9. The length of a rectangle is 3 cm longer than twice the width. If the area of the rectangle is 65 cm2,
find its length and the width.

Answers

Answer 1

Answer:

  length: 13 cm

  width: 5 cm

Step-by-step explanation:

You may be aware that 65 = 5×13. We note that 13 is 3 more than twice 5, so these are the dimensions of the rectangle:

  5 cm wide; 13 cm long

__

If you want so solve this algebraically, you can let w represent the width. Then the length is 2w+3 and the area is ...

  A = LW

  65 = (2w+3)(w)

In standard form, this equation is ...

  2w^2 +3w -65 = 0

To factor this, you look for factors of 2×(-65) = -130 that have a sum of 3. Those would be ...

  -130 = (-10)(13)

Then the factored equation is ...

  2w^2 +13w -10w -65 = 0

  w(2w+13) -5(2w+13) = 0

  (w -5)(2w +13) = 0   ⇒   w = 5, -13/2

The positive solution makes sense in this problem, so ...

  width = 5 cm

  length = 2(5) +3 = 13 cm


Related Questions

- The line AB has equation 5x – 2y = 7. The point A has coordinates (1, -1) and the point B has coordinates (3,k). (a) (i) Find the value of k. (ii) Find the gradient of AB. (b) Find an equation for the line through A which is perpendicular to AB. (c) The point C has coordinates (-6, -2). Show that AC has length pV2, stating the value of p. ​

Answers

Step-by-step explanation:

For finding k we'll have to plug in the x-value of the coordinate (3,k) into the equation, and solve for the y:

5(3) - 2y = 7

15 - 2y = 7

2y = 8

y = 4 => k =4

2) I assume the gradient is the slope of the line. If so, just isolate the y in the original equation and see what's the coefficient of the x:

-2y = -5x + 7

y = (5/2)x + 7/2 => the gradient is 5/2

3) the condition of perpendicularity is expressed by the following relation:

a * a' = -1

Where a is the slope of the first line and a' of the second line. We need to find a' that will be:

-1/a = -1/(5/2) = -2/5

The perpendicular line will be:

y = (-2/5)x + b

We need to find  b, and we know that this line passes through A (1,-1):

-1 = (-2/5)*1 + b

b = -1+(2/5) = -3/5

The equation will be:

y = (-2/5)x - 3/5.

4) I don't know what that symbol means (pV2).

A tree of unknown height casts a shadow that is 18 feet long. If a person that is 5 ft 7 in casts a shadow that is 4 ft long, then how tall is the tree in feet?

Round your answer to the nearest integer. Do not include feet in your answer.

Answers

Answer:

25.

Step-by-step explanation:

5 ft 7 in = 5.583 ft.

We have 2 similar triangles here.

If h is the height of the tree, then:

h / 5.583 = 18/4

h = 18*5.583/4

h = 25.12 ft

The height of the tree is approximately 25.12 feet.

What is Ratio?

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

The ratio of the shadow lengths is equal to the ratio of the object heights.

In other words, if we let H be the height of the tree in feet and h be the height of the person in feet, we have:

H/h = 18/4

We can find h by converting the person's height to feet. Since 1 inch is equal to 1/12 foot, the person's height in feet is 5 + 7/12 = 5.58 feet.

Substituting this value into the equation above and solving for H, we get:

H = (18/4) x 5.58 feet

= 25.12 feet

Therefore, the tree is around 25.12 feet tall.

Learn more about the Ratio here:

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G(x)=4.8x -5

I needed help finding the slope

Answers

Answer:

Slope is 4.8

Step-by-step explanation:

[tex]{ \tt{G(x) = 4.8x - 5}} \\ [/tex]

Answer: The Answer is 4.8

A square is a quadrilateral with four equal sides and four 90 degree angles. Is quadrilateral ABCD a square?

Answers

Answer: yes

Step-by-step explanation:

A complex shape with measurements 6 inches, 5 inches, 4 inches, 3 inches, 4 inches, 2 inches, 6 inches, 10 inches. What is the perimeter of the shape?

Answers

Answer: 40

Step-by-step explanation: do 6 add 5 add 4 add 3 add 4 add 2 add 6 add 10


An elevator company claims "for every 15 inches of cable, we can hold up to 32 pounds". Each elevator comes with a standard length of 18 inches for their cable. If an elevator has a
weight limit of 800 lbs, how many additional inches of cable were used?

Answers

375 inches of cable were used for an elevator with weight limit of 800 lbs

Let y represent the weight in pounds and x represent the inches of cable.

Since y and x are proportional:

y = kx,

k is the constant of proportionality.

15 inches of cable, we can hold up to 32 pounds. Hence:

32 = 15k

k = 2.13 pounds per inch

y = 2.13x

For a weight of 800 lbs, y= 800:

800 = 2.13x

x = 375 inches

375 inches of cable were used for an elevator with weight limit of 800 lbs

Find out more on equation at: https://brainly.com/question/2972832

It is for my final, please help!

Answers

Answer:

The answer will be the third one.

Step-by-step explanation:

Hope it helps

which among the following​

Answers

We have:

[tex]1-\frac{1}{3} >0[/tex]    ;   [tex]1- \frac{11}{17}>0[/tex]  ;    [tex]1-\frac{132}{157}>0[/tex]   ⇒ right

[tex]\frac{-1}{7}, \frac{-51}{107},\frac{-347}{949} <0[/tex]  ⇒ wrong

[tex]\frac{7}{5}, \frac{131}{47} ,\frac{945}{711} >1[/tex] ⇒ wrong

ANSWER: [tex]\frac{1}{3} ,\frac{11}{17} ,\frac{132}{157}[/tex]

ok done. Thank to me :>

Elsa is selling bracelets at craft shows to raise money for an animal shelter.

She is also accepting additional cash donations. She plans to give 75% of the

money from all bracelet sales and donations to the shelter. She will use the

remaining money to buy more supplies. Bracelet sales and donations from

the first craft show are represented by the expression 24n + 32, where n

represents the amount Elsa charges for each bracelet. The second craft

show sales and donations is represented by the expression 40n + 56. If Elsa

charges $4 for each bracelet, how much money will she donate to the

Answers

Answer:

$258

Step-by-step explanation:

75% = 0.75 when we divide by 100 to convert a percentage to a decimal

75% of total sales = money donated

Total sales = sales from first show + sales from second show

                  = 24n+32 + (40n+56)

                  = 64n + 88

0.75 of (64n+88) = money donated

                            = 0.75 * (64n+88)

                            = 48n + 66

substitute 4 for n, as she charges $4 for each bracelet

money donated = 48*4 + 66 = 258

What positive acute angle is
Зл/4

related to?

Answers

Radians can be converted to degrees using the formula degrees = radians * (180/pi)

So,

degrees =

3pi/4 * (180/pi)

= 135 degrees

Answer:

[tex][tex]\purple{\rule{45pt}{7pt}}\blue{\rule{45pt}{999999pt}}[/tex]

[tex][tex]\purple{\rule{45pt}{7pt}}\blue{\rule{45pt}{999999pt}}[/tex]

[tex][tex]\purple{\rule{45pt}{7pt}}\blue{\rule{45pt}{999999pt}}[/tex]

[tex][tex]\purple{\rule{45pt}{7pt}}\blue{\rule{45pt}{999999pt}}[/tex]

2...

Marsha is driving 630 total miles on a trip. She has already driven 2/5 of the distance. How far has Marsha driven?

Answers

Answer:

Marsha has driven 252 miles

Step-by-step explanation:

In order to figure out the problem, you take the total distance and multiply it by the fraction she has gone. This would be 630*(2/5) which would equal 252. Thus, Masha has driven 252 total miles.

Hope this helps!

Answer: 252 miles

Step-by-step explanation:

Convert 62% into a fraction

Answers

Answer:

62% = 31 / 50

Step-by-step explanation:

62/100

if you need to simplify then it would be 31/50

21
4x + 5
E
חו
What is the value of x?

Answers

Answer:

don't know

Step-by-step explanation:

A car is traveling at 20 miles per hour during rush hour. How far does the car travel in 1 minute and 45 seconds?

Answers

Answer: 7/12 miles

Step-by-step explanation:

20mph = 20/60 miles per minute = 1/3 miles per minute

1 min 45s = 1 min + 3/4 min = 7/4 min

1/3 x 7/4 = 7/12 miles

The distance travelled by car with the given speed and time is 7/12 miles.

What is the speed?

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, a car is traveling at 20 miles per hour during rush hour.

Time =1 minute and 45 seconds

= [tex]1\frac{45}{60}=1\frac{3}{4}[/tex]

= 7/4 minutes

Now, 20 miles per minute

= 20/60 miles per minute = 1/3 miles per minute

We know that, Distance =Speed×Time

= 1/3 ×7/4

= 7/12 miles

Therefore, distance travelled by car is 7/12 miles.

To learn more about the speed, distance, and time visit:

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Need help. I don't understand this question.

Answers

Answer:

The first is 1 and the second is 28 i believe

Step-by-step explanation:

Hope this helps:)

25. Which is a solution of the inequality y
(3,-5)

(2,-1)

(4,1)

(6,-4)

Answers

Step-by-step explanation:

B

D

A

с

2

2-1

1

2

3 4 5

2 1

2

2 4 5

A

B

2-1

1

2

B

5 4 3 2 1

1

2 3 4 5

The area of a square pond is 1000m2.A path of uniform width is surrounded outside the pond and its area is 369m2.find the outer length of the path​

Answers

Answer:

631 m²

Step-by-step explanation:

Outer length of park = Total area - Area of pond

Outer length of park = 1000 - 369

Outer length of park = 631 m²

Answer:

Hope it will help you a lot.

Solve the equations below exactly. Give your answers in radians, and find all
possible values for t in the interval 0 (less than or equal to ) t (less than or equal to) 2 pi
If there is more than one
answer, enter your solutions in a comma separated list.

(a) sin (t) = - square root of 3 divide by 2
when t=

(b) cos (t) = 1/2
when t=

Answers

Answer:

See below (along with unit circle attached)

Step-by-step explanation:

[tex]sin(t)=-\frac{\sqrt{3}}{2}[/tex]

[tex]t=\frac{4\pi}{3},\frac{5\pi}{3}[/tex]

[tex]cos(t)=\frac{1}{2}[/tex]

[tex]t=\frac{\pi}{3},\frac{5\pi}{3}[/tex]

It really helps to use the unit circle! I've attached it below for your convenience. Keep in mind that a point on the unit circle is defined by [tex](cos(\theta),sin(\theta))[/tex] where [tex]\theta[/tex] is measured in radians.

SOMEBODY HELP NO LINKS PLZ AND THANK YOU
The cost of a dog walker for n hours is given by f(n)=5 +10n. Which statement is true
A for each additional hour of service, the price of the dog walker increases by $ 15
B for each additional hour of service, the price of the dog walker increases by $5
C for each additional hour of service, the price of the dog walker increases by $10
D for each additional hour of service, the price of the dog walker decreases by $10

Answers

Answer:

C for each additional hour of service, the price of the dog walker increases by $10

Step-by-step explanation:

substitute any hour in f(n)=5+10n

for example, 1hr is 5+10×1=$15

2hr is 5+10×2=$25

3hr is 5+10×3=$35

4hr is 5+10×4=$45

and so on....

you can see that the price increases every $10

A2 + B2
Best answer gets a brainliest and thank and 5 star

Answers

Answer:

a+b)(a-b)

(Step-by-step explanation:

-PLEASE HURRY
8. Given: x2 – 2x + 5, find :
1.f(2)
2.f(-3)
3.f(0)
4.f(5) - f(-2)
5.f(1) + f(6)
-

Answers

Answer:

Step-by-step explanation:

     f(x) = x² - 2x + 5

1)   f(2) = (2)² - 2(2) + 5 = 5

2) f(-3) = (-3)² - 2(-3) + 5 = 20

3)  f(0) = (0)² - 2(0) + 5 = 5

4) f(5) - f(-2) = (5)² - 2(5) + 5 - [(-2)² - 2(-2) + 5 = 20 - 13 = 7

5) f(1) + f(6) = (1)² - 2(1) + 5 + [(6)² - 2(6) + 5 = 4 + 29 = 33

12. TEKS 21
A customer paid a total of $6.00 for 68 copies at a print shop. Some of the copies were
black-and-white coples, and the rest were color copies.
.
Each black-and-white copy cost $0.08.
Each color copy cost $0.15.
.
Which system or equations can be used to find b, the number of black-and-white copies,
and c, the number of color copies that the customer paid for at the print shop?


Answers

The system or equations can be used to find b, the number of black-and-white copies,

and c, the number of color copies that the customer paid for at the print shop is

b + c = 68

b + c = 680.08b + 0.15c = 6

Given:

Total amount paid = $6.00

Total copies = 68

cost of black-and-white copy = $0.08

cost of color copy = $0.15

let

number of black-and-white copies = b

number of color copies = c

The equation:

b + c = 68

b + c = 680.08b + 0.15c = 6

Therefore, the system or equations can be used to find b, the number of black-and-white copies,

and c, the number of color copies that the customer paid for at the print shop is

b + c = 68

b + c = 680.08b + 0.15c = 6

Learn more about equation:

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Find the value for x.​

Answers

Answer:

4x + 22

Step-by-step explanation:

Given that (-5,-6) is on the graph of f(x), find the corresponding point for this function -1/3f(x).

Answers

Answer:  (-5, 2)

Explanation:

We multiply the y coordinate by -1/3 because of the notation (-1/3)*f(x). Recall that y = f(x). The x coordinate stays the same.

The kinetic energy, k, the amount of energy that a moving object has, can be found for a particular roller coaster by the radical function v equals the square root of the quantity 2 times k over the 1,000 period If the velocity, v, of the roller coaster is 10 meters per second, what is the kinetic energy?

200,000 Joules
10,000 Joules
50,000 Joules
5,000 Joules

Answers

The kinetic energy of the roller coaster is 2000Joules

Given the formula for expressing the velocity of the roller coaster is given as:

[tex]v = \sqrt{\frac{2k}{1000} }[/tex]

Given the following parameter:

v = 10m/s

Substitute the given parameter into the formula to have:

[tex]10 = \sqrt{\frac{2k}{1000} }[/tex]

Square both sides of the equation:

[tex](10)^2=(\frac{2k}{1000} )^2\\100=\frac{4k^2}{1,000,000} \\4k^2=100,000.000\\k^2=\frac{100,000,000}{4} \\k^2=4,000,000\\k=2000Joules[/tex]

Hence the kinetic energy of the roller coaster is 2000Joules

Learn more on subject of formula here: https://brainly.com/question/657646

Answer:

You need to use √2k/1000 formula.

2000 joule is the correct answer.

It cost Faith $9.10 to send 91 text messages. How many text messages did she send if she spent $17.60?

Answers

Answer:

176

Step-by-step explanation:

9.10 / 91 = 1/10

17.60 x 1/10 = 176

Th stalest tree in the world is a red wood in red wood national and state parks .it is 379feet tall .how many yards is this

Answers

Answer:

126 1/3 yards

Step-by-step explanation:

1 foot = 1/3 yard

379 feet = 379/3 yard= 126 1/3 yards

What is the measure of angle DCE? Use numbers only.

Answers

Answer:

156 degrees

Step-by-step explanation

First we need to figure out what X is. To do that we set up the equation 7x+3=8x because vertical angles are congruent. After solving that we get x=3. We plug 3 back into each equation and we get that angle ACE equals 24. Since angle ACE and angle DCE are supplementary we know that they will equal 180 so we subtract 24 from 180 and get 156 as the final answer.

Hope this helps!

3/5 * 5/7 / 3/14 - 2/5​

Answers

Answer:

3/5*5/7*14/3-2/5

8/5...

Find the equation that represents the proportional relationship in this graph, for y in terms of x.

Answers

Answer:

y = 0.4 x

Step-by-step explanation:

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