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Luda [366]
2 years ago
15

The length of a rectangle is eight more than twice its width. The perimeter is 88 feet. Find the dimensions of the rectangle.

Mathematics
2 answers:
vodka [1.7K]2 years ago
7 0

Answer:

length: 31

width: 12

Step-by-step explanation:

l=8+2w

p=2l+2w=88

(8+2w)+(8+2w)+w+w

16+6w=88

6w=72

w=12

l=8+2(12)

l=32

sorry if this was confusing

masya89 [10]2 years ago
7 0

Answer:

l=32 and w=12

Step-by-step explanation:

Given: The length of a rectangle is eight more than twice its width. The perimeter is 88 feet.

To find: The dimensions of the rectangle.

Solution:

It is given that the length of a rectangle is eight more than twice its width.

Let the width of the rectangle be w.

So, the length of the rectangle=2w+8

We know that the perimeter of a rectangle is 2(l+w)

Here, perimeter of rectangle=88

So, we have

2(2w+8+w)=88

\implies2w+w+8=44

\implies3w=44-8

\implies3w=36

\implies w=12

Therefore, width of the rectangle is 12 feet

length=2\times12+8=32

Hence, length of the rectangle is 32 feet and width of the rectangle is 12 feet.

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Show that the three points whose position vectors are 7j+ 10k,-i + 6j+6k and - 4i + +9j + 6k form an isosceles right
Novay_Z [31]

Answer:

AB = √18 , BC=√18 and CA =4

AB²+BC²  = CA² and AB=BC

ΔABC isosceles right  angled triangle.

Step-by-step explanation:

Given vectors are  7j+ 10k,-i + 6j+6k and - 4i + +9j + 6k

A( 0,7,10), B( -1,6,6) C(-4,9,6)

AB⁻ = OB-OA = -I+6j+6k-(7j+10k) = -I-j-4k

AB = \sqrt{1+1+16} = \sqrt{18}

BC = OC-OB = -4i+9j+6k-(-I+6j+6k) = -3i+3j

BC=\sqrt{9+9} =\sqrt{18}

CA = OA-OC = 7j+10k - (- 4i + +9j + 6k ) = 4i-2j+4k

CA = \sqrt{16+4+16} =\sqrt{36} =4

Since AB²+BC²  = CA²

And AB=BC

Therefore it follows that ΔABC is a right angled isosceles triangle



3 0
2 years ago
NEED ASAP PLEASE HELP
sweet-ann [11.9K]

Answer:

Dilations produce similar figures because the image and pre-image will have congruent corresponding angles. The corresponding side lengths of the figures will be proportional based on the scale factor. The shape is preserved and the sides are enlarged or reduced by the scale factor

Step-by-step explanation:

6 0
1 year ago
Point T, the midpoint of segment RS, can be found using the formulas x = (6 – 2) + 2 and y = (4 – 6) + 6. What are the coordinat
Fiesta28 [93]

Question:

Point T, the midpoint of segment RS, can be found using the formulas x = (1/2) (6 – 2) + 2 and y = (1/2) (4 – 6) + 6. What are the coordinates of point T?

Answer:

T(4,5)

Step-by-step explanation:

Given

x = \frac{1}{2}(6 - 2) + 2

y = \frac{1}{2}(4 - 6) + 6

Required

Determine the coordinates of T

The coordinates of T can be represented as T(x,y)

To do this, we simply solve for x and y

x = \frac{1}{2}(6 - 2) + 2

Solve 6 - 2

x = \frac{1}{2}*4 + 2

Solve 1/2 * 4

x = 2 + 2

x = 4

y = \frac{1}{2}(4 - 6) + 6

Solve 4 - 6

y = \frac{1}{2}*-2 + 6

Solve 1/2 * -2

y = -1 + 6

y = 5

Hence, the coordinates of T(x,y) is:

T(x,y) = T(4,5)

5 0
2 years ago
Read 2 more answers
Hank invested a total of $20,000, part at 7% and part at 10%. How much did he invest at each rate if the total interest earned i
jolli1 [7]

Answer:

The amount invested at 7% is $12,000 while the amount invested at 10% is $8,000

Step-by-step explanation:

The given parameters are;

The total amount Hank invested = $20,000

The interest earned in one year = $1640

Hank invested part of the $20,000 at 7% interest and part of the $20,000 at 10%

Let the part invested at 7% = X and the part invested at 10% = Y, we have;

7% of X + 10% of Y = $1640 which gives;

0.07×X + 0.1×Y = $1640.....................(1)

X + Y = $20,000.................................(2)

Multiply equation (1) by 10 and subtract equation (1) from equation (2) to get;

X + Y - 10×(0.07×X + 0.1×Y) = $20,000 - 10×$1640

X - 0.7·X - Y - Y = $20,000 - $16,400 = $3,600

0.3·X = $3,600

X = $3,600/0.3 = $12,000

X = $12,000

Y = $20,000 - X = $20,000 - $12,000 = $8,000

Y = $8,000

Therefore, the amount invested at 7% = $12,000 and the amount invested at 10% = $8,000.

7 0
2 years ago
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Select the correct answer from each drop-down menu. A self-service car wash charges $4 for the initial 5 minutes plus an additio
arlik [135]

Answer: For m\geq15

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Nick does not has enough money to follow this recommendation.

Step-by-step explanation:

Given: A self-service car wash charges $4 for the initial 5 minutes plus an additional $0.75 for each minute after that.

Let y be the cost for car wash for m minutes then

y=4+0.75(m-5) such that at m= 5 , y=4 which is the cost for car wash (dollars) for first 5 minutes.

Also, A car enthusiast magazine recommends spending at least 15 minutes to properly wash a car.

For m\geq15

\\\Rightarrow\ y=4+0.75(m-5)\geq4+0.75(15-5)\\\Rightarrow\ y\geq4+0.75(10)\\\Rightarrow\ y\geq4+7.5\\\Rightarrow\ y\geq11.5

But Nick has $10 which is less than $11.5, so he does not has enough money to follow this recommendation.

7 0
2 years ago
Read 2 more answers
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