Answers
28/3 = 9.3333
The pen will be 9.3333 by 9.3333 meters
Related Questions
Describe the graph of the function at its roots.
f(x) = (x − 2)3(x + 6)2(x + 12)
At x = 2, the graph the x–axis.
A) Crosses
B) Touches
Answers
answers:
Describe the graph of the function at its roots.
f(x) = (x − 2)3(x + 6)2(x + 12)
At x = 2, the graph crosses the x–axis.
At x = −6, the graph touches the x–axis.
At x = −12, the graph crosses the x–axis.
The required solution of the given function, at x = 2 the graph crosses the x-axis.
Given that,
The graph of the function at its roots. f(x) = (x − 2)³(x + 6)²(x + 12)
To discuss At x = 2, the graph is the x-axis.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
The graph of the given function f(x) = (x − 2)³(x + 6)²(x + 12) is show,
From the graph, it is found that at x = 2, the graph passes through the x-axis.
Thus, the required solution of the given function, at x = 2 the graph crosses the x-axis.
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PLEASE help will mark brainliest algebra 2 . ... show your work
Answers
3x - 6= x + 4 .................distributive property
2x - 6 = 4 ......................addition property of equality
2x = 10 .........................addition property of equality
x = 5 ..............................division property of equality
In the diagram, KL = , LM = , and MN = . What is the perimeter of isosceles trapezoid KLMN? units units + units + units
Answers
The Perimeter of the isosceles trapezoid KLMN given the dimensions is;
3√2 + 2√5
How to find the Perimeter of a Quadrilateral?We re given the lengths of the isosceles trapezoid KLMN as;
KL = 2√2; LM = √5; MN = √2
We don't have the length of KN but we have the coordinates as;
K(-2, -4) and N(-1, -2)
Length of KN = √[(-2 - (-4))² + (-1 - (-2))]
Length of KN = √5
Thus;
Perimeter = 2√2 + √5 + √2 + √5
Perimeter = 3√2 + 2√5
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Solve.
x² + 4x + 4 = 18
A x=−4±3√ 2
B x=2±3√ 2
C x=4±9√ 2
D x=−2±3√2
Answers
x² + 4x + 4 = 18
A x=−4±3√ 2
B x=2±3√ 2
C x=4±9√ 2
D x=−2±3√2
[tex]x^2 + 4x + 4 = 18 \\ \\ x^2+4x+4-18= 0 \\ \\ x^2+4x-14=0 \\ \\ x_1_y_2= \dfrac{-b\pm \sqrt{b^2-4ac} }{2a} \qquad a= 1\qquad b= 4\qquad c= -14 \\ \\ \\ x_1_y_2= \dfrac{-4\pm \sqrt{4^2-4(1)(-14)} }{2(1)} \\ \\ \\ x_1_y_2= \dfrac{-4\pm \sqrt{16-(-56)} }{2} \\ \\ \\ x_1_y_2= \dfrac{-4\pm \sqrt{72} }{2} \\ \\ \\ x_1= \dfrac{-4+ \sqrt{72} }{2} \qquad\qquad x_2= \dfrac{-4+ \sqrt{72} }{2}\\ \\ \\ x_1= \dfrac{-4+ \sqrt{2^3*3^2} }{2} \qquad\qquad x_2= \dfrac{-4- \sqrt{2^3*3^2} }{2}[/tex]
[tex] x_1= \dfrac{-4+2*3 \sqrt{2} }{2} \qquad\qquad x_2= \dfrac{-4- 2*3\sqrt{2} }{2} \\ \\ \\ x_1= \dfrac{-4+6 \sqrt{2} }{2} \qquad\qquad x_2= \dfrac{-4- 6\sqrt{2} }{2} \\ \\ \\ x_1= \dfrac{-4}{2} + \dfrac{6 \sqrt{2} }{2} \qquad\qquad x_2= \dfrac{-4}{2}- \dfrac{ 6\sqrt{2} }{2} \\ \\ \\ x_1= -2 + 3 \sqrt{2} \qquad\qquad\quad x_2= -2- 3\sqrt{2} \\ \\ \\ \boxed{x= -2\pm 3\sqrt{2} } \to D) [/tex]
This was the correct answer, I even provided proof from my own test. Hope this helps!
The perimeter of an airplane ticket is 32 centimeters. The area is 60 square centimeters. What are the dimensions of the ticket
Answers
For this case what you should know is that the perimeter of the rectangle is given by:
P = 2w + 2l
The area of the rectangle is given by:
A = w * l
In both cases:
w: width
l: long
We have the following system of equations:
32 = 2w + 2l
60 = w * l
Solving the system we obtain:
The dimensions of the ticket are:
(10 cm) * (6 cm)
Answer:
the dimensions of the ticket are:
(10 cm) * (6 cm)
Note: see attached image for system solution
Find the value of x. Round the answer to the nearest tenth, if needed.
A.
5.3
B.
15.9
C.
31.7
D.
48.1
Answers
(4) Check my work please?
Answers
x/3 = 3/4
x*4 = 3*3
4x = 9
x = 9/4
AC = AD+DC
AC = 4+x
AC = 4+9/4
AC = 16/4 + 9/4
AC = 25/4
AB^2 + BC^2 = AC^2
5^2 + y^2 = (25/4)^2
25 + y^2 = 625/16
y^2 = 625/16 - 25
y^2 = 625/16 - 400/16
y^2 = 225/16
y = sqrt(225/16)
y = 15/4
A bag has a 6 dice and an 8 dice, a dice is picked at random. find the probability that a number 3 will be rolled.
Answers
hope this helps.
You bought 8 gumdrops for 2¢ apiece. For the same amount of money, how many gumdrops can you buy at 8¢ apiece? gumdrops
Answers
You can buy 32 gumdrops at 8¢ apiece for the same amount of money as buying 8 gumdrops at 2¢ apiece.
Explanation:To find out how many gumdrops you can buy at 8¢ apiece for the same amount of money as buying 8 gumdrops at 2¢ apiece, you need to compare the prices and calculate the equivalent quantity. Since the prices are different, you can set up a proportion to solve the problem:
2¢ / 8 = 8¢ / x
By cross-multiplying, you get:
2 * x = 8 * 8
Now, solve for x to find the number of gumdrops you can buy at 8¢ apiece:
x = (8 * 8) / 2
x = 32
Therefore, you can buy 32 gumdrops at 8¢ apiece for the same amount of money as buying 8 gumdrops at 2¢ apiece.
To find out how many gumdrops you can buy at 8¢ apiece for the same amount of money you spent on 8 gumdrops at 2¢ apiece, divide the total amount of money by the new price.
Explanation:To find out how many gumdrops you can buy at 8¢ apiece for the same amount of money you spent on 8 gumdrops at 2¢ apiece, divide the total amount of money by the new price:
Total amount of money = 8 gumdrops x 2¢ apiece = 16¢
Number of gumdrops you can buy at 8¢ apiece = Total amount of money / 8¢
Number of gumdrops you can buy = 16¢ / 8¢ = 2 gumdrops
So, for the same amount of money, you can buy 2 gumdrops at 8¢ apiece.
If f(x) = x2 + 1 and g(x) = x – 4, which value is equivalent to ? 37 97 126 606
Answers
Answer:
37
Step-by-step explanation:
its 37
The value of a composite function (f•g)(x) at x = 10 is 37 if the function f(x) = x² + 1 and g(x) =x - 4 option (A) 37 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is:
If f(x) = x² + 1 and g(x) = x - 4, which value is equivalent to (f•g)(10)?
3797126606We have a function:
f(x) = x² + 1
g(x) =x - 4
Plug x = 10 in the function g(x)
g(10) = 10- 4
g(10) = 6
Plug the above value in the function f(x)
(f•g)(10) = f(g(10)) = (6)² + 1
(f•g)(10) = 36 + 1
(f•g)(10) = 37
Thus, the value of a composite function (f•g)(x) at x = 10 is 37 if the function f(x) = x² + 1 and g(x) =x - 4 option (A) 37 is correct.
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You are reducing a map of dimensions 2 ft by 3 ft to fit on a piece of paper 8 in. by 10 in. what are the dimensions of the largest possible map that can fit on the page?
Answers
Answer:
The dimensions of the largest possible map that can fit on the page are 10 inches by [tex]6\frac{2}{3}[/tex] inches.
Step-by-step explanation:
You are reducing a map of dimensions 2 ft by 3 ft
Lets change them to inches.
1 foot = 12 inches
So, 2 feet = [tex]2\times12=24[/tex] inches
3 feet = [tex]3\times12=36[/tex] inches
So, dimensions are : 24 inches x 36 inches
[tex]\frac{24}{36}=\frac{2}{3}[/tex]
Since 10 inch will be the longer side, we can find the shorter side by :
[tex]\frac{x}{10}=\frac{2}{3}[/tex]
[tex]3x=20[/tex]
[tex]x=\frac{20}{3}[/tex]
or [tex]x=6\frac{2}{3}[/tex] inches
So, the dimensions of the largest possible map that can fit on the page are 10 inches by [tex]6\frac{2}{3}[/tex] inches.
The dimension of the largest possible map which can fit on the paper can be used is [tex] 6\frac{2}{3} \: inches \: by \: 10 \: inches [/tex]
Map dimension = 2 feets by 3 feets Area of paper = 8in by 10inConverting the map dimension to inches :
1 feet = 12 inches2 feets = 2 × 12 = 24 inches
3 feets = 3 × 12 = 36 inches
Scale factor = 24 / 36 = 2/3
Longer side of the paper = 10 inches
Using the scale to obtain the length of the shorter side :
2/3 = x/10
Cross multiply
3x = 2 × 10
3x = 20
x = (20 ÷ 3)
x = 6 2/3 inches
The dimension of the largest possible map would be [tex] 6\frac{2}{3} \: inches \: by \: 10 \: inches [/tex]
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Energy resources that exist in limited amounts and, once used, cannot be replaced except over the course of millions of years are called_____energy resources
Answers
Answer: Non- renewable
The energy is derived from various sources on the basis of origin the energy can be derived from the renewable and non-renewable sources of energy. Renewable sources are those, which are abundantly available in nature and they can be replenished after a single use. For example, sunlight energy, wind energy, tidal energy, geothermal energy. But non- renewable sources are those which are available in limited amount hence, are expensive and cannot be replenished once they are used. For example fossil fuels such as coal, petroleum and natural gas. These are the resources which takes millions of years for their formation. Their genesis takes place inside the earth's geosphere under high heat and pressure conditions and by the action of the soil microbes acting upon the dead remains of plants and animals.
On the basis of the above description, energy resources that exist in limited amounts and, once used, cannot be replaced except over the course of millions of years are called non- renewable resources energy resources
The masses of four planets in a solar system outside the Milky Way are given below. Mass of Planet A: 5.97 × 10 24 kg; Mass of Planet B: 3.30 × 10 23 kg; Mass of Planet C: 1.89 × 10 27 kg; Mass of Planet D: 4.87 × 10 24 kg What is the order of these planets from least to greatest mass?
Planet C; Planet B; Planet D; Planet A Planet C; Planet A; Planet D; Planet B Planet B; Planet D; Planet A; Planet C Planet A; Planet D; Planet B; Planet C\
Answers
Mass of Planet A: 5.97 × 10 24 kg;
Mass of Planet B: 3.30 × 10 23 kg;
Mass of Planet C: 1.89 × 10 27 kg;
Mass of Planet D: 4.87 × 10 24 kg
We observe that according to the scientific notation we have:
3.30 × 10 23 kg <4.87 × 10 24 kg <5.97 × 10 24 kg <1.89 × 10 27 kg
Therefore the order of the planets from lowest to highest mass is:
Planet B, Planet D, Planet A, Planet C
Answer:
Planet B, Planet D, Planet A, Planet C
The order of the planets from least to greatest mass is Planet B, Planet D, Planet A, Planet C.
To determine the order of the planets from least to greatest mass, we need to compare the given masses:
Mass of Planet A: 5.97 × 1024 kg
Mass of Planet B: 3.30 × 1023 kg
Mass of Planet C: 1.89 × 1027 kg
Mass of Planet D: 4.87 × 1024 kg
These masses help us rank the planets:
Planet B: 3.30 × 1023 kg
Planet D: 4.87 × 1024 kg
Planet A: 5.97 × 1024 kg
Planet C: 1.89 × 1027 kg
Therefore, the order of the planets from least to greatest mass is Planet B, Planet D, Planet A, Planet C.
James has $32 and earns $10 per week for his allowance. What is the initial value for the scenario described?
A.10
B.32
C.42
D.320
Answers
This answer is confirmed!
A wolf population and compound interest were both used as examples of exponential functions. How easy is it for you to see how these diverse examples relate to exponential functions
Answers
Wolf population and compound interest are exponential functions because both functions are in the form of m x [tex]a^x[/tex] as given below.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
An exponential function is denoted as f(x) = [tex]a^x[/tex]
Where x is a variable and a is a constant.
Now,
Wolf population:
Suppose the wolf population initially is 10.
It grows double every year.
This means,
The population of wolves after 3 years.
x = 3
P = 10 x 2³ = 10 x 2 x 2 x 2 = 80
P = 10 x 2³ is an exponential function.
Now,
Compound interest:
Principal = 10
Rate = 10% per year
Time = 3
Amount = P [tex](1 + r/n)^{nt}[/tex]
A = 10 [tex](1 + 0.1)^3[/tex]
A = 10 x 1.1³
This is an exponential function.
Thus,
Wolf population and compound interest are exponential functions.
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The answer is (A) I find it very easy to see the relationships and why they are all exponential functions.
To see why a wolf population and compound interest both relate to exponential functions, follow these steps:
1. Understand exponential functions: An exponential function has the form [tex]\( f(t) = a \cdot b^t \)[/tex], where a is the initial amount, b is the growth (or decay) factor, and t is time.
2. Wolf population:
- Suppose a wolf population grows at a constant rate of 5% per year.
- If the initial population is [tex]\( P_0 \)[/tex], the population after t years is [tex]\( P(t) = P_0 \cdot (1.05)^t \)[/tex], showing exponential growth.
3. Compound interest:
- For compound interest, if you invest P dollars at an annual interest rate of r, compounded annually, the amount after t years is [tex]\( A(t) = P \cdot (1 + r)^t \)[/tex], which is also an exponential function.
4. Conclusion:
- Both scenarios involve quantities growing by a constant percentage over time, fitting the exponential model.
Thus, the answer is: A. I find it very easy to see the relationships and why they are all exponential functions.
Complete question:- A wolf population, and compound interest were both used as examples of exponential functions. How easy is it for you to see how these diverse examples relate to exponential functions?
A. I find it very easy to see the relationships and why they are all exponential functions.
B. I have some difficulty seeing the relationships but understand why they are both exponential functions.
C. I don't see the relationships and am not sure why they are both exponential functions.
D. I do not understand what an exponential function is.
Find the total surface area of the triangular pyramid. Each of the faces (sides) has an area of 50.5 square inches.
Answers
A triangular pyramid (also called tetrahedron) is a polyhedron whose surface is formed by a base that is a triangle and triangular lateral faces that converge in a vertex that is called apex (or apex of the pyramid).
It will be composed, therefore, by 4 faces, the triangular base and three lateral triangles that converge at the vertex.
Thus, the surface area is:
As = 4 * (50.5) = 202 in ^ 2
Answer:
The total surface area of the triangular pyramid is:
202 in ^ 2
A basketball team played 66 games. they won 22 more than they lost. how many games did theyâ win? how many games did theyâ lose?
Answers
they lost 22 games
22+44 = 66
PLEASE HELP
I WILL GIVE BRAINILEST
Daniel, a 37-year-old male, bought a $160,000, 10-year life insurance policy. What is Daniel’s annual premium? Use the table.
$611.20
$728.00
$1268.80
$1652.80
Answers
Male, 35-39, 10-year
The figure in this category shows $4.55, telling us that the annual premium per $1000 of coverage is $4.55.
Daniel bought $160,000 worth of life insurance, so that is 160 one-thousands.
So, we multiply the annual premium per $1000 ($4.55 as identified) by 160 to give us our answer:
4.55×160= $728
Therefore, the answer is $728
Answer:
the answer is b 728
Step-by-step explanation:
what's the sum or difference
1. 4x^10-9x^10
2. 3y^5-10y^5
@kewlgeek555
Answers
1. -5x^10
Since both terms have an exponent of 5, they can both be subtracted.
2. -7y^5
Same reason as above.
Hope this helps!
helpppppppppppppppppppppppppppppppp
Answers
1/625
Explanation:
In case of multiplication of numbers with same base, we add the powers.
This means that:
a^x * a^y = a^(x+y)
Applying this to the given, we will find that:
(5^-1) * (5^-3) = 5^(-1-3)
= 5^-4
= 1/625
Hope this helps :)
(5 ^ -1) * (5 ^ -3)
Using properties of exponents we have:
(1/5) * (1 / (5 ^ 3))
Rewriting:
(1/5) * (1 / (125))
1/625
answer:
An equivalent expression is:
1/625
option 1
Point E is located at (–5, 2). Point M is the reflection of point E across the y-axis. What is the distance between E and M?
Answers
The distance between E and M is 10 units.
The reflection of point E across the y-axis, point M, is at (5, 2). The distance between these two points is 10 units.
Explanation:In the context of this problem, a reflection of a point across the y-axis inverts the sign of the x-coordinate while leaving the y-coordinate unchanged. Thus, if Point E is located at (-5, 2), the reflection of Point E, or Point M, would be located at (5, 2).
In terms of distance, it is important to remember that distance is always a positive value. Considering the x-coordinates, the distance from E to M is the absolute difference between their x-coordinates, which in this case is |-5 - 5| or 10 units.
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need answer plz smart people
Answers
13.
The radii are the lines that go from the exact center of the circle to anywhere on the circumference of the circle.
Here we can see that segments AB AD and AC go from the center to somewhere on the circumference, thus these segments are radii.
14.
Since the triangles are congruent, their corresponding angles are congruent. Given this, angle A is congruent to angle D and angle C is congruent to angle F.
A tip for future problems like this - you don't necessarily need to look at the diagram; the congruent statement gives you all the information you need about which angles correspond with each other and thus are congruent. Triangle ABC is congruent to triangle DEF: A corresponds to D, B corresponds to E, and C corresponds to F. This is useful because sometimes the triangles in the diagrams are not oriented the same way and its confusing to try to figure out which angles correspond.
15.
The diameter of a circle is the is a line that goes from a side through the center and to the other side of a circle.
The diameter is segment RS.
16.
Obtuse = greater than 90 degrees.
Acute = less than 90 degrees
Right = 90 degrees
Straight = 180 degrees (a straight line)
For this angle to be 90 degrees, it would have to be indicated by a little box in the corner; you must never assume an angle is 90 degrees, unless this information is explicitly stated in the question or shown in the diagram. This is not a right angle, nor is it a straight angle (it is not a straight line). That leaves obtuse and acute. Think: Is this greater than or less than 90 degrees? It is less than 90 degrees. The angle is acute.
So I need to add 2 teaspoons of conditioner for every 10 gallons of water in a tank. I have a 2.5-gallon tank, how much conditioner do I need to put in the tank? Please help I don't want my fish to die.
Answers
This is really just a simple equation:
2/10=x/2.5
Now, there are several ways you can really solve this, but i'll give you the basic version. You know for 10 gallons, you need 2 teaspoons. Divide, this means for every 1 teaspoon, you need 5 gallons. This here is a simplification.
Now, in order to get from 5 gallons per 1 teaspoon to 2.5 gallons per X teaspoons, you have to figure out the differences in what you know. 2.5 is half of 5, and what you do to one side of an equation, you do to the other. The first half was divided by half, so divide the second half (1 teaspoon) by half as well.
1/2=.5, AKA half.
2 teaspoons of conditioner for every 10 gallons
For 2.5 gallons, you need .5 teaspoons, or 2.46 ml.
Your answer is .5 teaspoons, basically HALF of a teaspoon.
~Hope this helps!
0.5 teaspoon of conditioner to 2.5 gallon of tank.
What is ratio?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.
Given
So, you need 2 teaspoons of conditioner for every 10 gallons of water.
2/10=x/2.5
Now, know for 10 gallons, you need 2 teaspoons. Divide, this means for every 1 teaspoon, you need 5 gallons. This here is a simplification.
x =0.5
2 teaspoons of conditioner for every 10 gallons
For 2.5 gallons, you need .5 teaspoons.
Hence 0.5 teaspoon of conditioner to 2.5 gallon of tank.
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A rectangular room is 6 6 meters longer than it is wide, and its perimeter is 28 28 meters. find the dimension of the room
Answers
We also know that the length is 6 meters longer than the width.
Based on this we can create the following formula to find the dimensions:
28= (w+6)+(w+6)+w+w
Then to solve, it's just simple algebra.
First, combine like terms: 28= w+w+w+w+6+6 28= 4w+12
The next thing we do is isolate the variable by subtracting 12 from each side: 28-12 = 4w+12-12 16= 4w
The next thing we do is divide both sides by the coefficient (4): 16/4 = 4w/4
And this gives us the answer that w=4.
Now to find the dimensions:
We know that the width is equal to 4.
We also know that the length is equal to 6 more than the width. If the width is 4 then the length is 4+6 or 10.
So there you have it, the dimensions of the room would be 4x10.
Find the number of real number solutions for the equation. x2 – 18 = 0
cannot be determined
1
0
2
Answers
For this case, the first thing you should do is rewrite the expression:
x ^ 2 - 18 = 0
x ^ 2 = 18
The solutions for this case are:
x1 = root (18)
x2 = -raiz (18)
Therefore the answer is:
2 solutions of real numbers.
Answer:
2
Answer:
The number of real roots is 2.
Step-by-step explanation:
Given,
[tex]x^2 -18 = 0[/tex]
We will find the number of roots by Descartes' rule of signs.
Let,
[tex]f(x)=x^2-18[/tex]
Since,
[tex]f(x) = + x^2 - 18[/tex]
That is, the change in the sign shows, the given polynomial has one positive real root.
Now, by putting x = - x,
[tex]f(-x)=(-x)^2- 18 = x^2 - 18[/tex]
[tex]\implies f(-x) = + x^2 - 18[/tex]
That is, the change in the sign shows, the given polynomial has one negative real root.
We know that, given polynomial has degree 2,
⇒ It only has 2 roots one is positive real and another is negative real,
⇒ f(x) having 2 real roots.
What is 7,433,654 rounded to the nearest 10,000
Answers
Here is your answer:
The proper answer for this question is "7,430,000".
3 is less than 5 which means it doesn't round up one.
Your answer is 7,430,000!
If you need anymore help feel free to ask me!
Hope this helps!
PLEASE HELP
7.05a
1. Find the first six terms of the sequence.
a1 = -6, an = 4 • an-1
A) 0, 4, -24, -20, -16, -12
B) -24, -96, -384, -1536, -6144, -24,576
C) -6, -24, -20, -16, -12, -8
D) -6, -24, -96, -384, -1536, -6144
2. Find an equation for the nth term of the arithmetic sequence.
-15, -6, 3, 12, ...
A) an = -15 + 9(n + 1)
B) an = -15 x 9(n - 1)
C) an = -15 + 9(n + 2)
D) an = -15 + 9(n - 1)
3. Find an equation for the nth term of the arithmetic sequence.
a14 = -33, a15 = 9
A) an = -579 + 42(n + 1)
B) an = -579 + 42(n - 1)
C) an = -579 - 42(n + 1)
D) an = -579 - 42(n - 1)
4. Determine whether the sequence converges or diverges. If it converges, give the limit.
48, 8, four divided by three , two divided by nine , ...
A) Converges; two hundred and eighty eight divided by five
B) Converges; 0
C) Diverges
D) Converges; -12432
5. Find an equation for the nth term of the sequence.
-3, -12, -48, -192, ...
A) an = 4 • -3n + 1
B) an = -3 • 4n - 1
C) an = -3 • 4n
D) an = 4 • -3n
6. Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.
A) an = 7 • (-3)n + 1
B) an = 7 • 3n - 1
C) an = 7 • (-3)n - 1
D) an = 7 • 3n
7. Write the sum using summation notation, assuming the suggested pattern continues.
5 - 15 + 45 - 135 + ...
A) summation of five times three to the power of the quantity n plus one from n equals zero to infinity
B) summation of five times negative three to the power of n from n equals zero to infinity
C) summation of five times three to the power of n from n equals zero to infinity
D) summation of five times negative three to the power of the quantity n plus one from n equals zero to infinity
8. Write the sum using summation notation, assuming the suggested pattern continues.
-9 - 3 + 3 + 9 + ... + 81
A) summation of the quantity negative nine plus six n from n equals zero to fifteen
B) summation of negative fifty four times n from n equals zero to fifteen
C) summation of negative fifty four times n from n equals zero to infinity
D) summation of the quantity negative nine plus six n from n equals zero to infinity
9. Write the sum using summation notation, assuming the suggested pattern continues.
64 + 81 + 100 + 121 + ... + n2 + ...
A) summation of n squared from n equals eight to infinity
B) summation of n minus one squared from n equals eight to infinity
C) summation of n squared from n equals nine to infinity
D) summation of n plus one squared from n equals eight to infinity
10. Find the sum of the arithmetic sequence.
17, 19, 21, 23, ..., 35
A) 260
B) 179
C) 37
D) 160
11. Find the sum of the geometric sequence.
1, one divided by two, one divided by four, one divided by eight, one divided by sixteen
A) one divided by twelve
B) 93
C) negative one divided by forty eight
D) thirty one divided by sixteen
12. An auditorium has 30 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?
A) 1170
B) 735
C) 1230
D) 600
13. Use mathematical induction to prove the statement is true for all positive integers n.
The integer n3 + 2n is divisible by 3 for every positive integer n.
14. A certain species of tree grows an average of 3.8 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall.
Answers
Since this exceeds the limit and I had to delete the last questions and I copied all the answers to a file that is attache. See the attachment with all the answers.
1) Question 1. Find the first six terms of the sequence: a1 = -6, an = 4 • an-1
Answer: option D) -6, -24, -96, -384, -1536, -6144
Explanation:
A(1) = - 6
A(n) = 4 * A(n-1)
n A(n)
1 - 6
2 4 * (-6) = - 24
3 4 * (-24) = - 96
4 4 * (-96) = - 384
5 4 * (-384) = - 1536
6 4 * ( -1536) = -6144
So, the first six terms are: -6, - 24, - 96, - 384, - 1536, - 6144.
2) Question 2: Find an equation for the nth term of the arithmetic sequence.
-15, -6, 3, 12, ...
Answer: option D) - 15 + 9(n - 1)
Explanation:
1. find the difference between the consecutive terms:
-6 - (-15) = -6 + 15 = 9
3 - (-6) = 3 + 6 = 9
12 - 3 = 9
So, the difference is 9, and you can find any term adding 9 to the previous.
2. Since the first term is - 15, you have:
First term, A1 = - 15 + 9(0) = - 15
Second term, A2 = - 15 + 9(1) = - 6
Third term, A3 = -15 + 9(2) = - 15 + 18 = 3
Fourth term, A4 = - 15 + 9(3) = - 15 + 27 = 12
3. So, the general formula is An = - 15 + 9 (n - 1), which is the option D)
3) Question 3. Find an equation for the nth term of the arithmetic sequence A14 = - 33, A15 = 9.
Answer: option B) An = - 579 + 42(n - 1)
Explanation:
1) Find the difference: 9 - (-33) = 9 + 33 = 42
2) A15 = A1 + 42 * (15 - 1)
=> A1 = A15 - 42(15 - 1)
A1 = A15 - 42(14)
A1 = 9 - 588 = - 579
Therefore, the formula es An = - 579 + 42(n - 1)
4) Question 4. Determine whether the sequence converges or diverges. If it converges, give the limit.
48, 8, 4/3, 2/9, ...
Answer: the sequence converges to 288/5
Explanation:
That is a geometric sequence.
The ratio is 1/6: 8/48 = 1/6; (4/3) / 8 = 4/24 = 1/6; (2/9)/(4/3) = 6/36 = 1/6.
The convergence criterium is that if |ratio| < 1 then the series, this is the sum of all the terms, converge to: A1 / (1 - ratio)
Then the limit 48 / (1 - 1/6) = 48 / (5/6) = 48*6 / 5 = 288/5
5) Question 5. Find an equation for the nth term of the sequence.
-3, -12, - 48, -192
Answer: - 3 * (4)^(n-1)
Explanation: clearly any term (from the second) is the previous term multiplied by 4.
The first term is -3
The second term is -3(4) = - 12
The third term is -3(4)(4)= - 48
The fourth term is - 3 (4)(4)(4) = - 192
So, the general formula for the nth term is -3 * 4^ (n-1)
6) Question 6. Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.
Answer: An =7 * (-3)^(n-1)
Explanation:
1) The fith term is the second term * (ratio)^3: A5 = A3 * (r)^3
2) A5 = 567, A2 = - 21 => r^3 = A5 / A2 = - 567 / 21 = - 27
=> r = ∛(-27) = - 3
3) So the first term is A1 = A2 / r = -21 / -3 = 7
4) The general formula is
An =7 * (-3)^(n-1)
7) Question 7. Write the sum using summation notation, assuming the suggested pattern continues.
5 - 15 + 45 - 135 + ...
Answer: option B) summation of five times negative three to the power of n from n equals zero to infinity
Explanation:
5 = 5
-15 = 5 (-3)
45 = 5(-3)^2
-135 = 5(-3)^3
=> 5 + 5(-3) + 5(-3)^2 + 5(-3)^3+....
Using the summation notation that is:
∞
∑ (5)(-3)^n
n=0
Which means summation of five times negative three to the power of n from n equals zero to infinity
8) Question 8. Write the sum using summation notation, assuming the suggested pattern continues.
-9 - 3 + 3 + 9 + ... + 81
Answer: option A) summation of the quantity negative nine plus six n from n equals zero to fifteen
Explanation:
Find the difference:
-3 - (-9) = - 3 + 9 = 6
3 - (-3) = 3 + 3 = 6
9 - 3 = 6
First term: - 9
Second term: - 9 + 6(1)
Third term: - 9 + 6(2)
nth term = - 9 + (n -1)
Summation = [- 9] + [- 9 + 6(1) + [-9 + 6(2)] + [-9 + 6(3) ]+ .... [-9 + 6(15) ]
Using summation notation:
15
∑ [-9 + 6n]
n=0
which means summation of the quantity negative nine plus six n from n equals zero to fifteen.
9) Question 9. Write the sum using summation notation, assuming the suggested pattern continues.
64 + 81 + 100 + 121 + ... + n2 + ...
Answer: A) summation of n squared from n equals eight to infinity
Explanation:
64 = 8^2
81 = 9^2
100 = 10^2
121 = 11^2
n^2
=>
∞
∑ n^2
n=8
which means summation of n squared from n equals eight to infinity
10) Question 10. Find the sum of the arithmetic sequence.
17, 19, 21, 23, ..., 35
Answer: 260
Explanation:
The difference is 2:
The sum is: 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35.
You can use the formula for the sum of an arithmetic sequence:
(A1 + An) * n / 2 = (17 + 35)*10/2 = 260
11) Question 11. Find the sum of the geometric sequence.
1, 1/2, 1/4, 1/8, 1/16
Answer: option D) 31/16
Explanation:
You can either sum the 5 terms or use the formula for the partial sum of a geometric sequence.
The formula is: Sum = A * ( 1 - r^n) / (1 - r)
Here A = 1, r = 1/2, and n = 5 => Sum = 1 * (1 - (1/2)^5 ) / (1 - 1/2) =
= [ 1 - 1/32] / [1/2] = [31/32] / [1/2] = 31 / 16
Consuela and her three friends order 2 pizzas. Consuela cuts each pizza into 8 equal slices. She saves 2 slices of pizza for her older brother, Then she and her friends share the rest of the pizza, each eating the same number of slices. What fraction of the 2 pizzas is left over?
Answers
x--------------> the number of slices eating by Consuela and her three friends
we know that
[total slices]=8*2=16 slices
[slices of pizza for her older brother]=2
x=16-2=14 slides
Consuela and her friends share the rest of the pizza, each eating the same number of slices---------> 14/4= 3.5 slides of pizza each (this part is not necessary, but it is shown in a didactic way)
the question is
What fraction of the 2 pizzas is left over?
[slices of pizza for her older brother]/[total slices]=2/16=1/8
the answer is (1/8)
Final answer:
To find the fraction of the 2 pizzas left over, calculate the total slices consumed and subtract from the total. Consuela and her friends ate 14 slices out of 16, leaving 2/16 or 1/8 of the 2 pizzas left over.
Explanation:
Consuela and her friends ordered 2 pizzas, each cut into 8 slices. Consuela saved 2 slices, then shared the rest equally. Each person ate 2 slices.
To find out what fraction of the 2 pizzas is left over, calculate the total slices consumed and subtract from the total.
Each pizza had 8 slices, so 2 pizzas have 16 slices in total.Consuela saved 2 slices, so she and her friends ate 14 slices in total.Thus, the fraction of the 2 pizzas left over is 2/16 or 1/8.A system of equations is graphed on a coordinate plane.
Which coordinates are the best estimate of the solution to the system of equations?
(6, 0)
(0, 5)
(1, 4)
(1, 5)
Answers
4x+2y = 10
-2(2x+3y = 12) -->
-4x-6y = -24
+4x+2y = 10
----------------
0 + -4y = -14
-4y = -14
-4y/-4 = -14/-4
y = 7/2 = 3.33
4x+2y = 10
4x+2(7/2) = 10
4x+7 = 10
4x = 3
x = 3/4 = 0.75
So the solution is at (0.75, 3.33)
closest is C) (1, 4)
PLZ HELP ME!!A dilation has center (0, 0). Find the image of the point A (-4, 6) for the scale factor 4.5.
A' =
A- (‑18, 27)
B-(0.5, 10.5)
C-(10.5, 0.5)
D-(27, ‑18)
Answers
Selection A (-18, 27).