If the length of a rectangle is 3 feet less then twice its width and the area is 54square feet what are its dimensions

QUESTION POSTED AT 10/10/2019 - 07:35 PM

Answered by answersmine AT 10/10/2019 - 07:35 PM

The length (L) of the rectangle can be written as a function of the width (W)L = 2W - 3:
Now since we know Area = Width*Length, we can write the area as a function of the width:
A = L*W = (2W-3)*W
Distributing the W inside the parentheses we have:
A = 2W^2 - 3W
We know the area is 54 ft^2, so we can rewrite it as:
2W^2 - 3W - 54 = 0
Now solve for W by factoring (or by applying the quadratic formula):
2W^2 - 12W + 9W - 54 = 0
Factor out a common 2W from the first two terms and a 9 from the last two terms:
2W(W-6) + 9(W-6) = 0
Regroup the terms to get our fully factored equation:
(2W + 9)(W-6) = 0
This gives us the roots W = 6 and W = -9/2, but width can't be negative so we have width = 6 ft. Then remember that the length L = 2W - 3, so our length is:
L = 2W - 3 = 2(6) - 3 = 12 - 3 = 9
So now we know that our rectangle is 9 feet long and 6 feet wide.
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Related questions

Analyze the diagram below and complete the instructions that follow. / Find the surface area of the composite solid if the base is a regular hexagon. Round your answer to the nearest hundredth. A. 471.53 m2 B. 615.53 m2 C. 709.06 m2 D. 802.59 m2

According to the image:
the right hexagonal pyramid surface area is given by the following formula:

S = 3√3 / 2) a² + 3a √h²+3a²/4
a = the base edge
h = the height of the pyramid

looking at the image  a =6m,  h =21m - 7m= 14m

so the surface area is S = 3√3 / 2) 6² + 3*6√14²+3*6²/4 =93.53+ 14.93=108.46 m²

for the another one
the figure is a prism hexagonal
its surface area is 
SA= 6ah +3√3 a²
a= base edge, h =height
in our case a =6m and h = 7m
so SA= 6*6*7 + 3√3 * 6²= 252 + 187 = 439 m²

finally, the surface area of the complete image is 
ST= S + SA = 108.46 m² + 439 m² = 547.52 m²
it is so approximate
 to B. 615.53 m2
look at the image

ANSWERED AT 17/10/2019 - 09:24 AM


QUESTION POSTED AT 17/10/2019 - 09:24 AM

What is the length of the hypotenuse in a right triangle with legs of length 14 and 48?

Answer: =50

Explanation: An unknown leg of a right triangle can be found using the Pythagorean theorem. Pythagorean theorem: a²+b²=c²

a²=14²+48²

a²=14²=14*14=196

a²=48²=48*48=2304

a²=196+2304

a²=196+2304=2500

a²=2500

a²=(25*100)=2500

a=5*10=50

A=50

Hope this helps!

Thanks!

Have a great day!

ANSWERED AT 17/10/2019 - 09:22 AM


QUESTION POSTED AT 17/10/2019 - 09:22 AM

A statue creates a shadow that is 30 feet long. the angle of elevation of the sun is 50 degrees. How tall is the statue and how would i calculate that?

The answer:
first, the angle of elevation, the shadow and the statue form an right triangle.
so, we know that for computing tangent, we use the main formula:

Tan = opposite side / adjacent side
let x be the length of the statue, it is the opposite side
30 feet long is the adjacent side
therefore, 
tan50°= x /30, 1.19 * 30= x, and the x=35.75 feet

ANSWERED AT 17/10/2019 - 09:22 AM


QUESTION POSTED AT 17/10/2019 - 09:22 AM

A 20-foot ladder is leaning against a tree. The bottom of the ladder is 12 feet away from the bottom of the tree. Approximately how high up the tree does the top of the ladder reach?

We want to use the Pythagorean theorem to find the missing length of the right triangle described in the word problem.

The Pythagorean Theorem is a^2 + b^2 = c^2, where a and b are the side lengths of the right triangle, and c is the hypotenuse.
If we know the lengths of two sides of a triangle, we can always find the length of the third side using this formula.

We're given the lengths of one of the sides (12) and the hypotenuse (20). We plug these numbers into our equation and then solve for x.
(x represents the how high the ladder reaches)

x^2 + 12^2 = 20^2
x^2 + 144 = 400
x^2 + 144 - 144 + 400 - 144
x^2 = 256

Now, find the square root of each side of the parenthesis.

√x^2 = √256
x = 16.

The answer is 16.

If there's anything you don't understand, I would highly recommend going to the website Khan Academy and watch his videos regarding it, he explains things much better than I ever could.

Hope this helps!!

ANSWERED AT 17/10/2019 - 09:20 AM


QUESTION POSTED AT 17/10/2019 - 09:20 AM

Select the measures that are equal. Mark all that apply. A. 4 Feet. B. 12 Yards. C. 36 Feet. D. 480 Inches. E. 15 feet. F. 432 inches.

12 yards, 432 inches and 36 feet are all equal
12 yards = 36 feet
36 feet = 432 inches

ANSWERED AT 17/10/2019 - 09:15 AM


QUESTION POSTED AT 17/10/2019 - 09:15 AM

Draw a quadrilateral that belong to any of these groups parrallelogram rectangle, square. explain why your shape does not belong to any of these groups

A trapezoid. It only has one pair of parallel sides, doesn't have four right angles and all sides are not the same length.

ANSWERED AT 17/10/2019 - 09:13 AM


QUESTION POSTED AT 17/10/2019 - 09:13 AM

What is the surface area of 120 x 110 x 4

The surface area of a rectangular prism is:

A=2(xy+xz+yz), where x,y, and z are its dimensions...in this case:

A=2(120*110+120*4+110*4)

A=2(13200+480+440)

A=2(14120)

A=28240 mm^2

ANSWERED AT 17/10/2019 - 09:11 AM


QUESTION POSTED AT 17/10/2019 - 09:11 AM

What is the surface area of 120 x 110 x 4

surface area is the area of all the faces on a shape so to speak.

2(120 x 110)=26,400

2(120 x 4)=960

2(110 x 4)=880

880+960+26,400=28,240

Surface area = 28,240

ANSWERED AT 17/10/2019 - 09:11 AM


QUESTION POSTED AT 17/10/2019 - 09:11 AM

Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y, and Z are all on line segment WZ. What is the area of circle C, which passes though points W and Z? 81 164 324 1296

Point D is the midpoint of the outer circle that we aim to find the area of

The circle has a diameter of WZ and radii of WC and CZ

We know that YZ=YD=10 cm

Let DC be x and CY be 10-x

The radius of the outer circle can be written as 8+8+x or 10+10-x which we can equate to find the value of x

8+8+x=10+10-x
16+x=20-x
2x=4
x=2

Therefore, the radius of the circle is 8+8+2=18

And hence the area of the circle is   \pi (18^{2})=324 \pi

ANSWERED AT 17/10/2019 - 09:07 AM


QUESTION POSTED AT 17/10/2019 - 09:07 AM

Please find the volume of each figure . Please show and explain all work or you will be reported do all and not some . 40) A 5m×3m×4m rectangular prism 41) A cube with edge of 6 ft 42) A cylinder with a height of 14 cm and base Diameter of 10 cm 43) A triangular prism with a base area of 15 square inches and height of 12 inches . 44) A cylinder with a base circumference of 8pi and height 7 45) A box has a volume of 24 ft^3 and base of 2 ft by 3 ft, what is the height ?

Volume formulas:
rectangle prism: l×w×h
cube: s^3
cylinder:(pi)r^2×h
triangle prism: (a×b/2)×h
cylinder:(pi)r^2×h
box:l×w×h

40) 5m×3m×4m =15m×4m= 60m^3

41) 6 ft × 6 ft ×6 ft = 36 ft × 6 ft = 216 ft^3

42) d=2r 10/2=5 r=5
3.14×5^2×14=78.5×14= 1099cm^3


43) 15=a×b/2 (area of trianlge)
15×12= 180in^3

44) c=2 (pi)r 8pi=2r (pi)
r=4
3.14×4^2×7=50.24×7=351.68

45) 24 ft^3 =2 ft × 3 ft × height
24=6×h
÷6 both sides
h=4ft

ANSWERED AT 17/10/2019 - 09:06 AM


QUESTION POSTED AT 17/10/2019 - 09:06 AM

A 12 ​-foot piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is x feet​ long, find the lengths of both pieces.

The shorter piece would be 3 feet long and the longer piece would be 9 feet long.

ANSWERED AT 17/10/2019 - 09:04 AM


QUESTION POSTED AT 17/10/2019 - 09:04 AM

Can someone help me find the area of the shaded region? is it just the area of the circle?

The shaded region is the area of the circle minus the area
of the pentagon.
A circle = pi * r^2
A circle = pi * 15^2
A circle = 706.5 cm^2

A regular pentagon = (a * p)/2 where a is the apothem, p is the perimeter.
The apothem id the perpendicular height from the midpoint of a side to the center of the pentagon.
To find the apothem you have to use a trig ratio.
A pent = (8.3 * 12*5)/2
A pent = 249 cm^2

Shaded region: circle - pentagon 706.5 - 249 = 457.5

ANSWERED AT 17/10/2019 - 09:04 AM


QUESTION POSTED AT 17/10/2019 - 09:04 AM

A parallelogram with sides of 6 and 10 has an area of 30. Find the measure of the small angle of the parallelogram.

Answer:

45

Step-by-step explanation:


ANSWERED AT 17/10/2019 - 09:02 AM


QUESTION POSTED AT 17/10/2019 - 09:02 AM

A triangle has two sides of lengths 5 and 12 what value could the length of the third party be check all apply 19 17 11 9 7 5

Answer: 11 and 9

Step-by-step explanation:

ANSWERED AT 17/10/2019 - 09:01 AM


QUESTION POSTED AT 17/10/2019 - 09:01 AM

The area of a square game board is 144 sq.in.whats the lenght of the sides of the board

Bear in mind that, a square is just a rectangle with all equal sides, thus, if say one side is length "x", all sides are "x" long then

check the picture below

ANSWERED AT 17/10/2019 - 09:01 AM


QUESTION POSTED AT 17/10/2019 - 09:01 AM

Point G lies between points F and H on . If the length of FH is 18 units, what is the value of x? 3 4 5 6

see the attached figure to better understand the problem

we know that

FH=FG+GH

FH=18 -------> equation 1

FH=4x+2x

FH=6x -------> equation 2

equate equation 1 and equation 2

18=6x

x=3

therefore

the answer is

x=3

ANSWERED AT 17/10/2019 - 08:49 AM


QUESTION POSTED AT 17/10/2019 - 08:49 AM

(LOTS OF POINTS, DUMB ANSWERS WILL BE REPORTED) What is the area of triangle ABC?

The answer is actually 7. I took the test.

ANSWERED AT 17/10/2019 - 08:38 AM


QUESTION POSTED AT 17/10/2019 - 08:38 AM

On a blueprint, the scale indicates that 6 cm represent 15 feet. What is the length of a room that is 9 cm long and 4 cm wide on the blueprint?

The scale length is 9cm and the scale is 6cm/15ft which is 3cm/5ft, so we can say:

9cm(5ft/3cm)=15ft for the length

If you wanted the width too...

4cm(5ft/3cm)=20ft/3  (6'8", 6ft 8in)

ANSWERED AT 17/10/2019 - 08:34 AM


QUESTION POSTED AT 17/10/2019 - 08:34 AM

What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple?

A Pythagorean Triplet is simply when all sides are integers, so we can check what x would be if it were the hypotenuse...

x^2=20^2+21^2

x^2=400+441

x^2=841

x=√841

x=29

ANSWERED AT 17/10/2019 - 08:30 AM


QUESTION POSTED AT 17/10/2019 - 08:30 AM

During the month of February, Fabulous Feet Shoe Mart sold 30 pairs of red loafers. After an ad campaign to boost sales, they sold 36 pairs in March. Find the percent of increase in sales. 23% 15% 20% 12%

Percent increase = 36-30/30 x 100
percent increase = 6/30 x 100

      20 percent

ANSWERED AT 17/10/2019 - 08:29 AM


QUESTION POSTED AT 17/10/2019 - 08:29 AM

find the area of the triangle defined by the following: a = 50, b = 20, γ = 105°.

A=side
b=base
γ=gamma

A=a b
 \frac{sin (y)}{2}

A=50*20* \frac{sin(105)}{2}

A≈482.96 m^2

ANSWERED AT 17/10/2019 - 08:25 AM


QUESTION POSTED AT 17/10/2019 - 08:25 AM

The surface areas of two similar solids are 1,008^cm and 1,372 cm^ The volume of the larger solid is 1,801cm ^3. Find the volume of the smaller solid. Round your answer to the nearest hundredth. A. 252.15cm^3 B. 1,134.16cm ^3 C. 1,323.18cm ^3 D. 1,372.19cm ^3

Answer:

Option B. 1134.16 cm³

Step-by-step explanation:

The surface area of two similar solids are 1,008 cm² and 1372 cm²

Since surface area is a two dimensional unit or surface area is the multiplication of two dimensions.

Ratio of the sides of the solids will be

Ratio of sides = \sqrt{\frac{1372}{1008} }

                       =\sqrt{\frac{4\times 343}{4\times 252}}

                       =\sqrt{\frac{343}{252}}=\sqrt{1.3611} = 1.167

Now ratio of volume of the solids will be cube of the sides.

\frac{\text{Volume of larger solid}}{\text{Volume of smaller solid}}=(\frac{1.167}{1} )^{3} = \frac{1801}{V}

By cross multiplication

V(1.167)³ = 1801

V = \frac{1801}{(1.167)^{3}}=\frac{1801}{1.588} = 1134.16 cm³

Option B. 1134.16 cm³ is the answer.

ANSWERED AT 17/10/2019 - 08:24 AM


QUESTION POSTED AT 17/10/2019 - 08:24 AM

The lens equation is 1f=1p+1q, where f is the focal length of the lens, p is the distance of the object from the lens, and q is the distance of the image from the lens. The formula to find q is

Answer:

The required formula is q=\frac{fp}{p-f}.

Step-by-step explanation:

The given equation is

\frac{1}{f}=\frac{1}{p}+\frac{1}{q}

where,

1. f is the focal length of the lens.

2. p is the distance of the object from the lens.

3. q is the distance of the image from the lens.

We have to rearrange the formula for q.

Multiply both sides by fpq.

\frac{fpq}{f}=fpq(\frac{1}{p}+\frac{1}{q})

pq=\frac{fpq}{p}+\frac{fpq}{q}

pq=fq+fp

Subtract fq from both the sides.

pq-fq=fp

Take out the common factor q.

q(p-f)=fp

Divide both the sides by (p-f)

q=\frac{fp}{p-f}

Therefore the required formula is q=\frac{fp}{p-f}.

ANSWERED AT 17/10/2019 - 08:22 AM


QUESTION POSTED AT 17/10/2019 - 08:22 AM