A used book store buys a hardback book for $1.50 and then sells it for $5. Over time, the store sells the same number of books it buys. The store manager can use the equation P(x)=5x−1.5x to determine the store's profit, P(x), where x is the number of books that the store sells. Which statement about the book store is true based on the profit equation?

A.The book store makes a profit of $5.00 for each hardback book that is sold.
B.The book store makes a profit of $3.50 for each hardback book that is sold.
C.The book store makes a profit of $4.50 for each hardback book that is sold.
D.The book store sells each hardback book for $3.50

Answers

Answer 1

A used book store buys a hardback book for $1.50 and then sells it for $5. Over time, the store sells the same number of books it buys. The store manager can use the equation P(x)=5x−1.5x to determine the store's profit, P(x), where x is the number of books that the store sells. Which statement about the book store is true based on the profit equation?

Cost Price of book, C.P.=$1.50

Selling Price of book, S.P.=$5

PROFIT=S.P. -C.P.

So, Profit=$5-$1.50=$3.50

So, Profit=$3.50 on each book

Or, we are given P(x)= 5x-1.50x

Or, P(x)=3.50x

For each book, we must divide the profit P(x) by x, that is, number of books

[tex] \frac{P(x)}{x}=\frac{3.5x}{x} [/tex]

[tex] \frac{P(x)}{x}=\frac{3.5*1}{1} [/tex]

[tex] \frac{P(x)}{x}=3.5 [/tex]

So, Profit for each book sold is $3.50

Answer:Option C

Answer 2

Answer:

Step-by-step explanation:

im too smort

Related Questions

Each of the 14 students in the art club needs 4 ounces of paint for a project. The art store sells paint only in 8-ounce bottles. How many bottles of paint does the art club president need to buy for the project?

Answers

Each bottle serves 2 students. He needs to buy 14/2 = 7 bottles.

Answer: The art club president need to buy 14 bottles of paint for the project.

Step-by-step explanation: Given that each of the 14 students in the art club needs 4 ounces of paint for a project. The art store sells paint only in 8-ounce bottles.

We are to find the number of bottles of paint that the art club president need to buy for the project.

We will be using the unitary method to solve the given problem.

Number of bottles filled by 8 ounces of paint = 1.

So, the number of bottles filled by 1 ounce of paint is

[tex]\dfrac{1}{8}.[/tex]

So, the number of bottles filled by 4 ounces of paint will be

[tex]\dfrac{1}{8}\times4=\dfrac{1}{2}.[/tex]

Now, number of bottles of paint needed by 1 student [tex]=\dfrac{1}{2}.[/tex]

Therefore, the number of bottles of paint needed by 14 students will be

[tex]\dfrac{1}{2}\times14=7.[/tex]

Thus, the art club president need to buy 14 bottles of paint for the project.

helppppppppppppppppppppppp

Answers

2x ^ 2 = 4x-7
We rewrite the polynomial:
2x ^ 2-4x + 7 = 0
Applying the resolver we have:
x = (- b +/- root (b ^ 2-4ac)) / 2a
x = (- (- 4) +/- root ((- 4) ^ 2-4 (2) (7))) / 2 (2)
x = (- (- 4) +/- root (16-56)) / 2 (2)
x = (- (- 4) +/- root (-40)) / 4
x = (2 +/- root (-10)) / 2
x = (2 +/- root (10) * i) / 2
Answer:
x = (2 +/- root (10) * i) / 2
option 3

Between the ages of 24 months and 6 years, the average child will gain _____ in height. 1 foot 1.5 feet 8 inches 4 inches

Answers

At that specific age range, the average child grows about 3in per year 24 months is 2 years old. 6-2 =4. there are 4 years that pass.

3in*4years =12in or 1 foot

What is the m∠ABC?

1)m∠ABC = 60°
2)m∠ABC = 67°
3)m∠ABC = 120°
4)m∠ABC = 127°

Answers

i believe it is 4)m∠ABC = 127°

we are given

m∠BCD =67

and m∠BDC=60

we know that

m∠ABC is exterior angle

m∠BCD and m∠BDC are interior angles

exterior angle is sum of interior angles

so, we can write it as

m∠ABC=m∠BCD+m∠BDC

now, we can plug values

and we get

m∠ABC=60+67

m∠ABC=127

so, option-4.........Answer

Using a straightedge draw a random triangle now carefully cut it out next amputate the angles by snipping through adjacents sides now move the angles together so the vertices all touch

Answers

This is usually used as a proof that triangles have 180°. Look at the attached figures. If you cut off angle A, angle B and angle C and rotate them so that their vertices touch, you form a half-circle out of them (or a straight line). We know that half a circle is 1/2 of 360° or 180; therefore all 3 angles in a triangle must add up to 180°.

It should be noted that a triangle is a polygon with three edges and three vertices.

What is a triangle?

A triangle is a simple closed curve or a polygon that is formed by three line segments.

It should be noted that triangles have 180°. In this case, looking at the attached figure, it can be deduced that the addition of the angles equals 180.

Learn more about triangles on:

https://brainly.com/question/17335144

please help im confused....

which ordered pair is a solution of the inequality?
2y+6<8
a. (4,13)
b. (-5,2)
c.(0,6)
d.(4,8)

Answers

Hello,

Here is your answer:

The proper answer to this question is option D "(4,8)".

Your answer is D.

If you need anymore help feel free to ask me!

Hope this helps!

Find the value of x. The diagram is not drawn to scale.

Answers

Answer:

C. [tex]x=99^{\circ}[/tex]

Step-by-step explanation:

We have been given a image. We are asked to find the value of x.

We can see that our given figure is a quadrilateral. We know that all interior angles of a quadrilateral add up-to 360 degrees.

[tex]x^{\circ}+y^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]

We can see that y and 116 degrees angles are linear angles, so we can set an equation as:

[tex]y^{\circ}+116^{\circ}=180^{\circ}[/tex]

[tex]y^{\circ}+116^{\circ}-116^{\circ}=180^{\circ}-116^{\circ}[/tex]

[tex]y=64^{\circ}[/tex]

Substitute [tex]y=64^{\circ}[/tex] in the equation:

[tex]x^{\circ}+y^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]

[tex]x^{\circ}+64^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]

[tex]x^{\circ}+261^{\circ}=360^{\circ}[/tex]

[tex]x^{\circ}+261^{\circ}-261^{\circ}=360^{\circ}-261^{\circ}[/tex]

[tex]x^{\circ}=99^{\circ}[/tex]

[tex]x=99[/tex]

Therefore, the value of x is 99.

y=x-8/x^2+4x-5 find any points of discontinuity for the rational function

a. x=5, x=1
b. x=-5, x=1
c. x=8
d. x=5, x=-1

Answers

Answer:

x=-5, x=1

Step-by-step explanation:

y=x-8/x^2+4x-5

[tex]y=\frac{x-8}{x^2+4x-5}[/tex]

When denominator becomes 0 in a rational function then there will be a break in the graph

To find any points of discontinuity for the rational function , we set the denominator =0 and solve for x

x^2 + 4x -5 =0

Now we factor x^2 +4x -5

product is -5 and sum = 4

5 * (-1) = -5

5 +(-1) = 4

(x+5)(x-1) =0

set each factor =0 and solve for x

x+5=0 , so x= -5

x-1=0 , so x= 1

x=-5, x=1 are the points of discontinuity for the rational function

Answer:

x=-5 , X=1

Step-by-step explanation:

Find an equation of the line that satisfies the given conditions. through (−1, −3); perpendicular to the line 2x + 7y + 2 = 0

Answers

2x + 7y + 2 = 0
2(-1) + 7(-3) + 2 = 0
-2 - 21 + 2 = 0
-21 = 0

Find the area of A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is

Answers

To find the area of the cylinder we need to find its volume first. Remember that the formula for the volume of a cylinder is [tex]V= \pi r^{2} h[/tex]
where:
[tex]V[/tex] is the volume
[tex]r[/tex] is the radius
[tex]h[/tex] is the height
From the question we know that [tex]A=175[/tex] and [tex]h=7[/tex]. Lets replace those values in our volume formula:
[tex]175= \pi r^{2} 7[/tex]
Now we can solve for [tex]r[/tex] to find our radius:
[tex]r^{2} = \frac{175}{7 \pi } [/tex]
[tex]r^{2} = \frac{25}{ \pi } [/tex]
[tex]r= \sqrt{ \frac{25}{ \pi } } [/tex]
[tex]r= \frac{5}{ \sqrt{ \pi } } [/tex]

Now that we know the radius, we can use the formula for the area of a cylinder [tex]A=2 \pi rh+2 \pi r^{2} [/tex]
where:
[tex]A[/tex] is the area
[tex]r[/tex] is the radius
[tex]h[/tex] is the height
We know now that [tex]r= \frac{5}{ \sqrt{ \pi } } [/tex] and [tex]h=7[/tex], so lets replace those values in our area formula:
[tex]A=2 \pi ( \frac{5}{ \sqrt{ \pi } } )(7)+2 \pi ( \frac{5}{ \sqrt{ \pi } })^{2} [/tex]
[tex]A= \frac{70 \pi }{ \sqrt{ \pi } } +50[/tex]
[tex]A=174.07[/tex]

We can conclude that the area of a cylinder that has a volume of 175 cubic units and a height of 7 units is 174.07 square units.

Part A: Jake rented a kayak at $26 for 3 hours. If he rents the same kayak for 5 hours, he has to pay a total rent of $42. Write an equation in the standard form to represent the total rent (y) that Jake has to pay for renting the kayak for x hours. (4 points)

Part B: Write the equation obtained in Part A using function notation. (2 points)

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

Answers

We can write the information we know as ordered pairs. The independent variable, or x, in this case would be the amount of time, and the dependent variable, or y, would be the amount of money. This is because the amount of money charged changes depending on the amount of time. This gives us the ordered pairs (3, 26) and (5, 42). Using the formula for slope we have:
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\ \\=\frac{42-26}{5-3} \\ \\=\frac{16}{2}=8[/tex]. A slope of 8 tells us that the hourly rental is $8. We can use this to back up and see what the rental fee is. When renting the kayak for 3 hours, Jake paid 26. We know that it costs $8 per hour; 8(3) = 24. This leaves us 26-24=$2 for the rental fee. The equation would then be
y = 8x + 2.
Writing this as a function would be f(x) = 8x + 2.
To graph this, we would label the x-axis as time (hours) and the y-axis as money (dollars). We would go up to the y-intercept, 2, and plot our point. (The y-intercept is 2 because in the form y=mx+b, b is the y-intercept; that's where our 2 is.) From here, we know the slope is 8=8/1, so we would go up 8 and over 1 to the right to plot our next point. Then we would draw our line between these two points.

Answer:

8x+2

fx= 8x+2

Step-by-step explanation:

a business analyst makes 20$ an hour for the first 42 hours he works during a week and 28$ an hour for each worked over 42 hours. which piecewise equation models his weekly pay y in dollars as it relates to the number of hours x that he has worked during the week

Answers

y=(20 × 42) + [28 × (x-42)]

Answer:

[tex]y=28(x-42)+840[/tex]

Step-by-step explanation:

Let he works for x hours in total.

We are given that he makes 20$ an hour for the first 42 hours

So, he earns in 1 hour = 20

He earns in 42 hours = [tex]20 \times42[/tex]

= [tex]840[/tex]

Now we are given that he earns $28 an hour for each hour worked over 42 hours.

Since he worked for 42 hours out of x hours .

So, remaining hours = x-42 hours

So,he earns for x-42 hours = [tex]28\times(x-42)[/tex]

y denotes his total earning of weekly

So, total earning [tex]y=28(x-42)+840[/tex]

Hence piecewise equation models his weekly pay y in dollars as it relates to the number of hours x that he has worked during the week is [tex]y=28(x-42)+840[/tex]

Please help I have 2 questions. Thank you.

Answers

1 is 30
2 is
3x + 2 = 2
3x = 0
x = 0

Which is the formula for the volume of a sphere with diameter d?

A. S= 4πd²
B. S= πd²
C. S= [tex] \frac{4}{3} [/tex]πd³
D. S= [tex] \frac{1}{6} [/tex]πd³

Answers

The answer for this problem is D because the diameter for the sphere is d, so the radius is 1/2d. Substituting that into the formula of finding a circle with radius x is [tex]/frac4/3 pi * x^3. We get 1/3* pi*1/2d^3, which equals 1/6*pi*d^3, or D.

Boyles law involves the pressure and volume of gas in a container. It can be repersented by the formula p sub 1 v sub 1= p sub 2 v sub 2. When the formula is solved for p sub 2, the results is

Answers

Final answer:

Boyle's Law can be rearranged to solve for p sub 2 (final pressure) using the formula p sub 2 = p sub 1 v sub 1 / v sub 2. This shows the inverse relationship between pressure and volume of gas at a constant temperature.

Explanation:

The question is asking to solve the formula representing Boyle's Law (p sub 1 v sub 1 = p sub 2 v sub 2) for p sub 2. Boyle's Law states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. To solve for p sub 2, you rearrange the formula to be p sub 2 = p sub 1 v sub 1 / v sub 2. This formula means that the final pressure (p sub 2) equals the initial pressure (p sub 1) times the initial volume (v sub 1), all divided by the final volume (v sub 2). Therefore, if the volume increases, the pressure decreases, and if the volume decreases, the pressure increases, keeping the gas's temperature constant.

Learn more about Boyle's Law here:

https://brainly.com/question/21184611

#SPJ12

ASAP PLEASE:

Segment RS is congruent to segment DF. Which congruence statement is true?

- RS ≅ DF
- RS ≅ SFD
- RS ≅ SF
- RS ≅ RD

Answers

Answer:

A. [tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]

Step-by-step explanation:

We have been given a circle and we are told that segment RS is congruent to segment DF.

We can see that segment RS corresponds to arc RS and segment DF corresponds to arc DF.

As both segments are congruent, therefore, both arcs will be congruent as well.

We can represent this information as:

[tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]

Therefore, option A is the correct choice.

LM¯¯¯¯¯¯¯ is the midsegment of trapezoid ABCD . AB=78 and DC=142 . What is LM ?

Answers

The midsegment has a length equal to the average of the base lengths.

LM = (AB +DC)/2
.. = (78 +142)/2
LM = 110

which rule describes the translation PQR --> P'Q'R'?

Answers

The "Pre Image" is the image that we started with, so the pink triangle.
The "Image" is the image that we ended with, so the blue triangle.

To determine how far we went from the pre image to the image, we can focus on one point, let's say point "P".

The pre image coordinates for point "P" are 2, 3.
The image coordinates for point "P'" are -1, 0.

To get from x value 2 to x value -3, we subtracted 3.
To get from y value 3 to y value 0, we subtracted 3.

So, our rule for this translation would be A, (x, y) ----> (x-3, y-3).

F(x) = x4/5(x − 6)2 find the critical numbers of the function

Answers

You can find the critical numbers by finding the derivative of the function and solving for 0.

F(x) = x(4/5)(x-6)(2) = x(8/5)(x-6) = (8/5)(x^2 - 6x)

Taking the derivative:
F'(x) = (8/5)(2x - 6)
F'(x) = 0 at x = 3,

critical number = 3

Final answer:

To find the critical numbers, differentiate the function using the product rule, set the derivative equal to zero, and solve for x. Critical numbers are where the derivative is zero or undefined, provided they are within the domain of the function.

Explanation:

To find the critical numbers of the function f(x) = x4/5(x − 6)2, you need to locate the values of x where the first derivative of the function is either zero or undefined. The first derivative can be calculated using the product rule and the power rule.

First, let's find the derivative:

f'(x) = d/dx [x4/5] * (x - 6)2 + x4/5 * d/dx [(x - 6)2]

After simplifying, you will get a derivative function where you can then set it equal to zero to find the critical points. The points where the derivative is zero are potential local maxima, minima, or points of inflection. Additionally, points where the derivative is undefined can also be critical points, if they are within the domain of the function.

Once you calculate and simplify the derivative, set it equal to zero and solve for x. You might find that you get explicit values of x, which are the critical numbers of the function. If the function's derivative does not exist at some point, that will also be a critical number.

Remember, critical numbers are only relevant if they are within the domain of the original function.

Which are the solutions to the quadratic equation 4x^2=64?

A. x=-16 and x=16

B. x=-8 and x=8

C. x=-4 and x=4

D.x=-2 and x=2

Answers

x=4 and x=-4 Your answer would be C.

Answer: x= -4, 4

Step-by-step explanation:

Jacey obtains a 30-year 6/2 ARM at 4% with a 2/6 cap structure in the amount of $224,500. What is the monthly payment during the initial period?

Answers

The answer is $1,071.80.

General Idea:

We need to make use of the below formula to find the monthly payment..

[tex] Monthly \; Payment\; =\; \frac{P \times \frac{r}{12}}{(1-(1+\frac{r}{12})^{-m})} \\ \\ Where:\\ P\; is\; Principal\\ r\; is\; rate\; in\; decimal\; form\\ m\; is\; number\; of\; monthly\; payments [/tex]

Applying the concept:

Given:

[tex] P=\$224,500\\ r=4\%=0.04\\ m=30\; year \times 12 \; months/year=360\\ [/tex]

Substituting the given in the formula we will get the monthly payment.

[tex] Monthly\; Payment\; =\; \frac{224500 \times \frac{0.04}{12}}{(1-(1+\frac{0.04}{12})^{-360})} =\frac{\frac{8980}{12}}{(1-0.301796)} =\frac{748.3333}{0.698204} \\ \\ Monthly \; Payment= \$1071.7975 [/tex]

Conclusion:

The monthly payment during the initial period is $1072.

Use the rules of significant figures to answer the following question:

67.31 - 8.6 + 212.198

A. 270.9
B. 271
C. 270.908
D. 270

Answers

Answer:

A. 270.9

Step-by-step explanation:

We know that the rule of significant figures for addition and subtraction states that 'the number of places after the decimal point in the result is equal to the least number of decimal places in each term.'

So, 67.31 - 8.6 + 212.198 = 67.31 + 212.198 - 8.6 = 279.508 - 8.6 = 270.908

Now, the resultant number is 270.908

Using the rule of significant figures, we get that, the number of places after the decimal point in 270.908 will be equal to the least number of decimal places i.e. 1 ( in 8.6 )

Hence, 67.31 - 8.6 + 212.198 = 270.9

A telephone pole is perpendicular to the ground. What is the size of the angle between the ground and the telephone pole? How do you know?

Answers

90 degrees
perpendicular just means the angle between the two planes, in this case the ground and the pole, is 90 deg :)

The values √8 and √14 are plotted on the number line.

What is the approximate difference in tenths between the two values?
0.5
0.9
1.1
2.4

Answers

Firstly, you have to count the number of spaces between the two points on the line, which gives you 9. Now, remember that you are counting between tenths on a number line, so you divide 9 by 10 to give you your answer, 0.9.

Answer:

The correct option is 2.

Step-by-step explanation:

The values √8 and √14 are plotted on the number line.

From the given number line it is clear that

[tex]\sqrt{8}\approx 2.8[/tex]

[tex]\sqrt{14}\approx 3.7[/tex]

We have to find the approximate difference in tenths between the two values √8 and √14.

[tex]\sqrt{14}-\sqrt{8}\approx 3.7-2.8[/tex]

[tex]\sqrt{14}-\sqrt{8}\approx 0.9[/tex]

The approximate difference in tenths between the two values is 0.9.

Therefore the correct option is 2.

need help thank thank you

Answers

im pretty sure number 10 is B

Which expressions are completely factored?

Select each correct answer.

A. 16a^5−20a^3=4^3(4a^2−5)

B. 24a^4+18=6(4a^4+3)

C. 30a^6−24a^2=3a^2(10a^4−8)

D. 12a^3+8a=4(3a^3+2a)

Answers

I’m pretty sure all of them are completely factored.

Answer:

Step-by-step explanation:

The only thing that you can factor out of B is 6, while the others are not in simplest form. Answer C can still factor out 2 and answer choice D can still factor out a. Answer choice can still be factored further using difference of squares.

Triangle RST is congruent to triangle WXY. If the area of triangle WXY is 20 square inches, then the area of triangle RST is _____.
40 in2
10 in2
20 in2
80 in2

Answers

The area of triangle RST is also 20 20 square inches

What are congruent triangles?

Triangles having equal side lengths and equal corresponding angles measures are called congruent triangles.

Given that, triangle RST is congruent to triangle WXY, the area of triangle WXY is 20 square inches,

We are asked to find the area of triangle RST,

Since, triangles RST and WXY are congruent, therefore, they will have congruent sides and angles,

That means, they will have equal area also,

ar (Δ RST) = ar (Δ WXY)

Therefore,

ar (Δ RST) = 20 square inches

Hence, the area of triangle RST is also 20 20 square inches

Learn more about congruent triangles, click;

https://brainly.com/question/22062407

#SPJ2

PLEASE HELP
7.06

1. Find the first six terms of the sequence.
a1 = -7, an = 4 • an-1

A) -7, -28, -112, -448, -1792, -7168
B) -28, -112, -448, -1792, -7168, -28,672
C) -7, -28, -24, -20, -16, -12
D) 0, 4, -28, -24, -20, -16

2. Find an equation for the nth term of the arithmetic sequence.
-13, -8, -3, 2, ...

an = -13 x 5(n - 1)
an = -13 + 5(n - 1)
an = -13 + 5(n + 2)
an = -13 + 5(n + 1)

3. Find an equation for the nth term of the arithmetic sequence.
a15 = -53, a16 = -5

A) an = -725 - 48(n - 1)
B) an = -725 + 48(n + 1)
C) an = -725 + 48(n - 1)
D) an = -725 - 48(n + 1)

4. Determine whether the sequence converges or diverges. If it converges, give the limit.
11, 44, 176, 704, ...

A) Diverges
B) Converges; 231
C) Converges; 3751
D) Converges; 935

5. Find an equation for the nth term of the sequence.
-4, -16, -64, -256, ...

A) an = 4 • -4n
B) an = 4 • -4n + 1
C) an = -4 • 4n
D) an = -4 • 4n - 1

6. Find an equation for the nth term of a geometric sequence where the second and fifth terms are -2 and 16, respectively.

A) an = 1 • (-2)n - 1
B) an = 1 • 2n
C) an = 1 • (-2)n + 1
D) an = 1 • 2n - 1

7. Write the sum using summation notation, assuming the suggested pattern continues.
4 - 24 + 144 - 864 + ...

A) summation of four times six to the power of n from n equals zero to infinity
B) summation of four times negative six to the power of n from n equals zero to infinity
C) summation of four times negative six to the power of the quantity n minus one from n equals zero to infinity
D) summation of four times six 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.
-3 + 6 + 15 + 24 + ... + 132

A) summation of negative 27 times n from n equals 0 to infinity
B) summation of negative 27 times n from n equals 0 to 15
C) summation of the quantity negative 3 plus 9 n from n equals 0 to infinity
D) summation of the quantity negative 3 plus 9 n from n equals 0 to 15

9. Write the sum using summation notation, assuming the suggested pattern continues.
343 + 512 + 729 + 1000 + ... + n3

A) summation of the quantity n minus 1 cubed from n equals 7 to infinity
B) summation of n cubed from n equals 7 to infinity
C) summation of n cubed from n equals 8 to infinity
D) summation of the quantity n plus 1 cubed from n equals 7 to infinity

10. Find the sum of the arithmetic sequence.
3, 5, 7, 9, ..., 21

A) 39
B) 120
C) 20
D) 23

11. Find the sum of the geometric sequence.
4 divided by 3, 16 divided by 3, 64 divided by 3, 256 divided by 3, 1024 divided by 3

A) 1363 divided by 3
B) 1364 divided by 15
C) 1364 divided by 3
D) 1363 divided by 15

12. An auditorium has 20 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) 390
B) 580
C) 620
D) 400

13. Use mathematical induction to prove the statement is true for all positive integers n.
10 + 20 + 30 + ... + 10n = 5n(n + 1)

14. A certain species of tree grows an average of 4.2 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 300 centimeters tall.

Answers

1. A. According to the expression a_n=4*a_n-1, each term after a1 is four times the previous term. The first term is -7 as given, 2nd term should be -7*4=-28, 3rd term is -28*4=-112, ... A is the correct answer.

2. B. The sequence is -13, -8, -3, 2... It's obvious that each term is equal to the previous term plus 5. This is an arithmetic sequence with initial term -13 and common difference 5. We know a1=-13, so a_n=-13+5*(n-1). The answer is B.

3. A. We are given a15=-53, a16=-5. The common difference of the arithmetic sequence is -5-(-53)=48. The formula for a_n term is a1+48*(n-1). We know that a15=-13; plug in n=15, a15=-53=a1+48*(15-1), a1=-725. So a_n=-725+48*(n-1).

4. Diverge. We are given a few terms, 11, 44, 176, 704... Observe that each term is four times the previous one. 11*4=44, 44*4=176, 176*4=704... This is a geometric series with common ratio>1. You can keep multiplying by 4 and the series goes to infinity, so it diverges.

5. D. We have -4, -16, -64, -256... Same as above, each term is four times the previous one. The initial term is a1=-4. The common ratio d=4. So a_n=a1*d^(n-1)=-4*4^(n-1)=-4^n. (D).

6. The answer is A. a2=-2, a5=16. Suppose the common ratio is D. a_n=a1*d^(n-1). a2=a1*d; a5=a1*d^4. Plug in a2 and a5: -2=a1*d, 16=a1*d^4. 16/-2=d^3=-8, d=-2, a1=1. So a_n=1*(-2)^(n-1).

7. B. We are given the sequence 4, -24, 144,... Each term is -6 times the previous one. The first term a0=4, the n^th term a_(n-1) is a1*d^n=4*(-6)^n. To express the sum, we simply have to use the sigma notation and sum 4*(-6)^n from n=0 to infinity. The answer is B.

8. D. We are given -3 + 6 + 15 + 24... 132. Each term is equal to the previous one plus 9. First term a0=-3, n^th term a_n-1 is -3+9*n. The last term is 132. 132 =-3+9n, n=15. So we have to sum -3+9n from n=0 to n=15.

9. B. 343 + 512 + 729 + 1000+... 343=7^3, 512=8^3, 729=9^3, 1000=10^3. This is a sequence of perfect cubes. Therefore, the sum is n^3 from n=7 to infinity. (The initial term is 343=7^3).

10. B. We are given 3, 5, 7, 9, ... 21. The common difference is 2. There are (21-3)/2+1=10 terms. The initial term a1=3, and last term is a10=21. The sum is (a1+a10)*10/2=(3+21)*10/2=120.

11. C. 4/3, 16/3, 64/3, 256/3, 1024/3. Each term is four times the previous one. This is a geometric series with initial term a1=4/3 and common ratio r=4. 1024/3 is the 5th term of the sequence. So sum=a1*(1-r^n)/(1-r)=4/3*(1-4^5)/(1-4)=-4/9*-1023=1364/3.

12. B. 10,12,14,... This is an arithmetic sequence. a1=10, and common difference d=2. There are 20 terms (20 rows). a20=a1+d*(n-1)=10+2*(20-1)=48. So the sum S=(a1+an)*n/2=(10+48)*20/2=580.

13. 10 + 20 + 30 + ... + 10n = 5n(n + 1). When n=1, this expression is true, since 10=5*1*(1+1). Suppose when n=k, this statement is true, then when n=k+1, the left side is 10+...+10n+10(n+1), the right side is 5(n+1)(n+2). The left side adds 10(n+1) compared to the previous one. The right side adds 5(n+1)(n+2)-5n(n+1)=5(n+1)(n+2-n)=10(n+1). So the statement holds true.

14. The height at week 0 is a0=300 (initial height). Common difference is 4.2 (weekly increment). a_n=300+4.2n. At week n, the height of the tree is 300+4.2*n centimeters.

Hello,
Please, see the detailed solution in the attached files.
Thanks

HELP SOMEONE SMART
What is the solution of the equation? Step by step.

Answers

As with any "solve for" problem, you undo what has been done to the variable, in reverse order.
Subtract 9, divide by 3, take the 5/3 power
.. 3*(a +4)^(3/5) +9 = 36 . . . . . original equation
.. 3*(a +4)^(3/5) = 27
.. (a +4)^(3/5) = 9
.. a +4 = 9^(5/3)
.. a = 9^(5/3) -4 ≈ 34.9407

The formula for volume of this rectangular prism is:

V = 2x 3 + 17x 2 + 46x + 40

Find an expression for the missing side length. Show all of your work for full credit.

Answers

By definition, the volume of a rectangular prism is given by:
[tex]V = (w) * (h) * (l) [/tex]
Where,
l: length
h: height
w: width
Substituting values we have:
[tex]2x ^ 3 + 17x ^ 2 + 46x + 40 = (w) * (x + 2) * (x + 4) [/tex]
From here, we clear the value of w.
[tex]w = (2x ^ 3 + 17x ^ 2 + 46x + 40) / ((x + 2) * (x + 4)) [/tex]
Factoring the numerator we have:
[tex]w = ((x + 2) * (x + 4) * (2x + 5)) / ((x + 2) * (x + 4)) [/tex]
Canceling similar terms we have:
[tex]w = 2x + 5 [/tex]
Answer:
The missing side is of length:
w = 2x + 5

The volume of a rectangular prism is the product of its dimension.

The missing side length is 2x + 5.

The volume is given as:

[tex]\mathbf{V = 2x^3 + 17x^2 + 46x + 40}[/tex]

Let the missing side be y.

So, we have:

[tex]\mathbf{V = (x + 2) \times ( x + 4) \times y}[/tex]

So, we have:

[tex]\mathbf{(x + 2) \times ( x + 4) \times y = 2x^3 + 17x^2 + 46x + 40}[/tex]

Factorize

[tex]\mathbf{(x + 2) \times ( x + 4) \times y = (x + 2) \times (x + 4) \times (2x +5)}[/tex]

Cancel out common factors

[tex]\mathbf{y = (2x +5)}[/tex]

Remove brackets

[tex]\mathbf{y = 2x +5}[/tex]

Hence, the missing side length is 2x + 5.