Answer:
a) P(n) is true for all 'n' in the set ; { 0,2,4,6,8 ….. }
b) P(n) is true for all 'n' in the set ; { 0,1,2,3,4,5 ............ }
Step-by-step explanation:
a) As P(0) is true
we will assume that
P(2) is trueP(4) is true P(6) is truethis simply means that ; P(n) is true for all 'n' in the set
{ 0,2,4,6,8 ….. }
b) since P(0) and P(1) are true
we will assume that
P( 0+2 ) = P(2) is truealso P(1) and P(2) are true
we will assume that
P(1+2) = P(3) is trueAlso from the previous answers it can be seen that P(2) + P(3) is true
we will assume
P(2+2) = P(4) is trueThis simply means that P(n) is true for all 'n' in the set
{ 0,1,2,3,4,5 ............ }
Find the lettered angles.
Find the volume of the composite figure. First, find the volume of the triangular prism. Triangular prism Volume = [?] ft 8 ft Rectangular prism Volume = [ ] ft 10 ft Total Volume of Composite Figure = [ ] ft 14 ft 10 ft
Answer:
1440ft^3
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
i already did it
given that f(x)=2x-5, find the value of x that makes f(x)=15
Answer:
x = 10
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
f(x) = 2x - 5
f(x) = 15
Step 2: Solve for x
Substitute in f(x) [Function]: 15 = 2x - 5[Addition Property of Equality] Add 5 on both sides: 20 = 2x[Division Property of Equality] Divide 2 on both sides: 10 = xRewrite: x = 10Marking brainliest!!
What should I put for the second question? I am confused. HELPP
Help me please please help me
what is the H.C.F of 2³×3²
Recall that the Fibonacci Sequence is defined by the recurrence relation, a0 = a1 = 1 and for n ≥ 2, an = an−1 + an−2 . a. Show that f(x) = 1 1−x−x 2 is the generating function of the Fibonacci Sequence. b. Find ???? and β such that 1 − x − x 2 = (1 − ????x)(1 − βx). c. Find A and B in terms of ???? and β, such that 1 1−x−x 2 = A 1−????x + B 1−βx. d. Use the results of the previous parts to obtain a formula for an.
Answer:
Step-by-step explanation:
From the given information:
[tex]a_n = a_{n-1} + a_{n-2}; \ \ \ n \ge 2 \\ \\ a_o = 1 \\ \\ a_1 =1 \ \ \ \ \ since \ \ a_o = a_1 = 1[/tex]
A)
[tex]a_n - a_{n-1} - a_{n-2} = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2}(a_n -a_{n-1}-a_{n-2} ) x^n = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2} a_nx^n - \sum \limits ^{\infty}_{n=2} a_{n-1}x^n - \sum \limits ^{\infty}_{n=2}a_{n-2} x^n = 0 \\ \\ \implies (a(x) -a_o-a_1x) - (x(a(x) -a_o)) -x^2a(x) = 0 \\ \\ \implies a(x) (1 -x-x^2) -a_o-a_1x+a_ox = 0 \\ \\ \implies a(x)(1-x-x^2)-1-x+x=0 \\ \\ \implies a(x) (1-x-x^2) = 1[/tex]
[tex]\mathbf{Generating \ Function: a(x) = \dfrac{1}{1-x-x^2}=f(x)}[/tex]
B)
[tex]If \ \ 1 -x-x^2 = (1 - \alpha x) ( 1- \beta x) \\ \\ \implies 1 -x - ^2 = 1 + \alpha \beta x^2 - ( \alpha + \beta )x \\ \\ \text{It implies that:} \\ \\ \alpha \beta = -1 \\ \\ \alpha + \beta = 1 \\ \\ \implies \alpha = ( 1-\beta) \\ \\ ( 1- \beta) \beta = -1 \\ \\ \implies \beta - \beta^2 = -1 \implies \beta - \beta^2 -1 = 0\\ \\ \beta = \dfrac{-(-1) \pm \sqrt{(-1)^2 -4(1)(-1)}}{2(1)}[/tex]
[tex]\beta = \dfrac{1\pm \sqrt{5}}{2} \\ \\ \beta = \dfrac{1 + \sqrt{5}}{2} \ \ and \ \ \alpha = \dfrac{1 - \sqrt{5}}{2}[/tex]
C)
[tex]\dfrac{1}{1-x-x^2}= \dfrac{A}{1-\alpha x}+ \dfrac{\beta}{1-\beta x} \\ \\ = \dfrac{A(1-\beta x) + B(1-\alpha x)}{(1-\alpha x) (1 - \beta x)} \\ \\ = \dfrac{(A+B)-(A\beta+B\alpha)x}{(1-\alpha x) (1-\beta x)}[/tex]
[tex]\text{It means:} \\ \\ A+B=1 \\ \\ B = (1-A) \\ \\ A\beta+ B \alpha =0 \\ \\ A\beta ( 1 -A) \alpha = 0 \\ \\ A( \beta - \alpha ) = -\alpha \\ \\ A = \dfrac{\alpha}{\alpha - \beta } \\ \\ \\ \\ B = 1 - \dfrac{\alpha }{\alpha - \beta} \implies \dfrac{\alpha - \beta - \alpha }{\alpha - \beta } \\ \\ =\dfrac{-\beta }{\alpha - \beta} \\ \\ \mathbf{B = \dfrac{\beta }{\beta - \alpha }}[/tex]
D)
[tex]\text{The formula for} a_n: \\ \\ a(x) = \dfrac{\alpha }{\alpha - \beta }\sum \limits ^{\infty}_{n=0} \alpha ^n x^n - \dfrac{\beta}{\beta - \alpha }\sum \limits ^{\infty}_{n=0} \beta x^n \\ \\ \implies \sum \limits ^{\infty}_{n =0} \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta}x^n \\ \\ a_n = \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta } \\ \\ \\ a_n = \dfrac{1}{\sqrt{5}} \Big (\Big( \dfrac{\sqrt{5}+1}{2}\Big)^{n+1}- \Big ( \dfrac{1-\sqrt{5}}{2}\Big) ^{n+1}\Big)[/tex]
Analyze the results of the correlation using the given residual plot.
Answer:
Last one
Step-by-step explanation:
Answer:Analyze the results of the correlation using the given residual plot.
Residual
Step-by-step explanation:
the sum of the three sisters' ages is 51. If ava is 6 years older than
Camila, and Camila is twice as old as Luna, what are the ages of the
three sisters?
Create an equation with only one variable.
9514 1404 393
Answer:
Luna is 9Camila is 18Ava is 24Step-by-step explanation:
We can express all of the ages in terms of Luna's age. Letting L represent Luna's age, we have ...
Luna's age: LCamila's age: 2LAva's age: 2L +6The total of their ages is then ...
L +2L +(2L+6) = 51 . . . . an equation with one variable
5L = 45
L = 9
Luna is 9, Camila is 18, and Ava is 24.
As the student council treasurer, you prepare the budget for your class rafting trip. Each large raft
costs $100 to rent and each small raft costs $40 to rent. You have $1,600 to spend. Write and
solve a linear equation to find the number of small rafts you can rent if you rent 12 large rafts.
Answer:
10 small rafts
Step-by-step explanation:
(1600- 1200) / 40 = 10
1600- 1200 = 400
400 / 40 = 10
12 large rafts costs $1200 so subtract that amount from you budget. If you do that you will have $400 left. So I divided $400 by the amount of money each small raft cost whitch was $40 per small raft so i got the quotient of 10.
Sorry if i worded that weirdly but you get the point.
P.s sorry if it isn't comlety correct but i did my best so... ya
im super confused pls help
Please give me the correct answer
Answer:
m∠4 = m∠1 + m∠3
Step-by-step explanation:
The measure of an exterior angle of a triangle is equal to the sum of its two opposite interior angles
Now, examining the given triangle, we can note that:
∠4 is an exterior angle
∠1 and ∠3 are its two opposite interior angles
Based on the givens and the above theorem, we can conclude that:
m∠4 = m∠1 + m∠3
Hope this helps :)
Answer:
her answer is correct please
The 1st flat-bar, or cross, or other operator means:
-9-(-7)
-9-(-7)
-9--7
-9+7
7-9
-2
---
hope it helps
Find the Surface area S of each prism (the numbers are 3,5,4,8)
Answer:
Did u ever get the answer to this?
Step-by-step explanation:
Find the volume of the cone th=20 in and r=8 in. Solve in terms of pi and round off the decimal to the
nearest tenths.
Answer:
426.7pi
Step-by-step explanation:
V = 1/3 pi r2h
1/3 × 22/7× 8 × 8 × 20
426.7 pi
The cashier determines that the customer's groceries total $156.75. If the sales tax is four percent, how much will the customer have to pay for their groceries, including tax?
The function f(x) = -(x + 5)(x + 1) is shown.
What is the range of the function?
10
8
O all real numbers less than or equal to 4
O all real numbers less than or equal to -3
O all real numbers greater than or equal to 4
O all real numbers greater than or equal to -3
6
2
-10
-8
4
-2
2
4
8
8
10
X
4
-6
8
-10
Answer:
a
Step-by-step explanation:
f(x)=-(x+5)(x+1)=-(x²+6x+5)=-(x²+6x+9-9+5)
=-(x+3)^2+4
Range: all numbers ≤4
If a rectangle has length x and width x+3, what is the perimeter of the rectangle in terms of x?
Answer:
[tex]4x+6[/tex] units
Step-by-step explanation:
Skills needed to solve: Order of Operations, Distributive Property, Perimeter Formula, Like Terms
1) To solve this problem, you need to understand the perimeter formula, and that is:
--> [tex]P = 2(L+W)[/tex]
P = Perimeter
L = Length
W = Width
2) Based on that, we are given that:
[tex]L = x[/tex] (since the length is x)
[tex]W = x+3[/tex] (since the width is x+3)
3) After that, we substitute in the values:
[tex]P = 2(L+W)[/tex]
[tex]P = 2(x+(x+3))[/tex]
[tex]x + (x+3) = x+x+3 = 2x+3[/tex] (with like terms and addition)
so: [tex]P=2(2x+3)[/tex]
Use distributive property, which is [tex]a(b+c) = ab+ac[/tex]
get: [tex]2(2x+3) = 2(2x) + 2(3)[/tex]
[tex]2(2x) = 4x[/tex]
[tex]2(3) = 6[/tex]
So: [tex]P = 4x+6[/tex]
Hope this helps and have a nice day!! :) :]
Graph the line x = 3.
Answer: this my graph
Step-by-step explanation:
What is the area of the shaded region?
Answer:
12 cm^2
Step-by-step explanation:
Triangle A'B'C' is the image of ABC under a dilation with a scale factor of 2.
What length of segment A'B?
The length of segment A'B' from the triangle A'B'C' is 6 units.
Given that, triangle A'B'C' is the image of ABC under a dilation with a scale factor of 2.
In the given triangle ABC, AB=3 units
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
2=Dimensions of the new shape/3
Dimensions of the new shape=6 units
Therefore, the length of segment A'B' from the triangle A'B'C' is 6 units.
To learn more about the scale factor visit:
https://brainly.com/question/22312172.
#SPJ1
A jury pool has 18 people that are married and 22 people that are not married, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of the following. (Give answer as a fraction or a decimal out to at least 4 places. If your answer is very small use scientific notation out to 4 decimal places for example 3.3421E-6.)
Factorise the following expressions.
Answer:
Q.1 a²+10a+24
splitting the middle.
a²+6a+4a+24
=a(a+6)+4(a+6)
(a+6)(a+4)
Q.2 x²+9x+18
splitting the middle
x²+6x+3x+18
x(x+6)+3(x+6)
(x+6)(x+3)
simplify the following 6(1/2+1/3)
Answer:
5
Step-by-step explanation:
use the distributive property
6 * 1/2 = 3
6 * 1/3 = 2
3 + 2 = 5
Hope this helped! Have a nice rest of ur day! Plz mark as brainliest!!!
-Lil G
3. Tim had 253 dollars to spend on 7 books. After
buying them he had 15 dollars. How much did each book cost?
Answer:
each book costs $34
Step-by-step explanation:
assuming that all the books cost the same,
253-15=238
238/7=34
Answer: Each book cost $34.
Step-by-step explanation:
First subtract 253-15.
253-15=238.
Then divide 238/7.
238/7=34
Hope this helps :)
.A boat can travel 280 miles on 56
gallons of gasoline. How much
gasoline will it need to go 110 miles
Answer:
22 gallons
Step-by-step explanation:
280 miles / 56 gallons = 5 miles per gallon
110 miles/5 mpg = 22 gallons
Can someone show me how to do this? I’m not sure how to do this
Directions: The points in the table lie on a line. Find the slope of the line. Then draw its graph.
Answer: Slope means the gradient. So find the equation of the line first then graph the points on the graph.
Step-by-step explanation:
y=mx+c *We want m*
m=(y2-y1)/(x2-x1)
m=(0-1)/(6-3)
m=-1/3
y=-1/3x+2 *(0,2) co-ordinate means it's the y-intercept=c*
I think the slope is -1/3 and then just plt the points on the graph manually.
Pls answer correctly I’ll give you brainliest
Answer:
1=2(4)+b
Step-by-step explanation:
slope intercept looks like this y=mx(or y=#x+#
if the slope is 2 the equation will be y=2x+b
to find b so x=4 and y=1 we can plug those numbers into the equation to find b
You measure the sides of a pool and find that it is 20 yards wide and 60 yards long.
30 points!
Approximately, how far would it be diagonally between corners of the pool?
63 yards
55 yards
67 yards
72 yards
Answer:
63
Step-by-step explanation:
Answer: 63
Step-by-step explanation:
GIVING 25 PTS URGENT
Answer:
D) 76 sq in
Step-by-step explanation:
It’s 4 triangles. A=1/2bh
1/2(8)(5)=20 (two of these)
1/2(8)(6)=24
1/2(4)(6)=12
20+20+24+12=76