A recursive definition for the set of all strings of a's and b's with odd lengths is:Base case: S(1) = {a, b}
Recursive case: S(n) = {as | s ∈ S(n-2), a ∈ {a, b}}
To create a recursive function for this set, we start with a base case, which is the set of all strings of length 1, consisting of either 'a' or 'b'. This is represented as S(1) = {a, b}.
For the recursive case, we define the set S(n) for odd lengths n as the set of strings formed by adding either 'a' or 'b' to each string in the set S(n-2).
By doing this, we ensure that all strings in the set have odd lengths, since adding a character to a string with an even length results in a string with an odd length. This process is repeated until we have generated all possible strings of a's and b's with odd lengths.
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This is confusing someone help please
Answer:
Below in BOLD.
Step-by-step explanation:
5x^2 - 6x - 2 = 0
Quadratic formula for ax^2 + bx + c = 0 is
x = [-b ± √(b^2 - 4ac)]/ 2a
Here we have a = 5, b = -6 and c = -2
so x = [-(-6) ± √((-6)^2 - 4*5*-2)]/ 2*5
= [ 6 ± √(36 + 40)] / 10
= 0.6 ± √76 / 10
= 0.6 ± 0.8718
= 1.4718, -0.2718
= 1.5, -0.3 to one decimal place.
x^2 + 3x = 40
x^2 + 3x - 40 = 0
We can factor this one:
(x - 5)(x + 8) = 0
x - 5 = 0 giving x = 5 and
x + 8 = 0 giving x = -8.
Answer x = -8, 5.
If f(x) = x-2, what is f¹(x)?
f¹(x) = 9x + 18
ƒ²¹(x) = x + 2
f¹(x) = 9x+2
ƒ¹ (x) = -2x +
Interchange x and y
[tex]\\ \tt\leadsto x=\dfrac{1}{9}y-2[/tex]
Solve for y[tex]\\ \tt\leadsto \dfrac{1}{9}y=x+2[/tex]
[tex]\\ \tt\leadsto y=9(x+2)[/tex]
[tex]\\ \tt\leadsto y=9x+18[/tex]
That's the inverse[tex]\\ \tt\leadsto f^{-1}(x)=9x+18[/tex]
Answer:
[tex]f^{-1}(x)=9x+18[/tex]
Step-by-step explanation:
[tex]f^{-1}(x)[/tex] is the notation for the inverse of a function.
The inverse of a function is its reflection in the line y = x.
Given function:
[tex]f(x)=\dfrac{1}{9}x-2[/tex]
To find the inverse of the given function:
Replace f(x) with y to get an equation for y in terms of x:
[tex]\implies y=\dfrac{1}{9}x-2[/tex]
Rearrange the equation to make x the subject:
[tex]\implies y+2=\dfrac{1}{9}x[/tex]
[tex]\implies 9(y+2)=x[/tex]
[tex]\implies x=9y+18[/tex]
Replace x with [tex]f^{-1}(x)[/tex] and y with x:
[tex]\implies f^{-1}(x)=9x+18[/tex]
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Rewrite each equation in factored form and solve using zero product property. Find the solutions of each equation. Use the notes about r * k = c and r + k = b. In the first problem c is 6 and b is -7. So you need the same r and k that multiply to be 6 but also add to be -7. The numbers you find will be the solutions
The factored form of the equation are as follows;
(d - 6)(d - 1) = 0(x + 9)(x + 9) = 0(u + 12)(u - 5) = 0How to write equation in factored form?Converting a quadratic function to factored form is called factoring.
Therefore,
let's factor the equation,
a.
d² - 7d + 6 = 0
d² - d - 6d + 6 = 0
d(d - 1) - 6(d - 1) = 0
(d - 6)(d - 1) = 0
b.
x² + 18x + 81 = 0
x² + 9x + 9x + 81 = 0
x(x + 9) + 9(x + 9) = 0
(x + 9)(x + 9) = 0
c.
u² + 7u - 60 = 0
u² - 5u + 12u - 60 = 0
u(u - 5) 12(u - 5) = 0
(u + 12)(u - 5) = 0
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What are the possible lengths of the third hallway? between 30 yards and 60 yards between 30 yards and 90 yards between 30 yards and 120 yards between 30 yards and 150 yards
The possible length of the third hallway is between 30 yards and 150 yards.
How to find the third length of a triangle?The hallway forms a triangle .
Therefore, using triangle inequality theorem, It states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
Hence,
90 + 60 > x
Where
x is the third side
x + 60 > 90
x + 90 > 60
Therefore, the possible length of the third hallway is between 30 yards and 150 yards.
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Answer:
D: between 30 yards and 150 yards
The angle measurements in the diagram are represented by the following expressions.
Answer:
X = 12
<B = 45°
Explanation:
From the diagram above:
Alternate exterior angles are equal. Therefore,
[tex]5x - 15 = 2x + 21 \\ collecting \: liketerms \\ 5x - 2x = 21 \: + 15 \\ 3x = 36 \\ dividing \: bothsides \: by \: 3 \\ \frac{3x}{3} = \frac{36}{3} \\ x = 12 [/tex]
For the measure of angle B
2x + 21°
2(12) + 21 = 24 + 21 = 45
Measure of angle B = 45°
Carlos found that the length of the diagonal of his laptop monitor is . If the manufacturer rounds to the nearest whole inch, what size is the monitor as measured by the diagonal
The size of the monitor as measured by the diagonal to the nearest whole inch, 17 inch.
What is square root?A number's square root is a quantity that, when multiplied by itself, yields the original quantity. There are two ways to calculate the square root of a number: method of prime factorization and division strategy.
For example, both 3 and –3 are square roots of 9
The length of the diagonal of his laptop monitor is squared root of 290
Let 'D' be the diagonal of the monitor.
The,
Diagonal = √290
Use long division method to solve the value,(attached in the file)
√290 = 17.029
= 17.03
Therefore, the value of √290 rounds to the nearest whole inch is 17 inch.
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The correct question is -
Carlos found that the length of the diagonal of his laptop monitor is squared root of 290. If the manufacturer rounds to the nearest whole inch, what size is the monitor as measured by the diagonal? 12 17 97 245
pls help :,)
What is the area of this triangle?
units²
Answer:
6 [tex]units^{2}[/tex]
Step-by-step explanation:
The formula for the area of a triangle is A = [tex]\frac{1}{2} bh[/tex]. The base in this case is the length of DE, 4 - 1 = 3 units. The height of this triangle is 1 + 3 = 4 units.
A = [tex]\frac{1}{2} bh[/tex] = [tex]\frac{1}{2} *3*4[/tex] = 6
A scale drawing of a house addition shows a scale factor of 1 in. = 3.3 ft. josh decides to make the house addition smaller, and he changes the scale of the drawing to 1 in. = 1.1 ft. what is the change in the scale factor from the old scale to the new scale? one-third two-thirds 2.2 3
3 is the scale factor that was changed from the previous scale to the new scale.
What is the scale factor?
The scale factor is a way to compare figures that appear to be similar but actually have distinct scales or measurements. Let's say two circles have similar appearances but different radii. A figure's scale factor indicates how much larger or smaller it is than the original figure.
What is the change in the scale factor?
A scale drawing is a condensed representation of an original image, structure, or object in terms of dimensions. The scale drawing is typically shrunk at a fixed dimension.
The change in the scale factor = larger scale / smaller scale
3.3 / 1.1 = 3
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Answer: 3
Step-by-step explanation:
Gerri purchases a coupon book with discounts for her favorite coffee shop. every coupon for the coffee shop offers the same discount. the table shows her total savings, y, based on the number of coupons, x, used from the book. a table showing coffee shop coupon savings with 2 columns and 6 rows. the first column, x, has the entries, 0, 5, 10, 15, 20. the second column, y, has the entries. negative 20, negative 10, 0, 10, 20.
Slope 2 and y intercept is 10
The question seems to be incomplete and complete and the complete question is shown in the image
The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases.
When x = 0, the corresponding y-value is the y-intercept. In the particular context of word problems, the y-intercept (that is, the point when x = 0) also refers to the starting value.
Y-intercept is the point at which the line intersects the y axis- meaning x = 0
From the table y = -20 when x= 0
y-intercept: -20
To find the slope
m = ΔY/ΔX
m = -20+10/0-5 = 2
Hence the slope is 2 and y intercept is 10
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ayuda por favor!!!!!!!!!!!!
La solución de la ecuación de valores absolutos es x = - 1 y la solución de la inecuación de valores absolutos es x ≥ 9/2 ∨ x ≤ 3.
¿Cómo resolver ecuaciones e inecuaciones de valores absolutos por medios algebraicos?
En esta pregunta debemos resolver una ecuación de valores absolutos y una inecuación de valores absolutos, cuya resolución requiere la aplicación de la definición de valor absoluto y procedimientos algebraicos:
|3 x - 1| = |3 · x + 7|
[tex]\left|\frac{3\cdot x - 1}{3\cdot x + 7} \right| = 1[/tex]
Por definición de valor absoluto:
[tex]\frac{3\cdot x - 1}{3\cdot x + 7} = 1\,\lor\,-\frac{3\cdot x - 1}{3\cdot x + 7} = 1[/tex]
[tex]3\cdot x - 1 = 3\cdot x + 7\,\lor \,- 3\cdot x + 1 = 3\cdot x + 7[/tex]
[tex]NaN \,\lor \, 6\cdot x = -6[/tex]
x = - 1
|4 · x + 3| ≤ 15
Por definición de valor absoluto:
- 4 · x + 3 ≥ - 15 ∨ 4 · x + 3 ≤ 15
- 4 · x ≥ - 18 ∨ 4 · x ≤ 12
x ≥ 9/2 ∨ x ≤ 3
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Find the value of X. Round to the nearest tenth HELP ASAP!!!!
Answer: 22.5
Step-by-step explanation:
[tex]\sin 64^{\circ}=\frac{x}{25}\\\\x=25 \sin 64^{\circ}\\\\x \approx 22.5[/tex]
A wall shaped like a trapezoid needs to be painted. The height of the wall is 16 feet and the bases are 20 feet and 24 feet. If one can of paint covers 20 square feet, how many whole cans of paint will the painter need to buy to paint the wall with one coat
Answer:
18 cans
Step-by-step explanation:
The number of cans of paint will be the least integer greater than or equal to the number required to cover the area of the trapezoid.
Area of a trapezoidThe area of the wall is given by the formula ...
A = 1/2(b1 +b2)h
where b1 and b2 are the bases, and h is the height.
We are given the values b1=20 ft, b2=24 ft, h=16 ft, so the area is found to be ...
A = 1/2(20 ft +24 ft)(16 ft) = 352 ft² . . . . . area of the wall
Cans of paintEach can of paint covers 20 ft², so n cans of paint will cover 20n square feet. We want to find the minimum integer value of n that satisfies ...
20n ≥ 352
n ≥ 17.6 . . . . . . . . . divide by 20
The next larger integer is 18.
The painter will need to buy 18 cans of paint.
3. A gardener uses 2 packages of lettuce seeds for 3 garden rows, each 5 feet long. How many packages of seeds does the gardener need to plant 45 feet of lettuce rows? Use the table to help.
Seeds (pkg) 2,4
Lettuce (rows) 3, 6
A 27
B 16
C 6
D 80
I need this with explanation please:(
Answer:
C) 6
Step-by-step explanation:
3 garden rows = 3*5 = 15 feet
we know we need 2 packages per each 15 feet
45/15=3 so 3 15 in 45, we just multiply 3 and 2 to get 6 packages
Call line that passes through the point x, y with a y intercept of b and a slope of m can be represented by the equation y=mx + b. a line is drawn on the coordinate plane that passes through the .3, -6 and has a slope of four the y-intercept of the line is
Answer: (0, -7.2)
Step-by-step explanation:
Substituting into point-slope form, the equation is
[tex]y+6=4(x-0.3)[/tex]
The y-intercept is when x=0, so substituting in x=0,
[tex]y+6=4(-0.3)\\\\y+6=-1.2\\\\y=-7.2[/tex]
So, the y-intercept is (0, -7.2).
Cost of 4 tables and 3 chairs is $225 and 3 tables and 4
chairs cost $195. Find the cost of 2 chairs and 1 table.
The cost of 2 chairs is = $30
The cost of 1 table = $60
Step-by-step explanation:
Let a table represent x
A chair represents y
4x + 3y = 225.......eq 1
3x + 4y = 195........eq 2
Use elimination method
x - y = 30
x= 30 + y...... Eq 3
Substitute the value of x into equation 1
4(30+ y) + 3y= 225
120 + 4y + 3y= 225
7y + 120= 225
7y= 225-120
7y= 105
y= 15
Substitute the value of y in eq 2
3x + 15 = 195
3x= 195-15
3x= 180
x= 60
Therefore, the cost of 2 chairs is 15 * 2= $30
The cost of 1 table = $60
Answer:
65
Step-by-step explanation:
Compare [tex]99![/tex] and [tex]50^{99}[/tex].
Hint: Identity [tex](a+b)(a-b)=a^2-b^2[/tex].
50^99 is greater than 99!
How to compare the numbers?The numbers are given as:
99! and 50^99
When the above numbers are estimated using a calculator, we have:
99! = 9.332622e+155
50^99 = 1.577722e+168
Next, we compare the exponents
168 and 155
168 is greater than 155
Hence, 50^99 is greater than 99!
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Ben has typed 180 and can type 30 words per minute. millie has typed 60 and can type 50 words per minute. how many minutes will it take for millie to catch up with ben.
The time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.
We assume the minutes taken by Millie to catch up with Ben to be x minutes.
The number of words Ben has already typed = 180.
The unit rate for Ben for the typing of words = 30 per minute.
Therefore, words typed by Ben in x minutes = 30x words.
Therefore, the total number of words typed by Ben = 180 + 30x words.
The number of words Millie has already typed = 60.
The unit rate for Millie for the typing of words = 50 per minute.
Therefore, words typed by Millie in x minutes = 50x words.
Therefore, the total number of words typed by Millie = 60 + 50x words.
As Millie needs to catch up with Ben after x minutes, the total number of words typed by them needs to be equal, that is, 60 + 50x = 180 + 30x, which is the required linear equation in one variable.
To find the minutes taken by Millie to catch up with Ben, we solve this linear equation in one variable as follows:
60 + 50x = 180 + 30x,
or, 60 + 50x - 30x = 180 + 30x - 30x {Subtracting 30x from both sides},
or, 60 + 20x = 180 {Simplifying},
or, 60 + 20x - 60 = 180 - 60 {Subtracting 60 from both sides},
or, 20x = 120 {Simplifying},
or, 20x/20 = 120/20 {Dividing both sides by 20},
or, x = 6 {Simplifying}.
Thus, the time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.
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0.00000007 as a fraction
Answer:
7/100000000
Step-by-step explanation:
to find this out we can start by saying that 0.7 is 7/10
every 0 in front of 7 after that is adding another 0 to 10
so
0.07 is 7/100
0.00000007 is 7/100000000
iteration-Find the first 3 iterates of the function look at pic pls help!!!!!
The first 3 iterates of the function are D. 3, -3, 9.
How to calculate the value?The function given is:
f(x) = -2x + 3
= -2(0) + 3
= 3
When x = 3
f(x) = -2x + 3
= -2(3) + 3
= -6 + 3
= -3
When x = -3
f(x) = -2x + 3
= -2(-3) + 3
= 9
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Which expression can be used to find the volume of the sphere?
A sphere with diameter 10 inches.
V = four-thirds pi r squared = Four-thirds (3.14) (5) squared
V = four-thirds pi r cubed = Four-thirds (3.14) (5) cubed
V = four-thirds pi r cubed = Four-thirds (3.14) (10) cubed
V = four-thirds pi r squared = Four-thirds (3.14) (10) squared
I think its (B)
V = four-thirds pi r cubed = Four-thirds (3.14) (5) cubed
can someone help me i know nothing about graphs
Answer:
The answer is B.
Step-by-step explanation:
The function F(x) = x would be the “parent function”. Meaning the +4 we see in G(x) would be a translation, because the function is not multiplied.
if you have ever seen the formula y = mx + b then you should be able to see that +4 would be referencing b in the linear equation, and because m is the same in both lines, we can say that the two functions only change is b, because b represents the y-intercept, if b was 0 in f(x)=x and was 4 in g(x)=x+4, the graph would be shifted 4 units up.
if you want to learn how to understand functions and linear equations, I recommend using khan academy. It is really helpfull in explaining topics of math.
What’s 1/6 to 3 dp does anyone know?
❄ Hi there,
[tex]\sf{\dfrac{1}{6}\approx0.167}[/tex], rounded to 3 DP (decimal places)
[tex]\left\vert\textsf{Decimal Places = Number of digits after the decimal point}\vert[/tex]
Why round? Because the entire number goes on for ever and ever.
So, we need to round. 1/6 rounded to 3 decimal places is 0.167. We have 3 numbers after the decimal point.
❄
Find the area of each figure as described or shown. Write final answer on blank provided. Show work. Include units as part of your answer. If needed, round answer to 2 decimal places.
Answer:
482.84u², 42.5cm², 51.5ft²
Step-by-step explanation:
1) A = 2(1 + √2)a²
A = 2(1 + √2)(80 / 8)²
A = 482.84units²
2) Square = 5²
Square = 25
T1 = 3 x 5 / 2
T1 = 7.5
T2 = 4 x 5 / 2
T2 = 10
Total = 10 + 7.5 + 25
Total = 42.5cm²
3) Rect = 4(8 + 3)
Rect = 44
T1 = 2 x 3 / 2
T1 = 3
T2 = 3 x 3 / 2
T2 = 4.5
Total = 3 + 4.5 + 44
Total = 51.5ft²
Find the nth term of the sequence 4, 7, 10, 13, …
Answer:
3n+1
Step-by-step explanation:
Subtract one from all the values, you get multiples of 3 in the equation 3n=nth term
So when you add one back, your equation is 3n+1=nth term
The angle measurements in the diagram are represented by the following expressions.
The angle measurements of angle B as represented in the diagram shown is 150°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the diagram:
∠A = ∠B (alternate interior angles)
Hence:
8x - 10 = 3x + 90
x = 20
∠B = 3(20) + 90 = 150°
The angle measurements of angle B as represented in the diagram shown is 150°
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Compared to the graph of f(x) = x², the graph of g(x) = (x − 2)² +3
is the result of translating f(x)
Answer:
Vertical shift up 3
Horizontal shift to the right 2
Brainliest, please :)
Answer:
Step-by-step explanation:
f(x) is moved 2 units to the right followed by 3 units up,
(X+m)(c+n) if m=5 and n=-7
Answer: -7/5
Step-by-step explanation:
x = - 5cm^2 - 7m^2 + 35/ m (5c - 7), C = (cross out the equal sign) 7/5 and m = (cross out the equal sign) 0 and n = -7/5
Help me with alg 2 please!
The probability that 5 boys would be selected would be 5/6720
How to determine the probabilityFrom the information given, the probability can be calculated using permutation
The formula for permutation is given as;
Permutation = [tex]\frac{n!}{n - r!}[/tex]
Where;
n is number of sets = 8r is the number of objects selected = 5Substitute the values into the formula
Permutation = [tex]\frac{8!}{8 - 5!}[/tex] = [tex]\frac{8!}{3!}[/tex] = [tex]\frac{40, 320}{6}[/tex] = 6720
The probability that 5 boys would be selected is 5/6720
Thus, the probability that 5 boys would be selected would be 5/6720
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ASAP PLEASE I NEED YouR HELP
Subtract − 4 b 2 + 4 b − 4 from 3 b 2 + 2 b − 5 .
Step-by-step explanation:
I assume the question really looks like
-4b² + 4b - 4 is to be subtracted from 3b² + 2b - 5.
so,
3b² + 2b - 5 - (-4b² + 4b - 4) =
= 3b² + 2b - 5 + 4b² - 4b + 4 =
= 7b² - 2b - 1
Which of the following shows the power of a power property
Answer: MULTIPLYING THE EXPONENTS!!!
Step-by-step explanation:
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