Mathematics High School

A wire 360 in. long is cut into two pieces. one piece is formed into a square and the other into a circle. if the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)?

Answers

Answer 1

The length of piece of wire for square = 230 inches

The length of piece of wire for circle = 130 inches.

The given length of  wire = 360 inches

Now let it cuts into lengths r' and r

Therefore,

⇒ r' + r = 360   ...(i)

Now let with length r' square is formed

Therefore,

Area of square = r'xr'

                         = (r')²

And with length of r circle is formed,

Area of circle = π r²

According to the question

Both area are same,

⇒ (r')² =  π r²

Taking square root both sides,

⇒ r' = √π r    ......(ii)

Now from (i) and (ii);

⇒ √π r + r = 360

⇒ r(1 + √π) = 360

⇒      2.77 r = 360

⇒              r = 129.96 ≈ 130 in

Then r' = 360 - 130

            = 230

Hence length are 130 inches and 230 inches.

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Related Questions

ABCD is a rectangle. The length of BD is 8 units and m

What is the length of AC and m

Answers

Do You Have A Picture So I Can Know Where The Points Go..

Round ​$0.6848 to the nearest cent.

Answers

$0.68. When you round a number when it comes to decimals, you need to round to the nearest 100ths place. 

JIMMMM! :)

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2^x and y = 4^x−2 intersect are the solutions of the equation 2^x = 4^x−2. (4 points)

Part B: Make tables to find the solution to 2^x = 4^x−2. Take the integer values of x between −4 and 4. (4 points)

Part C: How can you solve the equation 2^x = 4^x−2 graphically? (2 points)

Answers

Part A

The x coordinates are the inputs of the functions f(x) = 2^x and g(x) = 4^(x-2)

If we have some input x that leads to f(x) = g(x), then this x value is a solution. It makes the equation f(x) = g(x) true. This is why the x coordinate of the intersection point of y = 2^x and y = 4^(x-2) is the solution.

-------------------------------------------------------------------------
Part B

See attached for the table. See figure 1.

This is how you get the results you see in the table
Plug x = -4 into f(x) to get:
f(x) = 2^x
f(-4) = 2^(-4)
f(-4) = 0.0625

Do the same for g(x):
g(x) = 4^(x-2)
g(-4) = 4^(-4-2)
g(-4) = 4^(-6)
g(-4) = 0.000244140625

-------------------
Plug x = -3 into f(x) to get:
f(x) = 2^x
f(-3) = 2^(-3)
f(-3) = 0.125

Do the same for g(x):
g(x) = 4^(x-2)
g(-3) = 4^(-3-2)
g(-3) = 4^(-5)
g(-3) = 0.0009765625

-------------------
Plug x = -2 into f(x) to get:
f(x) = 2^x
f(-2) = 2^(-2)
f(-2) = 0.25

Do the same for g(x):
g(x) = 4^(x-2)
g(-2) = 4^(-2-2)
g(-2) = 4^(-4)
g(-2) = 0.00390625

-------------------
Plug x = -1 into f(x) to get:
f(x) = 2^x
f(-1) = 2^(-1)
f(-1) = 0.5

Do the same for g(x):
g(x) = 4^(x-2)
g(-1) = 4^(-1-2)
g(-1) = 4^(-3)
g(-1) = 0.015625

-------------------
Plug x = 0 into f(x) to get:
f(x) = 2^x
f(0) = 2^(0)
f(0) = 1

Do the same for g(x):
g(x) = 4^(x-2)
g(0) = 4^(0-2)
g(0) = 4^(-2)
g(0) = 0.0625

-------------------
Plug x = 1 into f(x) to get:
f(x) = 2^x
f(1) = 2^(1)
f(1) = 2

Do the same for g(x):
g(x) = 4^(x-2)
g(1) = 4^(1-2)
g(1) = 4^(-1)
g(1) = 0.25

-------------------
Plug x = 2 into f(x) to get:
f(x) = 2^x
f(2) = 2^(2)
f(2) = 4

Do the same for g(x):
g(x) = 4^(x-2)
g(2) = 4^(2-2)
g(2) = 4^(0)
g(2) = 1

-------------------
Plug x = 3 into f(x) to get:
f(x) = 2^x
f(3) = 2^(3)
f(3) = 8

Do the same for g(x):
g(x) = 4^(x-2)
g(3) = 4^(3-2)
g(3) = 4^(1)
g(3) = 4

-------------------
Plug x = 4 into f(x) to get:
f(x) = 2^x
f(4) = 2^(4)
f(4) = 16

Do the same for g(x):
g(x) = 4^(x-2)
g(4) = 4^(4-2)
g(4) = 4^(2)
g(4) = 16

Note that since the input x = 4 leads to the same output (16) this makes x = 4 a solution.

-------------------------------------------------------------------------
Part C

To solve graphically, you need to use the table in part B to draw a curve through the set of points. Then determine where the curves cross (if they cross at all). You may need to adjust the graph window if the intersection point is off the screen.

See figure 2 for the graph (attached as well). Point A in green is the intersection point. 
A = (4,16) 
so x = 4 is the solution to f(x) = g(x).


Hello there!

Part A: The point or points of intersection are the values of the variables which satisfy both equations at a particular point.

If [tex]y=2^x and y=4 ^{x-2} [/tex]  and the solution of which will satisfy both equations. This idea of equating the two equations is something that you would have come across before, maybe without realizing it.
Consider this:
[tex]x^2 + 6x + 9=0 This can also be looked at as being the two equations: y=x^2 +6x+9 and y=0 [/tex]
So the points of intersection are the roots in this case and satisfy the equation:
[tex]x^2 + 6x +9=0 This explains why it will be the solution to: 2^x = 4 ^{x-2} , because this is the equation formed at the intersection.[/tex]

Part B:
You just put integer values between -4 and 4 in each equation and when the output is the same for both that is the solution.

[tex]2^ ^{-4} = 0.0625 , [/tex] and [tex]4 ^{-6} = 0.000244[/tex]
[tex]2 ^{-3} = 0.125, [/tex] [tex]4 ^{-5} =0.000977[/tex]
[tex]2 ^{-2} =0.25[/tex] and [tex]4 ^{-4} =0.003906[/tex]
[tex]2 ^{-1}= -0.5,[/tex] and [tex]4 ^{-3} =0.01563[/tex]
[tex]2^0 =1[/tex] , and [tex]4 ^{-2} =0.0625[/tex]
[tex]2^1 = 2 [/tex] and [tex]4 ^{-1} =0.25[/tex]
[tex]2^2 =4 [/tex] and [tex]4^0 =1[/tex]
[tex]2^3 =8[/tex] and [tex]4^1=4[/tex]
[tex]2^4 =16, [/tex] and [tex]4^2 = 16 [/tex]  (This is the solution when x=4)


Part C:
To solve graphically you just plot the two equations [tex]=2^x[/tex] and [tex]y=4 ^{x-2} [/tex]
Together graph of [tex]y=2^x [/tex] and [tex]y=4 ^{x-2} [/tex]

The picture below is how the graph looks like.
Full Credit to my online calculator 'cause we don't have a graphing calculator here.

I hope I helped!


The new shanghai restaurant offers a choice of five appetizers, two choices of soups, and eleven choices of entrees for its lunch special. how many different complete lunches can be ordered from the restaurant's lunch special menu?

Answers

multiply the choices together
5*2*11 = 110

Final answer:

Using the Multiplication Principle, a customer can choose from 110 different complete lunch combinations by selecting one of each option (appetizer, soup, and entrée) from the menu at the New Shanghai restaurant.

Explanation:

To determine the total number of different complete lunches that can be ordered from the restaurant's lunch special menu, we apply The Multiplication Principle of counting. The principle states that if one event can occur in m ways and another independent event can occur in n ways, then the total number of ways both events can occur together is the product of m and n. In the context of ordering a lunch, each choice (appetizer, soup, and entrée) represents an independent event.

For appetizers, there are 5 choices.

For soups, there are 2 choices.

For entrées, there are 11 choices.

Following the Multiplication Principle, the total number of different complete lunches is calculated as follows:

5 appetizers × 2 soups × 11 entrées = 110 different complete lunches.

Therefore, customers have the opportunity to choose from 110 unique complete lunch combinations at the New Shanghai restaurant.

Mitch refuses to dine at a certain restaurant because he recalls reading two or three negative reviews of its service on a popular website. Mitch is falling prey to:

Answers

In this situation, we can actually see that Mitch was simply basing her taste on the information that is readily available to her. She does not even consider whether those reviews are legit or reliable. Mitch is falling into what we call as:

 

“the availability heuristic”

Final answer:

Mitch is falling prey to the bandwagon effect, where he avoids dining at a restaurant based on a few negative reviews he read online. The bandwagon effect is a cognitive bias that leads us to adopt beliefs or behaviors because we think everyone else is doing the same.

Explanation:

Mitch is falling prey to the bandwagon effect. The bandwagon effect is when someone adopts a certain belief or behavior because they believe that everyone else is doing it too. In this case, Mitch refuses to dine at a certain restaurant because of negative reviews he read on a popular website, assuming that those reviews reflect the majority opinion.



The bandwagon effect is a cognitive bias that can influence our decision-making process. It is important to be aware of this bias and make decisions based on objective information rather than simply following the crowd.

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HELLLLLPPP PLLEASEEE

Answers

Just looking at the formula, the original amount invested equals 728.
The answer is B

If you vertically compress the absolute value parent function, f(x) = |x|, by a factor of 3, what is the equation of the new function?
A. g(x) = |x – 3|
B. g(x) = |3x|
C. g(x) = 1/3 |x|
D. g(x) = 3|x|

Answers

That is correct. On APEX its C. g(x)= 1/3 |x|

what type of triangle has two angles at 70 degrees and one at 40 degrees

Answers

Isoceles Triangle.

By TWL

You make a large bowl of salad to share with your friends. Your brother eats 1/3 of it before they come over

Answers

Assume that the original amount of salad you made is "m".
Now, your brother ate 1/3 of the original amount.

This means that:
The amount left to be divided among your friends = m - (1/3) m = (2/3) m

Now, we need to divide this amount among the six friends of yours, therefore:
the amount that each friend gets can be calculated by dividing the (2/3) m which is the left portion of the salad by the number of friends as follows:
each friend receives = [(2/3) m] / 6 = (1/9) m

hard question ! Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her own expenses. After a month of driving from neighborhood to neighborhood and walking door-to-door, she figures out that her weekly earnings are approximately a linear function of the number of doors she knocks on. She writes the equation of the function like this: E(x) = 20x - 50, where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars. Which of the following are reasonable interpretations of the y-intercept of Jessica's function? Check all that apply.
A. Her expenses are $50 per week.
B. She can earn $20 per week even if she does not knock on any doors.
C. If she does not knock on any doors at all during the week, she will lose $50.

D. She will lose $20 per week if she does not knock on any doors.

Answers

The answer is C because she is using gas and not making money

Answer:

A and C

Step-by-step explanation:

Just answered on apex

A cylinder has a height of 6 meters and a diameter that is 6 times the measure of the height

Answers

What is the question?

Which type of triangle has one angle with a measurement greater than 90°? A. Obtuse B. Acute C. Isosceles D. Right

Answers

An obtuse angle is an angle with an angle measure greater than 90 degrees.
Obtuse Triangle has a measure bigger than 90

Sarah is 50 years old. she is twice as old as her friend bill and bill is 5 times as old as his sister jane. jane's mom is 12 times older than jane. what is the age difference between jane's mom and sarah?

Answers

10 years. Bill is 25, his sister is 5, and their mother is 60.

Sarah is twice as old as Bill so 2X=50 and X=25 so Bill is 25. Bill is 25 and bill is 5 times older than his sister Jane so 5n=25 N=5 so Jane is 5 years old. Jane's mom is 12 time older than Jane so 12x5=60 and so

60-50=10 so the answer is 10

Which shows the correct word and expanded forms for the decimal? 3.28
a. three and twenty-eight thousandths 3 + 0.2 + 0.08
b. three and twenty-eight thousandths 3 + 0.02 + 0.008
c. three and twenty-eight hundredths 3 + 0.2 + 0.8
d. three and twenty-eight hundredths 3 + 0.2 + 0.08?

Answers

The correct answer is:  [D]:
___________________________________________ 
    " three and twenty-eight hundredths ;  3 + 0.2 + 0.08 " .
___________________________________________
Note:  Given:  "3.28" .
_________________________
      3
   + 0.2
      0.08
____________
      3.28 ;
___________________________
  Note:  The whole number, "3" (three);  

            "twenty-eight hundredths" = 28/100 = 28 ÷ 100 = 0.28  ; 
___________________________________________________
          Note:  0.2 = 2/10 = 20/100 = 20÷100 = 0.20 = 0.2 ;
___________________________________________________
          Note:  0.08 = 8/100 = 8÷100 = 0.08 ;
___________________________________________________

Help me please don’t know how to do this and I have psat in a week.

Answers

Use the quadratic formula to solve for x (see attached image; we plug in a = 2, b = 7 and c = -15). Doing so leads to 
x = 3/2
x = -5

Since 3/2 = 1.5 is larger than -5, this means r = 3/2 = 1.5 and s = -5

Subtract r and s:
r - s = (3/2) - (-5)
r - s = (3/2) + (5)
r - s = (3/2) + (5/1)
r - s = (3/2) + (10/2)
r - s = (3+10)/2
r - s = 13/2

Therefore the final answer is B) 13/2

Find the parabola whose minimum is at (−12,−2)(−12,−2) rather than the point given in the book. the parabola's equation is y=x2+ax+by=x2+ax+b, where

Answers

The vertex form of the equation of a parabola is given by

[tex]y-k=a(x-h)^2[/tex]

where (h, k) is the vertex of the parabola.

Given that the vertex of the parabola is (-12, -2), the equation of the parabola is given by

[tex]y-(-2)=a(x-(-12))^2 \\ \\ y+2=a(x+12)^2=a(x^2+24x+144)=ax^2+24ax+144a \\ \\ y=ax^2+24ax+114a-2 \\ \\ y=x^2+24x+ \frac{114a-2}{a} [/tex]

For a = 1,

[tex]y=x^2+24x+112[/tex]

The parabola whose minimum is at (−12,−2) is given by the equation [tex]y=x^2+ax+b[/tex], where a = 24 and b = 112.

Help me with the first one please

Answers

D- 2x-1
plug in a number for x and you'll see

Can somebody please help me?

Answers

Again, look at the dotted line of y = x in the first picture. Which of the options given are symmetric across that diagonal line?

Please help me! And can you explain how you got that answer please?

Answers

The answer x = -3 is correct ; not really any mistakes made but they do seem to skip a step from 8^(-1) to 2^(-3) if that is confusing you.

8 = 2^(3) 
so
(8)^(-1) = (2^3)^(-1) = 2^(3*-1) = 2^(-3)

How long is the minute hand on a clock whose tip travels 15 cm from 1:15 to 1:30 to the nearest tenth?

Answers

Answer:

The length of minute hand is 9.5 cm

Step-by-step explanation:

We are given the minute hand move from 1:15 to 1:30

Time for 1:30 to 1:30 = 15 minutes

Tip of minute hand move 15 cm in 15 minutes.

In 60 minutes = 360°

   In  1 minute = 6°

In 15 minutes = 90°

Formula: [tex]\theta=\dfrac{L}{r}[/tex]

[tex]\theta=90^\circ[/tex]

Now we change [tex]\theta=90^\circ[/tex] into radian

[tex]Radian=\dfrac{\pi}{180^\circ}\times 90^\circ=\dfrac{\pi}{2}[/tex]

L=15 cm

R = Length of minute hand.

[tex]\dfrac{\pi}{2}=\dfrac{15}{R}[/tex]

[tex]R=\dfrac{30}{\pi}\approx 9.5[/tex]

Hence, The length of minute hand is 9.5 cm

Bill ate 1/4 pound of trail mix on his first break during a hiking trip. On his second break, he ate 1/6 pound. How many pounds of trail mix did he eat during both breaks? Explain.

Answers

Since we know that he ate 1/4 pound one time, and 1/6 another time, we have to add up the fractions. 

1/4+1/6

LCM of 4 and 6 = 12

3/12 + 2/12 

Add the numerators: 

5/12

So, he ate 5/12 of a pound of bars in both breaks. 

Hope this helps!
He ate 5/12 in all because 1/4 and 1/6 are equal to 3/12 and 2/12 and the sum of those two is 5/12






Which transformations will produce similar, but not congruent, figures?

Triangle PQR is reflected across the x-axis and then rotated 90° clockwise to form triangle P"Q"R" .

​ Triangle PQR ​ is reflected across the y-axis and then dilated by a scale factor of 6 to form ​ triangle P"Q"R" ​ .

​ Triangle PQR ​ is rotated 180° counterclockwise and then translated 11 units left to form ​ triangle P"Q"R" ​ .

​ Triangle PQR ​ is rotated 90° clockwise and then reflected across the y-axis to form ​ triangle P"Q"R" ​ .

Answers

its B i took the test its right

Multiplication property: if angle j equals 30 then 2m angle j equals

Answers

If m∡J=30, then 2(m∡J) = 2(30) = 60

A quadrilateral whose opposite sides are parallel and congruent and whose opposite angles are congruent is a ____. a. trapezoid c. kite b. heptagon d. parallelogram.
PLZ ANSWER ASAP!!

Answers

The answer is parallelogram.

Nick’s house is 4.28 miles from school. if nick’s average stride length is 3.1 feet, how many strides will it take him to walk to school?

Answers

7,289.80647 strides to walk 4.28 miles from school.

For items 14 and 15 use the following functions
f(x)=5x+1
g(x)=3x-4

14. Evaluate f(2), g(2), (f o g) (2), and (g o f)(2).

15. Write the composite functions h(x)=g(f (x)) and k(x)=f(g(x)).

Answers

To find f(2), plug in 2 for x. f(2) = 11 To find g(2), plug in 2 for x. g(2) = 2 To find (f o g) (2), plug in 2 for the composite function = 11. To find (g o f) (2) plug in 2 for the composite function = 29. g(f(x)) is when you plug in f(x) into g: 3(5x+1) - 4 = 15x - 1. f(g(x)) is when you plug in g(x) into f: 5(3x-4) + 1 = 15x -19.

Set up a proportion and use cross multiplication to solve. 100 is 250% of?

Answers

100/x =250/100
100 * 100 / 250 =x
X= 40

Answer:

[tex]40[/tex]  

Step-by-step explanation:

Let

x-------> the number

[tex]\frac{x}{100\%}=\frac{100}{250\%}[/tex]

[tex]x*250\%=100*100\%\\ \\x=10,000/250\\ \\x= 40[/tex]

PLEASE HELP!

Solve for t: A=P (1+rt)

Answers

A = P( 1 + rt)

A = P + Prt

A - P = Prt

(A - P)/Pr = t
Here are the steps to follow when it comes to solving for t. This is not the only way to do so

Step 1) A = P*(1+rt)

Step 2) A = P*(1)+P*(rt)

Step 3) A = P+P*(rt)

Step 4) A-P = P+P*(rt)-P

Step 5) A-P = P*(rt)

Step 6) A-P = t*(Pr)

Step 7) (A-P)/(Pr) = (t*(Pr))/(Pr)

Step 8) (A-P)/(Pr) = t

Step 9) t = (A-P)/(Pr)

----------------------------------------------

and here are the explanations for each step

Step 1) Nothing to do here. This is the original equation

Step 2) Distribute the outer P term into each inner term (1 and rt)

Step 3) Multiply P and 1 to get P*(1) = P

Step 4) Subtract P from both sides

Step 5) Simplify. Note how the P-P on the right side becomes 0P = 0 which goes away on the right side

Step 6) Rearrange the terms on the right side to go from P*(rt) to t*(Pr). 

Step 7) Divide both sides by Pr.

Step 8) Simplify. The Pr term on the right side divides with itself to get 1. Because 1 times anything is itself, we effectively have Pr cancel out and go away.

Step 9) Flip the equation so that the t is on the left side

----------------------------------------------

The answer is t = (A-P)/(Pr) which can be written as [tex]t = \frac{A-P}{Pr}[/tex]

The parenthesis in the equation t = (A-P)/(Pr) are important because we are specifying that we are dividing all of "A-P" all over all of "Pr"

If you randomly choose a letter in the word "mathematics", find the probability that you choose an "a".

Answers

The probability of any particular event occurring can be expressed as:

(number of desired outcomes)/(total number of outcomes)

Here, the total number of ways you can pick a single letter from the word "mathematics" is 11 (m, a, t, h, e, m, a, t, i, c, s), and the number of a's available to choose from is 2, therefore you have a 2/11 chance of choosing an "a" at random from the word "mathematics."

A rectangular park, with dimensions of 1500ft x 2000ft has a diagonal walking path that goes from corner to corner. How long is the walking path?

Answers

it'd 2500 ft hope this helps

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