Mathematics High School

George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.

a.
What is the area of the pool cover?
b.
What is the length of the rope?

Answers

Answer 1

so use a basic formula here:

area of a circle = πr²

and the circumference of a circle = πd

a)

therefore the area of the pool cover is π multiplied by the radius² (which is the diameter of the pool cover plus the extra 12 inches divided by two, so the radius is 21/2 or 10.5) is 346.36(to two decimal places.)

b)

Using the same diameter, we can work out the length of the rope by multiplying the diameter (10.5) by π, which is 32.99 (to two decimal places).

Related Questions

The three sides of sail A are each half the length of the three sides of sail B. How do the areas of the two sails compare?

Answers

answer

Area of sail A is 1/4 of area of sail B

Answer:

Step-by-step explanation:

It is B

The value of a treadmill bought new for $1000 decreases 5% each year. Use a graph to predict the value of the treadmill in 5 years.
A) ≈ $773.78
B) ≈ $857.38
C) ≈ $902.50
D) ≈ $814.50

Answers

The formula is
V (t)=V0 (1-r)^t
V (t)?
V0 1000
R 0.05
T 5 years

V (5)=1,000×(1−0.05)^(5)=773.78

The predicted value of the treadmill after 5 years, with an annual depreciation rate of 5%, is approximately $773.78. This calculation uses the exponential decay formula and corresponds to option A).

To predict the value of a treadmill in 5 years that was bought new for $1000 and decreases 5% each year, we can use the formula for exponential decay:

V = [tex]P(1 - r)^t[/tex]

Where:

V is the future value of the treadmill,

P is the original value ($1000),

r is the rate of decay (5% or 0.05), and

t is the time in years (5 years).

By substituting the values we have:

V = $1000(1 - 0.05)⁵

V = $1000(0.95)⁵

V = $1000(0.77378) = $773.78

Therefore, the predicted value of the treadmill after 5 years is approximately $773.78, which corresponds to option A).

In early spring, you are wanting to purchase 6 potted rose plants. The plants to choose from come in 8-inch pots that sell for $12 and 10-inch pots that sell fro $15. If you spend $78, which of the following are the equations for this scenario? Let x= number of 8 inch pots and let y = number of 10 - inch pots.

A. y+15y=6
12x+x=78

B. x+y=6
12x+15y=78

C. x+y=78
12x +15y=6(78

D. x+y=6
15x+12y=78

E. No solution

Answers

Things we know:
Six total pots = # of 10" + # of 8"
$78 total = cost of 10" + cost of 8"

So:
6 = x +y
and
78 = x*(cost of x) + y * (cost of y)
78 = x*12 + y*15

We need:
x+y=6  AND 12x+15y=78

So our answer can only be B. 

The difference of twice a number g and 10 is 24

Answers

The equation is 2g-10=24. To solve this, you need to get g by itself. So add 10 to both sides. You get 2g=34. Then, divided by 2 on each side. You get g=17. The answer to this is g=17. I hope this helps! ;)

Find the area of the shaded region.

Answers

Hi!

To find the area of a rectangle, multiply base times height.

5 x 10 = 50

Now we need to subtract the area of the non-shaded part.

2 x 2 = 4
50 - 4 = 46

The answer is 46

Hope this helps! :)
First, find the area of the shaded region plus the white region, which is 5*10, or 50. Now find the white region only, which is 2*2, or 4. Now subtract 4 from 50 to get the area of the shaded region only. You will get 46. So 46 is your answer.

Hope the explanation helped!

Please Help! Math Question!

Variable g is 8 more than variable w. Variable g is also 4 less than w. Which pair of equations best models the relationship between g and w?


A) g = w − 8
g = w + 4

B) w = 8g
w = g − 4

C) g = w + 8
g = w − 4

D) w = 8g
w = g + 4

Answers

"g is 8 more than w" means 
g = 8 more than w
g = 8+w
g = w+8

"g is also 4 less than w" means
g = 4 less than w 
g = w-4

The two equations are therefore:
g = w+8
g = w-4

which means the answer is choice C

Answer:

The answer is C.

g = w + 8

g = w − 4

Hope This Helps!

(03.01)

A newly made car will have a model number, a parts number, and a serial number. A model number is assigned by the manufacturer to identify each type of car. A parts number identifies one part of the smaller parts that make up the car. A serial number is unique to each car produced and identifies it.

Which relation is a function?
(parts number, serial number)
(model number, parts number)
(serial number, model number)
(serial number, part number)

Answers

The answer you want is letter C, have a good day

Answer:

Hi!

The corrects answers are:

•(serial number, model number)

Step-by-step explanation:

First, you have to understand the meaning of a function, that is an a relation but have the condition:

The input must be relationed with only one output.

The question says:

"A serial number is unique to each car produced and identifies it." so this will be you input, and will be related with only one model number.

Suppose you add two linear equations that form a system, and you get the result y = −2. how many solutions does the system have?

Answers

This system will have 1 solution <==

** if it were to end like 0 = 4, or 2 = -3....no variables and numbers that dont equal....this means no solutions.

** if u were to end up with 5 = 5, or -9 = -9...no variables and numbers that do equal, then u will have infinite solutions

** but if u end with y = -2 or x = 5...a variable equaling a number, then u will have 1 solution

Identify the x-intercept and y-intercept of the line
4x−2y=−12
4x−2y=−12
.
Select one:
a. The x-intercept is (0,-3) and the y-intercept is (6,0).
b. The x-intercept is (-3,0) and the y-intercept is (0,6).
c. The x-intercept is (4,0) and the y-intercept is (0,-2).
d. The x-intercept is (0,6) and the y-intercept is (-3,0).

Answers

4x−2y=−12
-2y = -4x - 12
y = 2x + 6

The y-intercept is b, in the equation y = mx + b.
So that means here the y-intercept is 6.

Now to get the x-intercept, you need to put the y at 0.

0 = 2x + 6
-6 = 2x
-3 = x

X-intercept is -3.

Also remember that the x and y intercepts look like this: (x, y). For the x-intercept, the y has to be at 0. For the y-intercept, the x has to be at 0.

So the answer is B.

The x-intercept is (-3,0) and the y-intercept is (0,6).

The correct option is B,

What are intercepts?

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

Given information:

4x - 2y = -12.

To find the x-intercept, we set y to zero and solve for x:

4x - 2y = -12

4x - 2(0) = -12

4x = -12

x = -3

So the x-intercept is (-3, 0).

To find the y-intercept, we set x to zero and solve for y:

4x - 2y = -12

4(0) - 2y = -12

-2y = -12

y = 6

So the y-intercept is (0, 6).

Therefore, the answer is b. The x-intercept is (-3,0) and the y-intercept is (0,6).

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Determine the domain of the function. f(x) is equal to four divided by x squared.
A. x ≥ 0
B. All real numbers except 0
C. All real numbers except 3
D. All real numbers

Answers

f(x)  = 4/x^2

Think what values of x give real values of f(x)

negative numbers are Ok  andso are positive ones 

What about x = 0? What is the value of 4 / (0)^2  ?

Find the coordinates of point l that lies along the directed line segment from N(14,4) to M(2,8) and partitions the segment in the ratio of 1:3

Answers

1. Drop the perpendicular from M to the x -axis, and the perpendicular from N to the y-axis.

Let these perpendiculars intersection be point A, with coordinates (2, 4).

[clearly A will have x coordinate equal to the x coordinate of M, and y coordinate equal to the y coordinate of N]

2. Let P be the point on NM such that |NP|/|PM|=1/3

3. Drop the perpendiculars from point P to AN and AM. Let the foot of these perpendiculars be points P' and P'' respectively.

4. By Thales theorem: |NP'|/|P'A|=1/3 and |AP''|/|P''M|=1/3

so let |NP'|=b, |P'A|=3b, |AP''|=c, |P''M|=3c, as shown in the figure


5. |AN|=14-2=12. 
    |AN|=4b so b=12/4=3

the x coordinate of P'=2+3b=2+9=11
the x coordinate of P= the x coordinate of P'=11

similarly |AM|=8-4=4
              |AM|=4c so c=1

the y coordinate of P'' is 4+c=4+1=5

the y coordinate of P = the y coordinate of P''=5





Answer: (11, 5)


How to divide fractions

Answers

When dividing fractions, what you do, is turn it into multipcation. You use the multiplicitve inverse (reciprocal) to multiply.

For example:

3/7÷ 5/8 = 3/7×8/5

Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division sign to multiplication and flip the second fraction. Let's try an example.

[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{5}{9}[/tex] can be rewritten as [tex]\frac{1}{2}[/tex] × [tex]\frac{9}{5}[/tex].

Now, we are simply multiplying fractions.

Multiply across the numerators and the denominators

[tex]\frac{1}{2}[/tex] × [tex]\frac{9}{5}[/tex] = [tex]\frac{9}{10}[/tex]

Therefore, [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{5}{9}[/tex] = [tex]\frac{9}{10}[/tex]

Lou’s Shoes is having its annual Flag Day Sale and is offering a 25% discount on all regularly priced shoes. Kayla spends $13.50 buying sandals and sneakers. Determine which equation represents how much Kayla will spend on sandals after the discount.

Answers

The easiest way to think of these is to put them in terms of percentages.  Obviously, if you are SAVING 25%, you are SPENDING 75%.  So if she SPENDS 13.50, we can easily use the 75% in an equation. $13.50 = .75x, with x being what the shoes cost originally.  The .75 indicates that she is spending 75% of what the original cost is. You don't have any examples to pick from, but this is the best way to explain what one of the equations could be.  You could also base it on money saved, but the equation is not quite as neat.

The equation represents how much Kayla will spend on sandals after the discount is $13.50 = 0.75x.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Lou’s Shoes is having its annual Flag Day Sale and is offering a 25% discount on all regularly priced shoes. Kayla spends $13.50 buying sandals and sneakers.

The equation can be written as:-

$13.50 = 0.75x.

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A video game sets the points needed to reach the next level based on the function g(x) = 12(2)x − 1, where x is the current level. The hardest setting promises to multiply the points needed in each level according to the function h(x) = 3x. How many points will a player need on the hardest setting of level 6?
A 18 points
B 384 points
C 4020 points
D 6912 points

Answers

I believe the x-1 is suppose to go in an exponent, so g(x) = 12(2)^(x-1). In this case, we're just going to plug in 6 for x in both g(x) and h(x) to get the total amount of xp. g(6) = 12(2)^(6-1) = 384, then h(6) = 3(6) = 18, so g(6)*h(6) = 384*18 = 6912, so D is the correct answer. Let me know if it was written differently than I interpreted it, tried it a few different ways until I got it to work.

Which inequality describes the graph?

Answers

Last one, y>= 3/4x-3.

The line is the same in all answers, so you may look at the inequality signs. The shaded area is on top, this means greater than, and the line is not dashed, so it belongs to the solution: greater or equal than
The  blue is above the white so it must be "greater-than".
Also, the division between the two is solid so it can be "equal to".
The answer is D

find the area and circumference of a circle with radius 4 in.

Answers

area = PI * radius ^ 2
area = 3.14159 * 4 ^ 2
area = 3.14159 * 16
area = 50.26544 square inches

circumference = 2 * PI * radius
circumference = 2 * 3.14159 * 4
circumference = 25.13272 inches

 



Answer is provided in the image attached.

There are 40 vehicles in a parking lot.Twenty percent of the vehicles are pickup trucks.How many pickup trucks are in the parking lot?

Answers

40 total vehicles....20% are pickup trucks....how many are pickup trucks

20% of 40....turn ur percent to a decimal..." of " means multiply

0.20(40) = 8.....there are 8 pickup trucks <==

Spencer Ward purchased a new riding mower for $1,989. He made a 15% down payment and financed the remainder. What amount did he finance?

Answers

The amount of the down payment is
1,989×0.15=298.35

Amount financed is
1,989−298.35=1,690.65

A rectangular table with sides in the ratio 3:5 has a perimeter equal to 240 inches. what is the area of the table in square inches?

Answers

Given that the rectangular table has sides with ratio 3:5 and perimeter, the side lengths will be as follows;
Total ratio=8
length=5/8*240=150 inches

width=3/8*240=90 inches
The area of the table will be:
A=length*width
=150*90
A=13,500 square inches

Identify each function as a constant, direct variation, absolute value, or greatest integer function.
g (x)=x+3

Answers

None of those describe this function.

It's not a constant function, because it is not equal to a constant (something that isn't a variable)

It doesn't show direct variation, because it can't be represented in the form
y = kx.

It isn't an absolute value function because the absolute value isn't taken anywhere.
If it was an absolute value function it would look something like this:
[tex]g(x) = |x+3|[/tex]

It isn't a greatest integer function, because the greatest integer isn't taken anywhere.
If it was a greatest integer function it would look something like this:
[tex]g(x) = \left \lfloor{x + 3}\right \rfloor[/tex]

Are you sure you typed that question right?

What is the ratio of the area of sector ABC to the area of sector DBE?
I am not quite sure how to do this. So far, since there are variables instead of numbers, I have got (pi)(r)^2:(pi)(3r)^2, but I know that is definitely wrong.

Answers

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}\qquad \begin{cases} \theta =\textit{angle in degrees}\\ r=radius \end{cases}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{\triangleleft ABC}{\triangleleft DBE}\qquad \cfrac{\frac{\beta \pi (2r)^2}{360}}{\frac{3\beta \pi (r)^2}{360}}\implies \cfrac{\beta \pi (2r)^2}{360}\cdot \cfrac{360}{3\beta \pi (r)^2}\implies \cfrac{\beta \pi 2^2r^2}{360}\cdot \cfrac{360}{3\beta \pi r^2} \\\\\\ \cfrac{\beta \pi 4r^2}{3\beta \pi r^2}\implies \cfrac{4}{3}[/tex]

Answer:

4/3

Step-by-step explanation:


why is a stem and leaf plot called a stem and leaf plot?

Answers

A stem and leaf plot is called a stem and leaf plot because it is a table where each number in a set gets broken up into stems and leaves.

Stem = the first digit, or digits
Leaf = the last digit 

Ex: The stem of 32 would be 3 and the leaf would be 2. 
     
Final answer:

A stem-and-leaf plot gets its name from the way the data is structured. The 'stem' represents the highest place value digits of the numbers in the dataset, and the 'leaf' represents the lower place value digits. These plots keep the actual numerical data intact, providing more detail than other data representations like bar graphs or histograms.

Explanation:

The term stem-and-leaf plot, also known as a stemplot, originates from the way data is structured in this type of graphical representation. The 'stem' in a stem-and-leaf plot stands for the highest place value digits of the numbers in the dataset, similar to the stem of a plant that holds up the leaves. The 'leaf' stands for the lower place value digits, similar to the leaves that extend from the stem. For example, in a dataset [23, 24, 33, 35], 2 and 3 would be stems, and the various units (3, 4 for 2 and 3, 5 for 3) would be leaves.

One of the main purposes of a stem-and-leaf plot is that it keeps the actual numerical data intact, as opposed to other graphical representations like bar graphs or histograms which group data into classes, thus providing a more detailed view of the data distribution.

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Which sequence of transformations will result in an image that maps onto itself?

Answers

The correct transformation to get result in an image that maps onto itself will be;

''Reflect over the y axis and then reflect again over the y axis''.

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The statement is,

'' A sequence of transformations will result in an image that maps onto itself''.

Now,

Since, We know that after two reflections over the same axis we get the original image.

Thus, we get;

The correct transformation to get result in an image that maps onto itself will be;

''Reflect over the y axis and then reflect again over the y axis''.

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Given the following geometric sequence, find the common ratio: {225, 45, 9, ...}.


5
-5
1/5
-1/5

Answers

in the sequence, a,b,c,d... the common ratio is b/a or c/b or d/c etc



so
common ratio in 225 and 49 and 9 is
49/225 or 9/45=1/5

the common ratio is 1/5

Answer:

1/5

Step-by-step explanation:

if trapezoid jklm is translated according to the rule (x,y) ,(x+8,y-3) what are the coordinates of point L

Answers

If the coordinates of L were (-5, -2) then you have to add 8 to the x value and subtract 3 from the y value.

-5 + 8 = 3
-2 - 3 = -5

New coordinates of L: (3, -5)

Hope this helps :)
Please give brainliest
Final answer:

With the given translation rule, to find new coordinates of a point L in trapezoid JKLM, apply it to the original coordinates by moving right by 8 units and down by 3 units. If original coordinates of L were (2,5), new coordinates will be (10,2).

Explanation:

In geometry, a translation is a type of transformation that slides a figure along a straight line. In this case, the translation rule given is (x, y) -> (x+8, y-3). This means that every point in the trapezoid is being moved 8 units to the right (increase in x-coordinate) and 3 units down (decrease in y-coordinate).

Per your question, to find the new coordinates of point L after the translation, you simply need to apply this rule to the original coordinates of point L. If for example, the original coordinates of point L were (2, 5), its new coordinates after the translation would be calculated as follows: (2+8, 5-3) = (10, 2).

This is how you find the new coordinates of a point after a translation in geometry.

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What is the are of the triangle below??

Answers

it is 9 squares high and the base is 6 squares wide

9*6 = 54

54/2 = 27

 area = 27 square units

If csc 0=8÷7 which equation represents cot 0

Answers

Answer: [tex]Cot\theta =\frac{\sqrt{15} }{7}[/tex]

Step-by-step explanation:

Since, given [tex]cosec\theta=\frac{8 }{7}[/tex]

And we know that [tex]Cot\theta=\sqrt{cosec^2\theta-1}[/tex]

Therefore, [tex]Cot\theta=\sqrt{cosec^2\theta-1} = \sqrt{(8/7)^2-1}= \sqrt{64/49-1}[/tex]

⇒[tex]Cot\theta=\sqrt{64-49/49}=\sqrt{15/49}=\sqrt{15}/7[/tex]

Thus,  [tex]Cot\theta =\frac{\sqrt{15} }{7}[/tex]


Answer:

CotA=√15/7

Step-by-step explanation:

cosecA=8/7=hypotenuse/perpendicular

We have to find cotA

We do this by right angled triangle

We use pythagoras theorem to find the base

Base²+Perpendicular²=hypotenuse²

Base²+7²=8²

Base²=15

Base=√15

cotA=Base/Perpendicular

     = √15/7

James, caleb and abigail bought a pizza. james ate 1/6 of the pizza, caleb ate 1/4 of the pizza what fracion did james and caleb eat together

Answers

You have to add 1/6 and 1/4. The only way to do that is to find a common denominator.  The lowest number that both 6 and 4 go into is 12:
[tex] \frac{1}{6} + \frac{1}{4} [/tex]
You have to multiply the 6 by 2 to get to 12, so you have to multiply the 1 by 2 to get the equivalent fraction of 2/12. Do the same with the 1/4: you have to multiply 4 by 3 to get to 12, so you have to multiply the 1 by 3 to get to the equivalent fraction of 3/12.
[tex] \frac{2}{12} + \frac{3}{12}= \frac{5}{12} [/tex]

A student solved a system of equations by elimination. The answer is not correct. Describe the error made in the part of the solution shown.

Answers

When multiplying by (-4) ---? -3*(-4)=12, not 3! lol

The error made in the part of the solution is when equation (2) is multiplied by -4 it is not multiplied both side .

What is elimination method?

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

According to the question

5x + 4y= 2 ------------------- (1)

3x + 3y = -3 ------------------- (2)

Now,

solving both equation by elimination method

Multiplying equation (1) by 3 and by 2 to equation (-4)

So, y  can be eliminated

3(5x + 4y)=2 * 3

15x + 12y = 6 -------------- (3)

-4(3x + 3y) = -3*-4

-12x - 12y = 12 -----------------(4)

Now,

Adding both eq(3) and (4)

3x = 18

x = 6

Putting value of x in eq(1)

5*6 + 4y = 2  

30 + 4y = 2

4y = 2 - 30

4y = - 28

y = -6

Hence, the error made in the part of the solution is when equation (2) is multiplied by -4 it is not multiplied both side .

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What is the solution to the inequality l2n+5l > 1

Answers

[tex]|2n+5| \ \textgreater \ 1\\ 2n+5\ \textgreater \ 1 \vee 2n+5\ \textless \ -1\\ 2n\ \textgreater \ -4 \vee 2n\ \textless \ -6\\ n\ \textgreater \ -2 \vee n\ \textless \ -3\\ n\in(-\infty,-3)\cup(-2,\infty)[/tex]

l2n+5l > 1

(2n+5) > 1
    2n > - 4
      n > -2

-(2n+5) > 1
    -2n - 5 > 1
      -2n  > 6
         n < -3

answer
n<-3 or n>-2
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