Answer:
21
Step-by-step explanation:
1, 1, 2, 3, 5, 8, 13, 21
The required eighth number in the Fibonacci sequence is 21.
Given that,
1, 1, 2, 3, 5, and 8 are the first six numbers of the Fibonacci sequence. what is the eighth number is to be determined
The sequence is defined as the specific pattern of numbers in which they are arranged.
Here,
given Fibonacci sequence is 1, 1, 2, 3, 5, 8
The Fibonacci numbers, sometimes known as Fn, are a set of numbers in mathematics where each number is the sum of the two numbers before it.
According to the above definition,
7 th number = 5th number + 6th number =
7 th number = 5 + 8 = 13
8th number = 8 + 13 = 21
Thus, the required eighth number in the Fibonacci sequence is 21.
Learn more about the Fibonacci sequence here,
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PLS HELP WILL MARK BRAINLIEST
[tex]f(a) = -4a +6a^3 - 15 -4a^2 \\\\\text{By the remainder theorem,}\\\\f\left(\dfrac 53 \right) = -4\left(\dfrac 53 \right) + 6 \left( \dfrac 53 \right)^3 - 15 - 4 \left(\dfrac 53 \right)^2 = -5\\\\\\ \text{Hence}~-5~ \text{is the remainder when f(a) is divided by}~ 3a -5[/tex]
[tex]\\ \sf\longmapsto 3a-5=0[/tex]
[tex]\\ \sf\longmapsto 3a=5[/tex]
[tex]\\ \sf\longmapsto a=\dfrac{5}{3}[/tex]
Using remainder theorem
[tex]\\ \sf\longmapsto f(a)=-4a+6a^2-4a^2-15[/tex]
[tex]\\ \sf\longmapsto f\left(\dfrac{5}{3}\right)[/tex]
[tex]\\ \sf\longmapsto -4(5/3)+2a^2-15[/tex]
[tex]\\ \sf\longmapsto -20/3+2(5/3)^2-15[/tex]
[tex]\\ \sf\longmapsto -20/3+2(25/9)-15[/tex]
[tex]\\ \sf\longmapsto -20/3+50/9-15[/tex]
[tex]\\ \sf\longmapsto (-60+50)/9-15[/tex]
[tex]\\ \sf\longmapsto -10/9-15[/tex]
[tex]\\ \sf\longmapsto -10-135/9[/tex]
[tex]\\ \sf\longmapsto -145/9[/tex]
[tex]\\ \sf\longmapsto 16\dfrac{-5}{9}[/tex]
Remainder=-5
Given that the area of a rectangle can be represented by 5x2-8x-4, write expressions to represent
the length and width of the rectangle. Show all work for credit.
Answer:
length: 5x + 2
width: x - 2
Step-by-step explanation:
Factors of 5
1, 5
Factors of 4
1, 4
2, 2
Sign
one positive, one negative
Factor 5x^2 - 8x - 4
(5x + 2)(x - 2) = 5x^2 - 10x + 2x - 4
(5x + 2)(x - 2) = 5x^2 - 8x - 4
Therefor
length: 5x + 2
width: x - 2
pls help! NO LINKS I WILL REPORT YOU
Is 70.61 a rational or irrational number?
Answer:
70.61 is a rational number
Step-by-step explanation:
This is because a rational number is either:
A whole number, like 70, whole number.
Is a terminating decimal, such as the one above 70.61, (A terminating decimal is a decimal that doesn't repeat.
And or has a pattern, or a recurring decimal, like 7.478478..., it repeats the decimal over and over, thus, rational.
Hope this helped you, have a great day.
Kylie borrowed a book from a library. The library charged a fixed rental for the book and a late fee for every day the book was overdue. The expression below shows the charges Kylie paid for the book when she returned it x days after the due date:
2 + 0.25x
What does the constant term of the expression represent? (1 point)
The late fee for the book
The fixed rental for the book
The number of books borrowed
The number of days the book was overdue
Answer:
it's "2+6556_789*4236+8765/987"
Step-by-step explanation:
837+208+363=find the sum by suitable rearrangement
Answer:
1,408
Step-by-step explanation:
208 + 363 + 837=1408
One number is 3 times another. If the difference between the numbers is 14, what is the larger number?
Answer:
21
Step-by-step explanation:
Create an equation: 3n - n = 14
Solve: 3n - n = 14
2n = 14
n = 7
Larger number: 3(7) = 21
Answer:
The numbers are 7 and 21.
Step-by-step explanation:
The difference is 14 and 7*3= 21
How to find extreme values of a function.
Answer:
See below
Step-by-step explanation:
Extreme values of a function are found by taking the first derivative of the function and setting it equal to 0. To determine if it's a minimum or maximum, we set the second derivative equal to 0 and determine if its positive or negative respectively.
Let's do [tex]f(x)=3x^4+2x^3-5x^2+7[/tex] as an example
By using the power rule where [tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex], then [tex]f'(x)=12x^3+6x^2-10x[/tex]
Now set [tex]f'(x)=0[/tex] and solve for [tex]x[/tex]:
[tex]0=12x^3+6x^2-10x[/tex]
[tex]0=2x(6x^2+3x-5)[/tex]
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-3\pm\sqrt{3^2-4(6)(-5)}}{2(6)}[/tex]
[tex]x=\frac{-3\pm\sqrt{9+120}}{12}[/tex]
[tex]x=\frac{-3\pm\sqrt{129}}{12}[/tex]
[tex]x=-\frac{3}{12}\pm\frac{\sqrt{129}}{12}[/tex]
[tex]x=-\frac{1}{4}\pm\frac{\sqrt{129}}{12}[/tex]
[tex]x_1=0,x_2\approx0.6965,x_3=-1.1965[/tex]
By plugging our critical points into [tex]f(x)[/tex], we can see that our extreme values are located at [tex](0,7)[/tex], [tex](0.6965,5.956)[/tex], and [tex](-1.1965,2.565)[/tex].
The second derivative would be [tex]f''(x)=36x^2+12x-10[/tex] and plugging in our critical points will tell us if they are minimums or maximums.
If [tex]f''(x)>0[/tex], it's a minimum, but if [tex]f''(x)<0[/tex], it's a maximum.
Since [tex]f''(0)=-10<0[/tex] then [tex](0,7)[/tex] is a local maximum
Since [tex]f''(0.6965)=15.822>0[/tex], then [tex](0.6965,5.956)[/tex] is a local minimum
Since [tex]f''(-1.1965)=27.18>0[/tex], then [tex](-1.1965,2.565)[/tex] is a global minimum
Therefore, the extreme values of [tex]f(x)=3x^4+2x^3-5x^2+7[/tex] are a global minimum of [tex](-1.1965,2.565)[/tex], a local minimum of [tex](0.6965,5.956)[/tex], and a local maximum of [tex](0,7)[/tex].
Hope this example helped you understand! I've attached a graph to help you visualize the extreme values and where they're located.
An investor invested a total of $3,000 in two mutual funds. One fund earned a 7% profit while the other earned a 3% profit. If the investor's total profit was $142, how much was invested in each mutual fund?
Answer:
Step-by-step explanation:
x= fund that got 7%
y= fund that got 3%
x+y=3000
.07x+.03y=142
y=3000-x
.07x+.03(3000-x)=142
.07x+90-.03x=142
.04x=52
x= 1300
x+y=3000
1300+y=3000
y=1700
1300 in the fund that earned 7%
1700 in the fund that earned 3%
Round 53,714.54 to the nearest a. thousandth. b. thousand.
pls help 3 x 2 + 6 (4+1) = ???
Answer:
17 IS THE ANSWER......................
Answer:
Your answer should be 36.
PLEASE HELP ITS URGANT WILL MAKE BRAINLIEST PLEASE HELP MEEE
Answer:
A is the answer
Step-by-step explanation:
look at the attached image
What is the range of this function?
4
-
co
8
7
18
-15
O A. {-4, -1, 15, 18}
O B. {-4,1,7,15}
OC. {-1,4, 8, 18}
O D. {-4, -1,1,4,7,8, 15, 18}
Answer:
Not sure but I think it's B.
what is an complementary angle?
Step-by-step explanation:
Angles whose sum is 90° .
For ex - 30° and 60°
Answer/Step-by-step explanation:
Complementary angle is two angle that add up to 90 degree.
Complementary angle also put together form a right angle.
ex:
To determine the complement, subtract the given angle from 90. 90 - 43 = 47° The complement of 43° is 47°.
rewrite in simplest form
9w-3(-w-8)
Answer:
12w + 24.
Step-by-step explanation:
distribute -3 to the equation in parenthesis. 9w - 3 (- w - 8). 9w + 3w + 24.
Two boxes are shown are cuboids
(Big box) : 50cm, 30cm, 20cm
little box: 10cm, 3cm, 4cm
how many of the smaller boxed would u need to fill in the bigger box? HELP
Answer:
25 little box will fit in the large box
Step-by-step explanation:
50×30×20=3000
10×3×4=120
so 3000/120=25
Answer: 25
Step-by-step explanation:
big cuboid=abc=50×30×20=3000cm3
little cuboid=10×3×4=120cm3
3000÷120=25
whats the answer????
Step-by-step explanation:
the general slope intercept form is
y = ax + b
a is the slope (and always the factor of x). it is expressed as ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point to another.
b is the y-intercept, the y value of the point, where the line crosses the y-axis (in other words : the y value when x = 0).
so, look at the chart. where do we see points with integer coordinates (these are the easiest to read correctly and work with) ?
I see for example (0, -6) and (4, -7).
to go from the first to the second point :
x changes by +4 units (from 0 to 4).
y changes by -1 unit (from -6 to -7).
the slope a is therefore -1/4.
and the first point i picked gives us also automatically the y-intercept (-6).
so, the line equation is
y = (-1/4)x - 6
b2 - 12a when a = 1/4 and b = 8
Answer:
13
Step-by-step explanation:
b2-12a
2(8)-12(1/4)
16-12/4
16-3
13
solve pls brainliest
Answer:
neither, neither, terminating, repeating
Reduce 36 to simplest form?
Answer:
[tex]2^{2} *3^{2}[/tex]
Step-by-step explanation:
You would have to prime factorize the number.
36=4x9
4=2x2
9=3x3
36=2x2x3x3
Answer:
36 reduced into simplest form is 12.
Step-by-step explanation:
12 is the simplest form of 36 because it has the smallest numerator and denominator possible to represent that amount.
If a fair coin is tossed 9 times, what is the probability, to the nearest thousandth, of
getting exactly 6 tails?
Answer:
16.4% quick maths, ya dig?
Write 0.012 as a fraction in simplest form.
Answer:
3/25Step-by-step explanation:
Remove The decimal,
= > 0.012 = 12/100
= > 3/25...ans
Hope it Helps you!!If x = 2, calculate the value of: 2x2 - x
what are the four functions that are increasing on the interval
Answer:
Tbh i don’t really know
Step-by-step explanation:
Ask someone else
7.5t= 45 Solve this.
Answer:
t = 337.5
Step-by-step explanation:
(7.5) * 7.5t = 45 * (7.5)
t = 337.5
Just some simple algebra, please mark me brainliest!
please help me with these 2 questions for a brainlist !
+give explanation to answer
Answer: Option 3 is the answer hope this helps!
Step-by-step explanation: Option 3
A small bowl of candy holds 75% as much as a large bowl of candy.
If the small holds 36 candy bars how much does the large hold?
Answer:
_____
Step-by-step explanation:
Im pretty sure it would be 45 ____
i’m physically begging for someone to help i do not understand
Answer:
Step-by-step explanation:
Need helpppppp!!!!!!!!!!
Answer: 12, 15, 11, 28
Explanation:
14. FC is half of AC so the length of FC is 12.
15. BD is 30 and half of that is BC or 15. AB and BC have same length so it is also 15.
16. ED and BE have same length so it is also 11.
17. BD is twice of AB so if AB is 14, BD will be 28.
Would appreciate a brainly <3
Andre rode his bike at a constant speed. He rode 1 mile in 8 minutes. Which of these equations
represents the amount of time tin minutes) that it takes him to ride a distance d of miles?
Andre rode 1 mile in 8 minutes. In 2 minutes he will ride 16 minutes, we know this because he is riding at a constant speed. Now, lets turn this into an equation. Due to the fact that the speed is consent at 8 minutes a mile, with d being the distance in miles, we can say that y = 8d
Lets test this equation out:
y = 8d 1 minute
y = 8
y = 8d 2 minutes
y = 16
I hope this helps! :)