Suppose we have the recursive formula of sequence, [tex]\displaystyle{f(n+1)=0.5f(n)}[/tex]. From this formula, we know that:
[tex]\displaystyle{f(2)=0.5f(1)}\\\\\displaystyle{f(3)=0.5f(2)}\\\\\displaystyle{f(4)=0.5f(3)}\\\\\displaystyle{f(5)=0.5f(4)}[/tex]
Since the first term of sequence is 120. Therefore, [tex]\displaystyle{f(1)=120}[/tex]. Since [tex]\displaystyle{f(4)=0.5f(3)}[/tex] then substitute in [tex]\displaystyle f(5)[/tex]:
[tex]\displaystyle{f(5)=0.5\cdot 0.5f(3)}[/tex]
Then substitute f(3) down to f(1):
[tex]\displaystyle{f(5)=0.5\cdot 0.5 \cdot 0.5 \cdot 0.5 \cdot 120}\\\\\displaystyle{f(5)=(0.5)^4\cdot 120}\\\\\displaystyle{f(5)=7.5}[/tex]
Therefore, f(5) = 7.5
solve problem below if you are smart.
18 points.
Answer:
See below
Step-by-step explanation:
48 + 3y = 90 degrees so y = 14 degrees
3x + 2x + 12 = 90 so x = 78/5 = 15.6 degrees
For j(x) = 4x − 2, find j of the quantity x plus h end quantity minus j of x all over h period
If j(x) = 4^(x - 2), the solving the given expression [j(x + h) - j(x)]/h gives;
[j(x + h) - j(x)]/h = (4^(x - 2))(4^(h) - 1)]/h
How to utilize laws of exponents?We are given the function as;
j(x) = 4^(x - 2)
Now, we want to solve the expression;
[j(x + h) - j(x)]/h
This gives us;
j(x + h) = 4^(x - 2 + h)
Thus, our expression is now;
[j(x + h) - j(x)]/h = [4^(x - 2 + h) - 4^(x - 2)]/h
Now, according to laws of exponents, we know that;
y³ × y² = y³ ⁺ ²
Thus;
4^(x - 2 + h) = 4^(x - 2) × 4^h
Therefore;
[4^(x - 2 + h) - 4^(x - 2)]/h = (4^(x - 2))(4^(h) - 1)]/h
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If ac = 57 find the measure of ab
9
30
6
27
Step-by-step explanation:
3x+4x-6=57
7x=63
x=9
AB=3x=3*9
AB=27
g(x)=6x-9 solve for when x is -8b
The solution to the equation g(x) = 6x - 9 whenx = -8b is g(-8b) = -48b - 9
How to evaluate the value of the function?From the question, the equation of the function is given as
g(x) = 6x - 9
Also, we have the value of the variable to be
x = -8b
So, we substitute -8b for x in the equation of the function
g(x) = 6x - 9
The above equation becomes
g(-8b) = 6(-8b) - 9
Open the brackets in the above expression
g(-8b) = -48b - 9
The above equation cannot be firther simplified
Hence, the solution is g(-8b) = -48b - 9
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I know it's hard but I beg you for help!
Answer:
use ASA
Step-by-step explanation:
since D=B, AB║CD
angle DEC=AEB (vertical angles)
AE=EC (given)
The midpoint M and one endpoint of CE are given. Find the coordinates of the other endpoint.
M(2,9) and C(4,12)
Hence, the coordinates of other point (x, y) are (0,6).
i.e. (x, y) → (0,6)
Let AB be the segment where
The coordinate M(2, 9) and C(4, 12)
and we have to find the point E.
Let us assume the other point is (x, y)
As we know that
The midpoint is halfway between the two end points, meaning midpoint coordinates are basically termed as the average of the corresponding endpoint coordinates.
Mid - point formula:
m = [tex]\frac{x_{1}+x_{2} }{2}[/tex]
n = [tex]\frac{y_{1}+y_{2} }{2}[/tex]
So,
Substituting M(2, 9) into C(4, 12):
2 = [tex]\frac{4+x_{2} }{2}[/tex]
9 = [tex]\frac{12+y_{2} }{2}[/tex]
Solve the Equation:
[tex]x_{2} = 0\\y_{2} = 6[/tex]
Express solutions in ordered pairs:
(0,6)
Hence, the coordinates of other point (x, y) are (0,6).
i.e. (x, y) → (0,6)
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Given h(x) = –x – 3, find h(-6).
To find h(-6), replace x = -6 into the function, as follows:
h(x) = -x - 3
h(-6) = -(-6) - 3
h(-6) = 6 - 3
h(-6) = 3
Jackson is comparison shopping for orange juice. He created a table to help him decide which package was the best deal.
Verify
REmember that the best deal is the deal with the less unit rate
so the order is
89 0z bottle is the best deal
64 oz cartoon
59 oz bottle
case of 24 10 oz bottles
10 oz bottle
therefore
Jason is not correct
The graph below shows Kate’s distance from her home(y), in miles, after a certain amount of time (x), in minutes:
The correct answer is Tim
She drives at a variable speed for 2minutes
A body is moving in simple harmonic motion with position function
s(t)= 4 + 5 cos t
Find the body’s velocity at t= 2π/3
The velocity of the body under simple harmonic motion is equal to - 5√3 / 2. (Correct choice: B)
How to find the velocity of a body under simple harmonic motion
Simple harmonic motion is a kind of self-sustained periodic motion that observed the following formula:
y = y' + Δy · cos ωt (1)
Where:
y' - Initial positionΔy - Amplitudeω - Angular frequency.t - TimeThe equation for the velocity of the body in simple harmonic motion is found differentiating (1):
v = - ω · Δy · sin ωt (2)
If we know that ω = 1, t = 2π / 3 and Δt = 5, then the velocity of the body is:
v = - 1 · 5 · sin (2π / 3)
v = - 5 · sin (2π / 3)
v = - 5 · √3 / 2
v = - 5√3 / 2
The velocity is equal to - 5√3 / 2.
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4. Understand Draw two lines of reflection through point A so that the composition of the reflections across the lines maps onto the image shown.
When a group of point is reflected across a line the distance of the points to the line must be equal, therefore the figure is inverted. With this in mind we can trace the intermediate step that is missing and finally draw the two lines.
Notice that the triangle get's inverted on each reflection around the lines.
11) At bank B, The value of us $700
is Bds $1.386. Calculate the
value of US $1.00 in BD $ at
this bank.
Answer:
Bds $ 1.98
Step-by-step explanation:
1386 bds / $ 700 * $ 1 = 1.98 Bds
find the value or measure. Assume all lines that appear to be tangent are tangent. X=
According to the secant-tangent theorem, we have the following expression:
[tex](x+3)^2=10.8(19.2+10.8)[/tex]Now, we solve for x.
[tex]\begin{gathered} x^2+6x+9=10.8(30) \\ x^2+6x+9=324 \\ x^2+6x+9-324=0 \\ x^2+6x-315=0 \end{gathered}[/tex]Then, we use the quadratic formula:
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where a = 1, b = 6, and c = -315.
[tex]\begin{gathered} x_{1,2}=\frac{-6\pm\sqrt[]{6^2-4\cdot1\cdot(-315)}}{2\cdot1} \\ x_{1,2}=\frac{-6\pm\sqrt[]{36+1260}}{2}=\frac{-6\pm\sqrt[]{1296}}{2} \\ x_{1,2}=\frac{-6\pm36}{2} \\ x_1=\frac{-6+36}{2}=\frac{30}{2}=15 \\ x_2=\frac{-6-36}{2}=\frac{-42}{2}=-21 \end{gathered}[/tex]Hence, the answer is 15 because lengths can't be negative.Part 1 of 2
Two of the most expensive cars in the world are car A and car B. The prices of these two cars differ by more than $10,000. The price of car Ais $130,745
a. Assuming that you do not know which model is more expensive, write an absolute value inequality that describes this situation. Use x for the price of car B.
b. What are the possibilities for the price of car B?
The absolute value inequality is given by | x-130745 | > 10000
and the possibility of Car B is x < 120745 or x > 140745
What is absolute value inequality?
Absolute value inequality are inequalities in algebra that involve algebraic expressions with absolute value symbols and inequality symbols. In simple words, we can say that an absolute value inequality is an inequality with an absolute value symbol in it. It can be solved using two methods of either the number line or the formulas.
x = price of car B
x-130745 = difference in price from car A to car B
If x is the larger price, then x-130745 will be positive. If x is the smaller price, then x-130745 is negative.
In short,
x-130745 > 0 when x > 130745
x-130745 < 0 when x < 130745
Using absolute value will give us
|x-130745| = positive difference in price
The result of an absolute value is never negative
We write the |x-130745| > 10000 to indicate that the difference in price is more than 10000 dollar
| x-130645 | > 10000
Part b.
We'll use the idea that if |x| > k, then x < -k or x > k
to get the following
|x-130745| > 10000
x-130745 < -10000 or x-130745 > 10000
x < -10000+130745 or x > 10000+130745
x < 120745 or x > 140745
Car B has a price less than $120,745
OR
Car B has a price greater than $140,745
So basically anything that is not between 120745 and 140745. The price has to be positive of course.
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find the slope of the line that passes through (1,5) and (9,8)
The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, the line passes through the points (1,5) and (9,8), then its slope is:
[tex]m=\frac{8-5}{9-1}=\frac{3}{8}[/tex]What is the fewest number of points you must plot in order to have examples of all four sets of numbers, including at least one positive and one negative integer? Explain.
To which sets do positive integers belong? Select all that apply.
A.
Integers
B.
Natural numbers
C.
Whole numbers
D.
Rational numbers
1) Two points are the minimum number of points that need to be plotted to have instances of all four groups of numbers.
2) The sets that positive integers belong to among the available are;
possibilities
Choices A, B, C, and D
1) There are two basic categories into which numbers are often divided:
- Rational numbers
- Irrational numbers
The four examples above are all different categories of rational numbers.
Positive integers are now by definition also known as whole numbers and natural numbers. Whole numbers and natural numbers can therefore be displayed in one graphic.
Since integers may be both positive and negative, as well as include fractions, another plot will be needed to display them.
In order to plot the fewest number of points necessary to provide examples for each of the four sets of numbers
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A grandfather wants to know the average height of all his grandchildren. He finds that the heights of his 9 grandchildren aregiven in inches by
mean = sum of the heights / number of grandchildren
[tex]=\frac{63+71+60+59+74+60+60+75+58}{9}[/tex][tex]=\frac{580}{9}[/tex][tex]\approx64.4[/tex]20 POINTS, GET MARKED AS BRAINLIST IF RIGHT
P (B U C) is 0.1675 when B and C are independent and P (B U C) is 0 when B and C are mutually exclusive.
What Are Independent Events?An Independent Event is defined as if the outcome of one event has no bearing on the outcome of the other, the two events are said to be independent events. Or, we may say that an event is considered independent if it does not affect the probability of another event. Probability-independent events mirror actual occurrences.
Let B and C be two events such that P(B) = 0.25 and P(C) = 0.67.
To determine P (B U C),
Given that B and C are independent.
Since B and C are independent events, we can just multiply the probabilities together, 0.25 × 0.67 = 0.1675
To determine P (B U C),
Given that B and C are mutually exclusive.
Since B and C cannot both occur at the same moment by definition because they are mutually exclusive, the answer is 0.
Therefore, P (B U C) is 0.1675 when B and C are independent and P (B U C) is 0 when B and C are mutually exclusive.
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how many integers are from 31 to 40
The number of integers from 31 to 40 is 10
What are integers?Integers are the set of positive whole numbers and negative whole numbers including zero. Examples are 5, 81, -56, 9, -2, 0, 17 etc.
From the question, we are to determine the number of integers there are from 31 to 40.
First, we will list all the whole numbers from 31 to 40.
The whole numbers from 31 to 40 are
31, 32, 33, 34, 35, 36, 37, 38, 39, and 40.
All of these numbers are positive whole numbers. Thus, they are integers.
The number of integers listed above is 10.
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The height (in inches) of a toy that moves up and down on a spring can be modeled by the function y= -(cos x)+2(cos x) (sin x) where x is time in seconds. Within the interval 0 < x < 6, when does the toy reach its minimum height? What is that height?
The correct option regarding the minimum height reached by the toy is:
A height of -1.76 inches at 5.647 seconds.
How to find the minimum value of the function?The function for the height of the toy in the spring after x seconds is modeled as follows:
y = -cos(x) + 2cos(x)sin(x)
It is a trigonometric function, hence there is no rule to find the minimum value of the function as there is for a quadratic function, for example.
Since there is no rule, we have to sketch the graph of the function in the given domain of 0 < x < 6.
Using a graphing calculator, the graph of the function is given at the end of the answer, with minimum point at (5.647, -1.76), hence the correct option is:
A height of -1.76 inches at 5.647 seconds.
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What is the value of x in the equation -2 = 5x + 3?
A 1
B 1/5
C-1
D-3 2/5
Answer:
C
Step-by-step explanation:
- 2 = 5x + 3 ( subtract 3 from both sides )
- 5 = 5x ( divide both sides by 5 )
- 1 = x
Find the zero of 3[2x-(3x-4)]-6(x-3)
First, simplify the expression:
[tex]\begin{gathered} 3\lbrack2x-(3x-4)\rbrack-6(x-3) \\ =3\lbrack2x-3x+4-6(x-3) \\ =3(2x)+3(-3x)+3(4)-6(x-3) \\ =6x-9x+12-6x+18 \\ =6x-9x-6x+12+18 \\ =-3x-6x+12+18 \\ =-9x+12+18 \\ =-9x+30 \end{gathered}[/tex]Then:
[tex]3\lbrack2x-(3x-4)\rbrack-6(x-3)=-9x+30^{}[/tex]To find the zero of the given expression, find the zero of -9x+30:
[tex]\begin{gathered} -9x+30=0 \\ \Rightarrow-9x=-30 \\ \Rightarrow x=\frac{-30}{-9} \\ \therefore x=\frac{10}{3} \end{gathered}[/tex]Therefore, the zero of the given expression is 10/3.
Brainliest if solved correctly
Answer:
1
Step-by-step explanation:
when there is no number, they are always 1.
1 multiplied by itself is always 1, so 1/1 is 1.
Hope this helps!
btw, brainliest if correct, ty!
Answer/Step-by-step explanation:
Simplify
x⁻⁵
-------
y³
Since the x on top has a negative exponent it must go down to the denominator.
So the answer would be:
1
-------
x⁵y³
I hope this helps!
what are possible dimensions of the rectangular area at the right
The expression used to depict area will be 9 / (3x - 1).
A rectangle may be defined as a closed figure with four sides and four interior angles. The interior angles are 90°.
The given expression for area = 27x - 9
Factorize 27x - 9
Taking 9 as greatest common factor outside, we get
27x - 9 = 9(3x - 1)
We know that the area of rectangle with dimensions length by breadth is given by:-
Area = Length x Breadth
Hence, the possible dimensions of the rectangle will be 9 / (3x - 1).
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Complete Question:
What are possible dimensions of the rectangular area at the right? if area is 27x-9.
Already got b I just need a
[tex]y=14x[/tex], where x is the number of gallons used and y is the distance driven in miles.
Walter is a waiter at the Towne Diner. He earns a daily wage of $50, plus tips that are equal to 15% of the total cost of the dinner he serves. What was the total cost of the dinners he served if he earned $170 on Tuesday?
Jason, this is the solution:
Walter's daily wage = $ 50
Tips = 15% of the total cost of the dinner he serves
Tuesday earnings = $ 170
Therefore,
Tips = 170 - 50
Tips = 120
For finding the cost of the dinners, we use Direct Rule of Three, as follows:
Percentage Cost
15 120
100 x
_____________________
120 * 100 = 15 * x
12,000 = 15x
Dividing by 15 at both sides:
15x/15 = 12,000/15
x = 800
The total cost of the dinners Walter serverd on Tuesday was $ 800
Write a quadratic equation in standard form with the given root(s) -7,3/4 and can you explain how you did it? i need it ASAP please and thank you
The quadratic equation with roots -7, 3/4 in standard form is
4x² + 25x - 21 = 0.
What is a quadratic equation?A quadratic equation is an algebraic equation of degree two and has exactly two roots real or imaginary or complex.
We know the roots of a quadratic equation are also factors of a quadratic equation.
If x = a and x = b are two roots of a quadratic equation then x - a = 0 and
x - b = 0 are the factors of a quadratic equation that can be formed by multiplying the two factors (x - a)(x - b) = 0.
Given that -7 and 3/4 are the roots.
∴ { x - (-7)}{ x - 3/4) = 0.
(x + 7)(x - 3/4) = 0.
x² + 7x -(3/4)x - 21/4 = 0.
x² + (25/4)x - 21/4 = 0.
4x² + 25x - 21 = 0.
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Three cards are drawn with replacement from a standard deck of 52 cards. Find the the probability that the first card will be a spade, the second card will be a red card, and the third card will be a queen. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Probability is expressed as
number of favorable outcomes/number of total outcomes
In a standard deck of cards, the total number of cards is 52.
There are 13 spades in a standard deck. Thus,
probability of selecting a spade = 13/52 = 1/4
There are 26 red cards in a standard deck of cards. Since the first card was replaced, the total number of cards remains 52.
probability of selecting a red card = 26/52 = 1/2
There are 4 queens in a standard deck of cards. Since the second card was also replaced, total number of cards is still 52. Thus,
Probability of selecting a queen = 4/52 = 1/13
Thus, the probability that the first card will be a spade, the second card will be a red card, and the third card will be a queen is
1/4 x 1/2 x 1/13
= 1/104
He invested $ at 8% and Sat 12%
An actor invests some money at 8%, and $36000 more than twice the amount at 12%. The total annual interest earned
from the investment is $26400. How much did he invest at each amount? Use the six-step method.
K
oney at 8%, and $360
This will be his initial investment. The amount for 8% will be 84000, and the amount for 12% will be 204000.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance.
When this equation is solved, we discover that the
value of the variable x is 7.
let x = the money invested at 8%
y = the money invested at 12%
an actor invests some money at 8% and 36,000 more than four times the amount at 12%
x = 36000 + 2y
total annual interest earned from the investment is 26400
0.08*x + 0.12*y = 26400
by solving the system of equations
x = 36000 + 2y
0.08*x + 0.12*y = 26400
solving the equations,
0.08(36000+2y)+0.12y=26400
2880+0.16y+0.12y=26400
y=84000
x=204000
The amount for 8% will be 84000, and the amount for 12% will be 204000.
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What is a ratio? And how do I find one if for example I had 4 and 6 ?
Ratio means the quantitative relation between two amounts showing the number of times one value contains or contained in order
example 4 and 6
for example
if we have 4 men and 6 women
we can say the ratio of men to women is 4 to 6
that is 4 : 6
and ratio can also means division
for 4 and 6
= 4 / 6
= 2 / 3
= 2 : 3
that is, for every 2 men we have 3 women