Answer:
f(n)=f(n-1)+f(n-2)
f(1)=1x
f(2)=1x
Step-by-step explanation:
This is the fibonacci sequence with each term times x.
Notice, you are adding the previous two terms to get the third term per consecutive triples of the sequence.
That is:
1x+1x=2x
1x+2x=3x
2x+3x=5x
3x+5x=8x
So since we need the two terms before the third per each consecutive triple in the sequence, our recursive definition must include two terms of the sequence. People normally go with the first two.
f(1)=1x since first term of f is 1x
f(2)=1x since second term of f is 1x
Yes, I'm naming the sequence f.
So I said a third term in a consecutive triple of the sequence is equal to the sum of it's two prior terms. Example, f(3)=f(2)+f(1) and f(4)=f(3)+f(2) and so on...
Note, the term before the nth term is the (n-1)th term and the term before the (n-1)th term is the (n-2)th term. Just like before the 15th term you have the (15-1)th term and before that one you have the (15-2)th term. That example simplified means before the 15th term you have the 14th and then the 13th.
So in general f(n)=f(n-1)+f(n-2).
So the full recursive definition is:
f(n)=f(n-1)+f(n-2)
f(1)=1x
f(2)=1x
Which one of these would be geometry or is it none of the above.
The midpoint, M , of segment AB has coordinates (2,−1) . If endpoint A of the segment has coordinates (−3,5) , what are the coordinates of endpoint B ?
The coordinates of endpoint B are?
the coordinates of endpoint B are (7,7)
Answer:
Solution given:
M(x,y)=(2,-1)
A[tex](x_{1},y_{1})=(-3,5)[/tex]
Let
B[tex](x_{2},y_{2})=(a,b)[/tex]
now
by using mid point formula
x=[tex]\frac{x_{1}+x_{2}}{2}[/tex]
$ubstituting value
2*2=-3+a
a=4+3
a=7
again
y=[tex]\frac{y_{1}+y_{2}}{2}[/tex]
$ubstituting value
-1*2=5-b
b=5+2
b=7
the coordinates of endpoint B are (7,7)
Consider the quadratic function:
f(x) = x2 – 8x – 9
Vertex: (StartFraction negative b Over 2 a EndFraction, f (StartFraction negative b Over 2 a))
Answer:
x=-b/2a=8/2=4
y=16-8*4-9=16-32-9= - 25
(4, - 25) ,,
In ∆ABC ,D and E are points on the sides AB and AC respectively such that DE is parallel to BC , 1) If AD= 2.5 cm ,BD = 3cm ,AE = 3.75 cm find length of AC. 2) If AD = 4 cm , AE =8cm ,DB =x – 4 cm ,EC =3x -19 cm , find x 3) I f AD =2cm ,BD = 4cm , show that BC = 3 DE
Answer:
1). AC=8.25cm
2). DB=7cm & EC=14cm
3). See Explanation
Step-by-step explanation:
According To the Question,
Given That, In ∆ABC, D and E are points on the sides AB and AC respectively such that DE is parallel to BC.
1). If AD= 2.5 cm ,BD = 3cm ,AE = 3.75 cm find length of AC.
Well we can apply Basic proportionality Theorem.
Since DE ║ BC ⇒ Sides are proportional and the angles are equal.
⇒ AD / BD = AE / EC
⇒ 2.5 / 3 = 3.75 / EC
On Solving we get,
⇒ EC * 2.5 = 3.75 * 3
⇒ EC * 2.5 = 11.25
⇒ EC = 11.25 / 2.5
⇒ EC = 4.5 cm
Thus,
AC = AE + EC
⇒ AC = 3.75 + 4.50
⇒ AC = 8.25 cm
Hence the measure of AC is 8.5 cm.
2). If AD = 4 cm , AE =8cm ,DB =x – 4 cm ,EC =3x -19 cm
Well we can apply Basic proportionality Theorem.
Since DE ║ BC ⇒ Sides are proportional and the angles are equal.
⇒ AD / BD = AE / EC
⇒ 4 / (x-4) = 8 / (3x-19)
on solving we get,
⇒ 3x-19 = 2(x-4)
⇒ 3x-19 = 2x-8
⇒x=11
Thus, DB =x–4 ⇒ 11-4 ⇒ DB=7cm
And, EC =3x-19 ⇒ 3×11-19 ⇒ EC=14cm
3). If AD=2cm , BD= 4cm , show that BC = 3 DE
Thus, AB = AD + DB = 2+4 = 6cm
Well we can apply Basic proportionality Theorem.
Since DE ║ BC ⇒ Sides are proportional and the angles are equal.
⇒ AD/AB = DE / BC
⇒ 2 / 6 = DE / BC
on solving we get
⇒ BC = 3 DE Hence, Proved
true or false,the diagonal of a rectangle is longer than any of its sides. I want the answer with explanation If u don't I will report
Answer:
True
Step-by-step explanation:
Yes! The diagonal of a rectangle is longer than any of its sides.
Consider PQRS as a rectangle. It is known to us that each interior angle of a rectangle measures 90°. Now, after making the diagonal of the rectangle PQRS, the rectangle has been split into 2 right-angled triangles i.e, ∆PRS and ∆RPQ. In the right angled triangle, hypotenuse is always the longest side. Here, in ∆PRS and ∆RPQ, the bases are RS and QP ; perpendiculars are PS and QR and both triangles' hypotenuse is PR. As, hypotenuse is always the longest side, so PR will be longer than RS,QP,PS and QR. Clearly, the diagonal of a rectangle is longer than any of its sides.
the sum of all the exponents on all the variables of a term
plsss answer
Answer:
Answer: for polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial
.
Serenity has a points card for a movie theater.
She receives 80 rewards points just for signing up.
She earns 11.5 points for each visit to the movie theater.
She needs 195 points for a free movie ticket.
.
.
Write and solve an equation which can be used to determine v, the number of visits
Serenity must make to earn a free movie ticket.
Evaluate without a calculator:
CSC -120°
Answer:
- [tex]\frac{2\sqrt{3} }{3}[/tex]
Step-by-step explanation:
Using the identity and the exact value
csc x = [tex]\frac{1}{sinx}[/tex] and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
- 120° is in the third quadrant where sin < 0 , then
csc - 120° = - sin60° , then
csc - 120°
= [tex]\frac{1}{-sin60}[/tex]
= - [tex]\frac{1}{\frac{\sqrt{3} }{2} }[/tex]
= - [tex]\frac{2}{\sqrt{3} }[/tex] ( rationalise the denominator )
= - [tex]\frac{2}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]
= - [tex]\frac{2\sqrt{3} }{3}[/tex]
The equivalent value of the trigonometric relation cosec ( -120 )° = 2√3/3
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
We know that the cosecant function is defined as the reciprocal of the sine function:
cosec (θ) = 1 / sin(θ)
Therefore, to evaluate cosec(-120°), we first need to find sin(-120°).
We know that sine is an odd function, which means that sin(-θ) = -sin(θ). Therefore,
sin(-120°) = -sin(120°)
We can now use the fact that the sine function has a period of 360 degrees, which means that sin(120°) is the same as sin(120° - 360°) = sin(-240°).
Using the same logic as before, we get:
sin(-240°) = -sin(240°)
Now , from the trigonometric relations , we get
Now, we can use the fact that sin(240°) = sin(240° - 360°) = sin(-120°), which means that:
sin(-240°) = -sin(-120°)
Therefore, we have:
sin(-120°) = -sin(120°) = -sin(-240°) = sin(240°)
Now, we can use the unit circle or trigonometric identities to find sin(240°). One way to do this is to draw a 30-60-90 degree triangle in the third quadrant of the unit circle, with the angle of 240° as the reference angle:
In this triangle, the opposite side (O) has a length of √3, the adjacent side (A) has a length of -1, and the hypotenuse (H) has a length of 2.
Therefore, sin(240°) = O/H = (√3)/2.
Finally, we can use the definition of the cosecant function to find cosec(-120°):
cosec(-120°) = 1/sin(-120°) = 1/sin(240°) = 1/((√3)/2) = 2/√3 = (2√3)/3.
Hence , cosec(-120°) is equal to (2√3)/3.
To learn more about trigonometric relations click :
https://brainly.com/question/14746686
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The
method would be the best for solving this
system of equations:
6x + 4y = 8
- 4y = 12
Enter the answer
Answer: [tex]\huge\boxed{x=3\frac{1}{3} \quad ;\quad y=-3}[/tex]
Step-by-step explanation:
[tex]\displaystyle\ \Large \boldsymbol+\ \left \{ {{6x+4y=8} \atop {-4y=12}} \right. \Longrightarrow\\\\\\ 6x+ 4y\!\!\!\!\!\diagup-4y\!\!\!\!\!\diagup=12+8 \\\\6x=20 \\\\x=\frac{20}{6} =\frac{10}{3} =3\frac{1}{3} \quad ; \quad y=-3[/tex]
[tex] {2}^{x} - 3( {2}^{x + \frac{1}{2} } ) + {2}^{2} = 0[/tex]
Can someone solve this equation?
Answer:
[tex]x = log_{2}( \frac{4+12 \sqrt{12} }{17} ) [/tex]
Step-by-step explanation:
I have attached the explanation above. hopefully this help
Answer: [tex]\Large\boxed{x=log_2\frac{12\sqrt{2}+4}{17}}[/tex]
Step-by-step explanation: [tex]\displaystyle\ \bigg{2^x-3(2^{x+\frac{1}{2} }})+2^2=0 \qquad ; \ \ \boxed{t=2^x} \\\\t-3t\sqrt{2} +4=0 \\\\ t(1-3\sqrt{2} )=-4 \\\\ t=\frac{4}{3\sqrt{2} -1} \cdot \frac{3\sqrt{2}+1 }{3\sqrt{2}+1 } =\frac{12\sqrt{2}+4}{17} \\\\\\2^x=\frac{12\sqrt{2}+4}{17} \\\\x=log_2 \ \ \frac{12\sqrt{2}+4}{17}[/tex]
The graphs below have the same shape. What is the equation of the blue graph?
Answer:
the answer is D
Step-by-step explanation:
Answer:
werwegwrvetvytby46bu46unu46e8mn667mmmm
Step-by-step explanation:m7
ui 6ei 67i77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777mmm
ratio of 55 paise is to 1 rupees
Answer:
You have to equal the unit first,
as 1 Rupee = 100 paise,
so,
55paise: 100paise,
= 11:20
I hope it hepled : )
Solve for x. Round to the nearest tenth of a degree, if necessary
Answer:
29.4 is the correct answer, it's rounded up so that you don't have to accidentally get it wrong like I did, lol
Step-by-step explanation:
log8-log4 ÷ log4-log2=
top cylinder: 6 in, 8 in
botton cube: 9 in, 9 in, 15 in
The volume of this figure is _____ cubic inches.
Answer:
1441.08 in^3
Step-by-step explanation:
Volume of rectangular prism = 15 * 9 * 9 = 1215 in^3
radius = 3 in
Volume of the cylinder = 3^2 * 3,14 * 8 = 226.08 in^3
Total volume = 1215 + 226.08 = 1441.08 in^3
Answer:
HJHJGHJHG
Step-by-step explanation:
JGHU45565677689789
Which of the following is an arithmetic sequence
Answer:
First one.
-3 is added to the previous term.
Solve for x.
Help me please
Answer:
x = 24
Step-by-step explanation:
Mathematically, in a cyclic quadrilateral; two opposite angles are supplementary
what this mean is that the opposite angles add up to equal 180 degrees
mathematically, we have this as;
(4x + 9) + (3x + 3) = 180
4x + 3x + 3 + 9 = 180
7x + 12 = 180
7x = 180-12
7x = 168
x = 168/7
x = 24
A marketing researcher interviews a large number of respondents and asks them a set of questions that are listed in a questionnaire. The respondents are required to select a response from a given set of options. In this case, the researcher is _____.
Answer: conducting quantitative research
Step-by-step explanation:
Quantitative research refers to the collection and the analysis of numerical data. Quantitative research can be used in making predictions, and testing casual relationships.
Quantitative research methods emphasize the numerical analysis of data which can be collected through questionnaires, polls, surveys etc.
Solve for x. Round to the nearest tenth, if necessary.
Answer:
15.4 (rounded to 1dp)
Step-by-step explanation:
ILL GIVE BRAINLIEST PLZ ANSWER
Answer:
-6
Step-by-step explanation:
y = -6x - 5
The equation is put in slope intercept form
( y = mx + b )
Where m = slope and b = y intercept
-6 is in the spot of "m"
Meaning that the slope would be -6
Answer:
slope is -6
Step-by-step explanation:
y = mx+b
m is slope :)
b is the point, where the line intersects the y axis
What is the slope of the line? What is the y-intercept of the line? y = 5/4x - 3
Answer:
m = 5/4
y intercept = -3
Step-by-step explanation:
The given equation of the line is ,
[tex]\implies y = \dfrac{5}{4}x -3[/tex]
We know that the Standard equation of Slope Intercept Form of the line is,
[tex]\implies y = mx + c[/tex]
Where ,
m is slope c is y interceptOn comparing to the Standard form of the line we get ,
[tex]\implies Slope = \dfrac{5}{4}\\[/tex]
[tex]\implies y - intercept= -3 [/tex]
general slope intercept form of a straight line is, y = mx + c
Slope of the line (m) = 5/4,
y-intercept of the line if when x=0 i.e.
y = 5/4x - 3
y = 5/4×0 - 3
y = -3
Answered by GAUTHMATH
Jon recently drove to visit his parents who live 270 270 miles away. On his way there his average speed was 24 24 miles per hour faster than on his way home (he ran into some bad weather). If Jon spent a total of 12 12 hours driving, find the two rates.
Answer:
He drove there at 60 mph, and he drove back at 36 mph.
Step-by-step explanation:
one way distance = d = 270 miles
average speed on way back = s
average speed on the way there = s + 24
time driving there = t
time driving back = 12 - t
average speed = distance/time
distance = speed * time
going there:
270 = (s + 24)t
270 = st + 24t
going back
270 = s(12 - t)
270 = 12s - st
We have a system of equations:
270 = st + 24t
270 = 12s - st
Solve the first equation for t.
t(s + 24) = 270
t = 270/(s + 24)
Substitute in the second equation.
270 = 12s - s[270/(s + 24)]
270 = 12s - 270s/(s + 24)
Multiply both sides by s + 24.
270s + 6480 = 12s^2 + 288s - 270s
12s^2 - 252s - 6480 = 0
Divide both sides by 12.
s^2 - 21s - 540 = 0
(s - 36)(s + 15) = 0
s = 36 or s = -15
The average speed cannot be negative, so we discard the solution s = -15.
s = 36
s + 24 = 60
Answer: He drove there at 60 mph, and he drove back at 36 mph.
Evaluate the expression. 37
Answer:
[tex]2187[/tex]
Step-by-step explanation:
[tex] {3}^{7} \\ = (3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3) \\ = 2187[/tex]
Hope it is helpful....Answer:
2187
Step-by-step explanation:
3*3=9
9*3=27
27*3=81
81*3=243
243*3=729
729*3=2189
can anyone answer this? (2y²-3xy)÷y.
Answer:
2y - 3x
Step-by-step explanation:
Given
(2y² - 3xy) ÷ y
Divide each term on the numerator by y , that is
[tex]\frac{2y^2}{y}[/tex] - [tex]\frac{3xy}{y}[/tex] ( cancel y on numerator/ denominator of both fractions )
= 2y - 3x
a same side interior angles pf two parallel lines is three times the other same side interior angle. find the measures of these two angles
Answer:
45 and 135
Step-by-step explanation:
Same Side Interior Angles = 180
x + 3x = 180
4x = 180
x = 45
3x = 135
Answer:
Angle 1 = 45 degrees
Angle 2 = 135 degrees
Step-by-step explanation:
All same side exterior angles are supplementary so if one is three times the other which means a ratio of 3:1.
180/4 = 45
First angle = 45 degrees
Second angle = 135 degrees
Find the value of c
1.)[tex](4)^{3c}*(4)^{5c}=4/16[/tex]
[tex]\displaystyle\ \boxed{a^m\cdot a^n=a^{m+n}}\\\\4^{3c} \cdot 4^{5c}=\frac{4}{16} \\\\4^{3c+5c}=4^{-1}\\\\8c=-1\\\\c=-\frac{1}8}[/tex]
Que
pr
The table shows a
proportional relationship. X
y228 45.6 6 8.4 8 11.2
Complete the equation that
represents the table. Ente -
V
re
Answer
49 votos
Answer:
???
Step-by-step explanation:
A bakery offers 4 different flavors of cake, 3 types of icing, 6 toppings, and 3 different sizes. If one option is chosen from each list, how many different cakes are possible? *
Answer:
216 different cakes are possible.
Step-by-step explanation:
Given that a bakery offers 4 different flavors of cake, 3 types of icing, 6 toppings, and 3 different sizes, if one option is chosen from each list, to determine how many different cakes are possible the following calculation must be performed:
4 x 3 x 6 x 3 = X
12 x 18 = X
216 = X
Therefore, 216 different cakes are possible.
Question 1 Tell whether this table represent a proportional relationship. Give the constant proportionality.
O yes, k= 2/9
yes, k= 9
O not proportional
Answer:
yes , k = 9
Step-by-step explanation:
The equation of a proportional relationship is
y = kx ← k is the constant of proportion
To find k divide both sides by x
[tex]\frac{y}{x}[/tex] = k
Check each ordered pair in the table
k = [tex]\frac{18}{2}[/tex] = 9
k = [tex]\frac{45}{5}[/tex] = 9
k = [tex]\frac{63}{7}[/tex] = 9
Thus the relationship is proportional with k = 9
a package is accidentally dropped from a helicopter from a height of 3,136ft. if the equation for height as a function of time is h(t) = -16t^2 + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the package to hit the ground?
Answer:
t = 14 seconds
Step-by-step explanation:
Given that,
A package is accidentally dropped from a helicopter from a height of 3,136ft.
The equation for height as a function of time is :
[tex]h(t) = -16t^2 + \text{initial height}[/tex]
So,
[tex]h(t) = -16t^2 +3,136[/tex]
When it hits the ground, h(t) = 0
So,
[tex]-16t^2 +3,136=0\\\\-16t^2=-3136\\\\t^2=\dfrac{3136}{16}\\\\t^2=196\\\\t=14\ s[/tex]
So, it will take 14 seconds for the package to hit the ground.
