A piece of wire 32cm Long is cut into two parts. Each part is bent to form a square. Given that the total area of the two squares is 34cm square, find the perimeter of each square
Answers
The possible perimeters for the squares are 20 cm and 12 cm, depending on how the wire is cut.
Let's denote the length of one part of the wire as x and the length of the other part as 32−x. Each part is bent to form a square.
The perimeter (P) of a square is given by 4 × side length.
The side length of the first square ([tex]S_1[/tex] ) is x/4, and the side length of the second square ([tex]S_2[/tex] ) is (32−x)/4.
The total area of the two squares is given as [tex]34cm^2[/tex] , so we can write the equation:
[tex]S^2_1 + S^2_2 = 34[/tex]
Substitute the expressions for [tex]S_1 and S_2[/tex] :
[tex](\frac{x}{4})^2 + (\frac{(32-x)}{4})^2 =34[/tex]
Now, solve for x:
[tex]\frac{x^2}{16} + \frac{(32-x)^2}{4} =34[/tex]
Multiply both sides by 16 to get rid of the denominators:
[tex]x^2 +(32-x)^2=544[/tex]
Expand and simplify:
[tex]x^2+1024-64x+x^2 =544[/tex]
Combine like terms:
−64x+480=0
Divide the entire equation by 2 to simplify:
−32x+240=0
Now, factor the quadratic equation:
(x−20)(x−12)=0
So, x=20 or x=12.
If x=20, the lengths of the two parts are 20 cm and
32−20=12 cm.
If x=12, the lengths of the two parts are 12 cm and
32−12=20 cm.
Now, we can find the perimeter of each square by multiplying the side length by 4:
For x=20, the perimeter is [tex]4 \times \frac{20}{4} = 20 cm[/tex]
For x=12, the perimeter is [tex]4 \times \frac{12}{4} = 12 cm[/tex]
So, the possible perimeters for the squares are 20 cm and 12 cm, depending on how the wire is cut.
Related Questions
find the number of liters in 90 gallons
Answers
in the inverse variation function, what happens to the output when the function's input value is divided by 3?
Answers
Answer: The function's output value will get multiplied by 3
Step-by-step explanation:
Two variables x (input value) and y (output value) are said to be in inverse variation if [tex]xy=k[/tex] for some constant k.
The equation for inverse variation can be written in the form :-
[tex]y=\frac{k}{x}[/tex], where k is a constant.
When the function's input value is divided by 3, then the new input value would be
[tex]x_1=\frac{x}{3}[/tex]
Now, the equation to find the new output value corresponding to new input value would be
[tex]y_1=\frac{k}{x_1}\\\Rightarrow y_1=\frac{k}{\frac{x}{3}}\\\\\Rightarrow y_1=3(\frac{k}{x})\\\\\Rightarrow y_1=3y[/tex]
Hence, When the function's input value is divided by 3, then the function's output value will get multiplied by 3.
guys please assist me
this is a system of equation word problem
Answers
.. 20t +100h = 10000 . . . . . . the total value of the payment was $10,000
.. t - h = 20 . . . . . . . . . . . . . . . she gave him 20 more twenties than hundreds
Using an augmented matrix, the solution can be found to be
.. t = 100
.. h = 80
She gave the crook only 100 20s, so did not meet the requirement for 105 twenty-dollar bills. Polly did not give him enough.
justin runs at a constant rate, traveling 17km in 2 hours whats the equation
Answers
17km/2 h=8.5 km/hour
Justin's constant rate of running can be represented by the equation
=17/2 =8.5, where r is his speed in kilometers per hour. This indicates that Justin runs at a steady pace of 8.5 kilometers per hour.
To find the equation that represents Justin's constant rate of running, we can use the formula for speed, which is distance divided by time. Given that Justin travels 17 km in 2 hours, we can use these values to determine his speed.
Step 1: Identify the variables:
Let's denote:
d as the distance traveled (in kilometers)
t as the time taken (in hours)
r as the rate or speed (in kilometers per hour)
Step 2: Write down the formula for speed:
Speed =Distance/Time
Step 3: Plug in the given values:
We know that Justin travels 17 km in 2 hours. So,
d=17 km and t=2 hours.
Step 4: Calculate the speed:
=17/2=8.5 km/hr
Step 5: Write down the equation:
Now that we know Justin's speed is 8.5 km/hr, we can express it as an equation:r=8.5
So, the equation representing Justin's constant rate of running is:
r=8.5
This equation states that Justin's speed is always 8.5 kilometers per hour, regardless of the distance he travels. It's a linear equation because his speed remains constant over time
complete question=
Justin runs at a constant rate, traveling 17 kilometers in 2 hours. What is the equation that represents Justin's rate of running?"
The inverse of f(x)
Answers
x=-6y+12
x-12=-6y
-1/6x+2=f^-1(x)
The function f(x) = −(x + 5)(x + 1) is shown.
What is the range of the function?
a.all real numbers less than or equal to 4
b.all real numbers less than or equal to −3
c.all real numbers greater than or equal to 4
d.all real numbers greater than or equal to −3
Answers
Since the shading would go from 4 all the way to negative infinity, the answer is all real numbers less than or equal to 4.
Best of luck!
Range of the given function is all real numbers less than or equals to 4.
What is the range of the function?The range of a function is the set of all its output values.
According to the given equation we have
f(x) = -(x+5)(x+1)
Let, y = -(x+5)(x+1)
To find the range of the given function, we will substitute different values of x.
At, x = -5
y = f(-5) = -(-5 +5)(-5+1) =0
At, x = -4
y = f(-4) = -(-4 + 5)(-4 + 1) = -(1)(-3) = 3
At, x = -2
y = f(-2) = -(-2+5)(-2+1) = -(3)(-1) =3
At, x = -3
y = f(-3) = -(-3 + 5)(-3 + 1) = -(2)(-2) =4
Similarly, we will find for the other values of x.
So, the coordinates are (-5, 0), (-4, 3), (-3, 4), (-2,3)
And the graph using this coordinates are already given. Here, the set of outputs are the values of y. So we can see that the range of the given function is all real numbers less than or equals to 4.
Learn more about the range of the function here:
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Please help quickly for 5 stars and brainliest!!
1. Omar set off a rocket in a field. The height h of the rocket in feet can be roughly estimated using the formula
h = -16t^2 + 128t, where t is the time in seconds. How long will it take the rocket to reach a height of 240 feet?
2. Josefina tosses a ball upward with an initial velocity of 76 feet per second.
She tosses it from an initial height of 2 feet. Find the approximate time that the ball hits the ground.
Use the function h(t) = -16t^2 + 76t + 2
Round to the nearest second.
3. Brandi, an amateur skier, begins on the "bunny hill," which has a vertical drop of 200 feet.
Her speed at the bottom of the hill is given by the equation v^2 = 64h, where the velocity v is in feet per second
and the height h of the hill is in feet. Assuming there is no friction, approximate Brandi's velocity at the bottom of the hill.
Answers
Height h = 240 feet
We insert it into formula.
[tex]240 = -16 t^{2} +128t[/tex]
Now we solve this for t:
[tex]16 t^{2} -128t +240 = 0 /16 \\ t^{2} - 8t +15 =0 \\ t_{1} = 5 t_{2} = 3[/tex]
We have two answers as the rocket will pass this height on it's way up and down.
2.
Height h = 0 feet
We insert it into formula.
[tex]0=-16 t^{2} +76t + 2[/tex]
Now we solve this for t:
[tex]16 t^{2} - 76t -2 = 0 /2 \\ 8t^{2} - 38t - 1 = 0 \\ t_{1} = 5 t_{2} = -1[/tex]
We do not consider solution -1 as the time can not be negative. Our solution is 5s.
3.
Height at bottom of hill h = 0 feet
We insert it into formula.
[tex] v^{2} = 64 * 0 = 0 ft/s[/tex]
Which unit would you use to measure the weight of an elephant? mg g kg km
Answers
The proof that HG ≅ EG is shown. Given: G is the midpoint of KF KH ∥ EF Prove: HG ≅ EG What is the missing reason in the proof? Statement Reason 1. ∠EGF ≅ ∠HGK 1. vert. ∠s are ≅ 2. KH ∥ EF 2. given 3. ∠F ≅ ∠K 3. alt. int. ∠s are ≅ 4. G is the midpoint of KF 4. given 5. FG ≅ KG 5. def. of midpt. 6. △FEG ≅ △KHG 6. ? 7. HG ≅ EG 7. CPCTC SAS ASA AAS HL
Answers
Solve for X:
X + 25 = 45
Answers
All you have to is isolate the X variable :)
X + 25 = 45
X = 45 - 25
X = 20
I hope this helps :))
Hope this helps ;)
The figure below shows triangle NRM with r2 = m2 + n2:
Triangle NRM has legs m and n, and r is the length of its longest side.
Ben constructed a right triangle EFD with legs m and n, as shown below:
Triangle EFD has legs m and n and hypotenuse f.
He made the following table to prove that triangle NRM is a right triangle:
Statement Reason
1. r2 = m2 + n2 Given
2. f2 = m2 + n2 Pythagorean Theorem
3. f2 = r2 Substitution
4. f = r Square Root Property of Equality
5. Triangle NRM is congruent to triangle EFD ?
6. Angle NRM is a right angle CPCTC
7. Triangle NRM is a right triangle Angle NRM is a right angle
Which reason best fits statement 5?
SSS Postulate
SAS Postulate
AAA Postulate
AAS Postulate
Answers
and given that ⇒ r² = m² + n²
Ben constructed a right triangle EFD with legs m and n
so, both of the triangles NRM and EFD have legs with sides m and n
beside that the third side of NRM is equal to the third side EFD, i.e ⇒ r = f
which is proved from the statement number 4
So, the sides of the triangle NRM are congruent to the sides of triangle EFD
So, the reason which best fits statement 5 is ⇒ [tex]\framebox {SSS \ Postulate} [/tex]
Answer:
Option "SSS postulate" is correct.
Step-by-step explanation:
Given that: Triangle NRM has legs m and n, and r is the length of its longest side.
and r² = m² + n².
Now, Ben constructed a right triangle EFD with legs m and n.
and in statement 4, it is proved that f=r.
So, all the three sides of the triangles NMR and EFD are congruent.
So, the triangles are congruent bt the SSS Postulate.
⇒ option "SSS postulate" is correct.
how do you do #8,9,10 ?? thank you !!
Answers
.. 3 represents a vertical expansion factor of 3
.. 2 represents a left shift of 2 units
9. g(x) = -2f(x)
.. 2 represents a vertical expansion factor of 2
.. the minus sign is a reflection across the x-axis
10. g(x) = f(x -1) +3
.. 3 represents a vertical shift upward by 3 units
.. -1 represent s right shift of 1 unit
30 POINTS!!! HELP PLEASE!
Model each scenario with an equation and a sketch. Solve for the missing value and u. Use complete sentences to interpret the solution. In your final answer, include your equation, sketch, interpretation, and all calculations necessary for the solution.
1.) To get home from school, Bob walks four blocks north and three blocks east. What is the straight line distance between Bob’s house and his school?
2.)One of the requirements of your summer window-washing job is to provide yourself with all of the necessary supplies, including a fourteen foot ladder. When you arrive at your first job, you place your ladder on the ground six feet from the base of the house and lean it towards a second story window, only to realize that the ladder doesn’t reach the window. Given the length of the ladder and its current position, what is one possible height of the second story window? (Hint: There is more than one correct answer.)
3.) In a softball diamond, each of the bases, including home plate, are equidistant from each other. Although the name implies differently, a softball diamond is in the shape of a square. Given that the distance between the bases is unknown, determine an expression for the straight line distance between first and third bases.
4.) A sailboat drifts 600 meters west, makes a turn and sails 800 meters south. How far is the sailboat from its original position?
Answers
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]. Using our coordinates we have:
[tex]d=\sqrt{(4-1)^2+(5-1)^2} \\=\sqrt{3^2+4^2} \\=\sqrt{9+16} \\=\sqrt{25} \\=5[/tex] His house is 5 blocks from the school in a straight line.
#2) The ladder (14 ft) forms the hypotenuse of a right triangle, with the legs being the distance from the house (6 ft) and the height of the ladder (b ft). This gives us:
[tex]6^2+b^2=14^2 \\36+b^2=196[/tex]
Subtract 36 from both sides:
[tex]36+b^2-36=196-36 \\b^2=160[/tex]
Take the square root of both sides:
[tex]\sqrt{b^2}=\sqrt{160} \\b=12.6[/tex]
One possibility for the height of the second story window is 13 feet, since it is longer than 12.6.
#3) The distance from 1st base to 3rd base forms the hypotenuse of a right triangle, with each leg being equal to s, the side length of the square formed by the baseball diamond. Using the Pythagorean theorem we have:
[tex]s^2+s^2=d^2[/tex], where d is the distance from 1st to 3rd. Combining like terms gives us [tex]2s^2=d^2[/tex]. Taking the square root of both sides we have [tex]\sqrt{2s^2}=\sqrt{d^2} \\s\sqrt{2}=d[/tex] (this is due to the fact that square root cancels a squared variable, so s comes out of the radical sign).
#4) The straight distance from the boat's original position to its new position forms the hypotenuse of a right triangle, with the legs being the distance west (600) and the distance south (800) it traveled. Using the Pythagorean theorem we have:
[tex]600^2+800^2=d^2 \\360000+640000=d^2 \\1000000=d^2[/tex]
Taking the square root of both sides we have
[tex]\sqrt{1000000}=\sqrt{d^2} \\1000=d[/tex]
The straight distance between the two points would be 1000 meters.
find the greatest common factor: 14a^4 + 35a^9
Answers
Adam wrote a check for $38 to pay his monthly gas bill, but when balancing his checkbook, he accidentally recorded it as credit rather than as a debit. How will his check register compare to his monthly bank statement when he receives it?
Answers
Answer: the balance in his check register will be $76 over the balance on his bank account
Which equation of the least squares regression line most closely matches the data set?
Note: The variable x represents the years after 1970.
Y= -5.7x-67
Y= -0.98x+65
Y= -0.17x+76
Y= -5.7x +67
Answers
The 4th selection is appropriate.
Answer:
D. [tex]y = -5.7x + 67[/tex]
Step-by-step explanation:
Let us take the year 1970 as the 0th year.
So, the corresponding table of values is,
x y
0 65
2 58
4 45
6 32
8 21
Using the linear regression calculator, we see that,
The closest equation of the regression line is [tex]y = -5.7x + 67[/tex].
What is the slope of the line that passes through (10,0) and is parallel to y=1/2x+3
Answers
Explanation: The slope of the given line y = 1/2x+3 is 1/2 as its the coefficient in front of the x. Any line parallel to this will also have a slope of 1/2. Parallel lines have equal slopes. The info about (10,0) is unneeded. It was likely put in there to throw you off.
In order to circumscribe a circle on a triangle, which line must you construct?
a.median
b.altitude
c.diagonal
d.perpendicular bisector
Answers
Explanation:
By definition, a circumscribe circle passes through the three vertices of the triangle and to its constrution, you have to draw the triangle and then construct a perpendicular bisector to each side of it. The point where these perpendicular bisectors intersect each other, will be the center of the circle. Then, you should place the compass on the center point to draw the circle.
The answer is in fact perpendicular bisector
In the game of roulette, a player can place a $55 bet on the number 3434 and have a startfraction 1 over 38 endfraction 1 38 probability of winning. if the metal ball lands on 3434, the player gets to keep the $55 paid to play the game and the player is awarded an additional $175175. otherwise, the player is awarded nothing and the casino takes the player's $55. what is the expected value of the game to the player
Answers
In the game of roulette, a player can place a $5 bet on the number 34 and have a 1/38 probability of winning. if the metal ball lands on 34, the player gets to keep the $5 paid to play the game and the player is awarded an additional $175. otherwise, the player is awarded nothing and the casino takes the player's $5. what is the expected value of the game to the player
we know that
P(winning) = 1/38
P(losing) = 1-1/38 = 37/38
Expected value = 175*1/38 - 5*37/38
175/38 - 185/38 = - 10/38 =-$0.2632
The player's expected value is -$0.2632 ( is losing)
How do I find the slope of (2,3) and (5,9) by showing all of my work
Answers
(Hint: y is the rise and x is the run. To find slope, we need to know the change in “y” and the change in “x.” That is where the formula comes from)
2 will be x1
3 will be y1
5 will be x2
9 will be y2
You will get 3-9/2-5
Then: -6/-3
Then: 2
The slope is 2.
(Although this works with linear functions, for non-linear functions we use derivatives. I’m assuming you are using a linear function. Assuming the two points are on a linear function, the slope is 2)
what are the lengths of the other two sides of the triangle?
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If CDEF ≅ MNPQ, then ≅ DE ≅
a. NP
b. PQ
c. NQ
d. MN
* there's no picture this is all the information the question gives me *
Answers
Answer:
The correct option is a.
Step-by-step explanation:
It is given that CDEF ≅ MNPQ.
We need to find the side of MNPQ which is congruent to the side DE.
The corresponding parts of congruent figures are congruent.
Since CDEF ≅ MNPQ, therefore the corresponding sides of both figures are congruent.
[tex]CD\cong MN[/tex]
[tex]DE\cong NP[/tex]
[tex]EF\cong PQ[/tex]
[tex]CF\cong MQ[/tex]
The side NP is congruent to side DE. Therefore the correct option is a.
Nina has 2 cups of flour. However, this is only 1/4 of the amount of flour she needs for a bread recipe. How many cups of flour does the recipe call for?
Answers
Nina has 2 cups of flour.
However, 2 cups of flour is only 1/4 of the amount of flour she needs for a bread recipe.
Therefore, quantity of flour which Nina needs for a bread recipe is four times the present quantity
The cups of flour which Nina needs for a bread recipe = 2 / (1/4)
= 2 *4 cups
= 8 cups
Hope this helps..!!
Thank you :)
kangaroo wants to arrange the twelve numbers from 1 to 12 in a circle in such a way that any neighboring numbers always differ by either 1 or 2 which of the following pairs of numbers have to be neighbors
Answers
The neighbors of 12 must be 11 and 10.
The neighbor of 11 must be 9, and the neighbor of 10 must be 8, and so on and so forth, until you get a unique arrangement.
A group of kindergartners and first graders were asked whether or not they can ride a bike. This table shows the relative frequencies of the rows for the two-way table representing this situation. Select from the drop-down menus to complete the statement. The percent of kindergartners surveyed who can ride a bike is (choose-greater than ,less than, equal to) the percent of first graders surveyed who can ride a bike.
Can ride a bike Cannot ride a bike
Kindergartners. 0.32. 0.68
First graders. 0.56. 0.44
Answers
Answer: The percent of kindergartners surveyed who can ride a bike is less than the percent of first graders surveyed who can ride a bike.
Step-by-step explanation:
Given: The table shows the relative frequencies of the rows for the two-way table representing this situation.
The relative frequency for kindergartners surveyed who can ride a bike=0.32
Then, the percent of kindergartners surveyed who can ride a bike=[tex]0.32\times100=32\%[/tex]
The relative frequency for First graders surveyed who can ride a bike=0.56
Then, the percent of First graders surveyed who can ride a bike=[tex]0.56\times100=56\%[/tex]
Clearly, 32 is less than 56.
Therefore, the percent of kindergartners surveyed who can ride a bike is less than the percent of first graders surveyed who can ride a bike.
An accountant pays 8% per year simple intrest, in year 1 the amount in the account is $850 how much is the account in year 6?
Answers
[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \$850\\ r=rate\to 8\%\to \frac{8}{100}\to &0.08\\ t=years\to &5 \end{cases} \\\\\\ A=850[1+0.08(5)]\implies A=850(1.4)[/tex]
A = P(1 + rt) where A is the total amount of principle and interest: P is the initial investment; r is the rate of interest; and t is the time
Using P = 850, r = .08, and t = 5
A = 850(1+ .08(5))
A = 850(1.4)
A = 1190 the amount in the account in year 6
Can someone help me please?
Answers
A quadrilateral with two sets of parallel sides and four right angles is a
parallelogram
rhombus
rectangle
trapezoid
Answers
thats the answer
1
Which mathematical symbol would best fill in the blank to compare the two real numbers? 7.6 repeating____55 squared
<
>
=
≈
2
Convert 11.42424242 … to a rational expression in the form of a/b , where b ≠ 0.
42/999 with 11 whole number
42/9990 with 11 whole number
42/99 with 11 whole number
99/42 with 11 whole number
3
Order the set of numbers from least to greatest: -5/6, -5, -26 squared, -31/6
4
Identify the number that does not belong with the other three. Explain your reasoning
50.1 reapting , -50/2, , -50.1, 50 squared
Answers
1. 7.6 repeating ____ 55 squared
Find 55 squared.
7.6 < 3025
7.6 is less than 7.4.
2. We already know we have 11 as the whole number.
When you have a repeating decimal, you can keep it as a fraction but use 99 as the denominator.
42/99 with the 11 whole number is the answer.
3. -31/6, -5, -5/6, -26^2 <== least to greatest.
-31/6= -5.16667 -26^2= 676
4. I think the 50 is the square root. Everything else can be represented as a fraction or ratio. The square root of 50 is irrational, and cannot be represented by a fraction or ratio. 50 squared is the one that doesn't belong.
I hope this helps!
~kaikers
A 72?? sector in a circle has an area of 16.4?? yd??.
What is the area of the circle?
Use 3.14 for pi.
Enter your answer as a decimal in the box.