Mathematics High School

Which of the following situations models a geometric sequence? Select all that apply.

Answers

Answer 1

Answer:

Options 1, 3, 4.

Step-by-step explanation:

We will check each and every option given here.

1) Amount of cell phone users increases by 33% every year.

Its a geometric sequence because the number of users are increasing exponentially every year.

2) Amount of cakes in bake sale increases by 3 each year the fundraiser is held.

amount of cakes is increasing with a common difference of 3 so it's an arithmetic sequence.

3).Uranium loses half of its weight every 415 years.

Exponential decay in every 415 years. So geometric sequence with a common ratio of 1/2.

4).A family of rabbits doubles in size every 3 months.

Exponential series again so geometric sequence with a common ratio of 2.

5).Car drives at a constant speed of 58 mph.

Its a linear function representing an arithmetic sequence with a common difference of 58 mph.

6). Number of students increases by 122 every year.

An arithmetic sequence with a common difference of 122.

7). Number of pieces of chalk in a class room decreases by 10 throughout the school year.

It's an arithmetic sequence having common difference of 10.

Answer 2

Amount of cell phone users increase by 33% every year. Uranium loses half of its weight every 415 years. A family of rabbits doubles in size every 3 months. Then the correct options are A, C, and D.

What is a geometric sequence and how to find its nth terms?

Suppose the initial term of a geometric sequence is a and the term by which we multiply the previous term to get the next term is r.

Then the sequence would look like

a, ar, ar², ar³,..... (till the terms to which it is defined)

Amount of cell phone users increase by 33% every year.

It's a geometric sequence because the number of users is increasing exponentially every year.

Uranium loses half of its weight every 415 years.

Exponential decay every 415 years. So geometric sequence with a common ratio of 1/2.

A family of rabbits doubles in size every 3 months.

Exponential series again so geometric sequence with a common ratio of 2.

Then the correct options are A, C, and D.

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Related Questions

Given: line segment AB is 10 inches long. Find the length of A'B' if AB is dilated to form A'B' with a scale factor of 1 2 . A) 1 2 inches B) 5 inches C) 10 inches D) 20 inches

Answers

ANSWER

[tex]|A'B'| = 5 \: units[/tex]

EXPLANATION

The formula for calculating the scale factor is

[tex]k = \frac{image \: length}{object \: length} [/tex]
Or

[tex]k = \frac{ |A'B'| }{ |AB|} [/tex]

Where k is the scale factor.

We were given
[tex] |A'B'|=10[/tex]

This is the image length.

We substitute the scale factor and the image length in to the formula to get,

[tex] \frac{1}{2} = \frac{ |A'B'| }{ 10} [/tex]
Multiply both sides by 10 to get,

[tex] \frac{1}{2}\times 10= |A'B'|[/tex]

[tex]|A'B'| = 5 \: units[/tex]

Answer:

Option (b) is correct.

The length of A'B' is 5 inches.

Step-by-step explanation:

Given : line segment AB is 10 inches long. AB is dilated to form A'B' with a scale factor of [tex]\frac{1}{2}[/tex]

we have to find the length of A'B'

Dilation of a figure is the increase or decrease in the length of the figure by a fixed scaling factor. if scaling factor is greater than 1 , then figure size increases, and if scaling factor is less than 1 , then figure size decreases.

Here, scaling factor is [tex]\frac{1}{2}[/tex] which less than 1 , so line segment A'B' decreases.

New image = scaling factor × original image

that is A'B' = [tex]\frac{1}{2}\times 10=5[/tex]

Thus, the length of A'B' is 5 inches.

Option (b) is correct.

$394.63781 Round to the nearest dollar

Answers

Hello,

Here is your answer:

The proper answer to your question is "$390.00

Here is how:

394.63781=$390

Your answer is $390!

If you need anymore help feel free to ask me!

Hope this helps!

$395 would be your answer
.6 is higher than .4 so the dollar amount would go up one.
hope this helps

can you please help me thank you you will be given brainley

Answers

Vertex W corresponds to vertex Z; V corresponds to V, and Y corresponds to Y. Hence
ΔZVY ≅ ΔWVY . . . . . . corresponds to the 2nd selection

FAST HELP!! 30 POINTS!!!

what type of solutions do the methods for solving systems of equations find and how does this relate to setting the equations equal to each other

Answers

substitution method and elimination method. And how does it relate to setting equal to each other? It's where the two graphs intersect is where they have in common

Final answer:

Explanation of solutions for systems of equations and how setting equations equal to each other helps find solutions.

Explanation:

Solutions for systems of equations can be classified as unique, no solution, or infinitely many solutions. The method of setting equations equal to each other typically helps find the intersection points where the equations are simultaneously true, representing the solution to the system.

Item 14
POSSIBLE POINTS: 5
The total cost of repairing a car is the sum of the amount paid for parts and the amount paid for labor. You paid $132 for parts and $65 for each hour of labor. The total cost to repair the car was $229.50. How many hours did it take to repair the car?

Which equation best models this problem? Let x = number of hours worked

229.5 – 65 = 132x

132x + 65 = 229.5

132 + 65x = 229.5

132 + 65 = 229.50x

Answers

Lets work out the problem from the beginning. Let [tex]x[/tex] be the number of hours worked. We know that you paid $65 for each hour, and remember that the numbers of hours worked is [tex]x[/tex], so you paid for those hours [tex]65x[/tex]. We also know that you paid $132 for parts, a total cost of $229.5, so:
parts + worked hours = total cost
[tex]132+65x=229.5[/tex]
And now that we have our equation from the model, lets solve for [tex]x[/tex] to find how many hours took to the repair the car:
[tex]65x=229.5-132[/tex]
[tex]65x=97.5[/tex]
[tex]x= \frac{97.5}{65} [/tex]
[tex]x=1.5[/tex]

We can conclude that it took 1 and a half hour to repair the car.

If you were offered a job would you choose the one with the pay increase according to an arithmetic sequence formula or a geometric sequence formula? Justify your response.

Answers

I believe it would be the one with the Geometric sequence formula

Final answer:

For maximizing earning potential over time, a geometric sequence salary increase is typically more beneficial due to exponential growth, while an arithmetic sequence offers steady, predictable increases that may appeal to those who value consistency.

Explanation:

If offered a job with a salary increase tied to either an arithmetic sequence or a geometric sequence, the preferable option typically depends on the long-term financial goals and growth potential you are looking for. An arithmetic sequence will give you steady, predictable increases. However, a geometric sequence formula will often result in larger increases over time, especially if the ratio is 2 or more. Due to the exponential nature of a geometric sequence, your salary could grow significantly faster than with an arithmetic sequence. For example, if you start with a salary of $50,000, and the arithmetic sequence increase is $1,000 each year, after five years you would be earning $55,000. On the other hand, for a geometric sequence with a modest ratio of 1.05 (5% increase each year), you would start at the same $50,000 but after five years be earning approximately $63,814.

Considering this, if your primary goal is to maximize earning potential over time, the geometric sequence would be the more appealing option. However, if you value consistency and predictability in pay increases, or if the progression starts very low, an arithmetic sequence might be more in line with your personal financial planning.

What’s the answer to this problem???

Answers

rewrite the equation into slope intercept form:
8y = -5x+16

divide everything by 8 to get just y
y = -5/8x+2

the slope = -5/8

look at the picture below // 99 points // PLEASEE HELPP

Answers

It would be D right? Because they are obviously congruent, parallel and the same length. Just an educated guess..

Is given that the figure on the problem is a square, and we know that the square's sides are congruent or have the same length.

•The correct answer is letter D, Yes, the opposite sides are parallel, and all sides are the same length.

The temperature, T , of a given mass of gas varies inversely with its volume, V . The temperature of a certain gas with volume of 105 cm 3 is 30º C. What will be the temperature of the gas when it is compressed to a volume of 84 cm 3? 18.8º C 48º C 24º C 37.5º C

Answers

we know that

if the temperature T of a given mass of gas varies inversely with its volume V
then
T=k/V

Step 1
Find the value of k
for T=30º C and V=105 cm³
we have
T=k/V--------> k=T*V--------> k=30*105=3150 °C*cm³

therefore
for V=84 cm³
T=3150/84=37.5 °C

the answer is 37.5 °C

Final answer:

The temperature of a gas can be calculated using the formula for inverse variation, which is T1*V1 = T2*V2. By substituting the given values into the formula, we can find that the temperature of the gas when it is compressed to a volume of 84 cm^3 is 37.5ºC.

Explanation:

To solve this problem, we can use the formula for inverse variation:

T1*V1 = T2*V2

Given that T1 = 30ºC, V1 = 105 cm^3, and V2 = 84 cm^3, we can solve for T2:

T2 = (T1*V1)/V2 = (30*105)/84 = 37.5ºC

Therefore, the temperature of the gas when it is compressed to a volume of 84 cm^3 will be 37.5ºC.

PLEASE HURRY
Line segment CT contains the point C(−2, 5) and a midpoint at A(1, −3). What is the location of endpoint T? T(4, −11) T(3, −8) T(5, −1) T(−0.5, 1)

Answers

Point A is the midpoint of CT which means the ratio of CA:CT would be 1:2.
To find CT, you need to find the distance of CA then applies 2 times of the distance to the point C

Xca= Xa-Xc= 1- (-2)= 3
Yca= Ya- Yc= -3 -5= -8

Xt= Xc + 2* Xca= -2 + 2*3= 4
Yt= Yc + 2* Yca= 5 + 2*-8= -11
T(Xt, Yt)= T(4, -11)

The coordinate for point T would be (4, -11)

How to tell if a scatter plot is positive or negative or no ttend?

Answers

If the dots are going to the right, it's positive. If they're going to the left, they're negative.

And if the dots are both sides, there is no trend.

Use the clues to find the mystery number.
It is greater than 37,493.
It is less than 37,503.
It is an even number.
The value of the mystery number rounded to the nearest ten is less than the mystery number.
The value of the mystery number rounded to the nearest thousand is greater than the mystery number.

The mystery number is

Answers

the number is 37,500

Why are epidemics and pandemics a relatively recent phenomenon in human history?

Answers

For the greater part of man's opportunity on earth, populaces were little, scattered, and subordinate after chasing and assembling. Those infectious diseases that influenced people were either the consequence of unplanned contamination by zoonoses or lethargic contaminations that maybe had developed with people from their primate precursors. It was just because of the rural upheaval 6,000 to 8,000 years back and the resulting development of inactive populaces sufficiently substantial to help microorganisms particularly subordinate upon human has that epidemics and pandemics seem to have moved toward becoming piece of man's life (Cockburn 1963)

.help thanks please :)

Answers

the first one, bc=ef

The tables below show two functions. For each set of data:
a) Determine whether the data represents a linear function, exponential function or neither and explain why.
x f(x)
-2 18
-1 22
0 26
1 30
2 34
x g(x)
-2 2
-1 4
0 8
1 16
2 32

Rubric:
Points Concept Addressed
/2 Correctly determines whether each table represents linear, exponential or neither
/2 Correctly explains their answer.

Answers

The first table, representing f(x), is linear. The data have a constant rate of change or slope:
(between the first two points): m = (y₂ - y₁)/(x₂ - x₁) = (22-18)/(-1--2) = 4/(-1+2) = 4/1 = 4. The rate of change between any two points is the same:
(between the last two points): m = (34-30)/(2-1) = 4/1 = 4.

The second table, representing g(x), is exponential. The data points are multiplied by the same constant between successive points. 2*2 = 4; 4*2= 8; 8*2 = 16, etc.

A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of the enclosed area.

What is the maximum area that can be enclosed by the fencing?

Enter your answer in the box.

ft²

Answers

Let
y------> the length of the rectangle
x-----> the width of the rectangle

we know that
perimeter of the rectangle=2*[x+y]

Since the barn is used as one of the sides (let's say y) we can subtract y
we don't need fencing for this side
That makes the perimeter 2x + y
Since we have 300 feet of fencing
we set these equal:
2x + y = 300-------> y=(300-2x)------> equation 1

area of the rectangle=x*y
substitute the equation 1 in the area formula
Area=[(300-2x)]*x-----> Area=(-2x²)+300x

This is a quadratic equation
Since the leading coefficient is negative (-2) we know it opens downward
We are looking for the x-coordinate of the highest point called the vertex

using a graph tool
see the attached figure

the vertex is the point (75,11250)
that means for x=75 (width of the rectangle)

the area is 11250 ft²

the answer is
the maximum area that can be enclosed by the fencing is 11250 ft²

Answer:

The Answer is 11250 ft~

Step-by-step explanation:

I did the test and got it correct

What is the length of the base of a right triangle with an area of 20 m² and a height of 4 m? A.5 m B.10 m C.80 m D.160 m

Answers

to find the length, follow the equation l(w) = a

l or b = length or base
w or h = width or height
a = area

b x h = a
b x (4) = 20
4b = 20
4b/.4 = 20/4
b = 20/4
b = 5

A. 5m is your answer

hope this helps

El Generico public high school got a new flagpole. But they completely forgot to buy a cord and NO ONE knows how tall the flagpole is! To find out, they decided to use similar figures! As the sun was setting, Bob the janitor set up a 5-foot stick next to the flagpole and compared shadows. The 5-foot stick cast an 8-foot shadow. The shadow of the flagpole was 32-feet long.

Use rules of similar polygons to figure out how tall the flagpole is!

Answers

According to the rule of similar polygons the ratio of corresponding sides of two polygons will be the same. So in this case the ratio of original length and shadow of a stick and ratio of length of flagpole and its shadow will be the same.

Length of Stick = 5 feet
Shadow of Stick = 8 feet
Shadow of flagpole = 32 feet
Length of flagpole = x = ?

Using rule of similar polygon we can write,

[tex] \frac{5}{8}= \frac{x}{32} \\ \\ \frac{5}{8}*32=x \\ \\ x=20 [/tex]

Therefore, the length of flagpole will be 20 feet.

Factor this expression completely and then place the factors in the proper location on the grid. Note:
Place factors alphabetically in the grid! mn - 4 m - 5 n + 20

Answers

First we are going to group the terms that contains the common factor [tex]m[/tex] in one parenthesis, and the other ones in another parenthesis:
[tex]mn-4m-5n+20[/tex]
[tex](mn-4m)-(5n+20)[/tex]
Notice that our the terms in our first parenthesis have a common factor [tex]m[/tex], and the terms in our second one have the common factor [tex]5[/tex]. Lets factor those out:
[tex]m(n-4)-5(n-4)[/tex]
Now we have a common factor [tex](n-4)[/tex] in both terms, so we can factor those out as well:
[tex](n-4)(m-5)[/tex]

We can conclude that the completely factored expression ordered alphabetically is [tex](m-5)(n-4)[/tex].

the area of a trapezoid is 72.8 square feet. the length of one of its bases is 7.4 feet and the length of its other base is 10.8 feet. what is the height of the trapezoid?

Answers

[tex]\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}\quad \begin{cases} a,b=\stackrel{parallel~sides}{bases}\\ h=height\\ --------\\ A=72.8\\ a=7.4\\ b=10.8 \end{cases}\implies 72.8=\cfrac{h(7.4+10.8)}{2} \\\\\\ 72.8=\cfrac{18.2h}{2}\implies \cfrac{72.8\cdot 2}{18.2}=h[/tex]

Quadrilateral ABCD is inscribed in this circle. What is the measure of angle C? Enter your answer in the box.

Answers

Answer:

[tex]m<C=62\°[/tex]

Step-by-step explanation:

we know that

In an inscribed quadrilateral opposite angles are supplementary

In this problem

[tex]m<D+m<B=180\°[/tex]

[tex]m<C+m<A=180\°[/tex]

step 1

Find the value of x

[tex]m<D+m<B=180\°[/tex]

substitute the values and solve for x

[tex](x+20)\°+(3x)\°=180\°[/tex]

[tex]4x=180\°-20\°[/tex]

[tex]x=160\°/4=40\°[/tex]

step 2

Find the measure of angle A

[tex]m<A=(2x+38)\°=2(40\°)+38\°=118\°[/tex]

step 3

Find the measure of angle C

[tex]m<C+m<A=180\°[/tex]

substitute the values and solve for m<C

[tex]m<C+118\°=180\°[/tex]

[tex]m<C=180\°-118\°=62\°[/tex]

Rowan raised $640 In a charity walk last year.this year he raised 15% more than he raised last year. How much money did Rowan raise this year?

Answers

Compute 115% of $640

1.15 × $640 = $736

helpppppppppppppppppppp

Answers

What you must do for this case is to rewrite the expression carefully to find the correct answer.
You must respect the subtraction of fractions.
Group the terms correctly.
Factor when necessary.
Answer
option 1
See attached graph.

True or false All equilateral triangles are isosceles

Answers

Answer:

TRUE

Step-by-step explanation:

When all sides are the same length, at least one pair of sides is the same length.

Answer:

the answer is true

Step-by-step explanation:

Evaluate the expression Arcsec(sqrt 2). Do not use your calculator to answer this question. Do not express answer in decimals.

Answers

pi/4 radians
You're looking for the angle that has a secant of sqrt(2). And since the secant is simply the reciprocal of the cosine, let's take a look at that.
sqrt(2) = 1/x
x*sqrt(2) = 1
x = 1/sqrt(2)
Let's multiply both numerator and denominator by sqrt(2), so
x = sqrt(2)/2
And the value sqrt(2)/2 should be immediately obvious to you as a trig identity. Namely, that's the cosine of a 45 degree angle. Now for the issue of how to actually give you your answer. There's no need for decimals to express 45 degrees, so that caveat in the question doesn't make any sense unless you're measuring angles in radians. So let's convert 45 degrees to radians. A full circle has 360 degrees, or 2*pi radians. So:
45 * (2*pi)/360 = 90*pi/360 = pi/4
So your answer is pi/4 radians.

helppppppppppppppppppppppppppppppp

Answers

We write the expression:
((2 ^ (1/2)) * (2 ^ (3/4))) ^ 2
We use for this case the properties of lso exponents:
((2 ^ (1/2)) * (2 ^ (3/4))) ^ 2
((2 ^ (2/2)) * (2 ^ (6/4)))
((2 ^ (1)) * (2 ^ (3/2)))
((2 ^ (1 + 3/2))
((2 ^ (5/2))
answer:
((2 ^ (5/2))
option 2

Simplify the ratio 30 ml: 45 ml

Answers

In order to simplify a ratio you divide the two number with the greatest common factor(GCF).

In the ratio 30 ml :45 ml the GCF is 15
making the simplified ratio to be 2 ml:3 ml

The speed of an object in space is shown in the graph.

What is the slope of the line?
10
15
20
25

Answers

(6-3)/(0.4-0.2)
= 15

the slope of the line = 15
the answer is B.

Answer:

Option B is correct

Step-by-step explanation:

Formula for slope is given by:

[tex]\text{Slope} = \frac{y_2-y_1}{x_2-x_1}[/tex]

As per the statement:

Form the graph:

Consider two points:

(0.2, 3) and (0.4, 6)

then;

[tex]\text{Slope} = \frac{6-3}{0.4-0.2}[/tex]

⇒[tex]\text{Slope} = \frac{3}{0.2}[/tex]

⇒[tex]\text{Slope}= 15[/tex]

Therefore, the slope of the line is, 15

Monica wants to measure the dimensions of her rectangular lawn. If the longer side of the lawn is (x + 3) feet and the diagonal length is (x + 4) feet, which function can be used to find the shorter side of her lawn?
a.] [tex]s(x)= \sqrt{2x+7} [/tex]
b.] [tex]s(x)= \sqrt{2 x^{2} +14x+25} [/tex]
c.] [tex]s(x)= \sqrt{x^{2} +7x+12} [/tex]
d.] [tex]s(x)= {x^{2} +7x+12} [/tex]

Answers

the answer is the option A

let
y--------------- > short side
applying the Pythagorean theorem
(x+4)²=y²+(x+3)²
y²=(x+4)²-(x+3)²-------> x²+8x+16-x²-6x-9=2x+7
y=√(2x+7)

Let us try and solve it analytically. We have that the side=x+3 together with the short side=s and the diagonal=x+4 satisfy the Pythagorean Theorem. Then we have that [tex](x+4)^2=(x+3)^2+s^2[/tex]. This yields [tex]s^2+x^2+6x+9=x^2+8x+16[/tex]
which yields s^2=2x+7, hence a) is the correct answer.

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Please describe in detail using your vocabulary terms, directions, and the number of steps to explain how the pre-image became the image in this picture. Type your answer in a word document and upload it to this dropbox for me to grade. (5 pts)

Answers

From the pre-image, the pentagon is reflected across the Y axis. From the second pentagon that was reflected across the Y axis is another reflection across the X axis.

A reflection across an axis is when the image is flipped over that axis that is mentioned. This is happening two times starting with the original. First it crosses the Y axis which will be flipping it to the left. The X values in the original ordered pair would all be the opposite of the original.

Then it is reflected across the X axis which would be flipping it down. This time the y values end of the ordered pair would all be the opposite from the previous figure.

Final answer:

The pre-image becomes the image in a picture through transformations such as translation, rotation, reflection, or dilation.

Explanation:

The pre-image is the original figure before any transformations. The image is the new figure after a transformation has been applied to the pre-image. In this picture, the pre-image became the image through translation, rotation, reflection, or dilation.

Translation: The pre-image is moved in a specific direction without changing its shape or size.Rotation: The pre-image is turned around a fixed point by a certain angle.Reflection: The pre-image is flipped across a line to create the image.Dilation: The pre-image is either enlarged or reduced in size.

By applying one or more of these transformations to the pre-image, it can become the image in the picture.

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