find the indicated sum for each geometric series.Pleaseee someone help I need this before 10 pm. I tried to do it but I keep failing.
Answers
We will have that it is solved as follows:
[tex]\sum ^9_{k=1}256(\frac{1}{2})^{k-1}=256+128+64+32+16+8+4+2+1=511[/tex]***
To solve we replace the values in the formula given:
[tex]S_n=a_1(\frac{1-r^n}{1-r})[/tex]Now, we have to determine the ratio, which is 1/2, and since we want to know the value at n = 9 and the fist value of the series (a1) is 256, we replace it as well:
[tex]S_9=256(\frac{1-(\frac{1}{2})^9}{1-\frac{1}{2}})\Rightarrow S_n=511[/tex]Related Questions
what are the roots of the equation? x^2+24=14×
Answers
Therefore,
[tex]\begin{gathered} x^2-14x+24=0 \\ x^2-2x-12x+24=0 \\ x(x-2)-12(x-2)=0 \\ (x-2)(x-12)=0 \\ x=2 \\ or\text{ } \\ x=12 \end{gathered}[/tex]I just need help with how to turn the table into y=Mx+b and f(x). I know how to graph and find R.
Answers
Solution:
Given the table as shown below:
Using the equation:
[tex]y=mx+b\text{ ---- equation 1}[/tex]When x = 68, y equals 4.1.
Thus, substitute these values into equation 1
[tex]\begin{gathered} 4.1=m(68)+b \\ \Rightarrow68m+b=4.1\text{ ----- equation 2} \end{gathered}[/tex]When x = 71, y equals 4.6.
Similarly, we have
[tex]\begin{gathered} 4.6=m(71)+b \\ \Rightarrow71m+b=4.6\text{ ----- equation 3} \end{gathered}[/tex]From equation 2, make c the subject of the formula.
[tex]\begin{gathered} 68m+c=4.1\text{ } \\ \Rightarrow c=4.1-68m\text{ ---- equation 4} \end{gathered}[/tex]Substitute equation 4 into equation 3. Thus,
[tex]\begin{gathered} 71m+c=4.6\text{ } \\ \Rightarrow71m+(4.1-68m)=4.6 \\ \text{open parentheses} \\ 71m+4.1-68m=4.6 \\ \text{collect lik terms} \\ 71m-68m=4.6-4.1 \\ 3m=0.5 \\ \text{divide both sides by the coefficient of m, which is 3.} \\ \text{thus,} \\ m=\frac{0.5}{3} \\ \Rightarrow m=\frac{1}{6} \end{gathered}[/tex]Substitute the obtained value of m into equation 4.
thus,
[tex]\begin{gathered} c=4.1-68m \\ \text{where m=}\frac{1}{6} \\ \text{thus,} \\ c=4.1-68(\frac{1}{6}) \\ =4.1-11.33 \\ \Rightarrow c=-7.23 \end{gathered}[/tex]Hence, (x,y) Notation y=mx+c
[tex]undefined[/tex]If h(x)=x^2-5x+7, find each value
1. h(2)
2.h(-5)
3.1/3*h(-8)
Please and thanks!
Answers
Answer:
1) 1 2) 32 3) 37
Step-by-step explanation:
1) 2^2-5*2+7 = 1
2) (-5)^2 - 5*(-5) + 7 = 32
3) (-8)^2 - 5*(-8) + 7 = 111 and 111*1/3 = 111/3=37
Identify each pair of angles as corresponding, alternate interior, alternate exterior, or consecutive interior.1)2)3)
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the corresponding angles are in figure 1)
the consecutive interior angles are in figure 4)
the alternate exterior angles are in figure 2)
and there is no figure that is showing an alternate interior angle.
I just need to know the gosh darn answer I know what I’m supposed to be doing here I ughhh I’ve just been working on this problem for literally 8 minutes because I cannot seem to GET IT. Someone help me please
Answers
From the graph
The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry
Hence,
The vertex of the curve is at the point
[tex](3,-2)[/tex]v/w = 9. slove for v
Answers
Solve for v:
Using multiply and divide property of equality
[tex]\begin{gathered} \frac{v}{w}=9 \\ v=9w \end{gathered}[/tex]Six less than three times a number is the same as six times the number. Find the number.
Answers
Three times a number can be written like this:
[tex]3x[/tex]then, 6 less than three times a number is:
[tex]3x-6[/tex]since this expression is the same as six times the number, we have:
[tex]3x-6=6x[/tex]solving for x, we get the following:
[tex]\begin{gathered} 3x-6=6x \\ \Rightarrow-6=6x-3x=3x \\ \Rightarrow x=-\frac{6}{3}=-2 \\ x=-2 \end{gathered}[/tex]therefore, x = -2
I need help in math can you please help me
Answers
In this case the first step is to find the radius of the circle. Use the pythagorean theorem to do this:
[tex]\begin{gathered} r^{}=\sqrt[]{2^2+2^2} \\ r=\sqrt[]{4+4} \\ r=\sqrt[]{8} \\ r^2=8 \end{gathered}[/tex]Now, use the center and the radius to find the equation of the circle
[tex]\begin{gathered} (x-(-2))^2+(y-2)^2=r^2 \\ (x+2)^2+(y-2)^2=8 \end{gathered}[/tex]-16 + x = -30 is -14
Answers
hello
let's solve for x in this question
[tex]-16+x=-30[/tex]collect like terms
to do this, take all variables of x to one side of the equation and the non-variables to the other side
[tex]\begin{gathered} -16+x=-30 \\ x=-30+16 \\ x=-14 \end{gathered}[/tex]x = -14
Three runners are training for a marathon. One day, they all run about ten miles each at their own constant speed.The graph shows how long, in minutes it takes Runner #1 to run d miles The equation relates to Runner #2s distance (in miles) with time (in minutes) is t=8.5dRunner 3s information is in the tableWhich of the three runners has the fastest pace?? (Runner 1, 2 or 3)Explain how you know.
Answers
for runner #1
From the graph, it is clear that runner 1 completes 2 miles in 20 minutes
for runner #2,
t = 8.5 d
put d = 2 miles,
t = 8.5 x 2 = 17 minutes.
so runner 2 completes 2 miles in the 17 minutes,
for runner #3
it is given in the table that,
runner 3 completes 2 miles in 18 minutes,
so, from the above results, it is clear that runner 2 completes 2 miles in less time from others,
thus, runner 2 has the fastest pace.
i have solved your problem in the answer tab.
if you have any doubt with this solution then let me know.
Which of the following must have diagonals that are perpendicular bisectors of each other? Selectall that apply.ParallelogramRectangleRhombusSquareTrapezoid
Answers
SOLUTION
All the quadrilaterals are similar in properties to that of a parallelohram, so the all special cases of paralleligram, Rhombus, Rectangle, and Square
10 The box plots summarize the high temperatures recorded in two different cities. The temperature was recorded for six days. Franklin: Troy: 4 + + 56 58 60 62 64 66 68 70 72 74 High Temperature + 76 78 Which statement best describes the data represented in the box plots? (6.13A, RS, RC4) F For half the days in Franklin, the high temperature was less than 64º. G For half the days in Troy, the high temperature was between 59° and 73°. H The range in high temperatures for Franklin is 18. The interquartile range for Troy is 11.
Answers
Here, we are given a box plot.
Given:
Franklin:
Median = 71
Lower quartile = 66
Upper quartile = 76
Lowest value = 63
Highest value = 77
Troy:
Median = 64
Lower quartile = 62
Upper quartile = 73
Lowest value = 59
Highest value = 77
The range is the difference between the lowest value and the highest value.
In a box plot the interquartile range can be said to be the difference between the lower quartile and the upper quartile.
Let's find the interquartile range for both Franklin and Troy.
Interquartile range:
Franklin = 76 - 66 = 10
Troy = 73 - 62 = 11
The interquartile range for Franklin is 10.
The interquartile range for Troy is 11
Therefore, the statement that best describes the data represented in the box plots is:
The interquartile range for Troy is 11
ANSWER:
J. The interquartile range for Troy is 11
In physics class, Carrie learns that a force, F, is equal to the mass of an object, m, times its acceleration, a. Shewrites the equation F=ma.Using this formula, what is the acceleration of an object with F=7.92 newtons and m=3.6 kilograms?
Answers
Given:
F=7.92 newtons
m=3.6 kilograms
Required:
To find the value of accelaration a.
Explanation:
Since we know that
[tex]F=ma[/tex]Where m= mass
F= force
Now substitute the given values in the formula.
[tex]\begin{gathered} 7.92=3.6\times a \\ a=\frac{7.92}{3.6} \\ a=2.2 \end{gathered}[/tex]Final answer:
Thus the accelaration of the object is the
[tex]2.2\text{ m/sec}^2[/tex]First blank options: does not change or change 2nd blank options: a constant, a decreasing, or an increasing 3rd blank options: can or cannot 4th blank options: is or is not PLEASE do 27 also
Answers
As given by the question
There are given that the graph.
Now,
For finding the linear function, first choose two points from the graph.
Then,
The point is:
[tex](1,\text{ 1) and (2, 2)}[/tex]Then,
Find the slope of the given line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2-1_{}}{2_{}-1_{}} \\ m=\frac{1}{1} \\ m=1 \end{gathered}[/tex]Now,
From the equation of the two-point form:
[tex]y-y_1=m(x-x_1)[/tex]Then,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1_{}=1(x-1_{}) \\ y-1_{}=x-1_{} \\ y-1-x+1=0 \\ y-x=0 \\ y=x \end{gathered}[/tex]hence, the correct answer is yes, the given function is linear.
Find the image of G when AIMG is rotated 180 around the origin,0 (-1,3)(-2,-4)(2,4)0 (2-4)
Answers
We will have that the original point G has coordinates (-2, 4). If we were to rorate the whole shape by 180° and deterine the new coordinates of the point G, we would have that those new coordinates would be:
[tex]G^{\prime}(2,-4)[/tex]When is it better to use the sine function and when is it better to use the cosine function when modeling sinusoids behavior
Answers
A sine function is as shown below
A cosine function is as shown below
The combination of both sine and cosine function is as shown below
It can be observed from the above combination that:
Cosine is better when the maximum is on the y- axis and sine is better if the midline is at the center.
Use slope-intercept form to write an equation of a line passing through the given point and having the given slope. Express the answer in standard form.P(−4, 1); m = 1
Answers
Recall that the slope-intercept form of the equation of a line is as follows:
[tex]\begin{gathered} y=mx+b, \\ where\text{ m is the slope of the line and \lparen0,b\rparen is the y-intercept.} \end{gathered}[/tex]Also, the standard form of the equation of a line is as follows:
[tex]\begin{gathered} Ax+By=C, \\ Where\text{ A, B, and C are integers and A>0.} \end{gathered}[/tex]Then the slope-intercept form of an equation with slope m=1 is as follows:
[tex]y=x+b.[/tex]Now, we know that the line passes through (-4,1), then:
[tex]1=-4+b.[/tex]Adding 4 to the above equation we get:
[tex]\begin{gathered} 1+4=-4+b+4, \\ 5=b. \end{gathered}[/tex]Therefore the slope-intercept form of the equation that passes through (-4,1) and has a slope of m=1 is:
[tex]y=x+5.[/tex]Adding -y-5 to the above equation we get:
[tex]\begin{gathered} y-y-5=x+5-y-5, \\ -5=x-y. \end{gathered}[/tex]Answer:
[tex]x-y=-5.[/tex]Translate the sentence into an equation. Six times the sum of a number and 2 equals 4. Use the variable b for the unknown number.
Answers
Given:-
Six times the sum of a number and 2 equals to 4.
Use the variable b for the unknown number.
So the sentence six times the sum of a number and 2 equals to 4 is,
[tex]6(b+2)=4[/tex]So the translated sentence into equation is 6(b+2)=4.
Convert the rational number below to a decimal. Round tothe nearest hundredth when necessary.911
Answers
Given the rational number below
[tex]\frac{9}{11}[/tex]We will use long division to convert it to decimal
From the above long division, the result is as shown below
[tex]\frac{9}{11}=0.81818\ldots[/tex]It can be observed that the result is a recurring decimal. converting the answer to the nearest hundredth will give us
[tex]\frac{9}{11}=0.81818\ldots\approx0.82(nearest\text{ hundredth)}[/tex]Hence, the conversion to the nearest hundredth gives 0.82
which of the following word problems can be solved using the inequality 9x+18>72, select two that apply A. Kelly already had $18 and will make $9 per hour mowing lawns how many hours X Miskelly work to save at least 72 B. a plant is currently 18 mm tall the plant grows at a rate of 9 mm every week how many weeks X will it take the plant to become taller than 72 mm C. Mackenzie plans on running more than 72 miles she has already ran a 18 miles and we'll run the same number of miles each day for the nine days how many miles X must she run each day in order to meet her goals
Answers
Given inequality : 9x + 18 > 72
A) A. Kelly already had $18 and will make $9 per hour mowing lawns how many hours X Miskelly work to save at least 72
Amount Kelly had + Amount she make in x hours = atleast to save 72
18 + 9x > 72
B) a plant is currently 18 mm tall the plant grows at a rate of 9 mm every week how many weeks X will it take the plant to become taller than 72 mm
Intial height of the plant + Hieght of the tree increase in x weeks = taller than 72mm
18 + 9x > 72
C) Mackenzie plans on running more than 72 miles she has already ran a 18 miles and we'll run the same number of miles each day for the nine days how many miles X must she run each day in order to meet her goals
Initial distance she cover + Distance travel in 9 days to meet the goal of 72
18 + 9x ≥ 72
Answer :
A) A. Kelly already had $18 and will make $9 per hour mowing lawns how many hours X Miskelly work to save at least 72
B) a plant is currently 18 mm tall the plant grows at a rate of 9 mm every week how many weeks X will it take the plant to become taller than 72 mm
How many triangles can be constructed with angles measuring 80º, 80º, and 40º?A noneB oneC more than one
Answers
One triangle can be formed
Looking at the angles, we can see that we have two angles that are equal
What this mean is that at any point in time, there will be two equal sides
Hence, following definition, we have it that the type of triangle that would be formed will be isosceles
Thus, we have one triangle that can be formed
Solve for X in the following inequality:-6x + 3 > -27
Answers
In order to solve the inequality for x, we can do the following steps:
[tex]\begin{gathered} -6x+3>-27\\ \\ -6x>-27-3\\ \\ -6x>-30\\ \\ 6x<30\\ \\ x<\frac{30}{6}\\ \\ x<5 \end{gathered}[/tex]Therefore the solution is x < 5.
The following chart gives values for a function N = N(t). Use averaging to estimate thevalue of N(45).
Answers
We know the value of N(40) and N(50). The average between this two values is:
N(45) = [N(40) + N(50)]/2
N(45) = [52.2 + 53.2]/2
N(45) = 52.7
find an equation for the line that passes through the points (-1,-5) and (-5,1)
Answers
The equation of line between two points is given as:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]plugging the values into the equation we have:
[tex]\begin{gathered} y-(-5)=\frac{1-(-5)}{-5-(-1)}(x-(-1)) \\ y+5=\frac{1+5}{-5+1}(x+1) \\ y+5=\frac{6}{-4}(x+1) \\ y+5=-\frac{6}{4}(x+1) \end{gathered}[/tex]Therefore the equation is:
[tex]y+5=-\frac{3}{2}(x+1)[/tex]I have final exams coming up and I’m trying to study for them but I’m just so confused on what I am doing
Answers
we have that
N 1
g(x)=2^x
For x=1, g(x)=2^1=2
For x=2, g(x)=2^2=4
For x=3, g(x)=2^3=8
so
the sequence is
2,4,8,16,...
N 2
we have
g(x)=2(2^x)
For x=1, g(x)=2(2^1)=4
For x=2, g(x)=2(2^2)=8
For x=3, g(x)=2(2^3)=16
so
the sequence is
4,8,16,32,...
N 3
we have
g(x)=(1/2)^x
For x=1, g(x)=1/2
For x=2, g(x)=1/4
Fr x=3, g(x)=1/8
so
the sequence is
1/2,1/4/1/8,1/16,...
N 4
we have
g(x)=(1/2)(2^x)
For x=1, g(x)=1
For x=2, g(x)=2
For x=3, g(x)=4
For x=4, g(x)=8
the sequence is
1,2,4,8,...
N 5
we have
g(x)=(1/2)(1/2)^x
For x=1, g(x)=1/4
For x=2, g(x)=1/8
For x=3, g(x)=1/16
For x=4, g(x)=1/32
the sequence is
1/4,1/8,1/16,1/32,...
Which of the following options represent the measure of arc ra ?
Answers
Explanation
For the given question, we will have to apply the rule for lines intersecting inside a circle
We will simply apply the rule
[tex]m Where[tex]\begin{gathered} mPK=2\times32.8=65.6^0 \\ mWe can now get the value of the measure of arc RA[tex]\begin{gathered} 71.4^0=\frac{1}{2}(mRA+65.6^0) \\ cross\text{ multiplying} \\ 2\times71.4^0=mRA+65.6 \\ \\ mRA=142.8^0-65.6^0 \\ mRA=77.2^0 \end{gathered}[/tex]Thus, the measure of the arc RA is 77.2 degrees
Option D is correct
how many students are in this survey and how many students do not play instruments?
Answers
Given data:
The number of students who play a sport and instrument are a=23.
The number of students who play a sport but not instrument are b=15.
The number of students who don't play sport but play instrument are c=18.
The number of students who don't play sport and instrument are d=4.
The expression for the total numbers of students are,
n=a+b+c+d
Substitute the given values in the above expression.
n=23+15+18+4
n=60
The expression for the students who donot play an instruments are,
x=b+d
Substitute the given values in the above expression.
x=15+4
=19
Thus, the total numbers of students are 60, and the students who donot play an instruments are 19.
Graph the line that passes through the point (2,-2) and is perpendicular to another line whose slope is -1.
Answers
Graph of the line that passes through the point (2,-2) and is perpendicular to another line whose slope is -1 has been plotted
The slope whose perpendicular to another line = -1
The slope of the main line will be = - (1/-1)
= 1
The line is passing trough the point (2,-2)
The point slope form is
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute the values in the equation
(y-(-2)) = 1(x-2)
y+2 = 1(x-2)
Rearrange the terms and make slope intercept form y = mx + b
y+2 = 1(x-2)
y+2 = x-2
y = x-2-2
y = x-4
Plot the graph using the slope intercept form
Hence, graph of the line that passes through the point (2,-2) and is perpendicular to another line whose slope is -1 has been plotted
Learn more about slope intercept form here
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Does this table represent a proportional relationship?ху0 22446YesNoMaybe
Answers
Answer
NO is the answer.
The table does not represent a proportional relationship.
Explanation
When two quantities x and y are said to be proportional to each other, this is represented by
y ∝ x
Introducing the constant of variation, k, we have
y ∝ x
y = kx
We can then solve for k knowing that for two proportinal quantities, the value of k will remain the same for corresponding values of x and y
x | y
0 | 2
2 | 4
4 | 6
y = kx
when x = 0, y = 2
y = kx
2 = (k) (0)
2 ≠ 0
This first shows that the two quantities aren't proportional
when x = 2, y = 4
y = kx
4 = (k) (2)
2k = 4
k = 2
when x = 4, y = 6
y = kx
6 = (k) (4)
4k = 6
k = (3/2)
The values of k aren't consistent through the values in the table, hence, we cvan see that this data in the table does not represent proportional relationship.
Hope this Helps!!!
let N be the middle number of three consecutive intergers. write and expression for the sum of these intergers
Answers
EXPLANATION
Since the consecutive numbers are numbers in order, the three consecutive numbers are the following:
Sum of three consecutive numbers:
(n-1) + (n) + (n+1)
Removing the parentheses:
n - 1 + n + n + 1 =
Adding like terms:
= 3n
The solution is 3n