A piece of cardboard is 5 centimeters longer than it is tall. The area of the piece of cardboard is 66 square centimeters. How many centimeters long is the piece of cardboard?

Answers

Answer 1

Answer:

12.244 cm long

Step-by-step explanation:

The area of a rectangle is equal to its height times its width, so if the piece of cardboard has an area of 66 square centimeters and is 5 centimeters longer than it is tall, we can write the following equation to represent the dimensions of the piece of cardboard:

height * (height + 5) = 66

To solve this equation, we can first divide both sides of the equation by the height of the piece of cardboard to get:

height + 5 = 66 / height

We can then subtract 5 from both sides of the equation to get:

height = 66 / height - 5

We can then multiply both sides of the equation by the height to get:

height^2 = 66 - 5 * height

We can then use the quadratic formula to solve for the height of the piece of cardboard:

height = (-5 +/- sqrt(5^2 - 4 * 1 * -66)) / (2 * 1)

The value of the square root in the quadratic formula must be positive, so we take the positive value for the height:

height = (-5 + sqrt(5^2 + 4 * 1 * 66)) / (2 * 1)

This simplifies to:

height = (5 + sqrt(61)) / 2

The height of the piece of cardboard is approximately 7.244 centimeters. Since the piece of cardboard is 5 centimeters longer than it is tall, it must be 5 + 7.244 = 12.244 centimeters long.

Therefore, the piece of cardboard is approximately 12.244 centimeters long.


Related Questions

KARLA has spent $33 on food. She bought milk, cheese, and meat. The milk cost half as much as the cheese and the meat cost four times as much as the cheese. Which equation will help you find the cost of the cheese?

KARLA has spent $33 on food. She bought milk, cheese, and meat. The milk cost half as much as the cheese

Answers

C+.5c+4c=$33 is the correct equation

SOLVE FOR X AND Y !! WILL GIVE BRAINLIEST

SOLVE FOR X AND Y !! WILL GIVE BRAINLIEST

Answers

Answer:

x=21, y=17

Step-by-step explanation:

180-42= 138

2x+138=180

2x= 42

x= 21

8y+2+2x=180

8y+2 + 42=180

8y= 136

y= 17

Answer:

x=21, y=68

Step-by-step explanation:

We're given that the quadrilateral on the left is a parallelogram as indicated by the arrow markings on the sides. We're also told that the angle on the right is 42 degrees. So, we can find the bottom right angle in the parallelogram by subtracting 42 from 180, because it forms a straight angle. 180-42 is 138. By the alternate interior angles theorem, 8y+2=138, because 138 is also the angle measure of the opposite corner. we also know that the bottom left angle in the parallelogram is the same as 2x. by the alternate interior angles theorem. Notice how the sides of the parallelogram with two arrow markings are parallel, which means that the bottom left angle and the 42 degree angle are congruent, or have the same measure, because of the parallel lines. This means that 2x=42, and the bottom left angle is 42. We can solve for x and y with simple algebra now. 8y+2=138, 8y=138-2, 8y=136, y=68. 2x=42, x=42/2, x=21. So, x is 21 and y is 68.

If a ring costs a jeweler $2100, at what price should it be sold to yield a profit of 50% on the selling price?

Answers

$1050
2100/2 = 1050
Meaning 50% is $1050

Using the slope formula, find the slope of the line through the given points. (4. - 2) and ( - 2, - 2)​

Answers

Answer:

- 0/6

Step-by-step explanation:

*I’m pretty sure you meant to type “(4, -2)” instead of “(4. -2)” Anyways…*

m = slope

m = change in y/change in x

m = y2 - y1/x2 - x1

Points: (4, -2) and (-2, -2)

m = -2 - -2/-2 - 4

m = 0/-6

The slope is - 0/6

Hi! I'm happy to help!

To solve this problem, we have to find the slope, which is rise over run, or how much the line rises and how far forward the line goes.

We find the slope using this formula (slope formula)

m(slope)=\(\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\)

This refers to the second y point minus the first y point, divided by the second x point minus the first x point. Y refers to the y axis, so that is the rise, because it is the difference of height in the line. X refers to the x axis, so that is the run, because it is the difference in how far it travels forward.

Our second y point is -2, our first y point is also -2. Our second x point is -2, and our first y point is 4. Let's plug in our values.

\(\frac{-2-(-2)}{-2-4}\)

Let's simplify this so there isn't a double negative.

\(\frac{-2+2}{-2-4}\)

Now, let's solve

\(\frac{0}{-6}\)

0 divided by -6, is still 0, so there is no slope or the slope is 0. This means that the line is horizontal and the y coordinate doesn't change.

I hope this was helpful, keep learning! :D

Which of the following is most likely the next step in the series ?​

Which of the following is most likely the next step in the series ?

Answers

Answer:

b

Step-by-step explanation:

it should be red because the colour is alternative

and next we should add a horizontal line

hence b is the next step

Answer:

I'm not sure but I guess the answer is option >D

Step-by-step explanation:

Find the height of the tower using the information given in the illustration.

Find the height of the tower using the information given in the illustration.

Answers

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Find the height of the tower using the information given in the illustration.

In computing the sum of an infinite series ∑ [infinity] , x = nn = 1suppose that the answer is desired with an absolute error less than e. Is it safe to stop the addition of terms when their magnitude falls below s? Illustrate with the series ∑[infinity] (0.99)^nn = 1

Answers

No, it is not safe to stop the addition of terms when their magnitude falls below s, even if the desired absolute error is less than e.

This is because the magnitude of the terms in the series may not decrease monotonically, and there may be large fluctuations in the magnitudes of the terms.
Therefore, it is necessary to use convergence tests, such as the ratio test or the root test, to determine if the series converges absolutely.

For the series ∑ (0.99)^n, we can use the ratio test to check for absolute convergence:

lim (n → ∞) |(0.99)^(n+1)/(0.99)^n| = 0.99 < 1

Since the limit is less than 1, the series converges absolutely. However, we cannot simply stop adding terms when their magnitude falls below a certain value s, as the magnitude of the terms in the series may not decrease monotonically.

Instead, we need to use the convergence test to determine the number of terms required to achieve the desired absolute error e.

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Can someone help me with this please?

Can someone help me with this please?

Answers

Answer:

okay i dont know if this will make sense but

Step-by-step explanation:

<_____* *________>

<---|------|-----|-----|-----|-----|----->

-2 -1. 0. 1. 2. 3

42/2 +9=???

what is the answer and how do you find the answer?!

Answers

42/2 is 21 then add 9 you’d get 30 as your final solution.

1 (c)
Gavin goes to Joti's shop.
He is making a circular blanket.
The finished blanket will have a radius of 0.325 m
It will have ribbon all around the edge.
He thinks he will need 2.5 m of ribbon.
Gavin knows that is about 3.1416
Round to 1 decimal place and use this value to work out how much ribbon
Gavin will have left if he buys 2.5 m
[4 marks]

Answers

Answer: 0.5m

Hope this helps!

PLEASE HELP, IGNORE ALL ANWSERS FILLED IN CURRENTLY I WILL GOVE BRAINLIST

PLEASE HELP, IGNORE ALL ANWSERS FILLED IN CURRENTLY I WILL GOVE BRAINLIST

Answers

Answer:

32.64°

Step-by-step explanation:

From triangle Given :

The sides of the missing angle given are the Adjacent and hypotenus.

Since the triangle is right angled, we can apply trigonometry :

cosθ = adjacent / hypotenus

Cosθ = 16 / 19

θ = Cos^-1(16/19)

θ = 32.6368

θ = 32.64°

Find
f '(a).
f(x) = 3 − 4x

Answers

Answer:

f'(a) = -4

Step-by-step explanation:

f(x) = 3 − 4x

Take the derivative of the function

f'(x) = -4

f'(a) = -4

2 : 6 : 7 = x : 36 : y

Answers

Answer:

x = 12, y = 42

Step-by-step explanation:

6 is multiplied by 6 to get 36 (lot of sixes lol)

So multiply everything else by 6

2 x 6 = 12

7 x 6 = 42

Answer:

d y/d x = y/x

Step-by-step explanation:

Help me out on this question

Help me out on this question

Answers

Answer:

the third one

Step-by-step explanation:

Answer 9 and 11 please only those.

Answer 9 and 11 please only those.

Answers

Step-by-step explanation:

11. -19/5

9.-9/10

i hope this helps

what is the answer to
-5x+y=-210

Answers

Answer:

y=−210+5x

Step-by-step explanation: easy

Find the equation of a line perpendicular to y=x−3 that contains the point (2,1). Write the equation in slope-intercept form.

Answers

perpendicular gradient (m) = -1
slope intercept form = y - y1 = m(x - x1)

y - 1 = -1 (x -2)
y - 1 = -x + 2
y = -x + 3

Find the area of each face of the triangular prism and the total surface area.
Drag each tile to its matching measurement. Each number may be used once or not at all.

Find the area of each face of the triangular prism and the total surface area.Drag each tile to its matching

Answers

9514 1404 393

Answer:

24160120200528

Step-by-step explanation:

The area of each triangular face is given by the formula ...

  A = 1/2bh

The triangular faces have a base of b=8 cm, and a height of h=6 cm. Their area is ...

  A = 1/2(8 cm)(6 cm) = 24 cm²

__

Each of the rectangular faces has a length of 20 cm. The width depends on which face is of interest. In each case, the area is given by ...

  A = LW

Bottom face: A = (20 cm)(8 cm) = 160 cm²

Back face: A = (20 cm)(6 cm) = 120 cm²

Sloped face: A = (20 cm)(10 cm) = 200 cm²

__

The total area is the sum of the areas of all of the faces and bases. There are two triangular bases, so the total area is ...

  (2×24 + 160 +120 +200) cm² = 528 cm²

what is 75 percent of 225? 30 57.25 75 168.75

Answers

Answer:

168.75

Step-by-step explanation:

hope this helps :3

if it did pls mark brainliest

Answer:

168.75

Step-by-step explanation:

Multiply 0.75 and 225 together

(0.75 = 75%)

0.75(225) = 168.75

So 168.75 is 75% of 225

Hope this helped :)

Brainliest?

What is the values of x and z?

What is the values of x and z?

Answers

Check the picture below.

What is the values of x and z?

Use f(x) = 1
2
x and f -1(x) = 2x to solve the problems.

f(2) =
1

f−1(1) =
⇒ 2

f−1(f(2)) =
⇒ 2

f−1(−2) =
1
⇒ -4

f(−4) =
2
⇒ -2

f(f−1(−2)) =
2
⇒ -2

In general, f−1(f(x)) = f(f−1(x)) =

Answers

Using the function f(x) = 1/2 x and the inverse of the function f⁻¹(x) = 2x, the solutions of the given are :

f(2) = 1, f⁻¹(1) = 2, f⁻¹(f(2)) = 2

f⁻¹(-2) = -4, f(-4) = -2, f(f⁻¹(-2)) = -2

Given a function,

f(x) = 1/2 x

And an inverse function,

f⁻¹(x) = 2x

We have to find the values of the following.

f(2) = 1/2 × 2 = 1

f⁻¹(1) = 2 × 1 = 2

f⁻¹(f(2)) = f⁻¹(1) = 2 × 1 = 2

f⁻¹(-2) = 2 × -2 = -4

f(-4) = 1/2 × 4 = -2

f(f⁻¹(-2)) = f (-4) = 1/2 × 4 = -2

So, in general, f⁻¹(f(x)) = f(f⁻¹(x))

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Please answer soon!!

Which angles are coterminal with 3л/2?
Select each correct answer.

A. 11л/2
B. -л/-2
C. -7л/-2
D. л/2

Answers

Answer:

  A, C

Step-by-step explanation:

You want to know which answer choices are angles that are coterminal with 3π/2.

Coterminal

Angles are coterminal when their terminal rays lie in the same position. In general, any angle will be coterminal with angles that are an integer multiple of 2π added to the original.

That is, an angle is coterminal with all angles that have the same value modulo 2π.

For the given angle and each of the answer choices, the attachment calculates the coefficient of π modulo 2. The ones that match the given angle are ...

 A. 11π/2 mod 2π = 3π/2

  C. -7π/-2 mod 2π = 3π/2

__

Additional comment

Both -π/-2 and π/2 match the angle π/2, which is not the same as 3π/2.

Of course, the minus signs in numerator and denominator cancel, so -7π/-2 is the same as 7π/2.

<95141404393>

Please answer soon!!Which angles are coterminal with 3/2?Select each correct answer.A. 11/2B. -/-2C.

What is the sum of two consecutive numbers is 141

Answers

Two consecutive numbers can be written as:
x , x+1

So their sum being 141
x + x +1 = 141

Combine and solve for c

2x = 140
x = 70

So two numbers are:

70,71

The two consecutive integers such that their sum is 141 will be 70 and 71.

What is a number system?

The number system is a way to represent or express numbers.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Let's say that two consecutive integers are x and x + 1.

x + x + 1 = 141

2x + 1 = 141

2x = 140

x = 70

So, x + 1 = 71

Thus, it will be 70 and 71.

Hence "The two consecutive integers such that their sum is 141 will be 70 and 71".

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If Aidan buys 5 guinea pigs at 20% off and each pig costs g dollars, what's an expression that shows
his total cost?

Answers

The expression for the total price is 4g

How to determine the expression for the total price

From the question, we have the following parameters that can be used in our computation:

Original price = g

Reduction = 20%

Number = 5

Using the above as a guide, we have the following:

Reduced price = Number of pigs * Original price * (1 - Reduction)

Substitute the known values in the above equation, so, we have the following representation

Reduced price = 5 * g * (1 - 20%)

Evaluate

Reduced price = 4g

Hence, the reduced price is 4g

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solve the equation
7x + 3 = 4x

Answers

The answer will be x= -1
solve the equation 7x + 3 = 4x

PLEASE HELP ILL GIVE BRAINLIEST !!! 100 POINTS !! NO FAKE ANSWERS !

PLEASE HELP ILL GIVE BRAINLIEST !!! 100 POINTS !! NO FAKE ANSWERS !

Answers

Answer:

20

Step-by-step explanation:

complex conjugate of 10+5i = 10-5i

10+5i + 10-5i = 20


Someone please help me. I will give you hella points I need this answer to like graduate type

Someone please help me. I will give you hella points I need this answer to like graduate type

Answers

Answer:

$9 and $7

Step-by-step explanation:

The first equation:

x + 2y = 23

The second equation:

2x + 3y = 39

Convert to slope-intercept form:

x + 2y = 23 ⇒ 2y = -x + 23 ⇒ y = -1/2x + 11.52x + 3y = 39 ⇒ 3y = -2x + 39 ⇒ y = -2/3x + 13

The graph is attached

Intersection point is (9, 7)

Adult tickets cost $9Child tickets cost $7
Someone please help me. I will give you hella points I need this answer to like graduate type

A research group at Nike decides to survey NCSU students for their preferences in clothing brands. They divide all students into groups according to the College they belong to (like College of Science, College of Architecture, etc.). Then they take a simple random sample of 50 students from EACH college. What kind of a sample is this

Answers

Answer:

Cluster sample

Step-by-step explanation:

i did it before

Somebody, please help a brother out :))

Answers

Okay soooo what do you need help with?

Answer:

ok just post another question and i will help u out just tell me what math u are doing

Step-by-step explanation:

A BluRay disc normally costs $22. This week it is on sale for 25% off the original price. How much money is discounted from the original price of the BluRay disc?

Answers

Answer:

$7.33

Step-by-step explanation:

22=3/4x

22/.75=22*4/3=29.3333333

$29.33-$22=$7.33

A discounted from the original price of the Blu-ray disc will be $5.5.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

Cost of a Blu-ray disc = $22

The sale on the cost of a Blu- ray = 25%

Now,

Find the discounted price of a Blu-ray as;

Discounted price = 25% of $22

                           = 25 x $22 / 100

                           = $550/100

                           = $5.5

Thus, A discounted from the original price of the Blu-ray disc will be $5.5.

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If a ___________service precedes the haircut, replace the vinyl cape and towel with a nylon cape and neck strip.