Leia cuts congruent triangular patches with an area of 63 square centimeters from a rectangular piece of fabric that is 27 centimeters long and 21 centimeters wide. How many of the patches can Leia cut from 33 pieces of the fabric?

Answers

Answer 1

Leia can cut a total of 297 triangular patches from 33 pieces of fabric, with each piece yielding 9 patches.

To calculate how many triangular patches can Leia cut from 33 pieces of fabric, we first need to find out how many patches can be cut from a single piece of fabric. The area of each triangular patch is 63 square centimeters. The area of the fabric is length * width, which is 27 cm * 21 cm = 567 square centimeters.

Now, if we divide the area of the fabric by the area of one triangular patch, we get the number of patches per fabric piece: 567 cm2 / 63 cm2 = 9 patches per fabric piece.

Since Leia has 33 pieces of fabric, the total number of patches she can cut is 9 patches * 33 pieces = 297 patches.

Related Questions

For what value of xis the square of the binomial 3x+1 is 9 times greater than the square of the binomial x–2?

Answers

The information tells us that (3x+1)²=9(x-2)², so this means that we must now solve this equation to find x.
First, we expand the parentheses on both sides using FOIL (Firsts, Outers, Inners, Lasts) :
(3x+1)(3x+1)=9(x-2)(x-2)
9x²+3x+3x+1=9(x²-2x-2x+4
Simplify:
9x²+6x+1=9(x²-4x+4)
Now expand the RHS (right-hand side) expression - multiply all the terms inside the parentheses by 9:
9x²+6x+1=9x²-36x+36
Now solve as you normally would to isolate x. Start off by subtracting 9x² on both sides:
6x+1=-36x+36
Add 36x on both sides:
42x+1=36
Minus 1 on both sides:
42x=35
Divide both sides by 42:
[tex]x= \frac{35}{42} [/tex]
which simplifies to
[tex]x= \frac{5}{6} [/tex]
I double checked this by substituting x back into the question and it worked, you can try doing this too for verification.

Final answer:

The value of x for which the square of the binomial 3x+1 is 9 times greater than the square of the binomial x−2 is obtained by equating (3x + 1)² to 9(x − 2)², which simplifies and solves to x = 5/6.

Explanation:

To find the value of x for which the square of the binomial 3x+1 is 9 times greater than the square of the binomial x−2, we need to formulate and solve an equation based on the given conditions:

(3x + 1)² = 9(x − 2)²

Expanding both sides gives us:

9x² + 6x + 1 = 9x² − 36x + 36

Now, by simplifying and solving for x, we find:

42x = 35

x = 35 / 42

x = 5 / 6

Therefore, the value of x is 5/6.

The diagonal of rectangle ABCD measures 2 inches in length What is the length of line segment AB?

Answers

Hi. I have found the diagram for this problem through other resources and I have it attached.

In the diagram, we already have the angles given so we just need to find the length of one side. Let's first find the length of segment CD since we are given the angles on that side of the rectangle.

We can find its length by applying SOHCAHTOA. We can either use the 60 or 30-degree angle but for this solution let's make use of 60 degrees. From SOHCAHTOA we know that sine of 60 is equal to the length opposite it (CD) over the hypotenuse which is the diagonal that is equal to 2 inches. Knowing this we can solve for CD:

[tex]sin(60)= \frac{CD}{2} [/tex]
[tex] \frac{ \sqrt{3}}{2}= \frac{CD}{2} [/tex]
[tex] \sqrt{3}=CD [/tex]

Since we have a rectangle, the measure of segment CD will just be equal to the measure of segment AB.

ANSWER: The length of line segment AB is √3 or 1.73 inches.

Answer:

Step-by-step explanation:

B on edge

9ax+9b-6=21

based on the equation above what is the value of ax+b

Answers

We have [tex]9ax+9b-6=21[/tex].

We add 6 to both sides. [tex]9ax+9b=27[/tex].

Now, to solve for [tex]ax+b[/tex], we factor out and divide by a 9 to get

[tex]9(ax+b)=27 \\ ax+b=3[/tex].

The value of equation ax + b is 3.

What is an equation?

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To find the value of ax + b, we need to isolate that expression on one side of the equation.

Starting with:

9ax + 9b - 6 = 21

We can add 6 to both sides:

9ax + 9b = 27

Then, we can factor out 9 from the left-hand side:

9(ax + b) = 27

Dividing both sides by 9, we get:

ax + b = 3

Therefore,

The value of equation ax + b is 3.

Learn more about equations here:

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Enrique charges $5 for every 1/5 hour he spends walking dogs.in the morning he walks buttons for 2/5 hour bruno for 1/5 hour and pepper for 3/5 hour. Monday thru friday. On saturdays he takes mimi diva and coco to the dog park for 4/5 of an hour. On wendsday this week it rained and pepper wanted to stay out for only 1/5 hour. How many hours did enrique spend with the dogs this week. Explain your method

Answers

Maybe You should go check out @AlwaysSmartKate

Shoe store A is having a sale in which every pair of shoes is 40% off the regular price.
Shoe store B is having a sale in which $40 is deducted from the regular price.

Richard is comparing the price of the same pair of shoes in both shoes in both stores.In both stores, the shoes normally sell for $120. Which store has the better bargain?

Answers

Store A because 40% off of 120$ will equal 72.

Store a where there is the 40% off, unless he's buying something less that $100 the percentage will always be the better deal than a solid amount off.

Margaret wants to call her friend overseas. There is a connection fee of $2 and a charge of $1.50 per minute. So the cost of the call is 2 + 1.5t dollars for t minutes.

Answers

Yes, because you take your connection fee which is $2 and since there is nothing that will change that you add the $2 to the cost per minute which is $1.50 per minute so you multiply the number of minutes (T) times $1.50 then add your $2

What is the circumference of a circle circumscribed around a rectangle with sides 10 cm and 24 cm?

Answers

if you can picture it , or sketch it. The diagonal of the rectangle (line connecting opposite corners) is the diameter of the circle. You can find the diagonal by using the Pythagorean theorem for a right triangle. The diagonal would be the hypotenuse.

10^2 + 24^2 = 676
sqrt(676) = 26

The formula for circumference is: diameter times pi.

C = 26pi

In a rhombus MPKN with an obtuse angle K the diagonals intersect each other at point E. The measure of one of the angles of a ∆PKE is equal 16°. Find the measures of all angles of ∆PKE and ΔPMN.

Answers

The rhombus has a couple of very interesting properties. The first is that the diagonals meet at 90o angles.

The second is that all the sides are congruent. That's actually the key to the problem (or one of them.

The third is that the diagonals are line segments that bisect the angles where the vertex of the angle is.

So just to make sure you understand what that last statement means <PKM = <NKM
K is the vertex of angle PKN

Now the really heavy duty stuff about your question.
Given
K is obtuse. Therefore <PKM can't be 16o because MKN would also have to be 16 degrees and together they don't add up to anything over 90o.
So the 16o angle is at <EPK

Remember that the diagonals meet at right angles. <PEK = 90o

Finally all triangles have 180o
< PKE = 180 - 16 - 90 = 74. So to review
<PKE = 74o
<EPK = 16o
<PEK = 90o That's one half the problem.

Moving on to triangle PMN
By the properties of parallel lines and a rhombus and isosceles triangles, that since PKN is bisected (rhombus property) Then PKN = 2* PKM =2*74 = 148o
The angle opposite <PKN is equal to <PKN so <PMN = <PKN
Since PKN = 148 then PMN = 148
Since KPN = 16o then PMN = 16o
Since triangle <PMN is isosceles <PNM = 16o

Summing up
PMN = 148o
MPN = 16o
MNP = 16o

That's both triangles solved. This is a really nice little problem. If you google properties of a rhombus, you will find all the properties I have used proven.

Answer:

m∠KEP = 90°

m∠EKP = 74°

m∠EPK = 16°

m∠N PM= 16°

m∠MNP = 16

m∠M = 148°

Step-by-step explanation:

If you do RSM those are the answers

A vegetable farmer fills 2/3 of a wooden crate with 5/7 pound of tomatoes. How many pounds of tomatoes can fit into one crate?

Answers

1 1/14 i think but not sure

5/7 pounds fill 2/3 crate

x= number of pounds of tomatoes that will fit in one crate

x=5/7 ÷ 2/3

multiply by the reciprocal
x=5/7 * 3/2
x=(5*3)/(7*2)
x=15/14

change to mixed fraction
x=1 1/14 or 1.07 pounds of tomatoes

1 1/14 pounds of tomatoes will fit in one crate.

Hope this helps! :)

for a rectangular solid with length 12 in width 2 in in height 15 in state the appropriate formula for volume and also find the volume

Answers

V= l • w • h= 12•2•15=360 in^3

A school sold small and large boxes of fruit as a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Let x represent the price of a small box and y represent the price of a large box. Solve the system to determine the price of each size box of fruit.

A The price of a small box of fruit is $10 and the price of a large box of fruit is $14.
B The price of a small box of fruit is $8 and the price of a large box of fruit is $14.
C The price of a small box of fruit is $10 and the price of a large box of fruit is $16.
D The price of a small box of fruit is $14 and the price of a large box of fruit is $16.

Answers

The answer is A.
5(10)+13(14)=232
50 + 182 =232

12(10)+7(14)=218
120 + 98 =218

The answer is y=14 and x= 10

What is the solution to a linear equation?

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218.

Then we have 5x+13y=232

12x+7y=218

Solving these two equations here we get y=14 and x= 10

Hence, The answer is y=14 and x= 10

Learn more about linear equations here:

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in 3/4 identify the role of 3. Then explain how to read tbis number

Answers

The role of 3 would be the numerator.
But how to read the number I’m not sure.

Answer:

The 3 is the numerator, To read the number is "three-fourths"

Step-by-step explanation:

I hope this helps!

If changes are made to a signature while using version 5.x signature files, are they visible in the router running the configuration?

Answers

I think that the changes will not be visible in the router running the configuration. This is because they are not part of the router configuration. The version 5.x signature is more advantageous it has an additional signature risk rating feature and it supports encrypted signature parameters.

The classroom encyclopedia set seems to fill a shelf that is 24 in long each book is 3/4 in thick how many books are in the classroom set

Answers

24 divided by 3/4= 24*4/3=32books

which number produces an irrational number when multiplied by 0.5

Answers

square root of 3
pi symbol

Find the equation of the plane through the point p=(5,5,4)p=(5,5,4) and parallel to the plane 5x+2y−z=−6.

Answers

If the required plane is parallel to the plane
Π : 5x+2y-z=-6
then they both have the normal vector <5,2,-1>

Given the required plane passes through the point (5,5,4), the new plane is defined by
5(x-5)+2(y-5)-1(z-4)=0
=>
plane: 5x+2y-z=31

William runs 5 meters in 20 steps. How many kilometers will he run if he takes 1,000 steps ?

Answers

This means 5 meters/20 steps = x/1,000 steps. 20 times 50 is 1,000, so 5 times 50 is 250 meters. 5/20 can be also reduced to 1/4 = x/1000. Use cross products rule to get 4x = 1,000. Divided both sides by 4 to get x = 250 meters.

Go help me anwser my question

what is the rate of decay, as a percent, for the following function n(x)=7(0.067)^x

Answers

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}\\\\ -------------------------------\\\\ n(x)=7(0.067)^x\implies n(x)=7(1-\stackrel{r}{0.933})^x \\\\\\ r=0.933\qquad r\%=0.933\cdot 100\implies r=\stackrel{\%}{93.3}[/tex]

Answer: The rate of decay is 93.3%.

Step-by-step explanation:

Since we have given that

The exponential function is given by

[tex]n(x)=7(0.067)^x[/tex]

As we know the general equation of exponential function that is given by

[tex]n(x)=a(1-b)^x[/tex]

Here, a denotes the initial value

1-b denotes the rate of decay.

So, On comparing both the equations, we get that

[tex]1-b=0.067\\\\b=1-0.067\\\\b=0.933=0.933\times 100=93.3\%[/tex]

Hence, the rate of decay is 93.3%.

Five hummingbirds drink 7.5 ounces of sugar water a day. How much sugar water is needed for 14 hummingbirds?

Answers

First, divide 7.5 by 5 to find out how much sugar water is needed for each bird.
Each bird needs 1.5 ounces per day.
Then just multiply that by 14 to get 15.5 ounces of sugar water.
Hope this helps!

Since 5 hummingbirds drink 7.5 ounces, we have to figure out how many ounces goes to only one.

You should divide 7.5 by 5, and that equals 1.5

Then you're going to multiply 1.5 by 14 because there are 14 hummingbirds

1.5 * 14 = 21

21 ounces of sugar water is needed for 14 hummingbirds.

How can you find the surface area of a composite solid made up of prisms

Answers

Asked and answered elsewhere.
https://brainly.com/question/8918751

a triangle has an area of 54 m2 and a height of 9m how long is the base of the triangle entered your answer in the box

Answers

Answer:
base of the triangle = 12 m

Explanation:
Area of the triangle = 1/2 * base * height
We are given that:
area = 54 m^2
height = 9 m

Substitute in the equation to get the base as follows:
Area of the triangle = 1/2 * base * height
54 = 1/2 * base * 9
108 = 9*base
base = 12 m

Hope this helps :)

The first thing you should know to solve this problem is that the definition of the area of the triangle is:
A =(1/2)* b * h
Where,
b: base
h: height.
Clearing the base we have:
b = 2*A / h
Substituting the values
b = 2*(54) / (9) = 12 m
Answer:
The base of the triangle is 12m long

a rectangle that is 2 inches by 3 Inches has been scaled by factor of 7 suppose you want to scale the copy back to its original size what scale factor would you use?

Answers

It would be 1/7 since you essentially are dividing by 7 to cancel out the original scaling.

This is about transformation of objects.

Scale factor back to original size = 1/7

We are told that the rectangle was scaled by a factor of 7.

What this means is that if the length and width are x and y respectively, then the new scaled measurements will be;

7x and 7y.

Now,for us to scale back to the original size, all we need to do is to divide the new scale measurements by a factor of 7.

This means the original size will be;

Length = 7x × 1/7

Width = 7y × 1/7

Thus,the scale factor will be 1/7 back to the original size.

Read more at; https://brainly.com/question/17292295

There are fewer than 8 gallons of gas in the tank how do I write an inequality for that

Answers

g<8 g as a variable for gallons

which equation is the inverse of y=100-x2

Answers

Answer:

Inverse of y = [tex]f^{-1}(x)[/tex] = [tex]\sqrt{100 -x}[/tex].

Step-by-step explanation:

Given : f(x) = y = 100 - x²

To find : Find inverse.

Solution : We have given that :

f(x) = y = 100 - x²

Step1) : Replace every x with a y and replace every y with an x .

x = 100 - y².

Step 2): Solve for y

On subtracting 100 from both sides

x - 100 = -y²

On multiplying both side by -1

100 -x = y²

Taking square root both sides and switching sides

y = ± [tex]\sqrt{100-x}[/tex].

Step3 ) : Replace y with [tex]f^{-1}(x)[/tex].

[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].

Therefore, inverse of y = [tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].

Answer:

A on edge

Step-by-step explanation:

The diagonals BF and CE divide the hexagon ABCDEF into two equilateral triangles and a square. Find the perimeter of the hexagon if BF = 3 cm. Answer: P = cm

Answers

18 cm
Because all the sides are the same size

Answer: The perimeter of the hexagon is 18 cm.

Step-by-step explanation: As given in the question, hexagon is shown in the attached figure.

The diagonals g and h divides the hexagon into two two equilateral triangles and one square .

Also, length of diagonal g = 3 cm.

We are to find the perimeter of hexagon.

We know that all the sides of a square are equal, so we have

length of b = length of h = length of e = length of g = 3 cm.

Since the two triangles are equilateral, so all their sides will be equal.

That is, length of a = length of f = length of g =length of c =length of d = length of h = 3 cm.

We know that the perimeter of a polygon is equal to the sum of the lengths of its sides.

Therefore, the perimeter of hexagon is given by

P = a + b + c + d + e + f = 3 + 3 + 3 + 3 + 3 + 3 = 18 cm.

Thus, the perimeter of the hexagon is 18 cm.

2 to the x power equals 512

Answers

2 to the 8th power = 512
Please make brainliest! ☺

The answer is 22.6 i believe, let me know if i got it right

C=
5\9
(F−32)

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

I.) A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5\9 degree Celsius.

II.) A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

III.) A temperature increase of 5\9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

A) I only
B) II only
C) III only
D) I and II only

Answers

the answer is D. hope this helps

A swimmer swam 49 kilometers in d days. what is the value of d if the swimmer swam an average of 3.2 kilometers daily?

Answers

the answer is the value of d is 15 days

Because d= 49/ 3.2= 15 days

which relation defined by mapping diagram is a function

Answers

Hello! A diagram is a function, when the domain of a number only has one range. By looking at this graph, A is eliminated, because 1 has more than one range. Exact same thing with C. The only diagram that shows a function is B, because no domain has more than one range. All of the numbers have one range, and that diagram makes a function. The answer is B.

Suppose that the polynomial function A(x) = - 0.0082x2 + 0.06x approximates a person's blood-alcohol level x hours after drinking 5 ounces of 80-proof whiskey. What is the person's blood-alcohol level after 3 hours?

Answers

Given that the blood-acohol level at time x is given by A(x)=-0.0082x²+0.06x. The blood-alcohol after 3 hours for a person who has drunk 5 ounces pf 80-proof whiskey will be:
A(3)=-0.0082(3)²+0.06(3)
A(3)=-0.0738+0.18
A(3)=0.1062
the amount of blood-alcohol after 3 hours will be 0.1062

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