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3 years ago

a rectangle consists of two identical squares with a common side. The perimeter of the rectangle is 27 inches. Find its area

Mathematics

2 answers:

aivan3 [116]3 years ago

8 0

Answer:

40.5

Step-by-step explanation:

sammy [17]3 years ago

3 0

Answer:

40.5 square inches

Step-by-step explanation:

Rectangle consists of two identical squares.

So, if the sides of square = x,

Then, Width of rectangle = x &

Length of rectangle = x +x = 2x

Perimeter of rectangle = 27 inches

2*(length + width) = 27

2*( 2x + x) = 27 {Combine like terms]

2* 3x = 27

6x= 27 {Divide both sides by 6}

x = 27/6

x = 4.5

Width = x = 4.5 inches

Length = 2x = 2*4.5 = 9 inches

Area of rectangle = length *width

= 4.5 *9

= 40.5 square inches

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3 years ago

Read 2 more answers

find the smallest number of terms of the AP "-54,-52.5,-51,-49.5" ....that must be taken for the sum of the terms to be positive

wel

The smallest number of terms of the AP that will make the sum of terms positive is 73.

Since we need to know the number for the sum of terms, we find the sum of terms of the AP

<h3>Sum of terms of an AP</h3>

The sum of terms of an AP is given by S = n/2[2a + (n - 1)d] where

n = number of terms,
a = first term and
d = common difference

Since we have the AP "-54,-52.5,-51,-49.5" ....", the first term, a = -54 and the second term, a₂ = -52.5.

The common difference, d = a₂ - a

= -52.5 - (-54)

= -52.5 + 54

= 1.5

<h3>Number of terms for the Sum of terms to be positive</h3>

Since we require the sum of terms , S to be positive for a given number of terms, n.

So, S ≥ 0

n/2[2a + (n - 1)d] ≥ 0

So, substituting the values of the variables into the equation, we have

n/2[2(-54) + (n - 1) × 1.5] ≥ 0

n/2[-108 + 1.5n - 1.5] ≥ 0

n/2[1.5n - 109.5] ≥ 0

n[1.5n - 109.5] ≥ 0

So, n ≥ 0 or 1.5n - 109.5 ≥ 0

n ≥ 0 or 1.5n ≥ 109.5

n ≥ 0 or n ≥ 109.5/1.5

n ≥ 0 or n ≥ 73

Since n > 0, the minimum value of n is 73.

So, the smallest number of terms of the AP that will make the sum of terms positive is 73.

Learn more about sum of terms of an AP here:

brainly.com/question/24579279

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4 0

2 years ago

Suppose you are going to form a committee of students and faculty. You have 10 total students and 11 total faculty to pick from.

zlopas [31]

Answer:

0.189

Step-by-step explanation:

We are using combination to solve for this.

C(n,r) = nCr = n!/r! (n - r)!

We have 10 total students and 11 total faculty = 21 people

Step 1

Selecting 3 students out of 10 total students

= 10× 9× 8×7×6×5×4×3×2×1/ 3×2×1 × 7×6×5×4×3×2×1/

= 120

Step 2

Select 6 faculty out of 11 faculty

11C6 = 11!/6!(11 - 6)!

= 11!/6! × 5!

= 11×10× 9× 8×7×6×5×4×3×2×1/6×5×4×3×2×1 × 5×4×3×2×1/

= 462

Step 3

Selecting 9 people out of 21 people to form a committee

21C9 = 21!/9!(21 - 9)!

= 21!/9! × 12!

= 293,930

Step 4

The fourth and final step of having a committee of 9 people =

(120 × 462)/293,930

= 55440/293,930

= 0.1886163372

Rounded to 3 decimal places = 0.189

Therefore, the probability that you select 3 students and 6 faculty = 0.189

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3 years ago

A.X'3+3x2 -10x = 24<br> x + 4

Nadya [2.5K]

Answer:

teach me plz this question

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3 years ago

What price do farmers get for the peach crops? in the third week of June, a random sample of 40 farming regions gave a sample me

prohojiy [21]

Given:
Sample size, n = 40
Sample mean, xb = $6.88
Population std. deviation, σ = $1.92 (known)
Confidence interval = 90%

Assume normal distribution for the population.
The confidence interval is
(xb + 1.645*(σ/√n), xb - 1.645*(σ/√n)
= (6.88 + (1.645*1.92)/√40, 6.88 - (1.645*1.92)/√40)
= (7.38, 6.38)

Answer: The 90% confidence interval is (7.38, 6.38)

6 0

3 years ago