Answer:
Explicit formula
f(n) = 2*2⁽ⁿ⁻¹⁾
Recursive formula
f(n) = aₙ₋₁ * r
Step-by-step explanation:
Since, Nathan has two parents, four grandparents, and so on, it would form a Geometric Progression (GP) series for the number of Nathan's ancestors as below:-
2, 4, 8, 16, 32, ....
First term (a₁) = 2
Common Ratio (r) = [tex]\frac{a_{2} }{a_1}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
So,
Number of ancestors of Nathan if we go back n generations = a₁r⁽ⁿ⁻¹⁾
Plugging in the values of a₁ and r, we get
f(n) = 2*2⁽ⁿ⁻¹⁾ [Explicit formula]
Now,
A geometric progression (GP) series is of the form,
a, ar, ar², ar³, ar⁴, ar⁵........
in which the first term a₁=a and other the terms are obtained by multiplying with r.
Observe that each term is r times the previous term. So, to get the [tex]n_{th}[/tex] term, we multiply [tex](n-1)_{th}[/tex] term by r.
i.e. aₙ = aₙ₋₁ * r
=> f(n) = aₙ₋₁ * r [Recursive formula]
Graph the functions and approximate an x-value in which the exponential function surpasses the polynomial function. In your final answer, include a copy of the graph. y = 2x2 + 7 y = 5(x-4)
Answer:
x-value is 6.87
Step-by-step explanation:
we are given
Polynomial as
[tex]y=2x^2+7[/tex]
Exponential as
[tex]y=5^{x-4}[/tex]
Firstly, we can draw graph
We can see that intersection point is (6.87,101.392)
so, x=6.87
At (6.97, 101.392) the exponential function surpasses the polynomial function.
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
Given, A system of equation y = 2x² + 7 and y = 5^(x - 4).
Now by graphing these two equations we observe that at 6.87 the exponential function surpasses the polynomial function.
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What is the answer to b in #10
Answer:
X=5 (Or (5,0))
Step-by-step explanation:
The Y intercept is when X=0
The X Intercept is when Y=0
Our equation is y=-4200x+21000
So let's rewrite it... First subtract 21,000 (Also, remember Y is 0)
0-21000=-4200x
-21000=-4200x
Now to get X alone, divide -21000 by -4200
This will give us 5=x, which is the same as x=5. There is your answer!
The slope means that the value decreases by -4,200 per year.
What can we say about the slope?Here we have the linear equation:
y = -4,200x + 21,000
We know that this equation relates the value of something, y, after x years.
So a slope will tell us how many units does the value increase or decraeses each year.
Here the slope is -4,200, which means that the price decreases by -4,200 dollars each year.
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What is the solution to the system of equations? X+3y=18 x+2y=14
Answer:
Solution to system is
x = 6 and y= 4
S.set={6,4}
Step-by-step explanation:
The given equations are
x + 3y = 18 ................(i)
x + 2y=14 .................(ii)
Subtracting both equation
(x+3y)-(x+2y)=18-14
x+3y-x-2y = 4
y = 4
put the value of y in equation (i)
the equation becomes
x + 3(4) = 18
x + 12 = 18
subtracting 12 from both sides
x + 12 -12 = 18-12
x =6
Solution to system is
x = 6 and y= 4
S.set={6,4}
create a real life example using either temperature or money to compare -3 and -5
Example with temperature:
The temperature -3 degrees is warmer than -5 degrees. This applies to celsius or fahrenheit. You might also write "negative 3 degrees" as "3 degrees below zero"; the same applies for -5. The absolute difference between the two temperatures is 2 degrees.
=================================================
Example with money:
If your bank balance is -3 dollars and your friend's bank balance is -5 dollars, then your friend owes more money to the bank (s/he owes $2 more than you do).
Negative balances mean you are in debt. Another way to look at this is to consider you want to buy an item worth $10 but you only have $7. If the store owner lends you the difference, which you pay back later, then 7-10 = -3 is the amount of money on your balance sheet indicating you are in debt $3. The order of subtraction is important. Saying 10-7 = 3 shows a positive bank balance and you wouldn't be in debt (and still have $3 in your pocket).
=================================================
In either example, the value -3 is to the right of -5 on the number line so we would write the inequality -3 > -5 to say that -3 is larger than -5. Have a look at the image attached below.
You open a lemonade stand in your neighborhood and start off charging $1 per glass of lemonade. After two weeks, you decide that business is doing so well and the demand for lemonade is high so you raise your prices to $1.75. What was your percent increase in price?
Answer:
75% increase in price
Explanation:
75% of $1 is 75 cents
When using pi, do you use 3.14 or 3.141592653?
i always use 3.1415 but just to be safe use the pi symbol :)
pls help only b,d, and f
what polynomial identity will prove that 117=125-8
Answer:
Difference of cubes polynomial identity prove that 117 =125-8
Step-by-step explanation:
Difference of cubes:- A polynomial in the form of [tex]a^3 -b^3[/tex] is called the difference of cubes.
The formula for difference of cubes is;
[tex]a^3 -b^3 = (a-b)(a^2+b^2+ab)[/tex]
To prove: 117 = 125 - 8
Take RHS
[tex]125-8 = 5^3 -2^3[/tex]
Apply difference of cubes;
[tex]5^3-2^3 = (5-2)(5^2+2^2+5\cdot 2)[/tex]
=[tex]3(25+4+10) = 3(39) = 117[/tex] = LHS hence proved!
Therefore, difference of cubes polynomial identity will prove that 117 = 125-8
5 ( 9 + d ) when d = 3
Answer:
60
Step-by-step explanation:
5 ( 9 + d )
Let d=3 and substitute it in
5(9+3)
According to PEMDAS, we do what is in the parentheses first
5(12)
Now we multiply.
60
Answer:
60
Step-by-step explanation:
5 ( 9 + d )
Let d=3 and substitute it in
5(9+3)
According to PEMDAS, we do what is in the parentheses first
5(12)
Now we multiply.
60
Which decimal is equivalent to 76/9?
Answer:
8.4444...
Step-by-step explanation:
So it's easier if we can write it first in mixed fractions. 9 x 8 is 72 and th is the highest we can go. So it becomes [tex]8\frac{4}{9}[/tex]. Then, if you just long divide 4 by 9 you get .44444.... So it is 8.4 repeating.
8.444 decimal is equivalent to fraction 76/9.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given a fraction of 76/9
Simplifying the above fraction,
=> 76/9
=> (72 + 4)/9
=> 8 + 4/9
=> 8 + 0.444
=> 8.444
Therefore, 8.444 decimal is equivalent to fraction 76/9.
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Need an answer thanks
How can you tell by looking at the coordinates of the two triangles that a’b’c’ is a 180 degrees rotation of abc
Answer:
D
Step-by-step explanation:
Under a rotation about the origin of 180°
a point (x, y ) → (- x, - y) → D
Note this only happens if the rotation is about the origin
Each bottle of apple juice costs $2.40 and each bottle of orange juice costs $2.20. If James has $50.80 and wants to buy 10 bottles of orange juice, how many bottles of apple juice can he buy using his remaining amount?
Answer:
12
Step-by-step explanation:
Orange juice: $2.20 per bottle.
10 bottles of orange juice cost 10 * $2.20 = $22.00.
We subtract the cost of the 10 bottles of orange juice from the amount of money he has to find out the amount he will have left for bottles of apple juice.
$50.80 - $22.00 = $28.80
After buying the 10 bottles of orange juice, he has $28.80 left.
We divide the money he has left for apple juice bottles by the price of one apple juice bottle to find out the number of apple juice bottles he can buy.
$28.80/$2.40 = 12
He can buy 12 bottles of apple juice.
PLEASE BE FAST !!!!!!
John bought 6 dumplings for $3.00. Let x represent the number of dumplings purchased, and let y represent the total cost. Graph the line that represents the proportional relationship.
15 POINTS
Answer:
I think this is right but I may be wrong
Step-by-step explanation:
Answer:
Easy! Y=0.5x
Step-by-step explanation:
First, we have to find unit rate.
6/6 = 1
3.00 / 6 = 0.5
Y=0.5x
Which triangle has hypotenuse of BD? Triangle BDA, TRIANGLE BDF, Triangle BDG, Or BDH
The hypotenuse of the ΔBAD is the side BD.
What is Hypotenuse of a Triangle?The longest side in a right angled triangle is called hypotenuse, it is the side which is opposite to 90° angle.
Steps:Step 1 : In the given cube, we should look at the face ABCD
Step 2 : Let us draw an imaginary line between the point B and D
Step 3 : Now the face ABCD is split into two triangles ΔBAD and ΔBCD respectively
Step 4 : The side opposite to the 90° angle of ΔBAD is BD
Hence the side BD is hypotenuse of ΔBAD.
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Beginning at 8:30 A.M., tours of the National Capitol leave every 15 minutes. Tours for the White House leave every 20 minutes. How often do the tours leave at the same time?
a quadrilateral has interior angles 85, 105 and 120 what is the measure of the 4th angle?
__________________
Answer: [tex]50^{\circ}[/tex]
Step-by-step explanation:
By the definition of quadrilateral,
A quadrilateral has four interior angles and the sum of all interior angle of a quadrilateral is always equal to [tex]360^{\circ}[/tex]
Here the measurements of three interior angles are [tex]85^{\circ}[/tex], [tex]105^{\circ}[/tex] and [tex]120^{\circ}[/tex]
Let the measurement of fourth angle is x degree.
Thus, [tex]85^{\circ}+105^{\circ}+120^{\circ}+x=360^{\circ}[/tex]
[tex]310^{\circ}+x=360^{\circ}[/tex]
[tex]x = 360^{\circ}-310^{\circ}=50^{\circ}[/tex]
Thus, the measure of fourth angle is [tex]50^{\circ}[/tex]
The measure of the 4th angle is 50 degrees.
Explanation:To find the measure of the fourth angle of a quadrilateral, we need to know that the sum of all the interior angles of a quadrilateral is always 360 degrees. Therefore, to find the measure of the fourth angle, we can subtract the sum of the other three angles from 360. In this case, the given angles are 85, 105, and 120 degrees, so the sum of these three angles is 85 + 105 + 120 = 310 degrees. To find the measure of the fourth angle, we subtract 310 from 360: 360 - 310 = 50 degrees.
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The length of s and hypotenuse
Answer:
A
Step-by-step explanation:
this is a standard right triangle 30-60-90
with legs 1 and [tex]\sqrt{3}[/tex] and hypotenuse 2, hence
s = [tex]\sqrt{3}[/tex] and h = 2
Answer:
A. [tex]\sqrt{3}[/tex] ; 2
Step-by-step explanation:
Since We have all the angles of the triangle and one side we can use SIN, COS, and TAN to find the missing side lengths. SIN which is [tex]sin(x) = \frac{opposite}{hypotenuse}[/tex] can be used to find the hypotenuse
[tex]sin(30) = \frac{1}{h}[/tex]
[tex]\frac{1}{sin(30)} = \frac{h}{1}[/tex] ..... inverse both sides
[tex]\frac{1}{sin(30)} = h[/tex]
[tex]2 = h[/tex]
Now we can use the Pythagorean theorem to find the missing length. The Pythagorean Theorem is [tex]a^{2} +s^{2} = h^{2}[/tex]. So we just plug in the values we already have and solve for s.
[tex]1^{2} +x^{2} = 2^{2}[/tex]
[tex]1+s^{2} = 4[/tex]
[tex]s^{2} = 3[/tex]
[tex]s = \sqrt{3}[/tex]
In Conclusion, s = [tex]\sqrt{3}[/tex] and h = 2
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Casey buys a bracelet. She pays for the bracelet and pays \$0.72$0.72 in sales tax. The sales tax rate is 6\%6%. What is the original price of the bracelet, before tax?
Answer:
$12.00
Step-by-step explanation:
If they paid $0.72 in tax and tax is 6% or .06 then you could create an equation like this: x * .06 = .72 with x representing the original cost of the bracelet. Now you can just solve for x like so:
x * .06 = .72
÷.06 ÷.06
x = 12
Answer:
$12.00
Step-by-step explanation:
the total entry price of the top of the Eiffel Tower during the low season of 95 Euros for 4 students and five teachers the total entry price is 173 euros and for 6 students and 10 teachers. find total entry price of the Eiffel Tower for a group of three students and 4 teachers
Answer:
74.30
Step-by-step explanation:
Let s = entry price for a student
Let t = entry price for a teacher
4s +5t = 95
6s+10t = 173
I will use elimination to solve this problem.
Multiply the first equation by -2
-2(4s +5t) = -2*95
Distribute
-8s - 10t = -190
Add this equation to the second equation to eliminate t
-8s - 10t = -190
6s+10t = 173
----------------------
-2s = -17
Divide by -2
-2s/-2 = -17/-2
s = 8.50
Now we need to find t
4s +5t = 95
Substitute s=8.50
4(8.50) +5(t) = 95
34 +5t = 95
Subtract 34 from each side
34-34 +5t = 95-34
5t = 61
Divide by 5
5t/5 = 61/5
t = 12.20
We want to find the cost for 3 students and 4 teachers
3s+4t
3(8.50) + 4(12.20)
25.50 + 48.80
74.30
Jackson used the process of completing the square to solve the equation 2x2−12x=−6.
Answer:
[tex]x=3-\sqrt{6},x=3+\sqrt{6}[/tex]
Step-by-step explanation:
we are given equation as
[tex]2x^2-12x=-6[/tex]
Since, we have to solve it by using complete square
so, firstly we will complete square
and then we can solve for x
step-1:
Factor 2 from both sides
[tex]2(x^2-6x)=-3\times 2[/tex]
step-2:
Simplify it
[tex]x^2-6x=-3[/tex]
step-3:
Add both sides 3^2
[tex]x^2-6x+3^2=-3+3^2[/tex]
now, we can complete square
[tex](x-3)^2=6[/tex]
step-4:
Take sqrt both sides
[tex](x-3)=-\sqrt{6},(x-3)=\sqrt{6}[/tex]
step-5:
Add both sides by 3
we get
[tex]x=3-\sqrt{6},x=3+\sqrt{6}[/tex]
What is the premium for $75000 for a 30 year old male for a 10 year policy ?
Answer: $286.50
If the AP (Annual Premium) $1000 for 30 yr male with 10 yr policy; $3.82...
75000/1000 = 75
75 x $3.83 = $286.50 AP
The premium for a 10-year, $75000 life insurance policy for a healthy 30-year-old male typically ranges from $10 to $20 per month. Actual pricing can vary based on health status, lifestyle, occupation and the specific insurance company's underwriting process. To get the most accurate premium, it's beneficial to shop around and compare quotes.
Explanation:The premium for a life insurance policy varies based on several factors including the age of the individual, the amount of coverage, policy term, and the individual's health status. The question doesn't provide enough information for an exact calculation as we do not know the general health status of the 30-year-old male, his occupation, lifestyle factors or the premium rates of the specific insurance company. However, we can give a general idea.
Assuming this individual is in good health, for a 30-year-old male, a $75000, 10-year term life insurance policy would typically cost between $10 to $20 per month. This is an average and the actual cost can vary greatly based on the factors mentioned.
Also, each insurance company has different pricing and underwriting processes, so it's important to shop around and compare quotes from different companies to ensure you're getting the best rate.
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Which is the largest decimal? 0.0688 0.667 0.68 0.6
The largest decimal is :
0.68
Because: In the tenths place, 6 is the biggest number. Now we go to the hundredths to see which one is the biggest. 8 Is the largest one out of them. But what about the 0's? The 0's at the end don't really matter. They are there to confuze you or to add more extra 0's. The 0 at the front of the decimal is also smaller then the 6. For example: 0.0175 < 0.68
Hope helps!-Aparri
The largest decimal among 0.0688, 0.667, 0.68, and 0.6 is 0.68. This can be determined by comparing each digit from left to right in the numbers. Hence, 0.68 is the highest.
To determine which is the largest decimal among 0.0688, 0.667, 0.68, and 0.6, we compare each decimal value:
0.06880.6670.680.6We start from the leftmost digit and compare:
First, look at the integer part left of the decimal point. All numbers are less than 1.Next, compare the tenths place: 0.0688 (0), 0.667 (6), 0.68 (6), 0.6 (6). So, 0.0688 is the smallest.For 0.667, 0.68, and 0.6: compare the hundredths place. Here, 0.6 (60), 0.667 (66), 0.68 (68). The largest is 0.68.Therefore, the largest decimal among the given numbers is 0.68.
Yesterday, Leila had d baseball cards. Today, she gave 10 away. Using , write an expression for the number of cards Leila has left.
Answer:
d - 10
Step-by-step explanation:
Because the amount of Leila’s baseball cards was d, subtract 10 from it to get Leila’s amount of baseball cards now.
d - 10
Answer:
d-10
Step-by-step explanation:
I don't know the word after "Using".
"Gave away" means having less, which means that you should subtract.
d-10
Solve the following system of equations . Plot the solution to the system on the provided graph
Answer:
(6, -3)
Step-by-step explanation:
I will solve this system using elimination.
[tex][tex]\left \{ {{-x+2y=-12} \atop {2x+3y=3}} \right.[/tex][/tex]
I will multiply [tex]-x+2y=-12[/tex] by 2 so that -x becomes -2x.
2(-x + 2y = -12)
Distribute.
-2x + 4y = -24
Now subtract this from the other equation.
2x + 3y = 3
-2x + 4y = -24
7y = -21
Divide both sides by 7.
y = -3
Now that we have the value of y, plug it into the original equation.
-x + 2(-3) = -12
Simplify.
-x - 6 = -12
Add 6 to both sides.
-x = -6
Divide both sides by -1.
x = 6
(6, -3)
Linda has $9.00 in her wallet. she buys a card for $1.17. she wants to buy some pens that cost $2.65. what is the maximum number of pens can she buy
Answer:
2 pens
Step-by-step explanation:
Let x represent the number of pens Linda buys. Since they cost $2.65 each, this gives us the expression 2.65x.
Adding the cost of the card to this gives us the expression 2.65x+1.17.
She has a total of $9.00; this gives us the equation
2.65x+1.17 = 9.00
Subtract 1.17 from each side:
2.65x+1.17-1.17 = 9.00-1.17
2.65x = 7.83
Divide both sides by 2.65:
2.65x/2.65 = 7.83/2.65
x = 2.95
We cannot buy a portion of a pen, so the most she can buy is 2 pens.
Answer:
The answer is 2 pens.
Step-by-step explanation:
Total amount Linda has in her wallet = $9
Amount spent on buying a card = $1.17
So, amount left with Linda = [tex]9-1.17=7.83[/tex]
Now, she wants to buy pens that cost $2.65, so the maximum number of pens she can buy are = [tex]\frac{7.83}{2.65}= 2.9[/tex]
But, pens cannot be in decimal, so the maximum pens she can buy are 2.
what is the recursive rule for this geometric sequence? 27, 9, 3, 1...
Answer:
Divided by 3.
They are all divided by 3.
Answer:
b(1)= 27
b(n)=b(n-1)* (-1/3)
Step-by-step explanation:
20 Points!!! Need Help ASAP!!! Will mark Brainliest!!!
Given: AB || CD, m
MA. 15
B. 33
C. 87
D. 93
Answer:
The answer is A
Step-by-step explanation:
5x + 18 = 7x - 12
Subtract 7x from both sides
5x + 18 - 7x = 7x - 12 - 7x
-2x + 18 = -12
Subtract 18 from both sides
-2x + 18 - 18 = -12 - 18
-2x = -30
Divide both sides by -2
-2x/-2 = -30/-2
x = 15
A cross-shaped pattern is made by arranging four identical rectangles around the side of a square, as shown in the diagram.
The area of the square is 36cm^2.
The area of each rectangle is one and a third times the area of the square.
Find the perimeter of the cross-shaped pattern.
Show your working and state the units of your answer.
Awarding 15 points. Please someone answer correctly quick, much appreciated x
Answer:
88 cm
Step-by-step explanation:
The side of the square = 6 cm, so the shorter side of each rectangle = 6 cms.
The area of each rectangle = 36 * 1 1/3
= 36 * 4/3 = 48 cm^2
So the longer side of each rectangle = 48 / 6 = 8 cms
Therefore, the perimeter of the whole figure
= 4( shorter sides ) + 8(longer sides)
= 4*6 + 8*8
= 24 + 64
= 88 cm (answer)
Bowl A contains 6 apples and 3 mangoes this can be written as, Bowl B contain 8 apples and 2 mangoes this can be written as. What is the difference between the bowls.
Answer:
Bowl B contains 2 apples more than Bowl A and Bowl A contains 1 mango more than Bowl B.
Step-by-step explanation:
Number of apples in Bowl A = 6
Number of mangoes in Bowl B = 8
Difference in apples = 8 - 6 = 2
So, Bowl B contains 2 apples more than Bowl A.
Number of mangoes in Bowl A = 3
Number of mangoes in Bowl B =2
Difference in mangoes = 3 - 2 = 1
So, Bowl A contains 1 mango more than Bowl B.
Bowl B has 2 more apples and 1 fewer mango compared to Bowl A. Thus, the primary differences are in the quantities of apples and mangoes in each bowl.
Step by Step Solution:
To understand the differences between Bowl A and Bowl B, let's break down the contents of each bowl:
Bowl A contains 6 apples and 3 mangoes.
Bowl B contains 8 apples and 2 mangoes.
Now, let's find the differences in the number of apples and mangoes between the two bowls:
Difference in Apples: Bowl B has 8 apples, and Bowl A has 6 apples. Therefore, the difference is 8 - 6 = 2 apples. Bowl B has 2 more apples than Bowl A.
Difference in Mangoes: Bowl A has 3 mangoes, and Bowl B has 2 mangoes. Therefore, the difference is 3 - 2 = 1 mango. Bowl A has 1 more mango than Bowl B.
In summary, Bowl B has 2 more apples and 1 fewer mango compared to Bowl A.