Answers
We are asked to calculate f(4) by means of the following function:
f(n) = f(n - 1)² - 5
As you can see, in order to calculate f(n) first we have to specify the value of f(n - 1), we are given the value of f(1), so we can calculate the value of f(2), then f(3) and finally f(4), like this:
f(2) = f(2-1)² - 5 = f(1)² - 5 = 2² - 5 = 4 - 5 = -1
Then, f(2) = -1, now we can calculate f(3) like this:
f(3) = f(3 - 1)² - 5 = f(2)² - 5 = (-1)² - 5 = -4
Then f(3) = -4, now we can calculate f(4) like this:
f(4) = f(4 - 1)² - 5 = f(3)² - 5 = (-4)² - 5 = 16 - 5 = 11
Then, f(4) equals 11
Related Questions
Number 9 please on this packet, I need it for a class presentation
Answers
9)
Let x represent the amount that she gets for 1/7 of a working day.
From the information given, she gets $35 for 1 working day. Thus, we can set up the equations as follows
35 = 1
x = 1/7
By crossmultiplying, we have
x = 35 x 1/7
x = 5
Ariel will earn $5 for working 1/7 of a day
simplify 3y -(2y - 3)/4
Answers
The expression is given
[tex]\frac{3y-(2y-3)}{4}[/tex]Simplify the expression
[tex]\frac{3y-2y+3}{4}=\frac{y+3}{4}[/tex]Hence the answer is
[tex]\frac{y+3}{4}[/tex]I need help with this math problem. It’s homework and I have been sitting here for 3 hours. Please please help me.
Answers
Given:
Coordinates (-3 , 2), (6 , 2), (6 , -4), (-3 , -4)
Required:
Area and Parameter
Explanation:
Formula to find the distance between two points
Distance between (-3 , 2), (6 , 2) and (6 , 2), (6 , -4)
[tex]\begin{gathered} d=\sqrt{(6-(-3))\placeholder{⬚}^2+(2-2)\placeholder{⬚}^2} \\ d=9 \end{gathered}[/tex]Final Answer:
I need help with number 28 I could be wrong but I think you need to use the rook to match the bishop number 25
Answers
Answer:
2 translation vectors.
[tex](A,3)\text{ }+\text{ u(4,0) }=\text{ (E,3)}[/tex][tex](E,3)\text{ + u(0,4) = (E, 7)}[/tex]Step by step explanation:
You have to move a rook from the green circle to the blue one.
Then you have to represent series of the translation vector
You should know that the tower only moves horizontally or vertically.
You first move it 4 blocks to the right
[tex](A,3)\text{ }+\text{ u(4,0) }=\text{ (E,3)}[/tex]Then you move 4 blocks up.
[tex](E,3)\text{ + u(0,4) = (E, 7)}[/tex]Volunteer drivers are needed to bring a students to the championship baseball game. Drivers either have cars, which can eat 4 students, or vans which can seat 6 students. The equation 4c +60 80 describes the relationship between the number of carse and number of vans v that can transport exactly so students 3 Explain how you know that this graph represents this equation number of vans 2 4 6 8 10 12 14 16 18 20 22 24 number of cars
Answers
One featue of the equation is that when c = 0
[tex]\begin{gathered} 4(0)+6v=80 \\ \therefore v=13.33 \end{gathered}[/tex]The other feature is that when v = 0
[tex]\begin{gathered} 4c+6(0)=80 \\ \therefore c=20 \end{gathered}[/tex]Therefore, our graph must contain the points (0, 13.33) and (20, 0), and looking at the graph given we see that it has exactly those points; hence, the graph represents the equation given
Solve the system of linear equations.7x + 2y = -88y = 4x
Answers
7x + 2y = -8 Equation 1.
8y = 4x Equation 2.
We solve for y in eq. 2; as follows:
y = 4x/8.
Now we replace y on eq. 1:
7x + 2(4x/8) = -8
7x + x = -8
8x = -8
x = -8/8
x = -1
Finally we replace x on eq 2:
8y = 4(-1)
8y = -4
y = -4/8
y = -1/2
One number is 9 more than another number. The sum of the numbers is 25. What is one of the numbers?A) 9B) 8C) 16D) 17
Answers
Answer
B) 8 or D) 17
Step-by-step explanation
Let's call x to one unknown number and y to the other number.
If one number is 9 more than another number, then:
[tex]y=x+9\text{ \lparen eq. 1\rparen}[/tex]Given that the sum of the numbers is 25, then:
[tex]x+y=25\text{ \lparen eq. 2\rparen}[/tex]Substituting equation 1 into equation 2 and solving for x:
[tex]\begin{gathered} x+x+9=25 \\ 2x+9=25 \\ 2x+9-9=25-9 \\ 2x=16 \\ \frac{2x}{2}=\frac{16}{2} \\ x=8 \end{gathered}[/tex]Substituting x = 8 into the first equation:
[tex]\begin{gathered} y=8+9 \\ y=17 \end{gathered}[/tex]Then, one of the numbers is 8 and the other one is 17
The cost to manufactute a hair clip is $.50. With a markip of 200 percent,what is the selling price of this hair clip?
Answers
The selling price of this hair clip will be $ 1.50.
Cost price of the clip is = $ 0.50
Markup price = 200 percent
Mark up price = 200 % of 0.5
Mark up price = 200 / 100 × 0.50
Mark up price = 2 × 0.50
Mark up price = $ 1
Selling price of the product will be:
SP = $ 0.50 + $ 1
SP = $ 1.50
Therefore, we get that, the selling price of this hair clip will be $ 1.50.
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Your question was incomplete. Please refer the content below:
The cost to manufacture a hair clip is $0.50. With a markup of 200 percent, what is the selling price of this hair clip?
Select all the lines that are perpendicular to 3x – y = 10. A. y = 3x + 5 B. y = –13x + 17 C. x + 3y = 27 D. y – 2 = 13(3x + 36)
Answers
The lines that are perpendicular to 3x – y = 10. is option C (x+3y= 27).
Line equation:
3x - y = 10
y = 3x - 10
here slope m = 3.
perpendicular line slope = -1/m = -1/3
so the perpendicular line must have slope m = -1/3
A.
y = 3x + 5
here slope m = 3
This line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.
B.
y = -13x + 17
here slope m = -13
This line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.
C.
x + 3y = 27
3y = -x + 27
y = -1/3(x) + 27/3
y = -1/3(x) + 9
here slope m = -1/3
This line is perpendicular to the 3x - y = 10 because here slope is equal to -1/3.
D.
y - 2 = 13(3x+36)
y = 39x + 468 - 2
y = 39x + 466.
here slope m = 39.
So this line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.
Therefore the lines that are perpendicular to 3x – y = 10. is option C (x+3y= 27).
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James invests 20k in an account that offers a compound interest rate of 8.3% per year for 6 years. I need to know which one is the correct answer 1. a(6)=20,000×(1+0.83)⁶‐¹2. a(6)=20,000×(1+0.083)⁶+¹3. a(6)=20,000×(1+0.083)⁶‐¹4. a(6)=20,000×(1+0.083)⁶
Answers
Given,
The principal amount is 20k.
The rate of interest is 8.3%.
The time period is 6 Years.
Required
The amount of investment after 6 years.
The amount is calculated as,
[tex]\begin{gathered} Amount=principal\times(1+\frac{rate}{100})^{time} \\ =20000\times(1+\frac{8.3}{1000})^6 \\ =20000\times(1+0.083)^6 \\ =20000\times(1+0.083)^6 \end{gathered}[/tex]Hence, the amount after 6 years is 2000 x (1 + 0.083)^6.
Find f[2) if f(x) = (x+ 1)^2 O9O6 O5
Answers
You have the following function:
f(x) = (x + 1)²
In order to determine the value of f(2) you replace the value x = 2 in the given function and make the operations, just as follow:
f(2) = (2 + 1)² simplify inside parenthesis
f(2) = (3)² 3² is the same as 3x3=9
f(2) = 9
Hence, the value of the function when x = 2 is f(2) = 9
A billboard has an area of 32 square meters. Express the area in square feet.
Answers
We will use the equivalency:
[tex]\begin{gathered} 1m=3.281ft \\ \frac{3.281ft}{1m}=1 \end{gathered}[/tex]Then, if we have an area of 32 m^2, we can multiply this value by the equivalency factor we wrote (as it is equal to 1) as:
[tex]\begin{gathered} A=32m^2\cdot(\frac{3.281ft}{1m})^2 \\ A=32m^2\cdot\frac{10.765ft^2}{1m^2} \\ A=344.48ft^2 \end{gathered}[/tex]Answer: the area is 344.48 sq ft.
match the following each letter may be used more than once.a. 12/15b. 15/12c. 9/15d. 9/12e. 12/9f. 15/9
Answers
We have a right triangle and we have to write some of the trigonometric ratios.
A trigonometric ratio relates a trigonometric function of an angle of the tiangle with a quotient of two of the sides of the triangle.
The basic trigonometric ratios are:
[tex]\begin{gathered} \sin (\alpha)=\frac{\text{Opposite}}{\text{Hypotenuse}} \\ \cos (\alpha)=\frac{\text{Adyacent}}{\text{Hypotenuse}} \end{gathered}[/tex]We can also write the trigonometric ratio for the tangent:
[tex]\tan (\alpha)=\frac{\sin (\alpha)}{\cos (\alpha)}=\frac{\text{Opposite}}{\text{Adyacent}}[/tex]Now, we can write sin(x):
[tex]\sin (X)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{YZ}{XZ}=\frac{12}{15}[/tex]The opposite side to X is YZ and the hypotenuse is XZ, so sin(X) = YZ/XZ = 12/15.
In the same way, we can calculate cos(x):
[tex]\cos (X)=\frac{\text{Adyacent}}{\text{Hypotenuse}}=\frac{XY}{XZ}=\frac{9}{15}[/tex]The tan(x) can be calculated as:
[tex]\tan (X)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{YZ}{XY}=\frac{12}{9}[/tex]For Z, the opposite and adyacent angles are different than for X, so we can write:
[tex]\tan (Z)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{XY}{YZ}=\frac{9}{12}[/tex]Answer:
sin(X) = 12/15
cos(X) = 9/15
tan(X) = 12/9
tan(Z) = 9/12
a recipe requires 7/8 sticks of butter for each 1 1/4 cups of flour. how many cups of flour to sticks of butter
Answers
In order to calculate the rate of cups of flour to stick of butter, just calculate the following quotient:
(1 1/4)/(7/8) = (5/4)/(7/8) = 5·8/7·4 = 40/28 = 20/14 = 10/7
Hence, the required rate is 10/7 or 10:7
that is, 10 cups of flour for 7 sticks of buttter
There are 25 popular trees currently in the park. Park workers will plant morepopular trees today. When the workers are finished there will be 80popular trees in the park. How many popular trees did the workers plant today?
Answers
Current trees = 25
trees when workers are finished = 80
Subtract the number of current trees (25) to the number of trees that are when the workers are finished:
80-25 = 55
The workers planted 55 trees today
what should be the value of k so that the trinomial is a perfect square trinomial ?
Answers
ANSWER:
5
STEP-BY-STEP EXPLANATION:
The perfect square trinomial is given as follows:
[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]Therefore, in this case would be:
[tex]\begin{gathered} x^2+2kx+25 \\ a=x \\ b=5 \\ (x+5)^2=x^2+2\cdot5x+25 \\ k=5 \end{gathered}[/tex]Therefore the value of k is 5
simplifying like terms and distributive property7b + 2(46 - 3)
Answers
We will solve as follows:
[tex]7b+2(46-3)=7b+92-6[/tex][tex]=7b+86[/tex]So, the solution is 7b + 86.
What is the new equation 1 when youmultiply by -1?
Answers
the equation will be
-x - y = 7
The function g is defined as follows.=gx+5x27If the graph of g is translated vertically upward by 3 units, it becomes the graph of a function f.Find the expression for fx.
Answers
f(x) = 5x²+10
Explanations:
Given the function g(x) expressed as:
[tex]g(x)=5x^2+7[/tex]If the function g(x) is translated vertically upward by 3 units to produce f(x), the resulting translation used will be given as:
[tex]f(x)=g(x)+3[/tex]Substitute the function g(x) into the translation rule to have:
[tex]\begin{gathered} f(x)=5x^2+7+3 \\ f(x)=5x^2+10 \end{gathered}[/tex]Therefore the expression for f(x) is 5x²+10
In an arithmetic sequence a18 = -10 and a40= 100 , write the explicit rule, the recursive rule, and find s30
Answers
Answer:
Explicit rule [tex]a_n=5n-100[/tex]Recursive rule [tex]a_1=-95,a_n=a_{n-1}+5[/tex]Sum of the first 30 terms [tex]-675[/tex]
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Let the first term be a and common difference be d.
Use equations for nth term and sum of the first n terms[tex]a_n=a+(n-1)d\\[/tex][tex]S_n=n(a+a_n)/2[/tex]Use the first equation to find the values of a and d[tex]a_{18}=a+17d=-10[/tex][tex]a_{40}=a+39d=100[/tex]Substract the first equation from the second and solve for d39d - 17d = 100 + 1022d = 110d = 110/22d = 5Find aa + 17*5= - 10a + 85 = - 10a = - 95Explicit rule[tex]a_n=-95+5(n-1)=-95+5n-5=5n-100[/tex]Recursive rule[tex]a_1=-95,a_n=a_{n-1}+5[/tex]Sum of the first 30 terms[tex]S_{30}=(-95-95+29*5)*30/2=(-45)*15=-675[/tex]The explicit rule is a(n) = - 95 + 5 · (n - 1), whose recursive rule is [tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 5. The 30th element of the arithmetic sequence is 50.
How to derive an arithmetic sequence
Arithmetic sequences are sets of elements generated by a formula of the form:
a(n) = a + r · (n - 1), for n ≥ 1
Where:
a - First element of the sequence.r - Common raten - Index of the n-th element of the sequence.Please notice that the common rate is the difference between any two consecutive elements of the sequence. The recursive form is described by the following form:
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + r
Now we should determine the elements of the explicit rule by solving the following system of linear equations:
n = 18
- 10 = a + r · (18 - 1)
a + 17 · r = - 10
n = 40
100 = a + r · (40 - 1)
a + 39 · r = 100
Then, we solve the system of linear equations by numerical methods:
(a, r) = (- 95, 5)
And the 30th element of the arithmetic series:
a(n) = - 95 + 5 · (n - 1)
a(30) = - 95 + 5 · (30 - 1)
a(30) = 50
And the recursive form is [tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 5.
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Quinn needs to collect at least 90 toys for a toy drive to earn community service credit. He has already collected 16 toys.
Answers
Let's define the next variable:
t: number of toys that Quinn still needs to collect
The number of toys that he already collected plus the number of toys that Quinn still needs to collect is: 16 + t
Quinn needs to collect at least 90 toys, then 16 + t must be greater than or equal to 90, that is,
16 + t ≥ 90
or
90 ≤ 16 + t
Subtracting 16 at both sides, we get:
90 - 16 ≤ 16 + t - 16
74 ≤ t
The following data points represent the number of flying saucers that are owned by each alien on planet nowhere. (a)Arrange the data from the least to greatest 1,4,2,21,8,27(b)Find the median number of flying saucers
Answers
The data that represent the number of flying saucers that are owned by each alien on planet nowhere is given below:
[tex]1,4,2,21,8,27[/tex](a)We sort the data from the least to greatest below.
[tex]1,2,4,8,21,27[/tex](b)The median is the middle number.
In this case, we have two numbers in the middle: 4 and 8
Therefore we find their average:
[tex]\begin{gathered} \text{Median}=\frac{4+8}{2} \\ =\frac{12}{2} \\ =6 \end{gathered}[/tex]Answer:
6 is the correct answer.
Step-by-step explanation:
Hi, I'm having a really hard time doing Multi Step Equations in Math, please help me.
Answers
You have the following equation:
4x - 3 = 2x + 5
In order to solve the previous equation, proceed as follow:
4x - 3 = 2x + 5 subtract 2x both sides
4x - 2x - 3 = 5 add 3 both sides
4x - 2x = 5 + 3 simplify like terms
2x = 8 divide by 2 both sides
x = 8/2
x = 4
Hence, the solution to the given equation is x = 4
Rebecca had $100 in her savings accountin the first week. She adds $45 each weekfor 5 weeks. The savings account balancecan be shown by a sequence.
Answers
Rebecca had $100
and each week, she add $45
Let the number of weeks is x
So, after x weeks, she will have y
y = 100 + 45x
See the following figure:
After 5 weeks, y = 100 + 45 * 5 = 325
============================================
After 1 week , y = 145
after 2 weeks , y = 190
after 3 weeks , y = 235
and so on
So, The savings account balance can be shown by a sequence.
The sequence will be: 145 , 190 , 235 , 280 , .......
The kind of this sequence will be arthimatic sequence , because there is a common defference between the terms of the sequence which = 45
Hello, I need some assistance with this homework question, please? This is for my precalculus homework. I submitted the answer x<-14 or x>-14 but it was incorrect Q4
Answers
To find the domain of the rational function we need to equate the denominator to zero and solve the equation, as follows:
[tex]\begin{gathered} x+14=0 \\ x+14-14=-14 \\ x=-14 \end{gathered}[/tex]Then, all the x-values are valid except x = -14, which makes the denominator equal to zero. Therefore, the domain of R(x) is:
[tex]\lbrace x|x\ne-14\rbrace[/tex]5m+3m+ 3 n- m + 6n +8
Answers
The given expression is
5m+3m + 3n - m + 6n + 8
We would simplify the expression by collecting like terms.
The terms containing m are like terms
The terms containing n are like terms
8 is a constant
Thus, we have
5m + 3m - m + 3n + 6n + 8
7m + 9n + 8
The final expression is
7m + 9n + 8
1. Combine like terms
5m + 3m - m = 7m
8 + 3 = 10
6n + n = 7n
Then you put them in an addition sentence
2. 7m + 7n + 10
What volume of ice cream is contained in a 10 cm-high ice cream cone with a base radius of 4 cm?
Answers
We would find the volume of the ice cream contained in the cone by applying the formula for determining the voume of a cone which is expressed as
Volume = 1/3 x pi x radius^2 x height
From the information given,
height = 10
radius = 4
pi is a constant whose value is 3.142
Thus,
Volume = 1/3 x 3.142 x 4^2 x 10
Volume = 167.57
rounding to the nearest whole number,
Volume = 168 cubic cm
If two planes leave an airport at the same time with one flying west at 520 miles per hour and the other flying east at 540 miles per hour, how long will it take them to be 3180 miles apart?
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
If two planes leave an airport at the same time with one flying west at 520 miles per hour and the other flying east at 540 miles per hour,
how long will it take them to be 3180 miles apart?
Step 2:
Let the distance of one of the planes flying west at 520 miles per hour be:
[tex]520\text{ x}[/tex]And let the distance of the other plane flying east at 540 miles per hour be:
[tex]540\text{ x}[/tex]where x , represents the time of flight in hours, such that:
[tex]\begin{gathered} 520\text{ x + 540 x = 3180} \\ 1060\text{ x = 3180} \\ \text{Divide both sides by 1060, we have that:} \\ x\text{ = }\frac{3180}{1060} \\ x\text{ = 3} \end{gathered}[/tex]CONCLUSION:
The time it will take them to be 3180 miles apart will be in 3 hours' time.
It costs mrs. barazal $245 for her and 6 people to take a day-long guided tour of the Everglades how much does the guided tour cost per person?
Answers
For Barazal and 6 persons the cost is $245
So, the number of persons = 7
so, the cost per person = 245/7 = $35
So
the guided tour cost per person = $35
the rest of the question say what is the length of the tangent line labeled X
Answers
To solve this problem, consider the following picture
By the tangent secant segment theorem we have the following equation
[tex]a^2=b\cdot(b+c)[/tex]Note that in our case, we have a=x, b=3 and c=9. So if we replace this values in the equation, we have
[tex]x^2=3\cdot(3+9)=3\cdot12=36[/tex]so, applying the square root on both sides, we get
[tex]x=\sqrt[]{36}=\pm6[/tex]Since x is a distance, it should be strictly positive, so we have that
[tex]x=6[/tex]