Mathematics College

Part 1:
A. Express the new length of the long side of the note card, once the two corners are removed.
B. Express the new width of the short side of the note card, once the two corners are removed.

Part 2:
Write a function A(x) that defines the area of the bottom of the box, once the corners are removed and the sides are folded up.

Part 3:
A. Suppose you want the bottom of your box to cover a total area of 16 in2. Set up an equation in standard form that will help you find the size (x) of the corner you need to cut in order for your box to have this area.
B. Solve this equation and take note of any extraneous solutions. Explain why the answer is extraneous, and clearly state the correct answer

Answers

Answer 1

The size of the corner you need to cut in order for your box to have this area is 0.5 inches

Part 1: A. Express the new length of the long side of the note card, once the two corners are removed.

The base length is given as:

Length = 7

When the edges are removed, the new length becomes

New length = 7 - x - x

Evaluate

New length = 7 - 2x

Part 1: B. Express the new width of the short side of the note card, once the two corners are removed.

The base width is given as:

Width = 4

When the edges are removed, the new length becomes

New width = 4 - x - x

Evaluate

New width = 4 - 2x

Part 2: Write a function A(x) that defines the area of the bottom of the box, once the corners are removed and the sides are folded up.

The area of the bottom of the box is calculated as:

Area = New length * New width

This gives

Area = (7 - 2x) * (4 - 2x)

Rewrite as:

A(x) = (7 - 2x) * (4 - 2x)

Part 3: Set up an equation in standard form that will help you find the size (x)

The area is given as:

Area = 16

So, we have:

(7 - 2x) * (4 - 2x) = 16

Expand

28 - 14x - 8x + 4x^2 = 16

Rewrite as

4x^2 - 14x - 8x + 28 - 16 = 0

Evaluate the like terms

4x^2 - 22x + 12= 0

Part 3: Solve this equation and take note of any extraneous solutions

We have:

4x^2 - 22x + 12= 0

Expand the equation

4x^2 - 24x - 2x + 12 = 0

Factorize the equation

4x(x - 6) - 2(x - 6) = 0

Factor out x - 6

(4x - 2)(x - 6) = 0

Solve for x

x = 0.5 or x = 6

The value of x = 6 is too big for the dimensions of the box.

So, x = 6 is an extraneous solution for the equation

Hence, the size of the corner you need to cut in order for your box to have this area is 0.5 inches

Related Questions

find the perimeter and area of the rectangle with vertices (1, -2), (1, 7), (-3, 7), and (-3, -2)

Answers

Answer:

Step-by-step explanation:

9+4+9+4=26

v= u + at, find v, when u = 12, a = 5 and t = 7

Answers

Answer:

V=47

Step-by-step explanation:

12+5x7

12+35

Answer:

Final velocity (v) = 47 m/s

Step-by-step explanation:

u = 12

a = 5

t = 7

v = ?

v = u + at (first law of motion)

v = 12 + (5 × 7)

v = 12 + 35

v = 47 m/s.

a population consists of the five measurement 2,3,6,5 and 7. what is the mean?

Answers

Answer:

4.6

Step-by-step explanation:

Find the vertex of the graph of the quadratic function f(x)=7x2+14x+10

Answers

Answer:

plazzz get lost bro fast

which explains how to find the quotient of the division below -3 1/3 / 4/9

Answers

KCF method
keep the first one the same, change the sign to multiplication, and flip the last fraction to its reciprocal.
(also change the first fraction to an improper fraction)
-10/3 x 9/4 = -90/12
-7.5 or -7 1/2

The solution set in interval notation is ??

Answers

Answer:

Step-by-step explanation:

The population of a school will increase by 3% per year. In 2005, the population was 127 students. Use a graph to find when the population will be
Enter the correct year in the box.

Answers

Using an exponential function, it is found that the population will be of 350 students in the year of 2039, 34.3 years after 2005.

What is an exponential function?

An increasing exponential function is modeled according to the rule presented as follows:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which the parameters of the equation is defined as follows:

A(0) is the initial amount of the function.r is the growth rate of the function, as a decimal.

In the context of this problem, the values of the parameters are given as follows:

A(0) = 127, which is the number of students in the reference year of 2005.r = 0.03, which is the yearly increase rate.

Hence the equation for the number of students in t years after 2005 is given as follows:

[tex]A(t) = 127(1.03)^t[/tex]

The number will be of 350 students when A(t) = 350, hence:

[tex]A(t) = 127(1.03)^t[/tex]

[tex]350 = 127(1.03)^t[/tex]

[tex](1.03)^t = \frac{350}{127}[/tex]

[tex]\log{(1.03)^t} = \log{\left(\frac{350}{127}\right)}[/tex]

[tex]t\log{1.03} = \log{\left(\frac{350}{127}\right)}[/tex]

[tex]t = \frac{\log{\left(\frac{350}{127}\right)}}{\log{1.03}}[/tex]

t = 34.3 years.

34.3 years = during the year of 2005 + 34.3 = 2039. This result is shown by the graph at the end of the answer.

Missing Information

The problem asks for when the population will be of 350 students.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

A recent General Social Survey asked respondents how many close friends they had. For a sample of 1467 people, the mean was 7.4 and the standard deviation was 11.0. The distribution had a median of 5 and a mode of 4.Based on these statistics, would you expect this distribution to be bell-shaped, left skewed, or right skewed?

Answers

Answer:

This distribution should be expected to be right skewed.

Step-by-step explanation:

Pearson skewness:

The skewness of a data set is given by the subtraction of the mean by the mode, divided by the standard deviation.

If the coefficient is positive, the distribution is right skewed.

If the coefficient is negative, the distribution is left skewed.

If the coefficient is sufficiently close to 0(+/- 0.05), the distribution is bell shaped.

In this question:

Mean 7.4, mode 4, standard deviation 11

(7.4-4)/11 = 3.4/11 = 0.31

Positive coefficient, so right skewed.

Question #4
The radius of a circle is 12 inches.
Enter the circumference of the circle, in inches. Round your answer
to the nearest hundredth.

Answers

Answer:

80.11 inches

Step-by-step explanation:

The formula to finding the circumference of a circle is:

C = 2πr (C = circumference, π = pi, r = radius)

Replace r with the radius:

C = 2π(12.75)

Now, multiply 2 times pi, then multiply that by 12.75, and the answer rounded

to the nearest hundredth is 80.11

This is the question I need the answer in 24 house or less please and thank u

Answers

Answer:

Vertex: (–9, 1)

Axis of Symmetry: x = –9

Step-by-step explanation:

x = 9 is the lowest point on the graph. This makes it the x-coordinate of the vertex and the axis of symmetry. Now count how many squares above the x-axis it is. It's 1 square above, right? This means the vertex is (–9, 1).

Hope this helps you. Have a great day!

Slope of (-2,-1) and (2,-3)

Answers

SLOPE is the picture.

Point-Slope form is y+1=-1/2*(x+2)

The y=mx+b form is y=-1/2x-2

i hope its not confusing lol

The earth travels 1,050 miles per hour.
At this rate, how many miles does the earth travel per day?

Plz Help God will Bless You!!

Answers

The earth travels 1,050 miles in an hour.

There are 24 hours in a day.

So multiply 1,050 by 24.

And you get 25,200.

The earth travels 25,200 miles in a day.

It will take 48 hours of work to complete the garden.
The garden must be finished in 3 days.
Each gardener works for 8 hours per day.
How many gardeners are needed?

Answers

6 Gardner’s because 48/8=6

100% of what equals 12

Answers

Answer:

Step-by-step explanation:

solve the equation 8 + b = 26 and b=

Answers

b=26-8
so the answer is b=18

B is equal to 18 hope this is correct

what is 23 + 23 - 789

Answers

Answer:

743

Step-by-step explanation:

23+23=46

789-46=743

Answer:

743

Step-by-step explanation:

Name all digits that can be the last digit of prime numbers.

Answers

Answer:

1,2,3,5,7,9

Step-by-step explanation:

I started by seeing all the digits (0-9) which are prime numbers.

A bucket contains 13 & 1/3 gallons of water and is 5/6 full. How many gallons of water would be in a full bucket?

Answers

Answer:

Step-by-step explanation:

Answer:

17 2+2+2+2+2+2+2+2+1

Step-by-step explanation:

the bucket contains 13 and 6

What is the area of the figure?

Answers

Answer:

졌던 냥 샷 세 새 새 휴 여ㅔ헤헤헤헤헤헤하리ㅎㄴ하왕허웋ㅇ헝후오ㅡ아ㅗ여ㅏㅕ라ㅕ라ㅗㅇ렁셔 요 쇽뎌ㅕ려래ㅛ요ㅓㅓㅛ요ㅏ다ㅛ 또훙서 유ㅓ가ㅗㅗ히ㅓ

ㅍ피ㅓ리ㅓ히ㅓㅓ히ㅗ챠ㅗㅗ료ㅡ쵸ㅏㅇ

Step-by-step explanation:

ㅇㅎ겨개ㅛ교ㅑ아ㅛ려ㅐㄹ서넣요ㅏㅗㅏ차ㅗ셔ㅏ 로 홀ㅛㅕㅑ쇼ㅑ겻효ㅕ 껴ㅛㅕㅛ교ㅑ교ㅐ료ㅏ래ㅕ새ㅕ리ㅕㅐㅕㅔㅑㅣㅕ셔ㅐ ㅕㅣ셔ㅐㄱㅕㅔ샹샹허텋요ㅑ오툐ㅏ어ㅣ래ㅕ촤쳐ㅐ료ㅑ와타ㅛ낳와탸ㅛ와촤야ㅛ 유ㅗㅡ촤우ㅗ퇴롸러ㅣ혀ㅣ라ㅛㅌ샤 ㅗㅣ래ㅛ려ㅣ랴ㅛ아ㅗ처ㅣ촤여ㅣ리ㅕㅓ쵸ㅐ려ㅣㅓㅓㅣ리ㅓㄹㅗㅏ려ㅣ려ㅣ려ㅣㅣㅕㅛㅑㅓㅛ나굣이셔서ㅣㅣ시서ㅣ서소니서서서성섯여ㅣ햐ㅔㅅ하ㅕㅓ퍄샤도ㅕㅐ요ㅏㅗ럇냐ㅛ려ㅔㅐㅈ서ㅕㅣ세ㅕ엿처억 ㅣㅕ려

Which of these best describes a pair of supplementary angles?

a . Two angles whose sum is 90°.

b . Two non-adjacent angles formed by the intersection of two lines.

c . Two angles whose sum is 180°

d . Two angles that share a common side and vertex with no common interior points.

Answers

Answer:

c . Two angles whose sum is 180°

Step-by-step explanation:

Hope it helps you in your learning process

How many 1/2 cup servings are in 6 cups of grapes?

Answers

Answer:

There are 12

Step-by-step explanation:

hope this helps.

There is 12 1/2 servings in 6 cups of grapes

Jocelyn boils 24 eggs. From experience, she knows that the shell of any given during the boiling process. If shells crack independently, what is the probability the boiling process with a cracked shell? Round to 2 decimal places.

Answers

Answer:

.62

Step-by-step explanation:

Keep it nice and simple.

Answer:

.62

Step-by-step explanation:

Here again are the results of a survey that students conducted at a mall. The students conducted this survey as part of a statistics project to determine if younger adults are more likely to have tattoos. At least one tattoo No tattoo Row Totals Age 18 - 29 170 320 490 Age 30 - 50 60 445 505 Column Totals 230 765 995 Which proportions are most useful in analyzing the relationship between age and tattoos? Group of answer choices 170 / 230 and 60 / 230

Answers

Answer:

1. 170/490 and 60/505

2. 320/490 and 445/505

Step-by-step explanation:

No options were given, but the question can still be answered

Given

[tex]\begin{array}{cccc}{} & {\ge 1\ tattoo} & {0\ tattoo} & {Row\ Total} & {18 -29} & {170} & {320} & {490} & {30 - 50} & {60} & {445} & {505} & {Column\ Total} & {230} & {765} & {995}\ \end{array}[/tex]

Required

Which proportion best compares age and tattoos?

The row data represents the age range of each group while the column data represents the amount of tattoo by each group.

So, to make comparison:

You simply pick a cell data and compare it to the row total.

Take for instance

For those who have at least 1 tattoo. The proportion to use are:

170/490 --- For age range: 18 - 29

60/505 --- For age range: 30 - 29

For those without tattoo. The proportion to use are:

320/490 --- For age range: 18 - 29

445/505 --- For age range: 30 - 29

15x > - 60

Help and I’ll give u brainlist :)

Answers

Answer:

most likely 1 or 20 but im not so sure tho

Evalute 4+(7-5)⁴?
PLEASE HELP

Answers

Answer:

The answer is 20

Step-by-step explanation:

(7-5)=2

2^4 = 16

16 + 4 = 20

Solve the equation
2x2 + 12x - 7 = 0
by completing the square.
Give your answers correct to 2 decimal places.
Show step by step please!!!!

Answers

Step-by-step explanation:

4+12x=7

12x=7-4

12x=3

X=3/12

X=0.25

Do
10 cm
10 cm
20 cm
form an triangle?

Answers

Answer:

No it is unable to form a triangle.

Step-by-step explanation:

It cannot be because one side is two times the other side, and there are two of the "other sides". It cannot form a triangle.

Answer:

Step-by-step explanation:

8) Which of the Prime number are
even numbers?
C
a) 0 & 2
b) 1 & 2
c) 2
ОО
d) None

Answers

Answer C is correct

A submarine is 84 feet below the surface of the water and descends 10 feet
deeper every minute. How many minutes will it take for the submarine to be
located 219 feet below the surface? Write and solve an equation,

Answers

Answer:

13.5

Step-by-step explanation:

219-84=135

10*13.5=135

so it would take 13.5 minutes to get to 219 since 84+135=219

19 tens is the same
as
Count forward by fives.

Answers

19 tens is 190 but i don’t know what you mean by count forward by fives

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