A. 5/10, -6/11, 7/12, -8/13
B. f(n) = n/(n+5)
C. Positive
What is a sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.
Here, we have
A. From inspection of the sequence, the pattern is:
Add 1 to the numerator of the previous term.
Add 1 to the denominator of the previous term.
Make every other term negative.
Hence, assuming the pattern continues, the next four terms in the sequence will be:
5/10, -6/11, 7/12, -8/13
B. An explicit formula for an arithmetic sequence allows you to find the [tex]n^{th}[/tex] term of the sequence.
f(1) = 1/6
f(2) = -2/7
We can see that the numerator is the position of the term (n) in the sequence. So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.
The denominator is 5 more than the position of the term in the sequence. So when n = 1 the denominator is 1 + 5 = 6, and when n = 2 the denominator is 2 + 5 = 7.
We observe that if the numerator (the value of n) is odd then the term is positive, and if the numerator (the value of n) is even then the term is negative.
Hence, the rule for the nth term is:
f(n) = n/(n+5)
If n is odd then f(n) is positive.
If n is even then f(n) is negative.
C. 53 is an odd number.
As the function f(n) is positive when n is odd, the sign of f(53) is positive.
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Simplify the below expression.
Answer:
x^-8.x^3
x^-8+3
x^-5
1/x^5
Step-by-step explanation:
Consider the graphs below. What are the explanatory variables?
D was the answer for me.
Answer:
its c
Step-by-step explanation:
I just took the test
for k(x)=4÷5x-6,determine k^-1(8)
The value of k⁻¹(8) in for k(x) = 4 ÷ 5x - 6 is 2/35.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Given, k(x) = 4 ÷ 5x - 6.
k(x) = (4/5x) - 6.
Let, y = k(x).
y = (4/5x) - 6.
(4/5x) = y + 6.
1/x = 5(y + 6)/4.
x = 4/{5(y + 6)}.
y = 4/{5(x + 6)}.
k⁻¹(x) = 4/{5(x + 6)}.
k⁻¹(8) = 4/{5(8 + 6)}.
k⁻¹(8) = 4/{5(14)}.
k⁻¹(8) = 4/70.
k⁻¹(8) = 2/35.
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help ! what's the value of x -
[tex] {x}^{4} + 4 = 100 \div 5[/tex]
Answer:
2
Step-by-step explanation:
100/5 = 20
x⁴ + 4 = 20
x⁴ = 20 - 4
x⁴ = 16
= 2 × 2 × 2 × 2
x⁴ = 2⁴
x = 2
Hence, the value of x is 2.
Repartos Equitativos: A:Repartir 21 chocolates en 5 niños (dividir) B:Repartir 10 chocolates en 3 niños (dividir)
Respuesta:
4 1/5 bombones
3 1/3 bombones
Explicación paso a paso:
Distribuir 21 bombones entre 5 niños;
21/5 = 4 resto 1
Por lo tanto, se le da 4 chocolates a cada niño y el 1 chocolate restante se divide en 5 partes iguales y se le da 1/5 a cada niño. Por lo tanto, cada niño recibe 4 1/5 chocolates.
Distribuir 10 bombones entre 3 niños;
10/3 = 3 resto 1
Por lo tanto, se le da 3 chocolates a cada niño y el 1 chocolate restante se divide en 3 partes iguales y se le da 1/3 a cada niño. Por lo tanto, cada niño recibe 3 1/3 chocolates.
HELP ASAP!!
Find the surface area of the figure. Round your answer to the nearest hundredth if necessary ^
Answer:
add all the sides together and if thats not it you learned something different from me:)
Answer: 384 yd
Step-by-step explanation: To find the surface area of a cube, simply calculate using this formula: [tex]SA=6a^2[/tex]. In this case, the [tex]a[/tex] is equal to 8 yards, input the number 8 into the formula.
[tex]SA=6(8)^2[/tex]
[tex]SA=384[/tex]
Hope this helped! ;)
What is the value of log2 log32?
the value of log2 log32 is 0.5899 and the base of the logarithm is raised to the value that was equated earlier and this expression is equal to the logarithm.
logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.J
The logarithmic equation that has the same solution as x-4=2^3 is log2(x-4)=3.
Logarithm
The logarithm of a number can be calculated from the following relationship:
Thus, the base of the logarithm is raised to the value that was equated earlier and this expression is equal to the logarithm.
So, we have that the third expression
Therefore, this expression is the one corresponding to x-4=2^3.
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convert each percent increase or decrease into a multiplier show work
a. 5 percent increase
b. 12 percent decrease
Answer:
a. 1.05
b. 0.95
Step-by-step explanation:
a. 5 percent increase
5% = 0.05
Because it is increasing, so we add 1
1 + 0.05 = 1.05
b. 12 percent decrease
12% = 0.12
Because it is decreasing, so subtract 1
1 - 0.05 = 0.95
So, the answer is
a. 1.05
b. 0.95
can you help with these 3 question pls it is due at 8 pm
Step-by-step explanation:
1. a + 130 =.180 ---> a = 50°
b + 130 + 120 = 360 ---> b = 110°
c + 120 = 180 ---> c = 60°
2. p + 44 = 180 ---> p = 136°
q + 44 = 180 ---> q = 136°
r = 44° (definition of vertical angles)
t = 34° (definition of vertical angles)
3. x = 50° (definition of vertical angles)
y = 50° (definition of alternate external angles)
Factor out the greatest common factor. If the greatest common factor is 1, just retype the
polynomial.
20q ^10 - 10q⁹+ 30q^8 + 20q^7
The greatest common factor of 20q¹⁰ - 10q⁹ + 30q⁸ + 20q⁷ is 10q⁷.
What is the greatest common factor?The GCF stands for greatest common factor. In this case, greatest can be changed to highest, and factor to divisor. The highest common factor is often referred to as the biggest common factor, highest common factor, or highest common divisor (GCD).
The largest number among all the common factors of the given numbers is known as the GCF (Greatest Common Factor) of two or more numbers. The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF. There are three main methods for calculating GCF: division, multiplication, and prime factorization.
the factor of 20q¹⁰ is 2*2*5*q*q*q*q*q*q*q*q*q*q
the factor of 10q⁹ is 2*5*q*q*q*q*q*q*q*q*q
the factor of 30q⁸ is 2*3*5*q*q*q*q*q*q*q*q
the factor of 20q⁷ is 2*2*5*q*q*q*q*q*q*q
So that the common factor of all the above terms is 2*5*q*q*q*q*q*q*q
the common factor of all the above terms= 10q⁷
So that the greatest common factor of 20q¹⁰ - 10q⁹ + 30q⁸ + 20q⁷ is 10q⁷.
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Anybody can help me with this ?
Answer: from left to right -3,-1,1,3,5
Step-by-step explanation:
Substitute the x value from the chart into the equation for each number.
Polly bought a bag of s sour candies. She ate 74 of the candies. Write an expression that shows how many sour candies Polly has now.
Answer:
s-74
Step-by-step explanation:
She ate 74 candies, out of the total S candies. So, if we do S-74, well find how many are left.
Find the number of 15% of it is equal to nine
Answer:
15% of 60 is equal to 9
Step-by-step explanation:
If this helps please mark as brainliest
HELP H>E>L>P help help
Answer:
i think b) option b
Step-by-step explanation:
lmk if this is incorrect
i will give brainly :) NO LINKS
I'm thinking of 3 whole numbers. Use the clues to find the values of the three mystery numbers:
Clue #1 - The middle number is 3 times the smallest number
Clue #2 - The largest number is 6 more than the middle number
Clue #3 - The sum of my 3 numbers is 34
Answer:
HAH DUM
Step-by-step explanation:
Find two consecutive odd integers such that the sum between twice the smallest and the biggest is 35.
Answer:
Consecutive odd numbers will be 11 and 13.
Step-by-step explanation:
Let the two consecutive odd integers are n and (n + 2).
From the given question,
Sum between twice the smallest and the biggest is 35.
Since, smallest number is 'n' and biggest is (n + 2)
Therefore equation will be,
2n + (n + 2) = 35
(2n + n) + 2 = 35
3n + 2 = 35
3n = 33
n = 11
And (n + 2) = 13
Consecutive odd numbers will be,
11, 13
The table shows the running speeds of 10 randomly selected lions
Step-by-step explanation:
speed (miles per hour) 48, 45, 50, 44, 46, 45, 42, 47, 45, 48. based on the data
The top speed of a lion is 48 miles per hour.
FOR 20 POINTS FIND X PLEASE!!
Hi there!
We can find the values of x using right triangle trig.
Recall: SOHCAHTOA
sin = O/H (Opposite / Hypotenuse)
cos = A/H (Adjacent / Hypotenuse)
tan = O/A (Opposite / Adjacent)
Thus:
6. A = 14, H = 15
cos x = 14/15
cos⁻¹ (14/15) = x
x = 21.04° ≈ 21°
7. O = 19, A = 23
tan x = 19/23
tan⁻¹(19/23) = x
x = 39.56° ≈ 40°
8. A = 9, H = 17
cos x = 9/17
cos⁻¹(9/17) = x
x = 58.03 ≈ 58°
9. O = 43, H = 45
sin x = 43/45
sin⁻¹(43/45) = x
x = 72.85° ≈ 73°
Suppose that g(x) = f(x) + 2. Which statement best compares the graph of
g(x) with the graph of f(x)?
A. The graph of g(x) is shifted 2 units down.
O B. The graph of g(x) is vertically stretched by a factor of 2.
C. The graph of g(x) is shifted 2 units to the right.
D. The graph of g(x) is shifted 2 units up.
Answer:
2 units up
Step-by-step explanation:
You have no stretch because no number in front and nothing is done to x do no movement to the sides
I need help with this
Answer:
27
Step-by-step explanation:
Area of Triangle x 2 = 3 * 3
The reason I did not divide it by 2 is because of how the other triangle is bound to have the same area. Just leave it as it is because later you're going to reach the same answer.
3 * 3 = 9
Rectangle Area = 6 * 3 = 18
18 + 9 = 27
ASAP
JUST THE ANSWER FR THIS TIME
Answer:
18
Step-by-step explanation:
You can use a calculator for this
60%*30=18
or, if you want to solve it by hand, 60% equals 0.6=6/10=3/5
(3/5)*30=90/5=18
Answer:
18
Step-by-step explanation:
have a nice day!!
find the values of X, Y, and Z
On applying the midpoint theorem the values of x, y, and z are 2, 10 and 8 respectively.
What is the mid-point theorem?
According to the midpoint theorem, the line segment connecting any two triangle sides' midpoints is parallel to and equal to half of the third side.
The outer triangle is ABC and the inner triangle is DEF.
It can be seen that sides AB, BC and AC are equally divided such that AD=DB,
BE=EC and
CF=FA.
So, this proves that point D, E and F are the middle points of AB, BC and AC respectively.
Now, according to the midpoint theorem -
DF = 1/2(BC)
Plugging in the values -
x = (5x-6)/2
2x = 5x-6
2x-5x = -6
-3x = -6
x = 2
Now, for side DE -
DE = 1/2(AC)
Plugging in the values -
12 = (2z+8)/2
24 = 2z+8
24-8 = 2z
16 = 2z
z = 8
Now, for side EF -
EF = 1/2(AB)
Plugging in the values -
y = 20/2
y = 10
Therefore, the values obtained are x=2, y=10 and z=8.
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The cost of 3 movie rentals and 7 boxes of candy is 16.60. The cost of 5 movie rentals and 2 boxes of candy is 13 how much does 1 box of candy cost ?
Answer:
212
Step-by-step explanation:
Which statements are necessary to prove the two triangles are congruent by SSS? (ASAP HELP PLS!!!)
Answer:
C
Step-by-step explanation:
To prove that two triangles are congruent using the SSS Congruence criterion, we must establish that all three sides of one triangle are equal to all the corresponding sides of the other.
Thus,
Side AD in ∆ADB is congruent to side AD in ∆ADC.
Side BD in ∆ADB is congruent to side CD in ∆ADC.
Side AB in ∆ADB is congruent to side AC in ∆ADC.
Therefore, based on the SSS congruence criterion, it is concluded that both triangles are congruent.
The statements necessary to prove that they are congruent by SSS is:
C.
Help with question 3
Answer:
All real numbers for both Range and Domain
R
or
(−∞,∞)
Kyle and Steve start at the same point and walk in opposite directions. If Kyle walks at 2 mph and Steve walks at 2 mph, how far apart will they be after 3 hours?
Answer:
12 miles
Step-by-step explanation:
Kyle's speed = 2 mph
Steve's speed = 2 mph
Time traveled = 3 hours
Distance apart after 3 hours
Distance moved by Kyle + Distance moved by Steve
Distance = Speed * time
Distance moved by Kyle = 2 * 3 = 6 miles
Distance moved by Steve = 2 * 3 = 6 miles
Total distance apart = 6 + 6 = 12 miles
Factor by gcf 6x2+3x+21 The 2 is supposed to be small.
Given:
The expression is:
[tex]6x^2+3x+21[/tex]
To find:
The factor of the given expression by GCF.
Solution:
It is given that,
[tex]6x^2+3x+21[/tex]
The terms of the given expression are [tex]6x^2,3x,21[/tex]. The greatest common factor of these terms is 3.
[tex]6x^2+3x+21=3\times 2x^2+3\times x+3\times 7[/tex]
So, taking out the GCF, the given expression can be rewritten as:
[tex]6x^2+3x+21=3(2x^2+x+7)[/tex]
Therefore, the factor form of the given expression by GCF is [tex]3(2x^2+x+7)[/tex].
How do you solve a 3 by 3 system of equations using matrices?
The solutions can be read off of the diagonal entries in the reduced matrix.
To solve a 3 x 3 system of equations using matrices, first we need to create the augmented matrix for the system of equations. The augmented matrix contains the coefficients of the variables and the constants for each equation on each row. Then we can use row operations to reduce the augmented matrix to reduced row-echelon form. This can be done by adding or subtracting rows to each other, multiplying or dividing a row by a non-zero number, and swapping two rows. After reducing the matrix to row-echelon form, we can back-substitute the solutions to the system of equations. The solutions can be read off of the diagonal entries in the reduced matrix. For example, if the matrix is reduced to the form [a b c d e f g h i] then the solution to the system of equations is x = d/a, y = e/b, and z = f/c.
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prove that cos x = sin x cot x.
Answer:
can u give me the brainliest
the answer is in the attached documents
Find the missing angle.
Answer:
x = 81
Step-by-step explanation:
180 (62 + 37) = x
81 = x
Hope this helps!
Answer:
81
Step-by-step explanation:
x + 37 + 62 = 180
x + 99 = 180
x = 180 - 99
x = 81