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2 years ago

5

The length of a rectangle is 1 m less than twice the width, and the area of the rectangle is 21 m?. Find the dimensions of the r

ectangle.

1 answer:

Vanyuwa [196]2 years ago

4 0

Answer:

length = 6

width = 3 1/2

Step-by-step explanation:

l = length

w = width

l = 2w-1

w(2w-1) = 21

2w² - 1 - 21 = 0

(2w - 7)(w + 3) = 0

w = 7/2 = 3 1/2

find 'l': l = 2(7/2) - 1 = 7-1 = 6

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A) Write the sequence of natural numbers which are multiplied by 3 ?

Volgvan

Answer:

a) 3, 6, 9, 12, 15,..., $3\cdot n$ , b) 4, 7, 10, 13, 16,..., $3\cdot n +1$ , c) Both sequences are arithmetic.

Step-by-step explanation:

a) The sequence of natural numbers which are multiplied by 3 are represented by the function $f(n) = 3\cdot n$ , $n\in \mathbb{N}$ . Let see the first five elements of the sequence: 3, 6, 9, 12, 15,...

b) The sequence of natural numbers which are multiplied by 3 and added to 1 is represented by the function $f(n) = 3\cdot n + 1$ , $n\in \mathbb{N}$ . Let see the first five elements of the sequence: 4, 7, 10, 13, 16,...

c) Both sequences since differences between consecutive elements is constant. Let prove this statement:

(i) $f(n) = 3\cdot n$

$\Delta f = f(n+1) -f(n)$

$\Delta f = 3\cdot (n+1) -3\cdot n$

$\Delta f = 3$

(ii) $f(n) = 3\cdot n +1$

$\Delta f = f(n+1)-f(n)$

$\Delta f = [3\cdot (n+1)+1]-(3\cdot n+1)$

$\Delta f = 3$

Both sequences are arithmetic.

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2 years ago

The largest 4 digit number exactly divisible by 88 is: a.9944 b.9768 c.9988 d.8888

serious [3.7K]

Answer:

A

Step-by-step explanation:

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2 years ago

At one store, Julia saved $10 with a coupon for 40% off her total purchase. At another store, the $29 she spent on books is

barxatty [35]

Let "a" and "b" represent the values of the first and second purchases, respectively.
0.40*(original price of "a") = $10
(original price of "a") = $10/0.40 = $25.00 . . . . divide by 0.40 and evaluate
a = (original price of "a") - $10 . . . . . . Julia paid the price after the discount
a = $25.00 -10.00 = $15.00

At the other store,
$29 = 0.58b
$29/0.58 = b = $50 . . . . . . . divide by the coefficient of b and evaluate

Then Julia's total spending is
a + b = $15.00 +50.00 = $65.00

Julia spent $65 in all at the two stores.

6 0

3 years ago

Explain whether rounding or compatible numbers gives a closer estimate for the product 48 x 123= 5904.

telo118 [61]

Compatible 50 x 120 = 6000

Rounding 50 x 123 =6150

Compatible numbers is closer estimate

4 0

3 years ago

Read 2 more answers

Find the number of elements in A1 ∪A2 ∪A3 if there are 100 elements in A1, 1000 in A2, and 10,000 in A3 if a) A1 ⊆ A2 and A2 ⊆ A

Stella [2.4K]

Answer:

Step-by-step explanation:

Given that there are 3 sets such that there are 100 elements in A1, 1000 in A2, and 10,000 in A3

a) If A1 ⊆ A2 and A2 ⊆ A3

then union will contain the same number of elements as that of A3

i.e. $n(A1 ∪A2 ∪A3)=n(A3) =10000$

b) If the sets are pairwise disjoint.

union will contain the sum of elements of each set

$n(A1 ∪A2 ∪A3) = 100+1000+10000=11100$

c) If there are two elements common to each pair of sets and one element in all three sets

We subtract common elements pairwise and add common element in 3

i.e. $n(A1 ∪A2 ∪A3) = 100+1000+10000-2-2-2+1\\= 10995$

5 0

3 years ago