61,36),(10,27),(76,52),(23,52)} represents a function, check if each x-value is associated with a unique y-value.
Check the x-values in the set: 49, 61, 10, 76, and 23. There are no repeated x-values. Still need to check if each x-value has a unique corresponding y-value.
Check the y-values: 13, 36, 27, 52, and 52. There is one repeated y-value, 52, for the pairs (76, 52) and (23, 52).
Conclusion: the y-value 52 is associated with 2 different x-values, therefore the given set of ordered pairs does not represent a function.
Two rectangles overlap, as shown below. Find the area of the overlapping region (which is shaded) if AB = BE = 2 and AD = ED = 4.
Answers
The area of the overlapping region is of: 6.25 units squared.
Area of a rectangleThe area of a rectangle of length l and width w is given by the multiplication of the dimensions, as follows:
A = lw.
The dimensions of the right triangle as follows:
Leg x.Leg 2.Hence the remaining leg on the overlapping region is:
4 - x, as AD = 4.
By symmetry, the other dimension of the overlapping region is also of:
4 - x.
Being also the hypotenuse of the right triangles.
The value of x can be found applying the Pythagorean Theorem as follows:
x² + 2² = (4 - x)²
x² + 4 = 16 - 8x + x²
8x = 12
x = 1.5.
Then the two dimensions of the shaded region are:
4 - 1.5 = 2.5.
Meaning that the area is of:
A = 2.5 x 2.5 = 6.25 units squared.
Missing information
The figure is missing and is given by the image at the end of the answer.
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A weatherman stated that the average temperature during July in Chattanooga is 80 degrees or less. A sample of 32 Julys is taken. The correct set of hypotheses is:________. a. H0: μ ≠ 80 Ha: μ = 80b. H0: μ 80 Ha: μ > 80c. H0: μ < 80 Ha: μ > 80d. H0: μ 80 Ha: μ < 80
Answers
Answer:
u <= 80
u > 80
Step-by-step explanation:
The happiest would be
Null hypothesis: u <= 80
Alternative hypothesis: u > 80
The correct set of hypotheses for the sample in July is H0: μ ≠ 80 Ha: μ = 80.
What is the null and alternative hypothesis?The null hypothesis H0 which is also known as the default hypothesis states that there is no relationship between the population parameters. The alternative hypothesis (H1 ) states that there is a relationship between the population parameters.
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The following information was obtained from the accounting records of Letty Stores for the financial year ended 30 June 2021:
R
Inventory (1 July 2020)
100 000
Sales
600 000
Purchases
400 000
Sales returns
2 000
Purchases returns
3 000
Drawings: Bank
1 000
Inventory (30 June 2021)
120 000
Additional information:
1. On 29 June 2021, the owner took inventory with a cost price of R20 000 for own use. This transaction has not yet been recorded.
The entity uses the periodic inventory control system.
Required:
Use the information provided above to calculate the cost of sales for the year ended 30 June 2021.
Answers
Answer:
333234
Step-by-step explanation:
333234$ for the next 4 years and the ecvation is 69$+-2$
Please help me with this math problem
Answers
Start off with the linear formula — y = mx + b
M is the slope find the slope by putting rise over run. In this case it is 5 as the rise and 5 as the run. This means 5(rise)/5(run) which is equivalent to 1. M is 1
B is the y intercept. In this case it is 2
You don’t have to show 1 as the slope because anything multiplied by one is itself so just get rid of the m and keep the x.
This leaves you with y = x + 2
Pls help extra points
Answers
Answer:
1 4
2 8
8 32
16 64
Step-by-step explanation:
2:8
8:32
16:64
A fourth of each
ADEF is translated 5 units straight up so that point F lands on the x-axis. where does point D land?
Answers
Point D would be translated to the point (0, 5).
What is translation?Translation is an aspect of geometry that moves plane shapes from one point to another along the cartesian coordinates without changing the form in which the shape exists.
Analysis:
Point D is at (0,0) if it is translated up from 0,0 the point D moves 5 units along the y-axis while x axis remain same. So that the new point of D becomes (0,5)
In conclusion, the point D will land at point (0,5)
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What is 5(x-2)-14x when x=4
Answers
Answer:
-46
Step-by-step explanation:
5 (x - 2) - 14x. x=4
5 (4 - 2) - 14(4) (distribute)
20 - 10 - 14(4) (multiply)
20 - 10 - 56 (subtract and solve.)
10 - 56 = -46 - solution
hope this helps (:
Learning Check Evaluate Algebraic Expressions Substitute for the given values. Then, solve using the order 2x + 10 when x = 5
Answers
Answer:
20
Step-by-step explanation:
2(5)+10=20
\(\huge \colorbox{pink}{Mathematics}\)
2x + 10 when x = 5
Solution\(2x + 10 \\ = 2(5) + 10 \\ = 10 + 10 \\ = 20\)
Answer: 20Correct me if I'm wrong
I hope it helps ^_^
Using the letters from the word ‘TRAPEZIUM’, how many combinations 5 letters can be formed such that they have exactly 3 consonants
Answers
Answer:
60
Step-by-step explanation:
TRAPEZIUM has 9 letters. 5 are consonants and 4 are vowels.
The number of possible combinations is:
₅C₃ × ₄C₂
10 × 6
60
The number of combination of 5 letters with exactly 3 consonants is 60.
What is a combination?It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.
The formula for combination is \(^nC_r\) = n!/r!(n - r)1
We have,
TRAPEZIUM
Number of consonant = 5
Number of vowels = 4
The number of ways 5 letters can be formed with 3 consonants.
= \(^5C_3 \times ^4C_2\)
= 5 x 2 x 6
= 60
Thus,
There are 60 combinations.
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30 POINTS HELPPPPP PLS Simplify the following. Do not Evaluate
30^7