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3 years ago

Find the area of this parallelogram. Be sure to include the correct unit in your answer.

Mathematics

1 answer:

jok3333 [9.3K]3 years ago

3 0

Answer:

1890 yd

Step-by-step explanation:

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andrey2020 [161]

First observe that if $a+b>0$ ,

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

3 0

1 year ago

What is 26/4, 6.45, 6 2/5, and 50/8 in order from least to greatest?

blagie [28]

26/4=6.50

6.45=6.45

6and 2/5=6.40

50/8=6.25

so it should be

least- greatest

50/8, 6 & 2/5, 6.45, 26/4

7 0

3 years ago

in a box full of oranges, apples, and pears in a ratio 2:5:6. What is the total weight of the fruits in the box if it was known

spin [16.1K]

Answer:

31.2 lbs

Step-by-step explanation:

Let 2x = weight of oranges

5x = weight of apples

6x = weight of pears

2x + 5x + 6x = total weight

2x = 4.8

x = 2.4

4.8 + 5(2.4) + 6(2.4) = 4.8 + 12 + 14.4

= 31.2 lbs

7 0

3 years ago

Challenge You buy 3.18 pounds of apples, 1.25 pounds of peaches, and 1.76 pounds of pears.

loris [4]

Answer:

6.19

Step-by-step explanation:

I hope this helps you

6 0

3 years ago

WILL MARK BRANLIEST A graph is shown below: Dotted line joining negative 1, negative 2 and 5,0 and the region above the line is

s2008m [1.1K]

Hello there!

<span>A graph is shown below: Dotted line joining negative 1, negative 2 and 5,0 and the region above the line is shaded. Which of the following inequalities is best represented by this graph? x − 3y > 5 x − 3y < 5 x − 2y > 5 x − 2y < 5

Answer:
</span><span>x – 3y < 5</span>

4 0

3 years ago