Find the dimensions of a rectangle whose width is 8 miles less than its length and whose area is 105 square miles

Answers

Answer 1

Area of a rectangle = w*l

w = width

l = length

In our problem,

Area = 105mi^2

l = x

w = x - 8

Let's plug our values into the formula above.

105mi^2 = x(x - 8)

Distribute the x

105mi^2 = x^2 - 8x

Subtract 105mi^2 from both sides.

0 = x^2 - 8x - 105

Let's factor the right side.

0 = (x - 15)(x + 7)

Set both terms equal to 0

x - 15 = 0

Add 15 to both sides.

x = 15

x + 7 = 0

Subtract 7 from both sides.

x = -7

Since the length cant be a negative number, 15 is the correct answer.

Length = x = 15 mi

Width = x - 8 = 15 - 8 = 7 mi

Answer 2

The length of the rectangle is 15 miles while the width is 7 miles.

What is a rectangle?

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

The perimeter of rectangle = 2( length + width).

Suppose the length is L while the width is W.

Area of rectangle = length × width.

L x W = 105

W = L - 8

By substitution,

L x (L - 8) = 105

L² - 8L - 105 = 0

L² - 15L + 7L - 105 = 0

L(L - 15) + 7(L - 15) = 0

(L + 7)(L - 15) = 0

L = -7, L = 15

Since length will not be negative thus L = 15 miles.

W = 15 - 8 = 7 miles

Hence "The length of the rectangle is 15 miles while the width is 7 miles."

For more about rectangles,

https://brainly.com/question/15019502

#SPJ2


Related Questions

Solve the equation algebraically. x^2-7x-1/7=0

Answers

Answer:

[tex]x1=\frac{49+\sqrt{2429}}{14} \\x2=\frac{49-\sqrt{2429}}{14} \\[/tex]

Step-by-step explanation:

[tex]x^2-7x-\frac{1}{7} =0\\7x^2-49x-1=0\\D=b^2-4ac=(-49)^2-4*7*(-1)=2429\\x1=\frac{49+\sqrt{2429} }{14} \\x2=\frac{49-\sqrt{2429} }{14} \\[/tex]

If f(x) = 2x + 4 and 9 (20) = x - 3, find f (g(x)).

Answers

Answer: D

Step-by-step explanation:

To find f(g(x)), you want to take g(x) and plug that into f(x). Since we are given f(x) and g(x), we can go ahead and do that.

f(g(x))=2(x-3)+4                  [distribute]

f(g(x))=2x-6+4                     [combine like terms]

f(g(x))=2x-2

Now, we know that f(g(x))=2x-2.

Gabby bought 5.15 kg of apples and 1.6 kg of oranges how much fruit did she buy in all

Answers

Answer:

6.75kg of fruit

Step-by-step explanation:

5 + 1 = 6

.15 + .6 = .75

6 + .75 = 6.75

Answer:

6.75

Step-by-step explanation:

Add 5.15 and 1.60

5.15

1.60

6.75

What is the sum of the solutions of the 2 equations
below?
8x = 12
2y + 10 = 22
A. 23
B. 71
7 1
C.
9
D. 10
E. 17.

Answers

8x = 12

Divide both sides by 8

x = 12/8 = 3/2

2y + 10 = 22

Subtract 10 from both sides.

2y = 12

Divide both sides by 2

y = 6

6 + 3/2 = 7 1/2

Answer:

7.5 or 7½

Step-by-step explanation:

8x÷4 = 12÷4

2x = 3

x = 3/2 = 1.5

2y + 10 = 22

2y = 12

y = 6

1.5 + 6 = 7.5 = 7½

Is 8 3/5 greater than 8 6/7

Answers

Answer:

no

Step-by-step explanation:

Answer:

8 6/7 is greater than 8 3/5

Step-by-step explanation:

Step 1:

8 3/5 = 8 21/35

Step 2:

8 6/7 = 8 30/35

Answer:

8 6/7 is greater than 8 3/5

Hope This Helps :)

10 x 1/5 in simplest form

Answers

Hey there!

ANSWER: [tex]2[/tex]EXPLANATION:

[tex]10*1/5[/tex]

Divide 10 by 5.

[tex]10/5=2\\2(ANSWER)[/tex]

Hope this helps!

[tex]-TestedHyperr[/tex]

Answer:

2.

Step-by-step explanation:

[tex]10 *\frac{1}{5} = 2[/tex]

A store is selling two mixtures of nuts in
-ounce bags. The first mixture has
ounces of peanuts combined with five ounces of cashews, and costs
. The second mixture has five ounces of peanuts and
ounces of cashews, and costs
. How much does one ounce of peanuts and one ounce of cashews cost?

Answers

Answer:

gfAnswer:Answer:Answer:Answer:Answer:Answer:Answer:

Step-by-step explanation:

fgAnswer:Answer:Answer:Answer:Answer:Answer:Answer:Answer:Answer:Answer:

Aretailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which
represents the situation, where x is the original cost of the item(s)?

Answers

Answer:

.65x(1.07) = 0.6955x

Step-by-step explanation:

In an arithmetic progession T7 =20 and T13 =38,. Find the first term and the common difference. ​

Answers

The first term is two.
The common difference is three. Hope this helps!

12x + 9 - 3x - 4. Please go fast!!!!

Answers

Answer:

9x +5

Step-by-step explanation:

combine like terms!

9x +5 combine like terms then subtract

3x 40° to Sum of angle measures: 180°​

Answers

Answer:

yes

Step-by-step explanation:

-2=12/x

pleasee answer

Answers

Answer:

Step-by-step explanation:

Find the derivative of the function. y = tan2(8θ)

Answers

Answer:

16tan(8θ)sec²(8θ)

Step-by-step explanation:

Given the question :

Find the derivative of the function. y = tan2(8θ)

y = tan²(8θ)

USing chain rule :

dy/dx = (du/dx) × (dv/du) × (dy/dv)

Let u = 8θ ; du/dθ = 8

v = tan u ; dv/du = sec²u

y = v² ; dy/dv = 2v

Hence,

(dy/dθ) × dv/du × dy/dv

8 * sec²u * 2v

Where v = tan u ; u = 8θ

8 * sec²8θ * 2tan8θ

16tan(8θ)sec²(8θ)

Simplify.

(3x2−2x+2)−(x2+5x−5)




4x2+3x−3

2x2−7x+7

2x2−3x−3

2x2+3x−3

Answers

Answer:

2x2+3x-3

Step-by-step explanation:

The first thing you want to do is find all the X2"s and add those together and that looks like this 3x2+(-x2) which would be 2x2. Then you want to find all of the x's and add them together which looks like this -2x+5x which is 3x. Then you find all the whole numbers without a variable and that's 2-5 which equals to be -3.

Compare -9 and square root -9

Answers

Answer:

-9 < 3i

Step-by-step explanation:

3i is bigger than -9 because 3i² is equal to -9

i means imaginary number

Hope this helps!

Use the distributive property to fill in the blanks below.

(8 x 5) + (8 x 2) = 8 x (_ + _)

Answers

The answer is anything that adds up to 7.
Examples: (5 + 2) or (3 + 4)

[tex]\boxed{\sf ab+ac=a(b+c)}[/tex]

[tex]\\ \rm\longmapsto (8\times 5)+(8\times 2)[/tex]

[tex]\\ \rm\longmapsto 8(5+2)[/tex]

[tex]\\ \rm\longmapsto 8(7)[/tex]

[tex]\\ \rm\longmapsto 56[/tex]

Helppppp!!!!!!! Gehjdhdhxjndhzjsvahsj

Answers

Answer:

don't worry bbg I got you give me a moment

Which of the following inequalities is graphed on the coordinate plane? ​

Answers

Answer: A

Step-by-step explanation:

This picture is very blurry, but the line appears to be a solid line. Since it is a solid line, it tells us that the inequality is ≤ or ≥. We can eliminate C and D. Now, the difference between A and B is the shading. Since the shading is showing that the numbers are increasing, we know that the inequality is ≥. Therefore, A is the correct answer.

If someone is good in theoram please help me I need help with task 3,4,5

Answers

Answer:

C²= A²+B²

Step-by-step explanation:

A) 10²=( Base)² + 6²

(Base )²= 10² - 6²:

100-36

= 64

Base = √ 64

8

B) 17² = 8² + (Height)²

(Height) ² = 17²- 8²

= 289-64

= 225

Height = √225

= 15

C) 2.5² = Base ² + 1.5 ²

Base² = 2.5 ²- 1.5²

6.25- 2.25

= 4

Base = √4

= 2

D) 41² = Base²+ 40²

Base²= 41²- 40²

1681-1600

= 81

Base = √81

=9

E)26²=Base² +10²

Base² = 26²- 10²

676-100

= 576

Base= √576

= 24

F)25²= Base²+ 7²

Base² = 25²- 7²

625- 49

=576

Base= √576

= 24

Point M is the midpoint of AB. The coordinates of point A are (-6, 1) and the coordinates of M are (-3,2).
What are the coordinates of point B?
The coordinates of point B are

Answers

Answer:

Let B(a,b) be x1, y1

A(-6,1) be x2,y2

midpoint M(-3,2) be (x,y)

using midpoint formula

(x,y)= [(x1+x2)/2, (y1+y2)/2)

(-3,2) = [(a-6)/2, (b+1)/2}

comparing corresponding value

-3 = (a-6)/2                           (b+1)/2 = 2

-6= a-6                                  b+1=4

a=0                                         b=3

coordinates of B = (0,3)

Estimate the difference.
689.2 - 263 = ?
To estimate the​ difference, first round each number to the nearest hundred.

PLZ HELP ME I AM STUCK ON THIS QUESTION :(

Answers

Answer:430.2

Step-by-step explanation:

Write an equation for the line that is parallel to y=-4x+2 and goes through (0,7)

Answers

Answer: y=-4x+7

Step-by-step explanation:

To find a parallel line, we know that the slope must be the same because parallel lines NEVER touch or cross. All we have to do is use the given point to find the y-intercept.

y=-4x+b

7=-4(0)+b            [multiply]

b=7

Now, we know that the final equation is y=-4x+7.

Answer:

The answer is

y = - 4x + 7

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

The original line is y = - 4x + 2

Comparing with the general equation above

Slope / m = - 4

Since the lines are parallel their slope are also the same

Slope of parallel line = - 4

So the equation of the line using point (0,7) and slope - 4 is

[tex]y - 7 = - 4(x - 0) \\ y - 7 = - 4x[/tex]

We have the final answer as

y = - 4x + 7

Hope this helps you

Find the weighted average of these values.


Value Weight

5.005.00 75.0%75.0%

6.006.00 15.0%15.0%

7.007.00 10.0%10.0%

Answers

Answers:

The Weighted Average = 5.35

Explanation:

The weighted average is given by:

W(avg) = v1*w1 + v2*w2 + v3*w3

v1.v2.v3 are the values

w1,w2,w3 are the weights

W(avg) = 5.00*0.75 + 6.00*0.15 + 7.00*0.10

W(avg) = 3.75+0.9+0.7

W(avg) = 5.35

Hence, the weighted average is equals to 5.35

Find two consecutive even integers such that four times the first equals three times the second

Answers

Answer:

1st: 2x

2nd: 2x+2

--------

Equation:

4(2x) = 3(2x+2)

-------

8x = 6x + 6

2x = 6

x = 3

-----

1st 2x = 6

2nd: 2x+2 = 8

Step-by-step explanation:

The two consecutive even integers such that four times the first equals three times the second is 6 and 8.

What is an integer ?

An integer is a number which has no decimal part.

According to the given question we have to find two consecutive even integers such that four times the first equals three times the second.

Let, the first even integer to be x.

∴ The second integer will be (x+2).          [ As every consecutive even                                                                                    

                                                                            integers comes after 2 digits]

Now, Four times the first equals three times the second which is

4x = 3(x+2)

4x = 3x + 6.

4x - 3x = 6

x = 6.

∴ The even integer is 6 and the second integer is 8.

learn more about these type of problems here :

https://brainly.com/question/12313844

#SPJ2

Lana uses 0.2 pounds of peaches in each mini pie she makes. How many mini pies can she make with 2.50 pound of peaches?

Answers

Answer:

12.5 mini pies or 12 depending on what it asks for

Step-by-step explanation:

Divide 2.50 by 0.2 to get 12.5

The answer can also be 12 because some teachers want students to know that you can't really make half a pie. Whatever your teacher prefers.  

1. Name the indicated geometric figures for the figure shown. Be sure to use correct notation.


A Name a point. _________

B Name a ray through Y. _________

C Name a line through Z. _________

D Name a plane. _________

Answers

Answer:

Step-by-step explanation:

A). There are three points given on the plane R.

    Point X, point Y and Point Z.

B). A ray from the point Y → [tex]\overrightarrow{XY}[/tex]

   A ray starting from point X and passing through Y to infinity.

C). Name of a line → [tex]\overleftrightarrow{YZ}[/tex]

    Aline passes through two points with both the ends directing towards infinity.

D). Name of a plane → Plane R or Plane XYZ

    A plane is defined by three points lying on the same surface.

Enter an algebraic expression to model the given context. Give your answer in simplest form.

The price s of a pair of shoes plus 6% sales tax.

The algebraic expression is

Answers

(s)+(s×0.06)=t

t is the total

s is the shoes

pls help math 15 points

Answers

3 x's at 1

4 x's at 1 1/4

3 x's at 1 1/2

1 x at 1 3/4

No x's at 2.

Now, let's combine all the recipes with 1 1/4

5/4 * 4 = 20 / 4 = 5 teaspoons

An angle measuring 3.6 radians is drawn in standard position?
In what quadrant will the terminal side of this angle lie?
Express your answer as a Roman numeral.

Answers

Answer:

III

Step-by-step explanation: I just took the quiz

9-6=3, 6+3=9, 3+6=9 what is the missing fact family?

Answers

Answer:

9-3=6

Step-by-step explanation:

An addition/subtraction fact family has 2 addition equations and 2 subtraction ones.

The question already states both addition ones, but only one subtraction

The subtraction one stated is 9-6=3

The opposite is 9-3=6

Hope this helps :-)

Other Questions
17. Choose the correct definite article: En la clase de ingls, yo tengo 1. _______cuadernos rojos.ellaloslas help help i need help please On what type of map would you see mountains, hills, plains and oceans? the people rule in this kind of government Consider the following cost structures for three oil producers: Fossils R UsGreen House OilsShale Ale Plant and property$900,000$1,500,000$1,000,000 Extraction costs (per barrel)$45$31$40 Capacity per day100,000 barrels140,000 barrels80,000 barrels If the price for a barrel of oil is currently $42, what is the amount of barrels produced by these suppliers? 5. If the lever arm is longer than the load arm, this lever system would bea class three lever systemb. a high speed systemc. a power systemd. disfunctional and is never seen in biological systems. Which one of the following is true of the structures labeled D in the cell membrane?A.They are membrane proteins.B.They are hydrophilic.CThey are carbohydrates.D.They are hydrophobic? The midpoint of AB is M (5,1). If the coordinates of A are (3,6), what are thecoordinates of B answers Describe two key differences between a savings account and an investment. NEED HELP!! Its easy but Im just dumb :/ The image shows the Viking Skalholt map from 1570. The map helps historians understand travels of the Vikings in a specific part of the world. A map of the Western Atlantic shows Britain, Ireland, Greenland, North America, and Winlandia. HELP PLEASE!!! What does this map show about the Viking civilization? It shows that the Vikings sailed to North America. It shows all the people whom the Vikings conquered. It shows the routes that the Vikings sailed around the world. It shows the people whom the Vikings encountered on their journeys. "All men are created equal..." is a direct quote in the Declaration of Independence, however, who was excluded from this statement? 100pts!!Plz answer me will mark as brainliest A bottle of hot sauce is 3/4 full. Leigh uses 2/9 of the contents of the hot sauce bottle for lunch. How much of a full bottle of hot sauce did Leigh use for lunch? A)26/36 B)5/36 C)1/6 D) 1/2 E) 1/3. PLEASE HELP. The youth is disgusted by the rumors and wishes the other soldiers would stop talking. After he scolds them, they are silent. True False 6. Alex wanted to find out what toothpaste made teeth the cleanest. Everyday she brushed her teeth with a different product and then took a plaque test to see how much plaque was left. She used Crest, Colgate, Close-up, and water. a. Independent Variable (IV): ______________________________________________ b. Dependent Variable (DV): ______________________________________________ c. Control: _____________________________________________________________ d. Constants:__________________ Solve for p if 2lpl = 4O {-8, 8)O{-4, 4)O (-2, 2) Which method is used to compute depletion?a. Double-declining-balance methodb. Straight-line methodc. Depletion methodd. Units-of-production method What is the equation of the line that is perpendicular tothe given line and passes through the point (3,0)?A. 3x+5y=-9B.3x+5y=9C.5x-3y=-15D.5x-3y=15 Why do the Mighty Ones not want the humans to have fire