Answers
Solution.
Given the sequence
[tex]3,18,108,648,3888[/tex]Test which kind of sequence it is
[tex]\begin{gathered} \frac{18}{3}=6 \\ \frac{108}{18}=6 \\ The\text{ sequence has a common ratio which is 6. } \\ Thus,\text{ it is a geometric sequence} \\ \end{gathered}[/tex][tex]\begin{gathered} The\text{ nth term of a geometric sequence can be determined by the formula} \\ a_n=ar^{n-1} \\ where\text{ a = 1st term} \\ r=common\text{ ratio} \end{gathered}[/tex][tex]a_n=3(6^{n-1})[/tex][tex]The\text{ answer is a}_n=3(6^{n-1})[/tex]Related Questions
the product of a number and 3, increased by 5, is 7 less than twice the number. write an equation
Answers
Answer:
[tex]3x + 5 = 2x - 7[/tex]
Find the average rate of change of f(x)=x2−x+2 on the interval [1,t].
Answers
The average rate of change of the function x²-x+2 on the interval [1,t] is t .
The Average Rate Of Change of the function g(x) on the interval [a,b] is given by the formula
Average rate of change = (g(b)-g(a))/(b-a) .
the function is given as x²-x+2
interval is given as [1,t] .
so a=1 and b=t .
f(a) = f(1) = 1²-1+2 = 1-1+2 = 2
f(b) = f(t) = t²-t+2
and , b-a = t-1
Substituting the values in the average rate of change formula , we get
Average rate of change = (t²-t+2-2)/(t-1)
= (t²-t)/(t-1)
taking t common from the numerator , we get
= t(t-1)/(t-1)
= t .
Therefore , the average rate of change of function x²-x+2 on the interval [1,t] is t .
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Fill in the empty spaces to complete the puzzle. In any row, the two left spaces should multiply to equal the right-hand space. In any column, the two top spaces should multiple to equal the bottom space.
Answers
Explanation:
We will find the expression for each space in the following order
To find the first expression, we need to find a number that multiplied by 6 is equal to 18. This number is 3 because
6 · 3 = 18
Then, for the second space, we need to factorize the expression 36x² + 144x + 108 as follows
36x² + 144x + 108 = 8(2x² + 8x + 6)
So, the expression that multiplied to 8 is (36x² + 144x + 108) is (2x² + 8x + 6).
The third space can be calculated by factorizing 2x² + 8x + 6 as
2x² + 8x + 6 = (x + 3)(2x + 2)
Therefore, the expression in the third space is (2x + 2)
Finally, for the fourth and fifth space, we need to multiply the expression to the left, so
6(2x + 2) = 6(2x) + 6(2) = 12x + 12
3(x + 3) = 3(x) + 3(3) = 3x + 9
Answer
Therefore, the answer is
$3.44 at the Farmers market at a grocery store the same oranges cost $8.40 for a bag of 20 find the better deal by calculating the unit rate for both locations how much would be saved per orange by purchasing oranges at the locations with the better deal solve the word problemFarmers market unit rate --------------grocery store unit rate ------------------better deal -------------how much is saved ------------A $0.01/ orangeslB $0.41 / orangeC grocery storeD Farmers marketE $0.43 / orangeF $0.40 / OrangeG $0.10 / Orange
Answers
Given :
At the farmer market : a bag of 8 oranges cost $3.44
At the grocery store : a bag of 20 oranges cost $8.4
So, the unit rate at the farmer market = 3.44/8 = $0.43/ orange
And the unit rate at the grocery store = 8.4/20 = $0.42/ orange
So, the better deal is the grocery store
how much is saved ?
the saving = 0.43 - 0.42 = $0.01/ orange
Write the phrase "8 more than 10 divided by x is 12" as a variable expression:
Answers
Answer:
10/x + 8 = 12
Step-by-step explanation:
10 divided by x = 10/x
8 more than 10 divided by x = 10/x + 8
The sum of a number and -4 is greater than 15. Find the number
Answers
x > 19
Explanation:
Let the number = x
The sum of a number and -4 = x + (-4)
The sum of a number and -4 is greater than 15:
x + (-4) > 15
Multiplication of opposite signs gives negative number:
x - 4 > 15
Collect like terms:
x > 15 + 4
x > 19
Question 7, pre calc, include the answer in bold please. I have bad WiFi so please finish question if I get disconnected so I can see it, thanks
Answers
Given the following function
[tex]f(x)=x^4-x^3+7x^2-9x-18[/tex]We want to find its roots. Since we already know that (x + 1) and (x - 2) are factors of this polynomial, we can divide our polynomial by those factors and factorize the result to get the other roots.
Let's start by dividing by the first factor
[tex]\frac{x^4-x^3+7x^2-9x-18}{x+1}[/tex]To divide a polynomial by other, we start by dividing the leading term of the dividend by the leading term of the divisor(this will be the first term of our result)
[tex]\frac{x^4}{x}=x^3[/tex]Then, we ultiply it by the divisor
[tex]x^3(x+1)=x^4+x^3[/tex]Subtracting this result from the dividend, we have
[tex](x^4-x^3+7x^2-9x-18)-(x^4+x^3)=-2x^3+7x^2-9x-18[/tex]This means that our division is
[tex]\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3+\frac{-2x^3+7x^2-9x-18}{x+1}[/tex]Repeating the whole process of division with the second term, we have
[tex]\begin{gathered} x^3+\frac{-2x^3+7x^2-9x-18}{x+1}=x^3-2x^2+\frac{9x^2-9x-18}{x+1} \\ \Rightarrow\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3-2x^2+9x-18 \end{gathered}[/tex]From this result, we can rewrite our function as
[tex]x^4-x^3+7x^2-9x-18=(x+1)(x^3-2x^2+9x-18)[/tex]Repeating this same process with the other know factor, the other division we have to solve is
[tex]\frac{(x^3-2x^2+9x-18)}{x-2}=x^2+9[/tex]Then, our function is
[tex]f(x)=(x^4-x^3+7x^2-9x-18)=(x+1)(x-2)(x^2+9)[/tex]Then, to find the roots we need to solve the following equation
[tex](x+1)(x-2)(x^2+9)=0[/tex]Since we have a product of 3 terms, the result will be zero if and only if one of the terms is zero. This means that the roots can be found by assuming each one is zero. The solutions for this equation are the same solutions for the following system
[tex]\begin{cases}x+1=0 \\ x-2=0 \\ x^2+9=0\end{cases}\Rightarrow\begin{cases}x=-1 \\ x=2 \\ x=\pm\sqrt[]{-9}=\pm3i\end{cases}[/tex]And those are the roots for our function. x = -1, 2, +-3i.
solve the equation 3x^2 - 5x + 1 = 0 expressing your answer correct to two decimal places
Answers
You have th following equation;
[tex]3x^2-5x+1=0[/tex]In order to find the solution to the previous equation, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, a = 3, b = -5 and c = 1. By replacing these values into the quadratic formula, you obtain:
[tex]\begin{gathered} x=\frac{-(-5)\pm\sqrt[]{(-5)^2-4(3)(1)}}{2(1)} \\ x=\frac{5\pm\sqrt[]{25-12}}{2}=\frac{5\pm\sqrt[]{13}}{2} \\ x=\frac{5\pm3.60}{2}=2.5\pm1.80 \end{gathered}[/tex]Hence, the solutions are:
x = 2.5 + 1.80 = 4.30
x = 2.5 - 1.80 = 0.70
what is the volume of a pipe that has a diameter of 8 meters and a height of 3 meters of water, round to the nearest tenth
Answers
The pipe is in the form of cylinder.
[tex]\begin{gathered} d\text{ = 8 m} \\ r\text{ = 4 m} \\ h\text{ = 3 m} \end{gathered}[/tex]The volume of the pipe is calculated as,
[tex]\begin{gathered} \text{Volume = }\pi\times r^2\times h \\ \text{Volume = 3.14 }\times\text{ 4}\times4\times3 \\ \text{Volume = 150.72 }\approx150.70m^3 \end{gathered}[/tex]Thus the volume of water is 150.70 cubic m .
How do you find the range in a graph like this?
Answers
Answer
y can take on any real number value except around 1 < y < 3 where none of the graphs have values around this region.
Hence, this is the range of the graph.
Explanation
The range of a function refers to the region of values where the fumction can exist. It refers to the values that the dependent variable [y or f(x)] can take on.
From the graph attached to this question, we can see that the function has different forms at different values of x.
But it is also evident that y can take on any real number value except around
1 < y < 3 where none of the graphs have values around this region.
Hence, this is the range of the graph.
Hope this Helps!!!
Which relation below is not a function
Answers
Answer:
0,0
Step-by-step explanation:
Two numbers can not equal another number
A ball is dropped from a state of rest at time T = 0.The distance traveled after t seconds is s(t) = 16t^2 ft.
Answers
ANSWERS
(a) 68 ft
(b) 136 ft/s
(c) 128 ft/s
EXPLANATION
(a) The time interval is from 4s to 4.5s, so the distance the ball travels from 4s to 4.5s is,
[tex]\Delta s=16\cdot(4.5)^2-16(4)^2=68ft[/tex](b) As stated, the average velocity is the quotient between the distance traveled and the time,
[tex]\frac{\Delta s}{\Delta t}=\frac{68ft}{0.5s}=136ft/s[/tex](c) Here we have to find the distance as we did in part b and then divide by the time interval,
[tex]\begin{cases}\lbrack4,4.01\rbrack\to\Delta s=1.28016\to V=1.28016/0.01=128.16ft/s \\ \lbrack4,4.001\rbrack\to\Delta s=0.128016\to V=0.128016/0.001=128.016ft/s \\ \lbrack4,4.0001\rbrack\to\Delta s=0.01280016\to V=0.01280016/0.0001=128.0016ft/s \\ \lbrack3.9999,4\rbrack\to\Delta s=0.01279984\to V=0.01279984/0.0001=127.9984ft/s \\ \lbrack3.999,4\rbrack\to\Delta s=0.127984\to V=0.127984/0.001=127.984ft/s \\ \lbrack3.99,4\rbrack\to\Delta s=1.2784\to V=1.2784/0.01=127.84ft/s\end{cases}[/tex]As we can see in the middle values, as the time interval is shorter - the difference approaches 0, the value of the velocity is closer to 128ft/s.
Hence, the estimated instantaneous velocity at t = 4 is 128 ft/s
FIND THE MEASURE OF EACH EXTERIOR ANGLE OF 40
Answers
Solution
The sum of exterior angles is 360º for any polygon
So then we can find the measure of the exterior angles like this:
360/40 = 9º
Evaluate the expression whenb= 48 c= 7simplify as much as possible
Answers
Given:-
[tex]\frac{b}{3}+2c^2[/tex]To find the simplified value when b=48 and c=7.
So now we simplify the solution by substituting the values of b and c in the given equation and get the required solution.
So now we simplify. so we get,
[tex]\frac{b}{3}+2c^2=\frac{48}{3}+2\times7\times7=16+98=114[/tex]So the simplified solution is 114.
Discuss the order of operations to explain why the expressions [(12÷(2+ 2)] ^3 and (12 ÷ 2) + 2^3 do not havethe same value.
Answers
The order of operations are different. Hence, the answers are not equal
Explanation:
Oder of operations using PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction)
[(12÷(2 + 2)]³ and (12 ÷ 2) + 2³
we solve seperately:
[(12÷(2+ 2)]³
we solve the parenthesis first:
(12 ÷ 4)³
then we apply division:
= (3)³
Then expand the exponent:
= 27
(12 ÷ 2) + 2³
we solve the parenthesis first:
6 + 2³
we expand the exponent:
6 + 8
we apply addition:
14
The order of operations are differnt. Hence, the answers are not equal
What is the solution to x^2 – 9x < –8?A. x < 1 or x > 8B. x < –8 or x > 1C. 1 < x < 8D. –8 < x < 1
Answers
INFORMATION:
We have the next inequality
[tex]x^2-9x<-8[/tex]And we must find its solution
STEP BY STEP EXPLANATION:
To solve it, we must:
1. Move all terms aside
[tex]x^2-9x+8<0[/tex]2. Factor x^2-9x+8
[tex](x-8)(x-1)<0[/tex]3. Solve for x
[tex]x=8\text{ or }x=1[/tex]4. From the values of x, we have these 3 intervals to test
[tex]\begin{gathered} x<1 \\ 18 \end{gathered}[/tex]5. Choose a test point for each interval
For the interval x < 1:
[tex]\begin{gathered} \text{ Using x }=0, \\ 0^2-9(0)<-8 \\ 0<-8 \end{gathered}[/tex]which is false. So, the interval is discarded.
For the interval 1 < x < 8:
[tex]\begin{gathered} \text{ Using x }=2, \\ 2^2-9(2)<-8 \\ -14<-8 \end{gathered}[/tex]which is true. So, the interval is maintained
For the interval x > 8:
[tex]\begin{gathered} \text{ Using x = 9,} \\ 9^2-9(9)<-8 \\ 0<-8 \end{gathered}[/tex]which is false. So, the interval is discarded.
Finally, the solution would be the interval that was maintained: 1 < x < 8.
ANSWER:
C. 1 < x < 8
Answer:
C. 1 < x < 8
Step-by-step explanation:
x² - 9x < -8
we will suppose some values for x to check which values will satisfy this inequality:
for x = 1
1(1-9) < -8 which is wrong
for x = 2
2(2-9) < -8 this is satisfying the inequality
for x = 8
8(8-9) < -8 which is wrong
let's take any negative value now,
let x = -2
-2(-2-9) < -8 which is wrong
thus x is the positive value which will always be greater than 1 and less than 8 for the given inequality.
You are redecorating your room and the only thing left to paint is your door. You're onlygoing to paint the side that faces the inside of your room. The door is 6 feet 10 inchestall and 30 inches wide. You need to know the surface area of the side of the door todetermine how much paint to buy. The hardware store sells paint by how much coversa square foot. What is the surface area of the garage door? Round your answer to thenearest square foot. (Hint: 1 square foot = 144 square inches) (gridded response)
Answers
The roblem tells us that a door needs to be painted on only one side that measures 6 ft and 10 in height by 30 in wide.
We need to find the area to be painted in order to buy the appropriate quantity of paint. The answer has to be given in square feet at the end.
We start by recalling that the door is represented by a rectangle, and the area of such is given by the height times the wid
Suppose you roll a pair of six-sided dice and add their totals.(a) What is the probability that the sum of the numbers on your dice is 9 or 12?
Answers
We know we're dealing with two dice. Since each die has 6 different possibilities, the outcomes of rolling two dice are given by:
6 × 6, which is 36. This will be our denominator.
How many ways can we get 9 or 12 with two dices?
For a sum of 9:
3 + 6 = 9
4 + 5 = 9
There are two possibilities.
For a sum of 12:
6 + 6 = 12
There is only one possibility.
Summing it up, there are 3 possibilities to get a sum of 9 or 12 with the two dice.
The events are independent events since neither of them can ever occur at the same time.
Thus, the probability will be:
[tex]\text{ Probability = \lparen Probability of getting 9\rparen + \lparen Probability of getting 12\rparen}[/tex]We get,
[tex]\text{ Probability = }\frac{2}{36}\text{ + }\frac{1}{36}\text{ = }\frac{3}{36}\text{ = }\frac{1}{12}\text{ \lparen simplified\rparen}[/tex]Therefore, the probability is 1/12.
Use the formula V=lwh and A=bg to complete the table below by evaluating the expression
Answers
we have that
the formula to calculate the area of a rectangle is equal to
A=L*W
we have
L=8.3 cm
W=4 cm
substitute
A=(8.3)*(4)
A=33.2 cm2
therefore
Formula A=L*W
Expression A=(8.3)*(4)
Solve A=33.2 cm2
Find the slope using the points (2,1) and (7,5). Justify your answer
Answers
a polynomial function has four turning points and two zeros. it’s degree could be ___? select all that apply 4567
Answers
SOLUTION
A polynomial function with real coefficients has four turning points and two zeros could be a degree 6 or any higher even degree because a polynomial with degree n has at most (n - 1) turning points.
So, it cannot be a degree 4.
It cannot be a degree 5 because it has two real zeros, and then three complex roots. A polynomial function with real coefficients cannot have an odd number of complex roots.
Answer:
6
Step-by-step explanation:
edge 23
Consider the function, Find the zeros or x-intercepts of f(x).
Answers
To find the x-intercepts, equate the function with zero as follows:
[tex]\begin{gathered} f(x)=0 \\ -16x^2+25x+10=0 \\ x=\frac{-25\pm\sqrt[]{(25)^2-4\times10\times-16}}{2\times-16} \\ x=\frac{-25\pm\sqrt[]{625+640}}{-32} \\ x=\frac{-25\pm35.5668}{-32} \\ x=-0.3302,1.8927 \end{gathered}[/tex]Hence the intercepts are -0.3302 and 1.8927
The intercepts are at points (-0.3302,0) and (1.8927,0)
Melissa works as a tutor for S12 an hour and as a waitress for S11 an hour. This month, she worked a combined total of 105 hoursat her two jobs.Lett be the number of hours Melissa worked as a tutor this month. Write an expression for the combined total dollar amount sheearned this month.
Answers
From the question
Melissa earns $12 an hour as a tutor
And $11 an hour as a waitress
Also,
This month, she worked a combined total of 105 hours
at her two jobs.
Let t be the number of hours Melissa worked as a tutor this month
Let w be the number of hours Melissa worked as a waitress this month
This implies
[tex]t+w=105[/tex]Since Melissa worked t hours as a tutor this month then
Total money earned as a tutor = $12t
Also,
Since Melissa worked w hours as a waitress this month then
Total money earned as a waitress this month = $11w
Therefore, the total combined earnings for the month is
[tex]\text{ \$12t }+\text{ \$11w}[/tex]a positive integer is nice if there is a positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to . how many numbers in the set are nice?
Answers
Answer:
A positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to The sum of four divisors is equal to 45360.
What is an integer?
Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The inverses of the equivalent positive numbers, which are additive, are the negative numbers. The boldface Z or blackboard bold "Z" is frequently used in mathematical notation to represent a collection of numbers.
Step-by-step explanation:
We know That total No. of factors
=product of (prime no′s power+1)
If N is the number of different divisors:
N=(p1+1)⋅(p2+1)⋅⋅⋅(pn+1)
100= 2^2 × 5^2
=2×2×5×5= (1+1)(1+1)(4+1)(4+1)
Then the integer n= a1^p1⋅a2^p2⋅⋅⋅⋅an^pn
For the smallest value: p1=4,p2=4,p3=1,p4=1
Then,
n=a1^4×a2^4×a3^1×a4^1
=24⋅34⋅51⋅71
=16⋅81⋅5⋅7
=45360
Hence, the positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to The sum of four divisors is equal to 45360.
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Algebra 2 The answer choices are: A. -3 less then or equal to x less then or equal to 6B. -4 less than x less then or greater to 1C. X greater than or equal to 1D. X greater to or equal to 6
Answers
Given:
A graph is given.
Required:
Find the interval of the domain that the graph of exponential function represents.
Explanation:
The graph of the exponential function is given as:
Consider these functions:/(=) =-{=2 + 51g(I) = =2 + 2What is the value of fg(-2))?
Answers
Answer: Provided the two functions, f(x) and g(x), we have to find the composite of these two functions at x = - 2:
[tex]\begin{gathered} f(x)=-\frac{1}{2}x^2+5x \\ \\ g(x)=x^2+2 \end{gathered}[/tex]
The composite function is as follows:
[tex]\begin{gathered} f(g(x))=-\frac{1}{2}(x^2+2)^2+5(x^2+2) \\ \\ \\ f(g(x))=-\frac{1}{2}[x^4+4x^2+4]+5x^2+10 \\ \\ \\ f(g(x))=-\frac{x^4}{2}-2x^2-2+5x^2+10 \\ \\ f(g(x))=-\frac{x^4}{2}-2x^2-2+5x^2+10 \\ \\ \\ f(g(x))=-\frac{x^4}{2}+3x^2+8 \\ \\ \\ f(g(-2))=-\frac{(-2)^4}{2}+3(-2)^2+8 \\ \\ \\ f(g(-2))=-\frac{(-2)^4}{2}+3(-2)^2+8=-8+12+8=12 \\ \\ \\ f(g(-2))=12 \end{gathered}[/tex]The answer is 12.
What is the gcf of 16 and 28
Answers
Answer:
4
Step-by-step explanation:
whic fracción is equivalente to 8/10
Answers
Given data
*The given fraction is 8/10
[tex]\frac{80}{100}=\frac{8}{10}[/tex]80/100 is the fraction equivalent to 8/10
Calculate the value of each expression.
1) (-5)
/
4
2) (-5)-(-/-)
3)-20
4)-20
(-20)
(4)
5)
Answers
Answer:
1) -15/4 or -3.75
2) 15/4 or 3.75
3) 5
4) -5
5) -5
Step-by-step explanation:
Estimate the difference between 7,472 and 3,827 by rounding each number to the nearest hundred.
Answers
Answer:
The difference is aproximately 3700.
Step-by-step explanation:
First, we'll round each number to the nearest hundred:
[tex]\begin{gathered} 7472\rightarrow7500 \\ 3827\rightarrow3800 \end{gathered}[/tex]Now, we can estimate the difference:
[tex]7500-3800=3700[/tex]This way, we can conlcude that the difference is aproximately 3700.