2. The width of a rectangle is 5 units less than the length. If the area is 150 square units, then find the dimensions of the rectangle.

Answers

Answer 1

Answer:

The length = x = 15 unitsThe width = x-5 = 10 units

Step-by-step explanation:

Let 'x' be the length of a rectangle

As the width of a rectangle is 5 units less than the length.

so

width of rectangle will be = w = x - 5 units

Area = 150 square units

Using the formula

Area = length × width

[tex]150=\left(x\right)\left(x-5\right)[/tex]

[tex]150=x^2-5x[/tex]

[tex]x^2-5x=150[/tex]

Subtract 50 from both sides

[tex]x^2-5x-150=150-150[/tex]

[tex]x^2-5x-150=0[/tex]

[tex]\left(x+10\right)\left(x-15\right)=0[/tex]

if

[tex]ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]

[tex]x+10=0\quad \mathrm{or}\quad \:x-15=0[/tex]

[tex]x=-10,\:x=15[/tex]

As length can not be negative. so

x = 15 units

Hence,

The length = x = 15 units

The width = x-5 = 15-5 = 10 units


Related Questions

Find the number whose arithmetic square root is 0.6

Answers

Answer: 0.36

Step-by-step explanation:

6/10 x 6.10= 36/100

A carpenter is building a rectangular shed with a fixed perimeter of 68 ft. What are the dimensions of the largest shed that can be built? What is its area?
The dimensions of the largest shed are _____ by _____.
The area of the largest shed is _____.

Answers

Answer:

The dimensions of the largest shed are 17 ft by 17 ft.

The area of the largest shed is 289 sq ft.

Step-by-step explanation:

Given that:

Fixed perimeter of the rectangular shed = 68 ft

To find:

The dimensions of the largest shed that can be built = ?

And

Area of the largest shed that can be built = ?

Solution:

First of all, let us have a look at the formula for perimeter of a rectangular shape shed:

Perimeter of a rectangle = 2 [tex]\times[/tex] (Length + Width)

68 = 2 [tex]\times[/tex] (Length + Width)

Length + Width = 34

The largest possible values are only in the case when the rectangle is a square.

i.e. Length = Width

Therefore values of length and width are:

Length = Width = [tex]\frac{34}{2} = 17\ ft[/tex]

Area of a square is given by the formula:

[tex]A = Side \times Side[/tex]

[tex]A[/tex] = 17 [tex]\times[/tex] 17  = 289 sq ft

The answer is:

The dimensions of the largest shed are 17 ft by 17 ft.

The area of the largest shed is 289 sq ft.

Classify the triangle shown by its sides and angles. Check all that apply.
73°
349
730
Equilateral
Scalene
Isosceles
Obtuse
Right
Acute
Equiangular

Answers

I think it might be scalene

Which table represents a linear function? Thanks! :)

Answers

Answer:

the first table

Step-by-step explanation:

Answer:

the first table

Step-by-step explanation:

this was on edjednuty

How do the final lines of “A Blessing” emphasize the author’s peaceful tone?

1 The final two lines, in which the speaker states, “I would break into blossom,” indicate that flowers blossom in the spring.
2 The final two lines, in which the speaker states, “I would break into blossom,” indicate the feeling of beauty and growth from contact with the horses.
3 The final two lines, in which the speaker states, “That if I stepped out of my body,” indicate the feeling of excitement when watching horses run.
4 The final two lines, in which the speaker states, “That if I stepped out of my body,” indicate the feeling of death and dying.

Answers

Answer:

4

Step-by-step explanation:

could someone please help me with #7 and #8?

Answers

Answer: I'm not sure If i'm right because I did this since 8th grade.

For number 7, I think it would be (the equation form)= 6 x  +  16

For number 8, I think it would be nothing because there is no solution.

Hope this helps:)

7. Plug in 3x + 8 for y in second equation
2(3x + 8) = 6x + 16
6x + 16 = 6x + 16
It would be all solutions

8. Plug in 4x + 5 for y in second equation
12x - 3(4x + 5) = 9
12x - 12x - 15 = 9
12x cancels out
-15 = 9
There would be no solution

Please need help thank you

Answers

free points since someone already answered

PLEASE HELP ME PLEASEEEEEEEEE

Answers

Answer:

5 week

Step-by-step explanation:

13.75/ 2.75

=5

Money Needed / Money Per Week = Number of Weeks

13.75 / 2.75 = 5

It will take 5 weeks.

x+ y + z = -3
3y - Z = 4
2x- y - 2z = -5

Answers

Answer:

(-3, 1, -1)

Step-by-step explanation:

x + y + z = -3  --> (1) 3y - z = 4   --> (2)2x - y - 2z = -5 --> (3)

Add up (1) and (2)

x + 3y + y + z - z = -3 + 4 ⇒ x + 4y = 1  --> (4)

Double (2) and subtract from (3)

2x - y - 2z - 2(3y - z) = -5 - 2(4) ⇒ 2x - y - 2z - 6y + 2z = -5 - 82x - 7y = -13 --> (5)

Double (4) and subtract (5)

2(x + 4y) - 2x + 7y = 2 + 13 ⇒ 2x + 8y - 2x + 7y = 15 ⇒ 15y = 15 ⇒ y = 1

Finding x

x + 4(1) = 1 ⇒ x = 1 - 4  ⇒ x = -3

Finding z

-3 + 1 + z = -3 ⇒ z = -1

So the answer is:

(-3, 1, -1)

Which value of x will make the fraction 10/x equivalent to 2/3?

I need this urgently!!!

Answers

Answer:

The value of x would be 15

Explanation:

10/x = 2/3

Cross multiply:

10 · 3 = x · 2

30 = 2x

30 ÷ 2 = x

15 = x

A liquid storage container is leaking at a rate of 2/3 gallon every 1/4 hour. What is the unite rate?

Answers

Answer:

2 gallons an hour

Step-by-step explanation:

This is a fraction equal to

2 gal ÷ 1 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 1

2 gal

÷ 1

1 hours

÷ 1

=

2 gal

1 hour

=

2 gal

hour

= 2 gal per hour

Answer:

3/8

Step-by-step explanation:

1/4 ÷ 2/3 = 3/8

Ashot borrowed $225, and paid $108 as an interest of eight years. What was the annual interest rate?

Answers

Answer:

6%

Step-by-step explanation:

I asked this same exact question, no one got the right answer, so I just guessed, and what do you know, I got the answer right! So here you go.

Answer:

6%

Step-by-step explanation:

108           x%

-------  =   --------

225          100%

3a. Find the volume of the 3-dimensional object. (enter only the number

Answers

Answer:

60 m^3.

Step-by-step explanation:

3*4*5.

Helpoooooooooooooooooooo

Answers

Answer:

1. x >/= -1

2. x < 4

3. x </= -1

4. x >/= -2

5. x < -3

6. x </= 7

Step-by-step explanation:

PLZ HELP!!! WILL GIVE U BRAINLIEST!!!

Answers

Answer:

Graph B is correct

(3,-1)

Step-by-step explanation:

Convert to slope-intercept form and find them on graph.

Answer:

Graph B and (3,-1)

Step-by-step explanation:

Step: Solve x−2y=5 for x:

x−2y=5

x−2y+2y=5+2y (Add 2y to both sides)

x=2y+5

Step: Substitute 2y+5 for x in 3x+15y=−6:

3x+15y=−6

3(2y+5)+15y=−6

21y+15=−6 (Simplify both sides of the equation)

21y+15+−15=−6+−15 (Add -15 to both sides)

21y=−21

(Divide both sides by 21)

y=−1

Step: Substitute−1for y in x=2y+5:

x=2y+5

x=(2)(−1)+5

x=3(Simplify both sides of the equation)

Answer:

x=3 and y=−1 or (3,-1)

A ​-gallon ​[gal] quantity of molten​ (liquefied) plastic is going to be used to make a​ 1-foot [ft] by​ 8-inch [in] plastic block. If liters​ [L] of the plastic is lost in the manufacturing ​process, how thick is the final plastic​ block, in units of inches ​[in]​?

Answers

Answer:

x  = 1,77 in

Step-by-step explanation:

Total volume of molten plastic to make  a block is

1 [gal] - 1 L (lost in the process)  =  3,7854 - 1  =  2,7854

Now the volume of the block is:

1 foot  * 8 inches * x ( thick of the block )

1 foot is 0,3048 meter  and 1 inch is 0,0254 meter

Then  in m³  the volume of the block is

0,3048 * 8 * 0,0254 * x  =  0,06193536 * x  [ m³ ]

That volume should be equal to  2,7854 / 1000

Therefore

 0,06193536 * x  = 2,7854 / 1000        x in m³

x = 2,7854 /61,93536  m

x  =  0,044972  m      and    1 m  =  39,37 in

x  = 1,77 in

Pam drivers 14,735 miles in one year. The next year she drivers 13,869 miles. How many miles did she Drive in all?

Answers

Answer:28604 in total

Step-by-step explanation:

just copy and paste hope this helps

Answer:

28604 miles

Step-by-step explanation:

Just add the two numbers to get the total number of miles:

  14735

+ 13869=

  28604

FInd the area of the circle

Answers

Answer:

A = 12.56 m²

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS

Geometry

Area of a Circle: A = πr²d = 2r

Step-by-step explanation:

Step 1: Define

d = 4 m

Step 2: Find r

Substitute:               4 = 2rIsolate r:                   2 = rRewrite:                    r = 2 m

Step 3: Find Area

Substitute:               A = π(2)²Substitute:               A = (3.14)(2)²Evaluate:                  A = (3.14)(4)Multiply:                   A = 12.56 m²

A company manufactures fuel tanks for cars. The total weekly cost (in dollars) of producing x fuel tanks is given by ... C(x) = 10000 +90x - 0.08x2 Find the exact cost of producing the 501st item.

Answers

Answer:

cost of producing the 501st item = $9.92

Step-by-step explanation:

The function representing the cost is given by;

C(x) = 10000 + 90x - 0.08x²

To get the cost of producing the 501st item, we have to first find the cost of producing 500 items and then do the same for 501 items then subtract the values gotten.

Thus;

C(500) = 10000 + 90(500) - 0.08(500)²

C(500) = 10000 + 45000 - 20000

C(500) = $35000

Similarly;

C(501) = 10000 + 90(501) - 0.08(501)²

C(501) = 10000 + 45090 - 20080.08

C(501) = $35009.92

cost of producing the 501st item = C(501) - C(500) = 35009.92 - 35000 = $9.92

A total of $5000 is invested: part at 5% and the remainder at 15%. How much is invested at each rate if the annual interest is $720?

Answers

Answer:

At 5% , $300 was invested

At 15%, $4,700 was invested

Step-by-step explanation:

Let the amount invested at 5% be $x and the amount invested at 15% be $y

x + y = 5000 ••••••(i)

Let’s work with the interest;

5% of x + 15% of y = 720

0.05x + 0.15y = 720 •••••(ii)

From i;

x = 5000-y

Insert this into ii

0.05(5000-y) + 0.15y = 720

= 250 - 0.05y + 0.15y = 720

250 + 0.1y = 720

0.1y = 720-250

0.1y = 470

y = 470/0.1

y = $4700

x = 5000-y

x = 5000-4700 = $300

Match the following.
Given A = (1, 2, 3, 4, 5) B = (2, 4, 6) C = (1, 3, 5)

Answers

Answer:

u have to put the pic of it then only we can understand this please put a pic

Determine the common difference, the fifth term, the nth term, and the 100th term of the arithmetic sequence.

7/5, 5/3,13/6,8/3

Answers

This question was not written properly

Complete Question

Determine the common difference, the fifth term, the nth term, and the 100th term of the arithmetic sequence.

7/6, 5/3, 13/6, 8/3

Answer:

a) Common difference = 1/2

b) Fifth term = 19/6

c) nth term = 7/6 + (n - 1)1/2

= 7/6 + n/2 - 1/2

d) 100th term = 152/3

Step-by-step explanation:

We solve using the formula for arithmetic sequence

an = a1 + (n - 1)d

a1 = First term

n= nth term

d = common difference

a) Common difference = Second term - first term or Third term - second term

= d = 5/3 - 7/6

d = LCD (Lowest Common Denominator = 15

d = 5 × 6 - 3 × 7/18

d = 30 - 21/15

d = 9/18

d = 1/2

b) Fifth term =

an = a1 + (n - 1)d

a1 = First term = 7/6

n= nth term = 5

d = 1/2

a5 = 7/6 + (5 - 1)1/2

a5 = 7/6 + (4)1/2

a5 = 7/6 + 4/2

a5 = 7/6 + 2

a5 = LCD = 6

= 7× 1 + 2 × 6/6

= 7 + 12/6

= 19/6

c) nth term

an = a1 + (n - 1)d

a1 = First term = 7/6

n= nth term = n

d = 1/2

= 7/6 + (n - 1)1/2

= 7/6 + n/2 - 1/2

d) 100th term

an = a1 + (n - 1)d

a1 = First term = 7/6

n= nth term = 100

d = 1/2

a5 = 7/6 + (100- 1)1/2

a5 = 7/6 + (99)1/2

a5 = 7/6 + 99/2

a5 = 7/6 + 99/2

a5 = LCD = 6

= 7× 1 + 3 × 99/6

= 7 + 297/6

= 304/6

= 152/3

Jonas is concerned about the amount of water he uses to wash his laundry. he made a table to show the number of gallons of water used by different washing machines to complete of laundry. use variables to represent the independent and dependent shown in the table and Use variables to represent the dependent variable and the independent variable in this sentence
Table:

Type of Washing Machine:

Older top Loanding,

New Standar Model,

Energy Efficient,

Age of washing Machine (years):

(6,4,2)

and

Gallons Of Water:

(42,28,14)



I do not understand your answer

The exercise asks who are the independent and dependent variables

Answers

In the case of Jonas and his washing machine the independent variables are:

Type of Washing Machine.

The dependent variables are:

Age of Washing Machine (years).Gallons of Water (42, 28, 14).Energy Efficient.

What is an independent variable?

The independent variable refers to all those variables that are tested experimentally, being manipulated by researchers in order to test a hypothesis.

Generally, the independent variable has the greatest influence on the result of the experiment, this means that it modifies all the dependent variables.

What is a dependent variable?

The independent variable refers to the qualities or characteristics whose behavior is affected by the independent variable. It is about the variable or variables that are measured in order to be able to interpret the results and confirm or discard a hypothesis.

According to the above, it can be inferred that the independent variables in the case of Jonas are the type of washing machine because this variable will directly affect the other variables.

For example, depending on the type of washing machine Jonas uses, it will consume different amounts of energy and will need different amounts of water.

Learn more about variable in: https://brainly.com/question/1029540

1,320 feet is what fraction of a mile?

Answers

Answer:

1/4

Step-by-step explanation:

divide the value in feet by 5280 because 1 mile equals 5280 feet.

Answer:There are 5280 feet in one mile; thus

1320/5280 = 1/4

Step-by-step explanation:

sorry if its not correct }:

Question
2. Determine
the
acute
angle
between the planes
x - 2y + 5z = 3
2x + y - 3z = 15.
Distance of a plane from the origin:​

Answers

Answer:

Acute angle between the two planes: approximately [tex]43^\circ[/tex].

Step-by-step explanation:

Find the normal vector of each plane:

The normal vector of the plane [tex]x - 2\, y + 5\, z = 3[/tex] is [tex]\displaystyle \begin{bmatrix}1 \\ -2 \\ 5\end{bmatrix}[/tex].The normal vector of the plane [tex]2\, x + y - 3\, z = 15[/tex] is [tex]\displaystyle \begin{bmatrix}2 \\ 1\\ -3\end{bmatrix}[/tex].

As the name suggests, there is a [tex]90^\circ[/tex] angle between a plane and its normal vector. The following four angles will correspond to the vertices of a quadrilateral:

The [tex]90^\circ[/tex] angle between the first plane and its normal vector.The angle between the normal vector of each plane.The [tex]90^\circ[/tex] angle between the second plane and its normal vector.The smallest angle between these two planes.

The sum of these four angles should be [tex]360^\circ[/tex]. Two of these four angles were known to be [tex]90^\circ[/tex]. Once the third angle (the angle between the two normal vectors) is found, subtractions would give the measure of the other angle (the smallest angle between these two planes.)

Make use of the dot product to find the angle between these two normal vectors. Let [tex]\theta[/tex] denote the angle between these two vectors.

[tex]\displaystyle \cos \theta = \frac{\begin{bmatrix}1 \\ -2 \\ 5\end{bmatrix} \cdot \begin{bmatrix}2 \\ 1 \\ -3\end{bmatrix}}{\sqrt{1^2 + (-2)^2 + 5^2} \cdot \sqrt{2^2 + 1^2 + (-3)^2}} \approx -0.73193[/tex].

Before continuing, notice that the smallest angle between the two planes would be [tex]360^\circ - 90^\circ - 90^\circ - \theta = 180^\circ - \theta[/tex].

Consider the identity: [tex]\cos\left(180^\circ - \theta\right) = -\cos \theta[/tex].

In other words, [tex]\cos\left(180^\circ - \theta\right)[/tex], the cosine of the smallest angle between the two planes (which the question is asking for) will be the opposite of [tex]\cos \theta[/tex], the cosine of the angle between the two normal vectors.

Therefore, the cosine of the smallest angle between the two planes will be [tex]-(-0.73193) = 0.73193[/tex].

Apply the inverse cosine function to find the size of that angle:

[tex]\arccos(0.73193) \approx 43^\circ[/tex].

1. Which equation represents the relationship shown in the table below? (1 point)

y = -x - 3
y=x-3
y = 2x - 3
y=-2x + 3

Answers

The third one is correct

The equation representing the relationship in the table is y = 2x - 3. The correct option is C.

What is an equation?

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between two or more variables.

Given data in the table:-

x              y

0              -3

1               -1

2              1

3              3

The equation satisfying the values of the table will be:-

y = 2x - 3

-3 = 2 x  0 - 3=-3

-1 = 2 x 1 - 3 =-1

1 = 2 x 2 - 3 = 1

3 = 2 x 3 - 3 = 3

Therefore, the equation representing the relationship in the table is y = 2x - 3. The correct option is C.

To know more about an equation follow

https://brainly.com/question/18831322

#SPJ5

Write each mixed number as a percent: 7 3/10

Answers

Answer:

730%

Step-by-step explanation:

Which type of cloud is mostly made up of ice crystals? A. Altostratus B. Cirrus C. Cumulus D. Stratus

I know not math But please help

Answers

Answer:

The answer is B

Step-by-step explanation:

look it up on google.

Answer:

The answer is B

Mostly its of B but some clouds are also made up of cmulus(option C)

Solve.
Question in a triangle, the measure of the first angle is four times the measure of the second
angle. The measure of the third angle is 78° more than the second angle. What is the
measure of the first angle?
17°
95°
68°
43°
< Previous
Next >
No new data to save last checked at 10:16 nm

Answers

Answer:

The first angle is 68.

Step-by-step explanation:

[tex]x_{1}+x_{2}+x_{3}=180\\x_{1} = 4*x_{2}\\x_{3}=x_{2}+ 78\\4*x_{2} + x_{2} + x_{2}+ 78 = 180\\6*x_{2}=102\\x_{2} = 17\\[/tex]

So [tex]x_{1}=68[/tex] and [tex]x_{3}=95[/tex]

danny bought a shirt that was first put on sale for 30% off that went on clearance for an additional 40% off. what is the markdown if the original price was $94.99

Answers

Answer:

The total is $28.50

Step-by-step explanation:

Other Questions
Bernard is an excellent chef. However, his beef steak did not turn out well. Bernard forgot that steak is tender and has less collagen, and he usedthe wrong cooking technique. Which is the correct technique that Bernard should have used?He should have used wet heat to ensure that the moisture content remains high.OB. He should have tenderized the steak using a mallet to pound it.Oc. He should have steamed the steak in a pan with closed lid.OD. He should have used dry heat without any moisture. Find the value of f(-7). how many conjugated forma of ser are there? [PICTURE ATTACHED] HELPis this correct? i dont really understand iti just picked math bc i dont know which subject it is and science isnt an option PLZ HELP I BEG YOU!!!!!!!!!!! MAX POINTS! FIRST ANSWER GETS BRAINLIEST !!!!!!!! PLEAAASE DO NOT ANSWER WITH NONSENSE I WILL REPORT AND YOU WILL NOT GET BRAINLIEST !!!!!!!! Academic and Workplace Skills Writing PracticeFor this assignment, choose one type of workplace document and create an example of it. Be sure to follow the format described in the lesson.Choose from these workplace documents:meeting minutesrsumif-then tablechecklistflowchartmemoYou may choose the information to put in your workplace document. If you choose a form that needs images, such as a flowchart, be sure your computer has the proper program for creating the diagram. Complete your assignment in a separate document and submit it when you are finished. PLEASE PLEASE HELP WILL GIVE A LOT OF POINTS! NEED HELP 45 POINTS PLZIs there enough information to prove that the triangles are congruent?If yes, provide the correct Triangle Congruence Postulate or Theorem and a congruence statement.If no, justify your answer. which is not a redox reaction?a. Formation of ammonium sulphate from ammonia and sulphuric acid b. formation of nitrogen monoxide from ammonia c. formation of sulphuric acid from sulphur d. formation of zinc from zinc sulphide help me please I just need a walkthrough or step by step process on how to get it so i can understand :) Select the correct answer.Select the italicized word that is not capitalized correctly.Many tourists go to Springfield, Arkansas, just to see the Ozark mountains.A. ManyB. ArkansasC. OzarkD. mountains Which source of funding would be most appropriate if you were starting abusiness from your home and you only needed to buy a computer and pay forInternet service to get started?A. Selling propertyB. Applying for a bank loanC. Using a credit cardD. Seeking venture capital How many five-symbol computer passwords can be formed using the letters A to J and the digits 3 to 6 how were kush and axum different Arteries carry oxygen-poorblood from the heart to the body's tissues and organs.O A TrueO B. False Around the world, ________ people rely on burning wood, coal or dried animal dung in open pits, stoves or fireplaces to heat their homes and cook. is the earth circle or flat 7. Calculate the average atomic mass of bromine. One isotope of bromine has an atomic mass of 78.92amu and a relative abundance of 50.69%. The other major isotope of bromine has an atomic mass of 80.92amu and a relative abundance of 49.31%. 12 time 10 times 10 times 10 A water slide starts at (0,144) and ends at (12,0) what is the slope of the slide