Hello there. To solve this question, we'll have to remember some properties about convergence of sequences.
Given the following sequence:
[tex]\mleft\lbrace a_1,a_2,\ldots,a_n\mright\rbrace[/tex]If it is a finite sequence, then it converges to its last term, that is the lim sup (or greatest term of the sequence).
If it is infinite, then the sequence only converges if this limit exists and is equal to zero, that is:
[tex]\lim _{n\rightarrow\infty}a_n=0[/tex]With this, we'll be able to determine whether the following sequence is convergent or not:
[tex]S=\mleft\lbrace8,108,208,308,408\mright\rbrace[/tex]Since it is a finite sequence, we already know it converges.
The lim sup of this sequence is its largest term, in this case, 408, and we write:
[tex]\limsup S=408[/tex]If it was an infinite sequence, on the other hand, we would have to determine the general term a_n and see if the limit is equal to zero.
Notice that there is a pattern between the values: the difference between two consecutive numbers is equal to 100.
In other words, it is an arithmetic progression with ratio equal to 100.
This means that we can use the following formula:
[tex]a_n=a_1+(n-1)\cdot r[/tex]Where a_1 = 8 and r = 100, therefore:
[tex]\begin{gathered} a_n=8+(n-1)\cdot100 \\ a_n=8+100n-100 \\ a_n=100n-92 \end{gathered}[/tex]And taking the limit as it goes to infinity, we have that:
[tex]\lim _{n\to\infty}a_n=\lim _{n\to\infty}100n-92=\infty[/tex]That is, the limit is not zero (not even a real number), so the sequence would not converge.
Question 3Factor the polynomial.16x^2+40x + 25
To factorize the given function you:
You can find if the equation correspond to a perfect square trinomial by knowing that the numbers 16x^2 and 25 are perfect squares (numbers that have a perfect sqare root) and the term 40x is equal to 2 times 4x*5. and 5.
Then,
[tex]\begin{gathered} 16x^2=(4x)^2 \\ 25=5^2 \\ 40x=2(4x)^{}(5) \end{gathered}[/tex]The equation follows the next general form to a perfect square trinomial:
[tex]a^2+2ab+b^2[/tex]Then, you can rewrite the given equation as:
[tex](4x)^2+2(5)(4x)+5^2[/tex]And knowing that:
[tex]a^2+2ab+b^2=(a+b)^2[/tex]You get that the given equation is equal to:
[tex](4x+5)^2[/tex]18 = 9 ( x + 8 ) solve for x
Answer:-6
Step-by-step explanation:
18=9x(n+8) so if "n" = -7 then -6+8 is 2, and 2x9 is 18
what is the value of 8 to the power of minus 3 over 4
The value of the number "8 to the power of minus 3 over 4" is found as -6561/16777216.
What is meant by the term power of a number?The power of a number is the number of multiples of that number. An exponent is a symbol that represents a number's power.When a number is "raised to a second power," it indicates that it has been multiplied together twice. Whenever a number is "raised to the fifth power," it indicates it has been multiplied by five. The reciprocal of the base is used to calculate the value of the number raised to the power of the a negative number.For the given number,
8 to the power of minus 3 over 4 can be written as;
= (-3/8)⁸
Expand the number to the 8th power.
= (-3/8)×(-3/8)× (-3/8)× (-3/8)× (-3/8)× (-3/8)× (-3/8)× (-3/8)
= -6561/16777216
Thus, the value of the number "8 to the power of minus 3 over 4" is found as -6561/16777216.
To know more about power of a number, here
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1, −3 − 4i; degree 3
If -3 - 4i is one of its zeros, -3 +4i is the another one
(x + 3 + 4i)*(x + 3 - 4i) = x^2 + 6x + 25 is the polynomial that contains these zeros.
Therefore, f(x) = (x-1)*(x^2+6x+25)
трана s 11 27-1.5 - 10 720 1 0 - Ayo ys agoga vo Anto 36-18-22 А) tarao utas se terre doүчно y-studio Critical thinking questions ту 25) Write a system of equations with the solution (4, -3).
We have to solve the system:
[tex]\begin{gathered} -\frac{5}{7}-\frac{11}{7}x=-y \\ 2y=7+5x \end{gathered}[/tex]To solve this system by elimination we have to add or substract a linear combination of the second equation from the first equation in order to eliminate one of the variables.
In this case we can multiply the first equation by 2 and add it to the second equation:
[tex]\begin{gathered} -y\cdot2=(-\frac{5}{7}-\frac{11}{7}x)\cdot2 \\ -2y=-\frac{10}{7}-\frac{22}{7}x \end{gathered}[/tex][tex]\begin{gathered} -2y+2y=(-\frac{10}{7}-\frac{22}{7}x)+(7+5x) \\ 0=-\frac{10}{7}-\frac{22}{7}x+7+5x \\ \frac{22}{7}x-5x=7-\frac{10}{7} \\ \frac{22x-5\cdot7x}{7}=\frac{7\cdot7-10}{7} \\ 22x-35x=49-10 \\ -13x=39 \\ x=\frac{39}{-13} \\ x=-3 \end{gathered}[/tex]Now we can use any of the two equations to find y:
[tex]\begin{gathered} -y=-\frac{5}{7}-\frac{11}{7}x \\ y=\frac{5}{7}+\frac{11}{7}(-3) \\ y=\frac{5}{7}-\frac{33}{7} \\ y=-\frac{28}{7} \\ y=-4 \end{gathered}[/tex]Answer: x=-3 and y=-4
Tommy spent $16 on two toys. The cost of each toy was a multiple of $4. What are the possible prices of the toys?
ok
Possible prices
Toy 1 Toy 2 Total Price
$12 $4 $16
$8 $8 $16
$4 $12 $16
These are the possible prices:
I need this answered, it’s from my prep guide I will include a pic of the answer options
Given the graph of the hyperbola:
[tex]\frac{(y+2)^2}{36}-\frac{(x+5)^2}{64}=1[/tex]The general equation of the given hyperbola is:
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]Where (h, k) is the center of the hyperbola
So, by comparing the equations:
Center = (h, k) = (-5, -2)
The hyperbola opens up and down
Since a =
[tex]a=\sqrt[]{36}=6[/tex]The coordinates of the vertices are: (h, k + a ) and (h, k - a)
h = -5, k = -2, a = 6
So, the coordinates are:
[tex](-5,-8),(-5,4)[/tex]The slopes of the asymptotes are:
[tex]\pm\frac{a}{b}=\pm\frac{6}{8}=\pm\frac{3}{4}[/tex]The equation of the asymptotes are:
[tex]\begin{gathered} y-k=\pm\frac{a}{b}(x-h) \\ y+2=\pm\frac{3}{4}(x+5) \end{gathered}[/tex]The 1/48 scale model of the building stood 11 inches high. What was the height of the actual building
SOLUTION
The ratio is 1 : 48. 1 for the model and 48 for real-life measurement of the building. This means for every inch of the model, we multiply by 48 to get the actual or real-life measure.
Therefore the actual height of the building is 11 x 48 = 528 feet
What is the slope to question 1,3,4,5,7
Answer:
The image is blurry, I cannot see it. Maybe take a better pic.
Step-by-step explanation:
HELP ME WITH THIS QUESTION PLEASE 35 POINTS
Answer:
Step-by-step explanation:
Ok:
So this means 3/4 of one big square it is asked to find=75 percent= 75/100=0.75
A train travelling at 20 m/s stops in 40 seconds. What is the acceleration of the train (numeric answers only - no units)
The equation of motion we will use is
[tex]v=u+at[/tex]Where
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
From the problem, we can figure out that the starting velocity, u, is 20. The time, t, is 40. The final velocity, v, will be 0.
Substituting, let's figure out acceleration, a :
[tex]\begin{gathered} v=u+at \\ 0=20+a(40) \\ 0=20+40a \\ 40a=-20 \\ a=-\frac{20}{40} \\ a=-\frac{0.5m}{s^2} \end{gathered}[/tex]The acceleration is negative because it is deceleration.
Tammy runs each lap in 8 minutes. She will run less than 72 minutes today. What are the possible numbers of laps she will run today? Use n for the number of laps she will run today. Write your answer as an inequality solved for n.
Tammy's rate is 8 minutes per lap. If she runs less than 72 minutes, then
[tex]\begin{gathered} 8x<72 \\ x<\frac{72}{8} \\ x<9 \end{gathered}[/tex]Hence, she will run less than 9 laps today.find the equation of a line that passes through (-3,10) and is perpendicular to y=3
Answer:
x = -3
Step-by-step explanation:
The line y = 3 is a horizontal line. So a perpendicular line is a vertical line. The form of the equation for a vertical line is
"x = anumber"
The information we have to work with is the point (-3, 10) A point is in the form (x,y). So we know that x is -3 and y is 10.
We need the x.
x = -3
This is the equation of the vertical line through (-3,10). It is perpendicular to the horizontal line
y = 3.
Answer:
x = -3
Find the antilog of 3.8226
Answer:
6646.6
Step-by-step explanation:
You want the antilog of 3.8226.
AntilogA scientific or graphing calculator, or any spreadsheet can tell you the value of 10 to that power, assuming this is a common log.
10^3.8226 ≈ 6646.6
__
Additional comment
If this is a natural log, then the base is e ≈ 2.718281828459045... instead of 10.
Most calculators have keys dedicated to the antilog functions. (Antilog may be a "2nd" or "Shift" function of a logarithm key.)
The width of a rectangular flower shop is 20 feet less than twice the length The perimeter is more than 70 feet Which inequality can be used to hnd a possible length of the shop in feet?
width (w)= 20 feet less than twice the length = 2x-20
x = length
Perimeter is more than 70 feet
Perimeter = 2w+2x
Replacing:
P= 2 (2x-20)+ 2x
Since the perimeter is more than 70:
2 (2x-20)+ 2x > 70
through (-2,3) and (0,2 )
The slope of the line that passes through the points (x1, y1) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Given that the line passes through (-2,3) and (0,2), then its slope is:
[tex]m=\frac{2-3}{0-(-2)}=-\frac{1}{2}[/tex]The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept
Replacing the point (0, 2) and m = -1/2 into the general equation, we get:
2 = -1/2(0) + b
2 = b
Then, the equation of the line is:
y = -1/2x + 2
Find all values of j for which the quadratic equation has one real solution.6x^2-5x+j=0Write your answer as an equality or inequality in terms of j.
SOLUTION
Given the question in the question tab, the following are the solution steps to solve the problem.
Step 1: Define the conditions for which a quadratic equation will have one real solution.
A quadratic equation has one real solution if the discriminant of the equation equals to zero. This means that:
[tex]\begin{gathered} D=0 \\ D=b^2-4ac=0 \end{gathered}[/tex]Step 2: Write out the quadratic equation given and the parameters
[tex]\begin{gathered} 6x^2-5x+j=0 \\ By\text{ comparisonn with }ax^2+bx+c=0, \\ a=6,b=-5,c=j \end{gathered}[/tex]Step 3: Substitute the values in step 2 in the equation in step 1 to solve for j
[tex]\begin{gathered} D=b^2-4ac=0 \\ (-5^2)-4(6)(j)=0 \\ 25-24j=0 \\ 25=24j \\ j=\frac{25}{24} \end{gathered}[/tex]Hence, the given quadratic equation will have one real solution when the value of j is equal to 25/24
An earthquake near New Zealand measured 4.2 on the Richter scale. I will send a picture of the rest of the question because it won't make sense if a type it here.
They give you the following formula:
R = log(A/Ao)
Where:
R = 4.2
log = Natural log
We need to solve for A, so:
Take the exponential function to both sides:
e^(4.2) = e^log(A/Ao)
66.68 = A/Ao
Multiply both sides by Ao
A = 66.7Ao
Given the equation negative 26 equals y over 13, solve for y.
Answer:
y = -338
Step-by-step explanation:
The equation will be,
→ -26 = y ÷ 13
→ y/13 = -26
Now the value of y will be,
→ y/13 = -26
→ y = -26 × 13
→ [ y = -338 ]
Hence, the value is -338.
siin. The scale used for a model of a kitchen isdimensions of the kitchen?1ft. In the model, the kitchen measures $2in. by 3 in.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Model
1 / 4 in = 1 1/2 ft
dimensions of the kitchen
2 1/2 in by 3 in
Step 02:
[tex]1\text{ }\frac{1}{2}\text{ ft = 1 + }\frac{1}{2}\text{ = }\frac{2+1}{2}=\frac{3}{2}\text{ ft}[/tex][tex]2\text{ }\frac{1}{2}in\text{ = 2 +}\frac{1}{2}\text{ = }\frac{4+1}{2}\text{ =}\frac{5}{2}in[/tex]Step 03:
1 / 4 in = 3 / 2 ft
[tex]\frac{5}{2}in\cdot\text{ }\frac{3\text{ / 2 ft}}{1\text{ /4 in }}\text{ = }\frac{5\text{ }}{2\text{ }}in\cdot\text{ }\frac{3\cdot4\text{ ft}}{2\cdot1\text{ in}}[/tex][tex]\frac{5}{2}in\cdot\text{ }\frac{12ft}{2in}\text{ = }\frac{5\cdot12\text{ }}{2\cdot2}=\text{ }15ft[/tex][tex]3\text{ in }\cdot\text{ }\frac{12ft}{2in}\text{ = }\frac{3\cdot12}{2}=18ft[/tex]The answer is:
b. 15 ft by 18 ft
Which of the following exponential equations is equivalent to the logarithmicequation below?In 6.12 = x
Given:
In 6.12 = x
Required:
To tell which option is correct
Explanation:
[tex]\begin{gathered} in\text{ 6.12=x log}_{a^n}=b\text{ a}^b=n \\ \\ in\text{ 6.12=log}_e6.12=x \\ \\ a=e,b=x,n=6.12 \\ \\ e^x=6.12 \end{gathered}[/tex]Required answer:
Option D
linear equations have expoments other than one on variables
A linear equation has the form:
[tex]\begin{gathered} f(x_1,x_2,\ldots,x_n)=a_0+a_1x_1+a_2x_2+\cdots+a_nx_n \\ \text{where }a_0,a_1,a_2,\ldots,a_n\in\mathfrak{\Re } \end{gathered}[/tex]So, the answer is false. The variables in linear equations could have only exponent 1, and could not multiply between them like x_1*x_2.
Help me answer as soon as possible, thank you!A and B only
Answer:
(a)4
(b)7
Explanation:
Given f(x) and g(x) defined below:
[tex]\begin{gathered} f(x)=\{(3,2),(5,1),(7,4),(9,3),(11,5)\} \\ g(x)=\{(1,3),(2,5),(3,7),(4,9),(5,11)\} \end{gathered}[/tex](a) f(g(3))
[tex]\begin{gathered} g(3)=7 \\ f\lbrack g(3)\rbrack=f(7)=4 \\ \implies f\lbrack g(3)\rbrack=4 \end{gathered}[/tex]The value of f(g(3)) is 4.
(b) (g o f)(9)
[tex]\begin{gathered} (g\circ f)(9)=g\lbrack f(9)\rbrack \\ f(9)=3 \\ g\lbrack f(9)\rbrack=g(3)=7 \\ \implies(g\circ f)(9)=7 \end{gathered}[/tex]The value of (g o f)(9) is 7.
To estimate the percentage of a states voters who support the current governor for reelection, three newspapers each survey a simple random sample of voters. Each paper calculates the percentage of voters in its sample who support the governor and uses that as an estimate for the population parameter. Here are the results:
When doing a sample of this kind, the papers are attempting to determine the actual percentage of voters that will vote a ceirtain way. The most accurate way to do this would be to ask everyone. As they cannot feasibly do this, the paper that asks the most number of people will likely be the most accurate.
The Tribune interviewed the most people at n= 900
Correct option: The Tribune at 73%
Which point is on both lines?с00BDАpoint Cpoint Apoint Bpoint D
Given:
The objective is to find the point that lies on both lines.
Explanation:
In the given figure, point D lies at the intersection of two lines.
So point D acts as a common point for line segment AB and CD.
Thus, point D lies on both lines of the figure.
Hence, point D is the correct answer.
I spend $360 on groceries and $240 on vegetables. what is the ratio of 360 to 240
SOLUTION
A ratio is an ordered pair of numbers a and b, where the raio of a to b is written as a / b where b does not equal 0.
Hence
The ratio of 360 to 240 is given as
[tex]\frac{360}{240}[/tex]reduce to the lowest fraction we have
[tex]\begin{gathered} \frac{360}{240}=\frac{36\times10}{24\times10} \\ \\ \text{divide out the common numbers } \\ \frac{36}{24} \end{gathered}[/tex]Then
[tex]\begin{gathered} \frac{36}{24}=\frac{6\times6}{4\times6}=\frac{6}{4} \\ \text{similarly} \\ \frac{6}{4}=\frac{3\times2}{2\times2}=\frac{3}{2} \end{gathered}[/tex]Hence the ratio of 360 to 240 in the simplest form is 3 to 2
I could use some help to find out Tony’s mistake(s)
To find the shaded area you subtract the area of the triangle from the area of the rectangle:
[tex]A_{shaded}=A_{rec\tan gle}-A_{triangle}[/tex][tex]\begin{gathered} A_{shaded}=w\cdot l-\frac{1}{2}b\cdot h \\ \\ A_{shaded}=(5cm)(11cm)-\frac{1}{2}(5cm)(3cm) \end{gathered}[/tex]Then, Tony's mistake was that he added the areas instead of subtract it.
The shaded are is:
[tex]\begin{gathered} A_{shaded}=55cm^2-\frac{15}{2}cm^2 \\ \\ A_{shaded}=55cm^2-7.5cm^2 \\ \\ A_{shaded}=47.5cm^2 \end{gathered}[/tex]Then, the shaded area is 47.5 square centimetersName Kuta Software - Infinite Algebra 2 Systems of Two Equations Solve each system by graphing. Date 1) y=-3x + 4 y= 3x - 2 2) y=x+2 x=-3
Lets make the graph of our systems of equations:
The blue line correspond to the equation x-y=3 and the red one correspond to 7x-y=-3. The lines intersect at point (-1,-4), then, the solution of the system is (-1,-4).
Determine whether x and y are proportional. Find the constant of proportion.5x=yO ProportionalO Not proportionalConstant of proportionality: k =
Given the equation
[tex]5x=y[/tex]We can rewrite it as:
[tex]y=5x\equiv y=kx[/tex]• It is a proportional equation.
,• The constant of proportionality, k=5
The radioactive substance uranium240 has a halflife of 14 hoursThe amount of a sample of uranium-240 remaining (in grams) after hours is given by the following exponential function A(i) = 3900 * (1/2) ^ (1/14)
GIVEN:
We are given the function that models the decay of the substance uranium-240.
[tex]A(t)=3900(\frac{1}{2})^{\frac{t}{14}}[/tex]Required;
Find the initial amount in the sample
Find the amount remaining after 50 hours.
Step-by-step solution;
What we have here is an exponential function with the variable t denoting the number of hours and A(t) denotes the population after t hours.
To determine the initial amount in the sample, we take t = 0 and solve as follows;
[tex]\begin{gathered} A(0)=3900(\frac{1}{2})^{\frac{0}{14}} \\ \\ A(0)=3900(\frac{1}{2})^0 \\ \\ A(0)=3900\times1 \\ \\ A(0)=3900 \end{gathered}[/tex]To find the amount remaining after 50 hours;
[tex]\begin{gathered} A(50)=3900(\frac{1}{2})^{\frac{50}{14}} \\ \\ A(05)=3900(\frac{1}{2})^{3.57142857143} \\ A(50)=3900\times0.0841187620394 \\ \\ A(50)=328.063171954 \\ \end{gathered}[/tex]Rounded to the nearest gram we now have;
[tex]A(50)=328gms[/tex]Therefore,
ANSWER:
Initial amount in the sample = 3900 grams
Amount after 50 hours = 328 grams