The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4 is ∑∞n=1 (2/3)(-4)ⁿ⁻¹
What are divergent geometric series?The next term in a geometric sequence is produced by multiplying the previous term by the same number across the whole series.
It can be given as,
a+ar+ar²+ar³+...
Here,
is the sequence's (a) initial term, and (r) stands for common ratio.
It should therefore be a series as geometric series diverge.
|r|>1
the first choice is,
3/5+3/10+3/20+3/40+ ...
The common ratio in this case is,
r = (3/10)/(3/5)
r= 1/2
The average ratio is below one. Option an is therefore incorrect.
second option given as,
-10+4-8/4+18/25- ...
Here, the common ratio is,
r = (4/-10)/(-2/5)
r= -2/5
The usual ratio for the second choice is (-2/5), which is below one. This alternative is also incorrect.
The common ratio in option number c is equal to -4. The common ratio's exact value is,
|r|=|-4|
|r|= 4
This common ratio has a greater absolute value than one. This is the best choice as a result.
The absolute value of this series' common ratio, or option number c, represents the geometric series that diverges.
∑∞n=1 (2/3)(-4)ⁿ⁻¹
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All of the following are suggestions of things to do if you have time left after completing the test except:
The correct option is B. Reread the directions for each section.
If you have time left after completing the test don't reread the directions for each section.
What is meant previewing a test?In order to find the various problem kinds and their point values during the test preview, you must read the complete test. Mark the questions that you can answer quickly and easily.
The benefits of previewing the test are-
You will probably be given credit for the answers even if you accidentally copied them from the scratch paper.Your effort on the scratch paper can earn you some points if a thoughtless mistake causes you to get the answer wrong.If you do make a mistake, it will be simpler to find it when the instructor goes through the test. By doing this, you can avoid making the same errors on your next exam.Therefore, resolve each issue by re-entering the solution into the equation or performing the opposing operation needed to provide the appropriate response. Do not leave the testing room until the bell has rung or after you have gone over each problem twice.
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The complete question is-
All of the following are suggestions of things to do if you have time left after completing the test except
A. Look at your answer sheet to make sure its filled properly
B. Reread the directions for each section
C. Return to the questioms you were unsure of
D. Make sure your answers correspond to the correct questions
Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown: A coordinate grid is shown from negative 5 to 0 to 5 on both x -and y-axes. A polygon ABCD has A at ordered pair 1, 3, B at ordered pair 3, 4, C at ordered pair 2, 1, D at ordered pair 1, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 3, 3, B prime at ordered pair negative 5, 4, C prime at ordered pair negative 4, 1, D prime at ordered pair negative 3, 1. Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?
Figure ABCD was translated 2 units to the right so as to obtain figure A'B'C'D'
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.
Figure ABCD was translated 2 units to the right so as to obtain figure A'B'C'D'
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Determine the equation of the parabola graphed below. A parabola is plotted, concave down, with vertex located at coordinates negative three and four.
The equation of parabola from graph is y = a(x + 1)² - 4.
According to the statement
we have to determine the parabola equation from the graphical representation.
So,
For this purpose we know that
Parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.
The general equation of parabola is y = a(x-h)2 + k
And The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
Considering the vertex given, we have that h = -1, k = -4, hence the equation is:
y = a(x + 1)² - 4
So, The equation of parabola from graph is y = a(x + 1)² - 4.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative one and negative four.
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Jeri finds a pile of money with at least $200. If she puts $80 of the pile in her left pocket, gives away 1/3 of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $200 of the original pile and kept the rest. What are the possible values of the number of dollars in the original pile of money? (Give your answer as an interval.)
The possible values of the number of dollars in the original pile of money is on the interval (200, 440)
How to solve Inequality Word Problems?We are told that Jeri finds a pile of money with at least $200.
Now, let x be the additional amount over the original amount of $200.
The greater side of the inequality will be expressed as;
Original pile = (200 + x)
After she gives away $80 and as such she has; (120 + x)
And she gives (1/3) of this away which means she will have;
= (1/3) (120 + x)
Thus, she must have (2/3) of this left
= (2/3)(120 + x) = amount in her right pocket
The lesser side of the inequality is expressed as;
(x + 200) - 200 = x
Thus, we now have that;
2[120 + x ]/3 > x
240 + 2x > 3x
240 > 3x - 2x
240 > x
x < 240
Thus, we can conclude that the original amount could be on the interval (200, 440)
The possible values of the number of dollars in the original pile of money is on the interval (200, 440)
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What is the
y-intercept
of this line?
Answer: (0, 3)
Step-by-step explanation:
The y-intercept of the line is where the line intercepts the y-axis. In other words, the coordinate value of the line when x is 0.
Answer: (3, 0)
Step-by-step explanation:
y-intercept = y=a number and x=0
So, y=3, x=0.
(3, 0)
The scatter plot below represents the amount of dog food a brand recommends based on the weight of the dog.
A
B
Amount of Food per Day (cups)
6
80
no association
negative linear association
● •
20
·
•
6
6
40
60
Weight of Dog (lb)
6
•
80
Which best describes the type of association shown in the scatter plot?
100
The best that describes the type of association shown in the scatter plot is positive linear association.
Given the scatter plot below represents the amount of dog food a brand recommends based on the weight of the dog.
Amount of Food per day cups:
20
40
60
No
We are required to find the type of association shown in the given scatter plot.
It is a positive linear association. The slope is positive so the linear association is also positive and linear mean generally in a line not on a curve like a nonlinear association.
Hence the given graph is of positive linear association.
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How do I solve question 6 through 8?
Solve for me
The equations of the functions are y = -4(x + 1)^2 + 2, y = 2(x - 2)^2 + 1 and y = -(x - 1)^2 - 2
How to determine the functions?A quadratic function is represented as:
y = a(x - h)^2 + k
Question #6
The vertex of the graph is
(h, k) = (-1, 2)
So, we have:
y = a(x + 1)^2 + 2
The graph pass through the f(0) = -2
So, we have:
-2 = a(0 + 1)^2 + 2
Evaluate the like terms
a = -4
Substitute a = -4 in y = a(x + 1)^2 + 2
y = -4(x + 1)^2 + 2
Question #7
The vertex of the graph is
(h, k) = (2, 1)
So, we have:
y = a(x - 2)^2 + 1
The graph pass through (1, 3)
So, we have:
3 = a(1 - 2)^2 + 1
Evaluate the like terms
a = 2
Substitute a = 2 in y = a(x - 2)^2 + 1
y = 2(x - 2)^2 + 1
Question #8
The vertex of the graph is
(h, k) = (1, -2)
So, we have:
y = a(x - 1)^2 - 2
The graph pass through (0, -3)
So, we have:
-3 = a(0 - 1)^2 - 2
Evaluate the like terms
a = -1
Substitute a = -1 in y = a(x - 1)^2 - 2
y = -(x - 1)^2 - 2
Hence, the equations of the functions are y = -4(x + 1)^2 + 2, y = 2(x - 2)^2 + 1 and y = -(x - 1)^2 - 2
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Quick algebra 1 question for some points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
[tex] \frac{y}{x} = \frac{1}{ - 3} \\ - 3y = x[/tex]
[tex] - 3(2) = 6 = x[/tex]
( - 6 , 2 ) Option aPOINTS!!!! PLS HELP LOOK AT PIC
Answer:
first option
Step-by-step explanation:
two solutions means 2 cutting points
10 points
help me, please!!!
Answer:
197.82 m^2
Step-by-step explanation:
The area of a circle is
a = πr^2 The radius is half of the diameter. They give us the diameter so we need to talk half of that number to use for the diameter. The diameter is the length from the center of the circle to the edge of the circle.
We will find the area of the big circle and subtract out the area of the little circle to bind the blue area.
Outer circle
a = πr^2
a = 3.14(12)^2
a = 3.14(144)
a = 452.16
Inner Circle:
a = πr^2
a = 3.14(9)^2
a = 3.14(81)
a =254.34
Lastly, subtract 254.34 from 452.16 to get 197.82
Lie is solving the quadratic equation by completing the square. 3x2 18x – 8 = 0 3x2 18x = 8
Answer: The answer is factor 3 out the variable terms
Step-by-step explanation:
If the probability of a student taking a math class is 0.70, the probability of taking a physics class is 0.30, and the probability of taking a math class and a physics class is 0.15, what is the probability of a student taking a math class or a physics class
The probability of a student taking a math class or a physics class is [tex]0.85[/tex] when the probability of a student taking a math class is [tex]0.70[/tex], the probability of taking a physics class is [tex]0.30[/tex], and the probability of taking a math class and a physics class is [tex]0.15[/tex]
How can we find the probability of taking math class or a physics class ?
Given in the question probability of the student taking class
[tex]p(M)=0.70\\p(P)=0.30\\p( M and P)=0.15[/tex]
So we use the probability union intersection formula
[tex]p(M or P)=p(M)+p(P)-p(M and P)[/tex]
Substitute the values
[tex]p(M or P)=0.7+0.3-0.15\\=0.85[/tex]
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Can someone help me on this pls? It’s urgent, so ASAP (it’s geometry)
Write formal proofs using HL Theorem.
Question 2
1) [tex]\overline{PR} \perp \overline{QS}[/tex], [tex]\overline{PQ} \cong \overline{PS}[/tex] (given)
2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)
3) [tex]\angle PRQ[/tex] and [tex]\angle PRS[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\triangle PRQ[/tex] and [tex]\triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)
5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)
Question 3
1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}[/tex], [tex]\overline{DE} \perp \overline{AB}[/tex] (given)
2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ACD[/tex] and [tex]\triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)
4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)
5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)
6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)
7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)
Your team decides to erect 8 tent frames that can each hold a tarp to provide shade and cover if needed. The area under each tarp is 25 feet wide and 40 feet long, and the top of the tarp will run the length of your seating area. Your tarp needs a slope of to allow runoff in case of rain. The frame will be 10 feet high around the outside. 5. How high does the center of the frame need to be?
The height of the center of the frame has to be 15ft.
How to solve for the height of the frameSlope of the tarp is given as 2/5
The height is said to be 10 feet
The width is given as 25
25/2 = 12.5
AB/BC = 2/5
AB/12.5 = 2/5
cross multiply to find AB
5AB = 25
AB = 5
The height = 10 feet + 5 feet
= 15 feet
Hence the center of the frame has to be 15 feet.
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Our company parking lot has cars, trucks, and motorcycles. The ratio of cars, trucks, and motorcycles is $4:3:2.$ If there are a total of $42$ cars and trucks, then how many motorcycles are there
There are 12 motorcycles in a company.
According to the statement
The ratio of cars, trucks, and motorcycles is 4:3:2.
The total number of cars and trucks is 42.
then
4x + 3x =42
7x = 42
x = 6.
now put these values in the ratio of vehicles.
Number of cars = 4*6 = 24
Number of truck = 3*6 = 18
Number of motorcycle = 2*6 = 12
So, There are 12 motorcycles in a company.
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Find the missing angle.
The missing angle of the right trapezoid is 126°.
Quadrilaterals
There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. The trapezoid is a quadrilateral that presents at least one set of parallel sides and the sum of the internal angles is 360°. The trapezoid classifications are:
Right trapezoid - it presents two right angles.Isosceles trapezoid - it presents the congruent non-parallel sides.Scalene trapezoid - it is one in which the non-parallel sides are not congruent.From the figure, it is possible to see that the image has two right angles. Thus, you have a right trapezoid.
Therefore, from the sum of internal angles, you can find the missing angle:
u+54+90+90=360
u=360-234
u=126
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[tex]\sqrt15-x +\sqrt3-x=6[/tex]
As currently written, solving for [tex]x[/tex], we have
[tex]\sqrt{15} - x + \sqrt3 - x = 6[/tex]
[tex]2x = \sqrt{15} + \sqrt3 - 6[/tex]
[tex]x = \dfrac{\sqrt{15} +\sqrt3 - 6}2[/tex]
I suspect you meant to write
[tex]\sqrt{15 - x} + \sqrt{3 - x} = 6[/tex]
Move one of the roots to the other side, then take squares on both sides.
[tex]\sqrt{15 - x} = 6 - \sqrt{3 - x}[/tex]
[tex]\left(\sqrt{15 - x}\right)^2 = \left(6 - \sqrt{3 - x}\right)^2[/tex]
[tex]15 - x = 36 - 12 \sqrt{3 - x} + (3 - x)[/tex]
[tex]12 \sqrt{3 - x} = 24[/tex]
Take squares again
[tex]\left(12\sqrt{3-x}\right)^2 = 24^2[/tex]
[tex]144 (3 - x) = 576[/tex]
[tex]432 - 144x = 576[/tex]
[tex]144x = -144[/tex]
[tex]\boxed{x = -1}[/tex]
3 quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Mr.Royal, tysm for the help!
#1
h(t)=-16t²+58t+2h(2.5)
-16(2.5)²+58(2.5)+2-16(6.25)+145+2147-10047ftAfter 2.5s the ball was at 47ft
#2
g(x)=x²-9g(0)
-9g(4)
4²-9=16-9=6g(7)
7²-949-940Range
{-9,6,40}#3
f(-3)=5f(0)=0f(1)=-3Arnold paid R2 599,99 for a car sound system in 1997 Assuming an average inflation rate of 7% per annum what did he pay for a sound system with the equivalent value in 2014
The value of the car in 2014 is 154709
How to determine the value?The given parameters are:
Initial, a = 599,99
Rate, r = 7%
The value of the car in t years is
Value = a * (1 + r)^t
This gives
Value = 59999 * (1 + 7%)^t
2014 is 17 years from 1997.
So, we have:
Value = 59999 * (1 + 7%)^14
Evaluate
Value = 154709
Hence, the value of the car in 2014 is 154709
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please help V'W'is a translation of VW Write the translation rule.
Answer:
(x+11), (y+15)
Step-by-step explanation:
the point v gets translated 11 points to the right, so the translation is x+11.
Point v also gets translated 15 points up, so the translation is y+15
Which of the following aquatic organisms is classified as a fish?
whale
jellyfish
octopus
shark
I think the octopus is right but i am not sure !
Answer:
Shark
Step-by-step explanation:
They have gills,scales,swim bladders to float,most produce eggs and also in ectothermic.
======================================================
Further explanation:
Whales are not fish. This is a common misconception many people have (the same goes for dolphins as well). Whales are mammals that don't have gills, which is why they occasionally come to the surface for oxygen. Despite "fish" being literally right in their name, jellyfish aren't fish. It's confusing I know. Jellyfish belong to the phylum Cnidaria, while fish belong to the phylum Chordata. Octopus aren't fish either. They are molluscs and are related to animals like snails, squid, and slugs.Sharks are fish. They have gills and fins like any other fish does.If f is greater than 0 but less than or equal to 90, and cos(22f-1)=sin(7f+4), what is the value of f?
The value of f from the given expression is 3
Sine and cosine functionGiven the expression below
cos(22f-1) = sin(7f+4),
This can also be expressed
cos(22f-1) = cos(90-7f-4)
cos(22f-1) = cos(86-7f)
22f - 1 = 86 - 7f
Collect the like terms
22f+7f = 86 + 1
29f = 87
f = 3
Hence the value of f from the given expression is 3
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you can afford to invest $150 per month in an annuity that earns 4% per year, compounded monthly. How long will it take before your investment is worth $6000?
The time it will take before your investment is worth $6000 = 7 years
Calculation of simple interestThe amount of money invested per month = $150
Therefore the amount principally invested yearly;
= 12 × 150 = $1,800
Simple interest = $6000
Rate = 4%
Time = ?
Using the formula for Simple interest (SI)= P×T×R/100
Make T the subject of formula,
T = SI × 100/P×R
T = $6000×100/1800×4
T = 600000/7200
T= 83 months/ 12 = 7 years
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Am what I’m writing is correct? I put 2+-2=0
The diagram ends at -2
The equation would be 2-4 = -2
Answer:
Step-by-step explanation:
Start on point 2
Ends on point -2
Then:
2 + a = -2
a = -2 - 2
a = -4
then the equation is:
2 + (-4) = 0
2 - 4 = 0
Corresponding Parts Of Congruent Figures Are Congruent
Please Help !!
In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.
Since we know that rigid motions preserve both the side length and angle measure, this ultimately implies that congruent segments have the same (equal) length.
Thus, line segment UV ≅ line segment XY i.e UV = XY and as such the side lengths are as follows:
SU = VX = 43 feet.
For the congruent angles, we have:
<J ≅ <K i.e m<J = m<K
m<S = m<V = 38°.
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area of the ceiling of a room 4 metre high is 48 metre square if the area of four walls of the room is 112 m square calculate the length and breadth of a room.
Answer:
Breadth=8
Length=6
OR
breadth = 6
length=8
Step-by-step explanation:
Area of 4 walls = 2(l+b)h
112=2.4(l+b)
112/8=l+b
14=l+b
l=14-b
Area of base or ceiling=l x b
48=(14-b).b
48=14b-b²
b²-14b+48=0
factorize it and we get
(b-6)(b-8)=0
taking b-6=0
b=6
l=14-6
l=8
Determine the perimeter of the figure.
Answer: 2x + 6y + 22 units
Step-by-step explanation:
The perimeter of a figure is the total length of all the sides of a figure.
Therefore, the perimeter can be found by adding up all the lengths of the figure.
Suppose that P is the perimeter of this figure, then
[tex]P = x+4+x+4+3y+7+7+3y\\[/tex]
Combining like terms, we get
[tex]P = 2x + 6y + 22[/tex]
Since we do not have any information on what the variables are, this is the perimeter of the figure.
I'm having a hard time with this question so someone help please
Answer:
7.7 km
Step-by-step explanation:
This question is asking you to find the third side of a triangle in which two sides and an angle not between them are given. The law of sines provides the necessary relationships.
Law of SinesThe Law of Sines tells you that triangle side lengths are proportional to the sine of the opposite angle. For this triangle TPJ, the relation is ...
t/sin(T) = p/sin(P) = j/sin(J)
We are given T=68°, p=5.2 km, t=7.5 km, and we are asked to find the length of j, the TP distance.
SetupWe know the sum of angles in a triangle is 180°, and the sine of an angle is equal to the sine of its supplement. This lets us fill in the Law of Sines equation like this:
7.5/sin(68°) = 5.2/sin(P) = j/sin(68°+P) . . . . . solve for j
SolutionThis can be solved in two steps. First, we find angle P, then we use that to find length j.
sin(P) = 5.2/7.5 × sin(68°) ≈ 0.642847
P = arcsin(0.642847) ≈ 40.0045°
Now, we can find j:
j = 7.5 × sin(68° +40.0045°)/sin(68°) ≈ 7.693 . . . km
The distance from the tower to the plane is about 7.7 km.
__
Additional comment
We have used T, P, and J to refer to the vertices at the tower, plane, and jet.
The triangle can also be solved using the Law of Cosines. In that case, the missing side will be the solution to a quadratic equation with irrational coefficients.
Which rule describes the translation below? on a coordinate plane, triangle s t u is shifted 3 units down and 5 units to the left to form triangle s prime t prime u prime. (x, y) right-arrow (x minus 5, y minus 3) (x, y) right-arrow (x 5, y 3) (x, y) right-arrow (x minus 3, y minus 5) (x, y) right-arrow (x 3, y 5)
In the figure, angle ZYX is measured in degrees. The area of the shaded sector can be determined using the formula StartFraction measure of angle Z Y X Over 360 degrees EndFraction (pi r squared).
Circle Y is shown. Line segments X Y and Z Y are radii. Sector X Y Z is shaded.
Which best explains the formula?
The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.
The central angle measure of the sector divided by the total angle measure of a circle multiplied by the circumference of the circle will yield the area of the sector.
The central angle measure of the sector multiplied by the area of the circle will yield the area of the sector.
The central angle measure of the sector multiplied by the circumference of the circle will yield the area of the sector.
The best explanation for the formula is: A. The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.
What is the Area of a sector of a Circle?The area of a sector of a circle equals measure of the central angle subtended by the sector over the angle measure of a full circle multiplied by the area of the circle.
A full circle has an angle measure of 360 degrees.
The area of a circle = pi(r²).
Therefore, the formula for the shaded sector of a circle would be represented by the formula: ∅/360 × πr².
Here, we have:
Central angle (∅) = measure of angle ZYX
Measure of full circle = 360 degrees
Area of a circle = πr². (area formula for the circle that contains the sector)
Therefore, the statement that best explains the formula, (m∠ZYX)/360 × πr², used for finding the shaded sector in the circle is: A. The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.
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Answer:
its the first answer "The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector."
Step-by-step explanation: i got it right because im smort