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3 years ago

Write a simplified polynomial expression in standard form to represent the area of the rectangle below.

2 answers:

6 0

Given:
Rectangle shape.
One side: 5x + 2
other side: x - 4

Area = length * width
Area = (5x+2)(x-4)
A = 5x(x-4) +2(x-4)
A = 5x² - 20x + 2x - 8
A = 5x² - 18x - 8

Sophie [7]3 years ago

6 0

Answer:

its ........................................................C

Step-by-step explanation:

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If tanA+sinA=m and tanA-sinA=n.prove that m^2-n^2=4√mn

mash [69]

Let $a=\tan A$ and $b=\sin A$ . Then

$m^2-n^2=(a+b)^2-(a-b)^2=(a^2+2ab+b^2)-(a^2-2ab+b^2)=4ab$

$\implies m^2-n^2=4\tan A\sin A$

and

$mn=(a+b)(a-b)=a^2-b^2$

$\implies4\sqrt{mn}=4\sqrt{\tan^2A-\sin^2A}$

The expression under the square root can be rewritten as

$\tan^2A-\sin^2A=\dfrac{\sin^2A}{\cos^2A}-\sin^2A=\sin^2A\left(\dfrac1{\cos^2A}-1\right)=\sin^2A(\sec^2A-1)$

Recall that

$\sin^2A+\cos^2A=1\implies\tan^2A+1=\sec^2A$

so that

$\tan^2A-\sin^2A=\sin^2A\tan^2A$

and assuming $\sin A>0$ and $\tan A>0$ , we end up with

$4\sqrt{\tan^2A-\sin^2A}=4\tan A\sin A$

so that

$m^2-n^2=4\sqrt{mn}$

as required.

5 0

2 years ago

A worker at a cabinet shop is cutting out pieces of wood for a dresser. He needs pieces that are 4 1/4inches long. Each saw cut

ella [17]

Answer: he will be able to make 19 full pieces

Step-by-step explanation:

1. Start off by making 7 feet into 84 inches so the measurements can match.

2. Add 4/14 inches and the 1/8 a inch together so you know how much is being taken off 84 inches. The amount will be 35/8 inches.

3. Divide 84 inches by 35/8 inches = 19 1/5

4. The whole number of the answer will be how many boards you can make from the board.

8 0

2 years ago

Your balance sheet shows $6,400 worth of inventory in hair products. Items are recorded in inventory at cost, and the average co

andreyandreev [35.5K]

Answer:

Units of hair products = 2634 units

Step-by-step explanation:

Given that:

Worth of products in the inventory = $6400

Average cost per unit = $2.43

Number of units = $\frac{Total\ worth}{Per\ unit\ cost}$

Number of units = $\frac{6400}{2.43}$

Number of units = 2633.73

Rounding off to nearest whole number = 2634 units

Hence,

Units of hair products = 2634 units

4 0

3 years ago

Solve the equation. Check your solution. 3x - 2 = 16

DedPeter [7]

X=6

16 plus 2 is 18 and divided by 3 is 6

3 0

3 years ago

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The sum of three consecutive even integers is 36. Let X represent the first integer X plus to represent the second integer and X

tatuchka [14]

$x,\ x+2,\ x+4-\text{three consecutive even integers}\\\\\text{The equation:}\\\\x+(x+2)+(x+4)=36\\\\3x+6=36\ \ \ \ |-6\\\\3x=30\ \ \ \ |:3\\\\x=10\\x+2=12\\x+4=14$

6 0

3 years ago

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