All categories

3 years ago

Each rectangle has its area written inside and the expression mod

Mathematics

1 answer:

dangina [55]3 years ago

6 0

Answer:

Length of the boxes are 17 in, 35 in, 17 in.

Step-by-step explanation:

The given question is incomplete: please find the complete question in the attachment.

A). From Box - (1)

Area of the box = 289 in.²

Expression that denotes the area of the box = 36x² - 12x + 1

So, 36x²- 12x + 1 = 289

(6x)² - 2(6)x + (1)² = (17)²

(6x - 1)² = (17)² [ Since (a² - 2ab + b²) = (a - b)²]

Given box is a square having sides = (6x - 1) in.

∵ (6x - 1)² = 17

⇒ 6x = 18

⇒ x = $\frac{18}{6}$ = 3

Now length of the sides = (6x - 1) = 17 in.

B) Box - (2)

Similarly, 25x²- 50x + 25 = 1225

(25x² - 50x + 25) = (35)²

(5x - 5)² = (35)²

5(x - 1) = 35 ⇒ x = 8

Here length of one side of the box is 5(x - 1) = 5(8 - 1) = 35in.

C). Box - (3)

49x² - 56x + 16 = 289

(7x)² - 2×(7x)(4) + 4²= (17)²

(7x - 4)² = (17)²

Length of each side = (7x - 4) in.

From, (7x - 4)² = (17)²

7x - 4 = 17

⇒ x = $\frac{21}{7}$

⇒ x = 3

Therefore, length of each side of the box = (7x - 4) = 17 in.

You might be interested in

Suppose a box of Cracker Jacks contains one of 5 toy prizes: a small rubber ball, a whistle, a Captain America decoder ring, a r

lakkis [162]

Answer:

11.42 boxes

Step-by-step explanation:

For the first box bought, there is a 100% chance of getting a unique toy (since you still don't have any). E₁ = 1.

After that, there is a 4 in 5 chance of getting a unique toy from the next box, the expected number of boxes required is:

$E_2 = (\frac{4}{5})^{-1} = 1.25$

For the next unique toy, there is now a 3 in 5 chance of getting it:

$E_3 = (\frac{3}{5})^{-1} = 1.67$

Following that logic, there is a 2 in 5 chance of getting the 4th unique toy:

$E_4 = (\frac{2}{5})^{-1} = 2.5$

Finally, there is a 1 in 5 chance to get the last unique toy:

$E_5 = (\frac{1}{5})^{-1} = 5$

The expected number of boxes to obtain a full set is:

$E=E_1+E_2+E_3+E_4+E_5\\E=1+1.25+1.67+2.5+5\\E=11.42\ boxes$

5 0

3 years ago

sweet-ann [11.9K]

Answer:

Step-by-step explanation:

<h3><em>The Answer is B, This is the answer beacuse R and S is true. There are some methonds you can do to help you solve any questions like these in the future. I hope this well help.</em></h3>

3 0

2 years ago

Read 2 more answers

When you multiply a mixed number by ___________ ,the product is equal to the mixed number. What do you put in the blank?

4vir4ik [10]

Answer:

Step-by-step explanation:

because 1/2 time 1 = 1/2

4 0

3 years ago

The seventh term of an arithmetic progression is equal to twice the fifth term. The sum

mario62 [17]

Answer:

a₁ = - 24

Step-by-step explanation:

The n th term of an AP is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₇ = 2a₅ , then

a₁ + 6d = 2(a₁ + 4d) = 2a₁ + 8d ( subtract 2a₁ + 8d from both sides )

- a₁ - 2d = 0 → (1)

The sum to n terms of an AP is

$S_{n}$ = $\frac{n}{2}$ [ 2a₁ + (n - 1)d ]

Given $S_{7}$ = 84 , then

$\frac{7}{2}$ (2a₁ + 6d) = 84

3.5(2a₁ + 6d) = 84 ( divide both sides by 3.5 )

2a₁ + 6d = 24 → (2)

Thus we have 2 equations

- a₁ - 2d = 0 → (1)

2a₁ + 6d = 24 → (2)

Multiplying (1) by 3 and adding to (2) will eliminate d

- 3a₁ - 6d = 0 → (3)

Add (2) and (3) term by term to eliminate d

- a₁ = 24 ( multiply both sides by - 1 )

a₁ = - 24

6 0

3 years ago

Complete the pattern

romanna [79]

1.) 376.2
2.) 37620
3.)376200.
3.) 3762000

hope that helped

7 0

4 years ago