A piece of wire is 76cm long. It is cut into two unequal parts and each part is bent into a square. The sum of the areas of the two squares is 205cm². Find the length of the shorter part of the wire.

Answers

Answer 1

Answer:

The length of the shorter part of the wire is 24 centimeters.

Step-by-step explanation:

Let [tex]L[/tex] the total length of the piece of wire, where [tex]L-x[/tex] and [tex]x[/tex] are the perimeters of the greater and lesser squares. All lengths are measured in centimeters. Since squares have four sides of equal length, the side lengths for the greater and lesser squares are [tex]\frac{L-x}{4}[/tex] and [tex]\frac{x}{4}[/tex]. From statement we find that the sum of the areas of the two squares ([tex]A[/tex]), measured in square centimeters, is represented by the following expression:

[tex]A = \left(\frac{L-x}{4} \right)^{2}+\left(\frac{x}{4} \right)^{2}[/tex] (1)

And we expand this polynomial below:

[tex]A = \frac{L^{2}-2\cdot L\cdot x +x^{2}}{16} + \frac{x^{2}}{16}[/tex]

[tex]A = \frac{L^{2}-2\cdot L\cdot x +2\cdot x^{2}}{16}[/tex]

[tex]2\cdot x^{2}-2\cdot L\cdot x +L^{2}-16\cdot A = 0[/tex] (2)

If we know that [tex]L = 76\,cm[/tex] and [tex]A = 205\,cm^{2 }[/tex], then the length of the shorter part of the wire is:

[tex]2\cdot x^{2}-152\cdot x +2496 = 0[/tex]

By the Quadratic Formula, we determine the roots associated with the polynomial:

[tex]x_{1} = 52\,cm[/tex], [tex]x_{2} = 24\,cm[/tex]

The length of the shorter part of the wire corresponds to the second root. Hence, the length of the shorter part of the wire is 24 centimeters.


Related Questions

find angle X on the given figure. m

Answers

Answer:

x = 61°

Step-by-step explanation:

In a rhombus, the diagonals bisect the angles, thus

∠ BAE = ∠ DAE = 29° , then ∠ A = 58°

∠ ADE = ∠ CDE = x , then ∠ D = 2x

In a rhombus, consecutive angles are supplementary

∠ A and ∠ D are consecutive angles , then

58 + 2x = 180 ( subtract 58 from both sides )

2x = 122 ( divide both sides by 2 )

x = 61°

solve for x round your answer to the nearest tenth

Answers

Answer:

13.7

Step-by-step explanation:

Pythagorean theorem converse

Answer:

The value of x is 13.7.

Step-by-step explanation:

☆We are going to use the Pythagorean theorem to solve this.

☆Pythagorean Theorem:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

☆Remmeber: a = leg, b = leg, c = hypotenuse or the diagonal.

☆Let's plug in according to the pythagorean theorem and solve!

[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {x}^{2} + {9.2}^{2} = {16.5}^{2} \\ {x}^{2} + 84.64 = 272.25 \\ \frac{ \: \: \: \: \: \: \: \: - 84.64 = - 84.64}{ {x}^{2} = \sqrt{187.61} } \\ x = 13.7[/tex]

Kate used 2/5 of a pound of sugar to bake cookies. She used another 3/4 of a pound of flour for the cookies. How many pounds of sugar and flour did she use in all? ASAP ANSWER PLS

Answers

Answer:

c. 1 3/20

Step-by-step explanation:

a guess hopefully you are right

y=x+3
y=x-3
Solve these equations​

Answers

Answer:

what is x?

Step-by-step explanation:

Answer:

No solutions

Step-by-step explanation:

The variable Q varies inversely as the cube of V. FK is the constant of variation, which equation represents this situation?

A. qv^3=k
B. q^3v=k
C. q/v^3=k
D. q^3/v=k

Answers

Step-by-step explanation:

When 2 variables are inversely proportional to each other, their product is a constant.

Since Q and V³ are inversely proportional to one another, QV³ = k. (B)

Please help please please ASAP

Answers

Answer:

choose the first one.

0.87

Answer:

Use your calculator

Step-by-step explanation:

Press the cos button COS(  - should look like that... Then fill it out COS(30) make sure to add the closed parenthesis so you dont get an error. And then BAM you got your answer and dont have to look anymore up. XD

What is the simplified form of
of (-7xº+5x²-x+6)-(-8x2 + x +3)?
ОА.
-x + 4x2 - x+3
OBX + 4x² - x+3
ocx - 4x² – 2-3
D. -15x + 6x? - X+9
Please I need help immediately

Answers

Note: Your answer choices remain a little unclear. But, I have solved the concept and solution, so you can easily figure it out.

Answer:

[tex]\left(-7x^0+5x^2-x+6\right)-\left(-8x^2+x+3\right)=13x^2-2x-4[/tex]

Step-by-step explanation:

Given the expression

[tex]\left(-7x^0+5x^2-x+6\right)-\left(-8x^2+x+3\right)[/tex]

solving the expression

[tex]=-7x^0+5x^2-x+6-\left(-8x^2+x+3\right)[/tex]

apply the rule: [tex]a^0=1,\:a\ne \:0[/tex]

[tex]=-7+5x^2-x+6-\left(-8x^2+x+3\right)[/tex]

[tex]=-7+5x^2-x+6+8x^2-x-3[/tex]

simplify

[tex]=13x^2-2x-4[/tex]

Therefore, the simplified form is:

[tex]\left(-7x^0+5x^2-x+6\right)-\left(-8x^2+x+3\right)=13x^2-2x-4[/tex]

Note: Your answer choices remain a little unclear. But, I have solved the concept and solution, so you can easily figure it out.

The five marathon runners weigh an average weight of 92 pounds, Nicole weighs 89 pounds, Jon weighs 95 pounds, Jenny and Kim weigh 90 pounds each, How much does Jordin weigh?

Answers

Answer:

Jordin weighs 96 pounds

Step-by-step explanation:

The Mean Value of a Data Set

The mean or average of a data set is found by adding all numbers and then dividing by the number of values in the set. Written as a formula:

[tex]\displaystyle \bar x=\frac{\sum x_i}{n}[/tex]

Where xi is the value of each data and n is the total number of values.

We are given the average weight of n=5 marathon runners:

[tex]\bar x=92[/tex]

Multiplying the formula by n and expanding the sum:

[tex]n\bar x=\sum x_i=x_1+x_2+x_3+x_4+x_5[/tex]

We are given the weighs of four of the runners:

[tex]5*92=89+95+90+90+x_5[/tex]

[tex]460=364+x_5[/tex]

Solving for x5:

[tex]x_5 = 460-364=96[/tex]

Jordin weighs 96 pounds

Find the circumference of a circle with radius of 18 in

Answers

Answer: 113.1 in.

Step-by-step explanation:

C=2πr=2·π·18≈113.09734in

Hope this helped! :)

Select the correct answer.
Determine which equation has the same solutions as the given equation.

x2 − 10x − 11 = 0

A.
(x − 5)2 = 21
B.
(x − 10)2 = 21
C.
(x − 10)2 = 36
D.
(x − 5)2 = 36

Answers

Answer:

D. [tex]\displaystyle (x - 5)^2 = 36[/tex]

Step-by-step explanation:

All you are doing is converting this Quadratic Equation to a Vertex Equation in Vertex Form by completing the square:

[tex]\displaystyle [\frac{b}{2}]^2 \\ \\ x^2 - 10x - 11 = 0 → x^2 - 10x + 25 - 36 = 0→ (x - 5)^2 - 36 = 0 \\ \\ (x - 5)^2 = 36[/tex]

It is that simple, is it not?

I am joyous to assist you at any time.

can someone pls help me !!!

Answers

Answer:

I dont know the answer, but I am going to give you a lot of luck, so good luck!

Step-by-step explanation:

Solve for x. I need help :,) thank you if you help!

Answers

Answer: if its a multiple of a 345 triangle then its congruent x is 36 if othersides ate multiples of 20 ie

Sides are

60 80 100 is a 345 right triangle

Step-by-step explanation:

plzz helpp guys
At the beginning of an environmental study, a forest covered an area of 1500 km . Since then, this area has decreased by 2.4% each year. Lett be the number of years since the start of the study. Let y be the area that the forest covers in km². Write an exponential function showing the relationship between y and t.​

Answers

Answer:

[tex]y = 1500(0.024)^t[/tex]

Step-by-step explanation:

Given

[tex]a = 1500km[/tex] -- initial area

[tex]b = 2.4\%[/tex] -- rate

[tex]t = time[/tex] --- (years)

Required

Represent as an exponential function

An exponential function has the form:

[tex]y = ab^t[/tex]

Where

[tex]a = initial\ value[/tex]

[tex]b = rate[/tex] and [tex]b \ne 1[/tex]

[tex]t= time[/tex]

Substitute values for a and b, we have:

[tex]y = 1500 * (2.4\%)^t[/tex]

Convert percentage to decimal

[tex]y = 1500 * (0.024)^t[/tex]

[tex]y = 1500(0.024)^t[/tex]

Hence, the exponential function that represents the scenario is: [tex]y = 1500(0.024)^t[/tex]

Divide. Write the quotient in lowest terms.
5 divide 3 1/3

Answers

Answer:

3/2 or 1 1/2

Step-by-step explanation:

5÷3 1/3

5/1 ÷ 10/3 because you have to get it into an improper fraction form in order to divide

5/1 × 3/10 because you have to multiply the first number by the reciprocal

5  and 10 cancel out so you would have 2 at the bottom

3/2 or 1 1/2

Draw an ordered stem and leaf diagram to show this information.
245, 250, 251, 253, 258, 264, 267, 269, 273, 276
Key:
2415 means

Answers

Answer:

24|5

25|0;1;3;8

26|4;7;9

27|3;6

Step-by-step explanation:

key in the bottom right:

24|5means 245

What is the area, in square feet, of the trapezoid below?

Answers

Answer:

68.75

Step-by-step explanation:

Measure the length of the parallel sides and add them together. Then multiply this number by the height of the area. Then multiply by ½ or divide by two to find the square footage of the trapezoid.  

13.6 + 5.9= 19.5

19.5 + 8 = 27.5

27.5 x 5 = 137.5

137.5 x 1/2 = 68.75

c2-1/4=0 equation maths ​

Answers

Answer:

c=1/8

Step-by-step explanation:

2c-1/4=0

2c=1/4

2c/2=1/4/2

c=1/4x1/2

c=1/8

This recipe makes 18 cupcakes.
Deepak only wants to make 12 cupcakes.
How much of each ingredient does he need?

Recipe: Makes 18 cupcakes
12 ounces butter
6 ounces sugar
9 ounces flour
3 eggs

Answers

Answer:

Deepak only wants to make 12 cupcakes. Recipe:  8 ounces butter  4 ounces sugar 6 ounces flour 2 eggs

Step-by-step explanation:

Answer:

8 ounces of butter, 4 ounces of suger, 6 ounces of flour, 2 eggs

Step-by-step explanation:

The difference of two numbers is 18. Their sum is 66. What are the numbers? List the numbers from least to greatest.

Answers


attack_panic
·
5y
Another solution is to solve one equation for one variable, and plug that into the other equation.

x + y = 66
x = 66 - y

(66 - y) - y = 18
66 - 2y = 18
-2y = 18 - 66
-2y = -42
-2y/-2 = -42/-2
y = 24

Now that you have y, plug that into the first equation and solve for x.

x + 24 = 66
x = 66 - 24
x = 42

Then plug your two answers into both original equations to verify.

x + y = 66
42 + 24 = 66
66 = 66 check

x - y = 18
42 - 24 = 18
18 = 18 check

How do you write 1/12 as a decimal?

Answers

Answer:

I think it's 0.083

Step-by-step explanation:

Answer:

0.0833333 (3 is repeating)

Step-by-step explanation:

One spring day, Zoey noted the time of day and the temperature, in degrees
Fahrenheit. During that time, the temperature rose, stayed steady, and fell, at
different rates! On the set of axes below, Zoey created a graph of temperature over
time.
How long did the temperature hold steady for?

Answers

Answer:

2 hours

Step-by-step explanation:

Each square=1 hour

2 squares= 2 hours

Lupe is the manager of the football team, and she has to plan a team dinner for Saturday night. She knows that one large pizza can feed 3 players and one sandwich tray can feed 4 players. Lupe needs to order enough food for the 72 players on the team. (a) Write a linear equation to represent the number of pizzas (x) and the number of sandwich trays (y) she could purchase to feed the football players.

Answers

Answer:

3x + 4y = 72

Step-by-step exlanation:

Number of pizzas = x

Number of sandwich trays = y

one large pizza can feed 3 players

one sandwich tray can feed 4 players

Total players = 72

The linear equation is

3x + 4y = 72

To rent a certain meeting room, a college charges a reservation fee of $38 and an additional fee of $7.40 per hour. The history club wants to spend less then $75.00 on renting the meeting room.

What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for t.

Answers

Answer:

the anwser is 55 easy hope this helps;)

Step-by-step explanation:

What is the range of the following numbers:

12,20,18,25,6

Answers

Answer:

19

Step-by-step explanation:

You need to find the biggest and smallest number; 25,6

Then you subtract 6 from 25

25-6=19

I hope this helps!!!!!!!

Answer:

19

Step-by-step explanation:

The range is the difference between the highest and the lowest number

So 6, 12, 18, 20, 25 and 25-6 = 19

Please help please please ASAP please please

Answers

Step-by-step explanation:

ac is the answer

.............

A baker needs 8 1/2 cups of flour for a sheet cake recipe. He has 4 2/3 cups of flour in a canister and buys 5 1/4 cups more.

How much flour does he have left after he makes the sheet cake?

Enter your answer as a mixed number in simplest form.
I dont know if i asked this question already but, I cant find it, but i need help now!

Answers

Answer: 1 5/12 cups of flour leftover

Step-by-step explanation: First, add 4 2/3 + 5 1/4. This gives you 9 11/12. 9 11/12 - 8 1/2 = 1 5/12.

The baker has [tex]1\frac{5}{12}[/tex] cups of flour left after making the sheet cake.

What is Fraction?

A fraction represents a part of a whole.

Given that  baker needs [tex]8\frac{1}{2}[/tex] cups of flour for a sheet cake recipe.

Baker has  [tex]4\frac{2}{3}[/tex] cups of flour in a canister and buys [tex]5\frac{1}{4}[/tex] cups more.

The flour he has in total =  [tex]4\frac{2}{3}[/tex] +  [tex]5\frac{1}{4}[/tex]

=14/3 +21/4

=56+63/12

=119/12

To find how much flour the baker has left after making the sheet cake, we can subtract the amount needed from the total amount:

119/12 - 17/2 = (119 - 102) / 12 = 17/12

Therefore, the baker has [tex]1\frac{5}{12}[/tex] cups of flour left after making the sheet cake.

To learn more on Fractions click:

https://brainly.com/question/10354322

#SPJ3

CAN SOMEONE HELP ME ??? This is areas and volumes of similar solids!!!!!! It’s urgent!!

Answers

Answer:

Step-by-step explanation:

let x be the unknown volume

5/7=50/x

x=70

Answer:

137.2 m³

Step-by-step explanation:

Given the ratio of sides a : b , then

ratio of volumes = a³ : b³

Here ratio of sides = 5 : 7 , then

ratio of volumes = 5³ : 7³ = 125 : 343

let x be the volume of the larger prism then by proportion

[tex]\frac{50}{125}[/tex] = [tex]\frac{x}{343}[/tex] ( cross- multiply )

125x = 17150 ( divide both sides by 125 )

x = 137.2

That is volume of larger prism is 137.2 m³

Help me please thank you

Answers

The answer is B= 8-D

6th Grade Math! Can you please help?

Answers

Answer:it is c and d

Step-by-step explanation:

What is it???????? Nada

Answers

Answer:

g(3)= -1

Step-by-step explanation:

from the graph f(3)= -1

so, g(3) = -4 * (-1) + 7 = 12

Other Questions
explain how improvements in technology have led to overfishing and the depletion of fish stocks in the oceans, HAS TO BE A PARAGRAPH LONG Describe the painting style of the Mayans. Which class were painters a part of? (Answer this question in 3-4 complete sentences.) Disclaimer Do NOT answer my question if you do not know the answer. Do NOT be disrespectful to someone else if they provided the wrong answer. Do NOT answer my question to point cheat.Thank you for answering! Have a lovely day or night, I hope to see you again soon! manita carries a box of mass 40kg. What is the wieght of the box? Answer 6-15 please!!FOR 10 POINTS!! Jackie's mother is 28 years old, which is four times Jackie's age minus eight years 1. A rift valley is evidence of what type of plate boundary? A) convergentB) dilvergentC) transtormD) transverse Sandy has 31 books in her library. She bought several books at a yard sale over the weekend. She now has 59 books in her library. How many books did she buy at the yard sale Read the poem.Ozymandiasby Percy Bysshe ShelleyI met a traveller from an antique land,Who saidTwo vast and trunkless legs of stoneStand in the desert. . . . Near them, on the sand,Half sunk a shattered visage lies, whose frown,And wrinkled lip, and sneer of cold command,Tell that its sculptor well those passions readWhich yet survive, stamped on these lifeless things,The hand that mocked them, and the heart that fed;And on the pedestal, these words appear:My name is Ozymandias, King of Kings;Look on my Works, ye Mighty, and despair!Nothing beside remains. Round the decayOf that colossal Wreck, boundless and bareThe lone and level sands stretch far away.What is the structure of "Ozymandias"?sonnetlimerickhaikufree verse The soccer team is planning to sell health bars for a fundraiser. The prices of purchasing health bars from two different companies are represented by the system of equations shown, where x is the number of bars purchased and y is the total cost in dollars. Company A: y=0.75x Company B: y=10+0.50x How many bars would the team need to purchase from each company in order for the total cost to be equal? The absolute age of a rock is the aproxmate number of years ago that the rock formed the absolute age of ingenious rock can best be determined by Nosotrosla clase de matemticas el jueves. Amanda buys 4 tickets to the baseball game for $24 each. Which equationshows the closest estimate of the total amount Amanda spends? Which equation shows the closest estimate of the total amount Amanda spends what is 15% of 80????? Help me PLEASE! Choose one answer! First one to answer get Brainliest!16.)Small, gradual changes in the color or size of a population.A.) MacroevolutionB.) EmbryologyC.) PhylogenyD.) Microevolution Sally has a discount card that reduces the price of her grocery bill in a certain grocery store by 5%. If c represents the cost of Sallys groceries, which expression represents Sallys grocery bill? In the mid-1800's, more than 70% of all immigrants to the United States entered through the city of New Orleans. HELP WILL GIVE 20 POINTS AND BRAINIEST. IF YOU GIVE YOU A SILLY ANSWER I WILL REPORT. PLEASE GIVE STEPSCalculate the difference between the final values of the following two investments after 3 years Write three facts about recessive heredity genes A stack of books is 5 feet 5 inches high. How high is it in inches? Which of the following would NOT be an enforcement responsibility of a local police officer?federal statutelocal ordinancestate lawinternational trade agreement