The length of a rectangle is eight times it's width. If the length was decreased by 10 meters and the width decreased by 2 meters the area would be decreased by 162 m. Find the original dimensions.

Answers

Answer 1
Alright, so l=8w (l=length, w=width, a=l*w or original area)

(l-10)*(w-20)=a-162

Substituting l for 8w and a for l*w and then 8w*w, we have
 (8w-10)(w-20)=8w^2-162=8w^2-160w-10w+200=8w^2-170w+200

8w^2-170w+200=8w^2-162 , so we subtract 8w^2 from both sides as well as subtract 200 to both to get -170w=-362, so w=362/170 and
 l= 8*362/170=2896/170 


Related Questions

Find the area of a sector that has a central angle of 40 and a radius of 2 cm. Round your answer to the nearest 100th. Use 3.14=

Answers

I think the answer is around 1.4 as you need to multiply the area by 1/9 after finding the real area. 

Webassign find the area of the region bounded by the parabola y = x2, the tangent line to this parabola at the point (6, 36), and the x-axis.

Answers

first find the tangent line

dy/dx=2x
at x=6, the slope is 2(6)=12
so
use point slope form
y-y1=m(x-x1)
point is (6,36)
so
y-36=12(x-6)
y-36=12x-72
y=12x-36

alright, so we know they intersect at x=6
and y=12x-36 is below y=x^2

so we do [tex] \int\limits^6_0 {x^2} \, dx - \int\limits^6_0 {12x-36} \, dx = \int\limits^6_0 {x^2-(12x-36)} \, dx = \int\limits^6_0 {x^2-12x+36} \, dx =[/tex]
[tex][\frac{x^3}{3}-6x^2+36x]\limits^6_0=(\frac{6^3}{3}-6(6)^2+36(6))-(0)=\frac{216}{3}-216+216=[/tex] [tex]72+0=72[/tex]

the area under the curve bounded by the lines and the x axis is 72 square units

Find the area of the larger regular pentagon if the smaller pentagon has an area of 43.01 inches^2. The side length of the small pentagon is 5 and the side length of the large pentagon is 8.

Answers

110.11 is the answer.

Someone help me please !!!

Answers

Answer:

1. 10

2. 12

3. Sqrt 130

4. Sqrt 45

Step-by-step explanation:

To find the missing side of a right triangle, use the Pythagorean Theorem. The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the legs with a being the smallest and c is the hypotenuse.

1. a=6, b=8, c=?

[tex]6^2+8^2=c^2\\36+64=c^2\\100=c^2\\10=c[/tex]

2. a=5, b=?, c=13

[tex]5^2+b^2=13^2\\25+b^2=169\\169-25=b^2\\144=b^2\\12=b[/tex]

3. a=7, b=9, c=?

[tex]7^2+9^2=c^2\\49+81=c^2\\130=c^2\\\sqrt{130}=c[/tex]

4. a=2, b=?, c=7

[tex]2^2+b^2=7^2\\4+b^2=49\\49-4=b^2\\45=b^2\\\sqrt{45}=b[/tex]

What is the precise definition of an angle? question 1 options:?

Answers

In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Which is heavier 9 5/8 pounds or 9 3/4 pounds

Answers

9 3/4 weighs more than 9 5/8 because 3/4 is larger than 5/8. You can draw this out if you like to see it visually, or you can divide 3 by 4 and 5 by 8 to see which is more! 5/8 = 0.625 while 3/4 = 0.75

The sum of two numbers is 33. Twice the first number minus the second number equals 18. Find both numbers.

Answers

We can call the two numbers x and y. Then, x + y = 33, and 2x - y = 18. We can use substitution to solve this problem:

y = 33 - x 

SO

2x - 33 + x = 18

3x = 51

x = 17

Now, we know x. We can use this to find y:

x + y = 33

17 + y = 33

y = 16

So, the numbers are 16 and 17. 

The both numbers are = 17 and 16

Solving for the unknown numbers

The sum of two numbers = 33

Let the two numbers be X and y.

therefore X + y = 33 ----> equation 1

Twice the first number minus the second number= 18.

That is,

2x - y = 18 -----> equation 2

From equation 1 make X the subject of formula;

X = 33 – y

substitute X into equation 2,

2(33 – y) - y = 18

66 – 2y – y = 18

66 – 3y = 18

66 – 18 = 3y

48 = 3y

y = 48/3

y = 16

Substitute y = 16 into equation 1

Therefore, X +16 = 33

X = 33 –16

X = 17

Therefore, he both numbers are = 17 and 16

Learn more about summation here:

https://brainly.com/question/14322177

What is -11-8-13(-10)? And how did you get you're answer

Answers

-11-8-13(-10)

First, multiply since multiplication goes before subtraction according to the order of operations.

-11-8+130

Then add and subtract from left to right.

-11-8= -19
-19+130=111

Final answer: 111

True or false the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle

Answers

The answer is TRUE!!!!!

Answer:

True

Step-by-step explanation:

Consider triangle ABC inscribed in the circle with center at point O. Point O is a point of intersection of perpendicular bisectors of sides AC, AB and BC. According to the attached diagram, points E, F and G are midpoints of sides BC, AC and AB, respectively.

Then

EB=EC;FC=FA;GA=GB.

Since segments OE, OF and OG are perpendicular bisectors of sides BC, AC and AB, then

m∠OBE=m∠OCE=90°;m∠OCF=m∠OAF=90°;m∠OBG=m∠OAG=90°.

You get three pairs of congruent triangles:

ΔOBE≅ΔOCE;ΔOCF≅ΔOAF;ΔOBG≅ΔOAG.

This gives you that

[tex]OB=OC=OA.[/tex]

Each of these segments is a radius of the circumscribed circle about a triangle ABC, then the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle.

If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?

Answers

52/2 = 26 ounces of cereal in 1 box
26 * 5 = 130 ounces of cereal in 5 boxes

Answer:

If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?

Step-by-step explanation:

If we have 52 ounces in 2 boxes, in 1 box we have: 52/2 = 26 ounces.

If we have 5 boxes and 26 ounces in each, we have: 5 x 26 = 130 ounces in total.

Please help me !!!!!!!!

Answers

It's C the missing side is 9 units long so since cosine is adjacent divided by hypotenuse it would be 9/41
41^2 - 40^2 = 1681 - 1600 = 81

side xy = square root 81 = 9

cosine(X) = Adj / Hypo
cosine(X) = 9/41
answer
C. 9/41

The cells of a certain culture of bacteria double every 6 minutes. If the culture contains 100 cells in the beginning, then the total number of cells P in this culture after t minutes is given by the exponential equation P = 100(2)t/6. Identify the number of minutes it will take for the number of cells to exceed 50,000.
A) 53 min
B) 49 min
C) 48 min
D) 54 min

Answers

Since the growth is exponential, therefore I believe the correct form of the equation is:

P = 100 (2)^(t / 6)

Where t / 6 is the exponent of 2

So to find for the amount of time needed to exceed the population of 50,000, all we have to do is to plug in that value in the equation and find for t. Therefore:

P = 100 (2)^(t / 6)

50000 = 100 (2)^(t / 6)

500 = 2^(t / 6)

log 500 = (t / 6) log 2

t / 6 = log 500 / log 2

t = 6 * 8.96578

t = 53.8 mins = 54 mins

 

Answer:

D. 54 min

A tea bag is shaped like a regular square pyramid. Each leg of the base is 4 cm, and the slant height is 5 cm. Find the VOLUME of the tea bag.

Answers

(16[tex] \sqrt{21} [/tex])/3
The volume of a pyramid is V=1/3Bh (One-third the area of the base times height). Since your pyramid has a square base, you have to find the area of the base, multiply it by the height, and then divide it by 3.

So, the area of the base is 4x4, which is 16, then you multiply it by the height, 5, and 16x5 is 80, and 80/3 is approximately 26.6

The answer would be 26.6 cm^3

HELP QUICK!!!
An ellipse has foci F1(9, 0) and F2(11, 6), and the point (1, 6) is on the ellipse. Identify the constant sum for the ellipse.
a 20
b 10
c 0
d 100

Answers

The first step is to find the distance from the given point to each of the two foci as follows:
Distance D1:
(D1)^2 = (9-1)^2 + (0-6)^2 = 100
D1 = 10
Distance D2:
(D2)^2 = (11-1)^2 + (6-6)^2 = 100
D2 = 10

The constant sum is the summation of the two distances as follows:
constant sum = D1 + D2 = 10 + 10 = 20

The correct choice is:
a) 20

Answer:   20

Step-by-step explanation:

Write an equation for the translation of the function. y = cos x; translated 6 units up

Answers

it's just y= cos(x)+6

Answer:

[tex]y=cos(x)+6[/tex].

Step-by-step explanation:

We are asked to write an equation for the translation of the function [tex]y=cos(x)[/tex] to 6 units upwards.

Let us recall transformation rules.

[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]

[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]

[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]

[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]

Since we need to shift our given function 6 units upwards, so we will add 6 to our given function outside the parenthesis as:

[tex]y=cos(x)+6[/tex]

Therefore, our required equation would be [tex]y=cos(x)+6[/tex].

Rectangular prisms A and B are similar.
The edge of prism B is 3 times that of prism A. How many times the volume of prism A is the volume of prism B?

Answers

27 times smaller or 1/27 because 3^3 equals to 27.
[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \textit{let's say the edge of A is \underline{k} long, then B's is \underline{3k}} \\\\\\ \cfrac{A}{B}\qquad \cfrac{k}{3k}\implies \cfrac{1}{3}\implies \cfrac{s}{s}\qquad thus \\\\\\ \cfrac{A}{B}\qquad \cfrac{1}{3}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{1}{3}=\sqrt[3]{\cfrac{s^3}{s^3}}\implies \left( \cfrac{1}{3} \right)^3=\cfrac{s^3}{s^3}\implies \cfrac{1^3}{3^3}=\cfrac{s^3}{s^3} \\\\\\ \cfrac{1}{27}=\cfrac{s^3}{s^3}[/tex]

At a sandwich shop they offer 3 kinds of bread, 5 kinds of meat, and 3 kinds of cheese. Each type of sandwich has a combination of exactly 3 ingredients: 1 bread, 1 meat, and 1 cheese. How many types of sandwiches are possible?

Answers

Final answer:

The sandwich shop could yield a total of 45 types of sandwiches based on the three categories provided; namely, bread, meat, and cheese. According to the counting principle in mathematics, you multiply the amount of options available from each category to get the total combinations possible.

Explanation:

In the scenario described, to determine the possible number of sandwiches, we need to analyze the provided combinations. We have 3 types of bread, 5 kinds of meat, and 3 kinds of cheese. Each sandwich exactly contains one item from each category.

To find out all possible sandwich combinations, we multiply the number of choices in each category. This is known as the counting principle.

So, the formula would be:
Number of sandwich combinations = Types of Bread * Types of Meat * Types of Cheese

Plugging the given numbers into this formula, we get:
Number of sandwich combinations = 3 * 5 * 3 = 45

So, there are 45 possible sandwich combinations available in this sandwich shop.

Learn more about Counting Principle here:

https://brainly.com/question/29594564

#SPJ12

Evaluate 9 - b when b = 8

Answers

9 - b = ?
9 - 8 = 1
So, your answer is 1. Hope this helps, please mark brainliest and have an amazing day!

Equations are expressions separated by an equal sign. The value of the expression 9-b is b is 8 is given as 1

Equations and expressions

Equations are expressions separated by an equal sign

Given the expression  9 - b

If b = 8, we will have to substitute the value of 8 into the expression to have:

f(b) = 9 - b

f(8) = 9 - 8

f(8) = 1

Hence the value of the expression 9-b is b is 8 is given as 1

Learn more on function and values here: https://brainly.com/question/2284360

Twenty times the square of a non-zero number is equal to 15 times the number

Answers

i think that the answer is 5

20x^2 = 15x
20x^2 - 15x = 0
5x(4x - 3) = 0 
5x = 0, x =0
4x -3 = 0, x = 3/4

answer
non-zero number is 3/4

Applying the distributive property, the expression becomes (3x)(–x) + (3x)(4) + (–5)(–x) + (–5)(4). What is the simplified product in standard form?

Answers

The answer is -3x^2 + 17x - 20.
(3x)(–x) + (3x)(4) + (–5)(–x) + (–5)(4)
= -3x^2 + 12x + 5x - 20
= -3x^2 + 17x - 20

hope it helps

Which algebraic expression represents “the difference of 54 and a number”?

Answers

For this case, the first thing we should do is define a variable.

We have then:

x: unknown number

Then, we write the algebraic expression that models the following problem:

the difference of 54 and a number.

We have then:

[tex]54-x[/tex]

Answer:

An algebraic expression that represents "the difference of 54 and a number" is:

[tex]54-x[/tex]

Answer:

A

Step-by-step explanation:

The sum of two numbers is 54 . the smaller number is 12 less than the larger number. what are the numbers?

Answers

Let x=one number and x+12= the other number.  Together the numbers=54.  Set up the equation:  x+x+12=54;  Combine the variables;  2x+12=54;  Subtract 12 from both sides of the equation;  2x=42; Divide both sides of the equation by 2;  x=21 is one number and 21+12=33 is the other number.  Check:  2(21) +12=54;  42+12=54;  54=54.

A quiz has 4 multiple-choice questions with 4 possible answer choices each. for each question, there is only 1 correct answer.a student guesses each answer at random. what is the probability of getting exactly 3 questions correct, to the nearest percent?(3 correct and 1 incorrect)

Answers

There are 4C3 ways of getting 3 out of 4 correct. This = 4.

The probability of getting  3 correct and 1 wrong in one of these ways is 
1/4 * 1/4 * 1/4 * 3/4  =  3/256

So required probability = 4 * 3/256  = 12/256  =  4.69 %   
5% to nearest percent.

Answer:    (quartered spinner)     (4)     (1/256)


Julio checked the temperature of a bag of frozen peas and found it was at −13°C. After he left the bag out of the freezer for an hour, its temperature rose to 8°C. What was the change in temperature in an hour?
a)−21°C
b)21°C
c)5°C
d)−5°C

Answers

The change is the difference final temperature less initial temperature.

ΔT = final temperature - initial temperature = 8°C - ( -13°C) = 8°C + 13°C = 21 °C.

So, the temperature raised 21 °C, and that is the change in temperature.

Answer: change = option b) 21°C.
The correct answer is option A



20 POINTS, PLEASE HELP ASAP!!!!

Answers

Question b)

17 minutes ⇒ 1 revolution = 2π
1 minute ⇒ 2π/17

Angle of rotation is 2π/17 per minute

Question c)

The period of the rotation is 2π/17 

The wheel starts rotating from the height of 5 meters from the ground and the maximum height is 125 meter from the ground.
The amplitude is 125 - 5 = 120 ÷ 2 = 60

The midline of the rotation is at 125 - 5= 120 ÷2 = 60 + 5 = 65 (this is the location of the centre of the wheel). This value is a shift of 65 from the zero midlines (which in this case would be the ground)

Question C

The movement of the wheel can be described as starting from 0° then reaching its peak at 180° and come back to its original position as it stops and it makes a complete circular turn 360°.

If we sketch this on a graph, we will obtain a curve of -cos(x)

We need to apply the period, the amplitude and the shift produced by this rotation into the equation [tex]y = -cos(x)[/tex]

The period is [tex] \frac{2 \pi }{7} [/tex] ⇒ [tex]f(t)=-cos( \frac{2 \pi }{7}t) [/tex]
The amplitude of 60 ⇒ [tex]f(t)=-60cos( \frac{2 \pi }{7}t) [/tex]
The shift of the midline by 65 units upwards ⇒ [tex]f(t) = -60cos( \frac{2 \pi }{7}t)+65 [/tex]

The final equation is
[tex]f(t) = -60cos( \frac{2 \pi }{7}t)+65 [/tex]

and the graph is shown in the third picture below

In 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg

Answers

ok so the ratio is 1:1

Answer: it’s 1:1

Step-by-step explanation:

From 75 campsites to 120 campsites

Answers

subtract 75 from 120

120-75 =45 more campsites

The volume of a cube depends on the length of its sides. This can be written in function notation as v(s). What is the best interpretation of v(4)=64

Answers

check the picture below.

Solve 2x + 5y = −13
3x − 4y = −8

Answers

2x+5y=-13
3x-4y=-8

Rearrange the first equation to solve for x in terms of y. This will be needed to apply the substition method.

2x+5y=-13
2x=-5y-13
x=-5/2y-13/2

Now plug this in for x in the second equation.

3(-5/2y-13/2)-4y=-8
-15/2y-39/2-4y=-8
-23/2y-39/2=-8
-23/2y=11.5
y=-1

Now plug this y value in to one of the original equations.
2x+5(-1)=-13
2x-5=-13
2x=-8
x=-4

Final answer: (-4,-1). <=============

To check:

2(-4)+5(-1)=-13
-8+5(-1)=-13
-8-5=-13
-13=-13
True

3(-4)-4(-1)=-8
-12-4(-1)=-8
-12+4=-8
-8=-8
True

Driving on the North West Express-way, Debbie averaged 62 miles per hour for 3 & one fourth hours. How far did she drive?

Answers

1/4 = 0.25

s0 3 1/4 = 3.25

62x3.25 = 201.50 miles = 201 1/2 if you need it in fraction form

Other Questions
HELP PLEASEWhat is the degree measure of the supplement of the complement of a 42-degree angle? Tony misplaced 7 stamps from his collection. He knows that each stamp of his worth $0.15 and that the total value of them is now only $5.55. write an -EQUATION- to determine the number of stamps (s) that tony originally had. The picture below shows a container that Sue uses to freeze water:What is the minimum number of identical containers that Sue would need to make 2,000 cm3 of ice? (Use = 3.14.) What is the discriminant of the polynomial below? 4x2 - 20x + 25 P = KT/V solve for k How big are viruses? A.Big enough to be seen by the naked eye but smaller than a human egg cell. B.Too small to be seen without the aid of an electron microscope. C.Too small to be seen without the aid of a light microscope. D.Big enough to be seen when cultured like bacteria. Which of the following describes a difference between the Declaration of Independence and the United States Constitution? Which sentence uses who correctly?From who did you receive the call?Who did you call?Who is the person that I should call?To who are you speaking? which statement best explains why President Lincoln was opposed to the Wade Davis Bill Are some rights more worthy of protection than others? Explain. Match the person to the description.1.AntinousHelen's husband2.MenelausNestor's son and Telemachus's chariot companion3.Pisistratusloyal servant of Telemachus4.PoseidonHelen's father5.Mentorone of Athena's disguises6.EurycleiaEarth-shaker7.Zeusmost vocal and violent suitor Net income is ________.a. the cash flow from the operations of the company during the period.b. not cash flow.c. the increase or decrease in cash flow for the period.d. earnings before interest and taxes. Write a complete c program that finds the square roots of all elements of type double in an array of size 8. your program should display the original array as well as the array of square roots. As of june 30, 2013, actual tigers company has assets of $100,000 and stockholders' equity of $30,000. what are the liabilities for actual tigers company as of june 30, 2013? How was the effect of imperialism on latin america similar to its effect on china (02.08 HC)Apply the principles of training to personal fitness goals. Your friend is working on lower body and has been doing one set of 8 bodyweight squats each day. Give specific suggestions on how your friend can apply the principles of progression and overload to her current squat routine to see improvement in lower body strength over time. Hi. What is the meaning of fluency? please help!Q- Missy makes two promises to herself as she leaves Pittman county. How does she fulfill the first promise to herself?A-She pledges to find a home in the West for herself and her mother.B-She decides to rename herself after the town in which she runs out of gas.C-She chooses to attend a community college on the Cherokee reservation.D-She uses a brochure from a gas station to identify the city she will call home. Where did the US government relocate the Cheyenne, Arapaho, and Plains Apache tribes? 20 PTS!!!David's company reimburses his expenses on food, lodging, and conveyance during business trips. The company pays $60 a day for food and lodging and $0.65 for each mile traveled. David drove 600 miles and was reimbursed $3,390. Part A: Create an equation that will determine the number of days on the trip. (3 points) Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points) Part C: How many days did David spend on this trip? (1 point) Steam Workshop Downloader