The explicit formula for this sequence exists as = (-9) + (n-1)6
Explain about the explicit formula ?We can use an explicit formula, as previously discussed, to determine the nth term in a series. The simplest meaning of explicit is precise or unambiguous. The reason the formula is explicit is that, if properly used, it can be used to find the nth term.
An arithmetic sequence can be expressed explicitly as a = a + (n - 1)d, and each term of the sequence can be computed without knowledge of the other parts. The nth term of an arithmetic, geometric, or harmonic series is usually the explicit formula.
Given: -9, -3, 3, 9, 15.
Because it is an arithmetic series, the supplied sequence.
Therefore, there is no difference between two consecutive terms.
For example, 3-(-3)=6 and (-3)-(-9)=6.
The nth term is now equal to a+(n-1)d.
as, a=-9
So, = -9+(n-1)6
= -9+6n-6
= 6n-15
so that =-9+(n-1)6.
The answer is option D
To learn more about explicit formula refer to:
https://brainly.com/question/24198356
#SPJ9
If you multiply three negative integers, will
the product always, sometimes, or never
be negative.
ASAP 30 POINTS HELP,
Find the range of the following piecewise function.
(see attachment)
[-1,27]
[18,-2]
[1,27]
[-4,0]
The range of the function will be equal to [-1, 27].
Function may be defined as an expression in which for every input variable there is only one output variable. The input variable is the variable x and also called as independent variable and output variable is the y variable and is also called as dependent variable. Domain of a function may be defined as the set of values of all the input values. Range of a function may be defined as the set of values of all the output values. For the domain -5 ≤ x < 3 we have function x² + 2. So, if we put -5 as x, we get the value equal to 27. Also, for the domain 3 ≤ x < 7 we have the function x - 4 and if we put the value 3 as x, we get the value equal to -1. Now, the range will be equal to [-1. 27].
Learn more about Range at:
brainly.com/question/4206663
#SPJ1
11. In Pam's neighborhood, 7 out of 25 houses are painted yellow. What percent of the houses are painted yellow? *
hello
to solve this question we should simply express this in percentage
[tex]\frac{7}{25}\times100=28\text{ \%}[/tex]from the calculation above, the percentage of houses painted yellow are 28%
solve x and graph solution on number line, 10th grade
Solution:
Given the inequality;
[tex]-10x>-90[/tex]Divide both sides of the inequality by -10 and change the sign;
[tex]\begin{gathered} \frac{-10x}{-10}<\frac{-90}{-10} \\ \\ x<9 \end{gathered}[/tex]Thus, the solution on the number line is;
helppppppppppppppppppp meeeeeeeeeeeeeeeeeeeee
Answer:
33
Step-by-step explanation:
3
The difference of two numbers is 16. But large number is five less than four times the smaller number. Find the two numbers.
Let x be the larger number and y be the smaller number.
Given the difference between two numbers is 16.
[tex]x-y=16\ldots\text{..}(1)[/tex]Given larger number is five less than four times the smaller number.
[tex]x=4y-5\ldots\text{.}\mathrm{}(2)[/tex]Now, solve the equation (1)
[tex]x=16+y[/tex]Put x in the 2nd equation.
[tex]\begin{gathered} 16+y=4y-5 \\ 4y-y=16+5 \\ 3y=21 \end{gathered}[/tex]Further solved as,
[tex]y=7[/tex]Now, put the value of y in equation (1)
[tex]\begin{gathered} x-y=16 \\ x-7=16 \\ x=16+7 \\ x=23 \end{gathered}[/tex]Thus,
[tex]x=23[/tex]Therefore, the two numbers are 23 and 7.
tanner writes a number that has 8 tens 2 ones. what number does tanner write
82
1) Since Tanner is going to write a number with 8 tens and 2 ones
Then we can write:
[tex]\begin{gathered} 8\text{ }\times10=80 \\ 2\times1=2 \\ 82 \end{gathered}[/tex]2) Tanner writes the number 82
Activity 1: Trigonometry
Find the supplement of an angle whose compliment is 62º.
Answer:
If the complement of an angle is 62°, then its supplement is 152°.
hope it helps u
branliest?
Right and solve any quality which can be used to determine v , The number of visits Nolan can make to his first free movie ticket.
Answer:
20 + 2.5v ≥ 40
v ≥ 8
Step-by-step explanation:
Nolan receives:
- fixed value: 20
- vari
write the answer in standard form(-3x^4+x^6-9x^5+2x^2-7)-(-2x^5+x-4x^2-x^4+12)
Let's make the operation:
[tex]\begin{gathered} (-3x^4+x^6-9x^5+2x^2-7)-(-2x^5+x-4x^2-x^4+12) \\ =-3x^4+x^6-9x^5+2x^2-7+2x^5-x+4x^2+x^4-12 \\ =x^6-7x^5-2x^4+6x^2-x-19 \end{gathered}[/tex]Therefore the answer is:
[tex]x^6-7x^5-2x^4+6x^2-x-19[/tex]A distribution of values is normal with a mean of 198 and a standard deviation of 74.5.
Find P10, which is the score separating the bottom 10% from the top 90%.
P10 =
Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
The probability P10 for a data with mean of 198 and standard deviation of 74.5 is P10 = 25.15%
As per the question statement, a distribution of values is normal with a mean of 198 and a standard deviation of 74.5 and we are supposed to find P(10), which is the score separating the bottom 10% from the top 90%.
Given mean (µ) = 48.5 , SD(σ) = 18.2
z = (X - μ) / σ, where X = data
X = 216.74
z = (216.74 - 198) / 74.5 = 0.2515 or 25.15%
Hence the probability P10 for a data with mean of 198 and standard deviation of 74.5 is P10 = 25.15%
Probability: The chance of happening of any event is its probability.Mean: The average of any given set of data is called mean and is calculated by dividing the sum of all observations by the total number of observations.Standard deviation: A number calculated to depict the degree of variation across the board for a group.To learn more about Probability, click on the link given below:
https://brainly.com/question/11234923
#SPJ1
I need help i dont understand
Answer:
2.50 + 1.50m = c
Step-by-step explanation:
Since he pays a fee of 2.50 when he enters the taxi were going to start with:
2.50 +
Now after its 1.50 for each mile so were going to do :
2.50 + 1.50m
Since we want to find the cost the equation will be:
2.50 + 1.50m = c
The graph below shows the solution set to which system of inequalities?
O A. ys x+2
y> 2x
y>-3
O B. y2 x+2
y< 2x
y2-3
O C. y< x + 2
ys 2x
W.3.
The correct answer is option C.
[tex]\begin{gathered} yWe can see that the solution set is all above a dotted line, parallel to the x axis at height y = -3. Then, the inequality that respresents this is:[tex]y\ge-3[/tex]With this, we can already rule out option A.
Next, we can see a slanted dashed line, that when x = 0, y = 2. The solution set is below this line. The inequality that represnts this is:
[tex]yThis rule out the option BThus, option C is the correct one.
Item 3What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=|4+x|? horizontal translation of 4 units rightvertical translation of 4 units upvertical translation of 4 units downhorizontal translation of 4 units left
As given by the question
There are given that the function
[tex]f(x)=|4+x|[/tex]Now,
According to the concept,
x+4 means, horizontal translation of 4 units left.
Hence, the correct option is D.
suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. suppose that it takes 100 workers 6 weeks to build 4 miles of Highway. how long will it take a 160 workers to build 16 miles of Highway?___weeks
Answer:
The amount of time it would take 160 workers to build 16 miles of Highway is;
[tex]15\text{ weeks}[/tex]Explanation:
Given that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers.
Let t represent the time in weeks, l represents the length of the highway in miles, and n represent the number of workers;
So, we have;
[tex]\begin{gathered} t\propto\frac{l}{n} \\ t=k\frac{l}{n} \\ k=\frac{nt}{l} \end{gathered}[/tex]Given;
it takes 100 workers 6 weeks to build 4 miles of Highway
[tex]\begin{gathered} n=100 \\ t=6 \\ l=4 \\ k=\frac{nt}{l} \\ k=\frac{100\times6}{4} \\ k=150 \end{gathered}[/tex]so, for 160 workers to build 16 miles of Highway the time it will take is;
[tex]\begin{gathered} n=160 \\ l=16 \\ k=150 \\ t=k\frac{l}{n} \\ t=150\times\frac{16}{160} \\ t=\frac{150}{10} \\ t=15 \end{gathered}[/tex]Therefore, the amount of time it would take 160 workers to build 16 miles of Highway is;
[tex]15\text{ weeks}[/tex]The question is in the image. Need help with #8
SOLUTION
The graph is a function
The domain is all real numbers apart from 0 given by the interval
(-∞,0) ∪ (0,∞)
The Range of the function is all positive numbers given by the interval
(0,∞)
The function is increasing on the interval
(-∞,0)
The function is decreasing on the interval
(0,∞)
Please help me: What is the y-intercept of the following equation?
To find the y-intercept, replace x=0:
[tex]\begin{gathered} y=3(0)+1 \\ =0+1 \\ =1 \\ \\ \therefore y=1 \end{gathered}[/tex]Therefore, the y-intercept of the given equation is 1.
A 2.7 meter ladder leans against a house forming a 30° angle with the house. Exactly how far is the base of the ladder from the house?
Given the information, we have the following right triangle:
notice that x represents the distance from the base of the ladder to the house.
Then, using the trigonometric function sine we have the following:
[tex]\begin{gathered} \sin (30)=\frac{\text{opposite side}}{hypotenuse}=\frac{x}{2.7} \\ \Rightarrow\frac{1}{2}=\frac{x}{2.7} \\ \Rightarrow x=2.7\cdot\frac{1}{2}=1.35 \\ x=1.35 \end{gathered}[/tex]thus, the base of the ladder is 1.35m from the house
What is the inverse of this function?
f(x) = 8√x, for x ≥ 0
O A. f¹(x) = 64x², for x ≥ 0
O B. f¹(x) = ², for x ≥ 0
O c. f¹(x) = 8x², for x ≥ 0
O D. f¹(x) = 1/64x², for x ≥ 0
The inverse of the function is 1/64x², for x≥0
What is a function?
Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the first documented treatment of the concept of function. Initially, functions expressed the idealized interaction of two changing quantities. A planet's location, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity). The realms of application of the idea of a function were substantially expanded at the conclusion of the 19th century when it was defined in terms of set theory.
The inverse of the function is given by option (D) 1/64x², for x≥0
To know more about function, click on the link
https://brainly.com/question/11624077
#SPJ9
Given, 115=1+6(5r+4), what is the value of 9r?
Answer:
9r=27
Step-by-step explanation:
you first are gonna multiply 6 into the 5r+4 then you are gonna have this: 115=1+30r+24then u add the 24 and 1 togetheryou get 115=30r+25then you subbtract 25 from both sidesyou get 90=30rthen you didvide 30 by both sidesyou get 3=rso now we multiply 9 cause we need the value of 9r and r=33*9=27The area of a rectangle is 3/5 square m² the width is 2/5 m a what is the area of the rectangle write your answer as a fraction in simplest form the length of the rectangle is meters how many times greater is the length than the rest write your answer in simplest form the length is times greater than the width
The length of the rectangle based on the information is 6/25 meters.
The length is 3/5 times more than the width.
How to calculate the length?From the information, the area of a rectangle is 3/5 square m² and the width is 2/5m. It should be noted that the length will be:
Length = Area / Width
Length = 3/5 ÷ 2/5
Length = 3/5 × 2/5
Length = 6/25
The length will s 6/25 meters.
The number of times that the length is more than the width will be:
= 6/25 ÷ 2/5
= 6/25 × 5/2
= 3/5 time.
Learn more about area on:
brainly.com/question/25292087
#SPJ1
Elias incorrectly finds the measure of
Answer:
105 degrees
Elias' mistake was that he added m
Explanation:
To be able to determine the measure of AFB, we have to 1st of all find the value of x.
Let's go ahead and solve for x as shown below;
[tex]m\angle AFD=m\angle\text{BFC (vertically opposite angles are equal)}[/tex][tex]\begin{gathered} 3x+3=2x+27 \\ 3x-2x=27-3 \\ x=24 \end{gathered}[/tex]Since we know the value of x, let's go ahead and solve for [tex]\begin{gathered} (3x+3)+m\angle\text{AFB}=180\text{ (sum of angles on a straight line)} \\ 3(24)+3+m\angle AFB=180 \\ 75+m\angle AFB=180 \\ m\angle AFB=180-75 \\ m\angle AFB=105^{\circ} \end{gathered}[/tex]
A right triangle has a hypotenuse of length 10 units and includes a 40° angle. What are the length of the other two size
1) Let's sketch this out to better grasp it:
2) Since the sum of the interior angles is 180º, we can write out the following to find the missing angle:
[tex]\begin{gathered} 40+90+\alpha=180 \\ 130+\alpha=180 \\ \alpha=180-130 \\ \alpha=50 \end{gathered}[/tex]3) We can find the lengths by using trigonometric ratios (sine, cosine, tangent).
[tex]\begin{gathered} \sin (40)=\frac{opposite\text{ leg}}{hypotenuse}=\frac{b}{10} \\ \sin (40)=\frac{b}{10} \\ b=10\cdot\sin (40) \\ b\approx6.43 \\ \\ \sin (50)=\frac{c}{10} \\ c=10\cdot\sin (50) \\ c=7.66 \end{gathered}[/tex]Leander planted 100 acres with soybeans and he plans to increase his field size by 3% each year. What is the growth factor?
We are given that the rate of growth is:
[tex]0.03.[/tex]Now, recall that the growth factor is:
[tex]1+rate\text{ of growth.}[/tex]Therefore, the growth factor is:
[tex]1+0.03=1.03.[/tex]Answer: [tex]1.03[/tex]Y=f(x+3) what is the transformation
Look at the construction being preformed in this diagram below
When we draw a perpendicular bisector, we are also:
1. Bisecting a line
2. Bisecting a line segment
A paralallel line is not correct. The draw is for bisecting AB, not for a parallel line to AB.
Therefore, the correct answers are:
A, C and D.
Question in picture will give brainlist
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
If 3x + 2y = 72 and 2y = 3z then 3x + 3z = 72.
This is due to the property of substitution.
Option E is the correct answer.
None of the above.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
3x + 2y = 72 _____(1)
2y = 3z ______(2)
Substitute (2) in (1) we get,
3x + 3z = 72
We got 3x + 3x = 72 using the property of substitution.
Thus,
If 3x + 2y = 72 and 2y = 3z then 3x + 3z = 72.
This is due to the property of substitution.
Option E is the correct answer.
None of the above.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
Find an equation for the perpendicular bisector of the line segment whose endpoints are (1,4)and(-9,-6)
The endpoints are (1,4) and (-9,-6). The equation for the perpendicular bisector of the line segments with given end points is x-y+3=0.
Given that,
The endpoints are (1,4) and (-9,-6).
We have to find the equation of the perpendicular bisector of the line segments with given end points.
First we have to find
The slope of the line m= [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m=(-6-4)/(-9-1)
m=-10/-10
m=1
Now,
The equation of the line is y-y₁=m(x-x₁)
Taking point (1,4)
y-4=1(x-1)
y-4=x-1
x-y+4-1=0
x-y+3=0
Therefore, the equation for the perpendicular bisector of the line segments with given end points is x-y+3=0.
To learn more about equation visit: https://brainly.com/question/10413253
#SPJ1
When completing a composition translation (more then one translation) we move from right to left?
Solve the system of functions, y2 = 3x and y = 7x.
We have the following system of functions:
[tex]\begin{gathered} y^2=3x \\ y=7x \end{gathered}[/tex]The second equation gives us an expression for y. We can replace y with these expression in the first equation:
[tex]\begin{gathered} y^2=(7x)^2=3x \\ 7^2\cdot x^2=3x \\ 49x^2=3x \end{gathered}[/tex]We can substract 3x from both sides:
[tex]\begin{gathered} 49x^2-3x=3x-3x \\ 49x^2-3x=0 \end{gathered}[/tex]The x is a factor of both terms on the left. Then we can rewrite this equation:
[tex]\begin{gathered} 49x^{2}-3x=0 \\ x(49x-3)=0 \end{gathered}[/tex]So we have that the product of two terms is equal to 0. This happens when any of them is equal to 0 so we have two equations:
[tex]\begin{gathered} x=0 \\ 49x-3=0 \end{gathered}[/tex]From the first we have x=0 and we can add 3 to both sides of the second equation:
[tex]\begin{gathered} 49x-3+3=0+3 \\ 49x=3 \end{gathered}[/tex]Then we divide both sides by 49:
[tex]\begin{gathered} \frac{49x}{49}=\frac{3}{49} \\ x=\frac{3}{49} \end{gathered}[/tex]So we have the two x-values of the solutions: x=0 and x=3/49. In order to find their respective y-values we can use any of the two original functions:
[tex]\begin{gathered} y=7x\rightarrow y=7\cdot0=0\rightarrow(x,y)=(0,0) \\ y=7x\rightarrow y=7\cdot\frac{3}{49}=\frac{21}{49}\rightarrow(x,y)=(\frac{3}{49},\frac{21}{49}) \end{gathered}[/tex]AnswerWe have two solutions: (0,0) and (3/49,21/49). We can round the values of the second solution:
[tex]\begin{gathered} \frac{3}{49}\cong0.06 \\ \frac{21}{49}\cong0.43 \end{gathered}[/tex]Then the solutions are (0,0) and (0.06,0.43). Then the answer is the fourth option.
