Either enter an exact answer in terms of .. or use 3.14 for ..

If the original square had a side length of

irina [24]

Answer:

Part a) The new rectangle labeled in the attached figure N 2

Part b) The diagram of the new rectangle with their areas in the attached figure N 3, and the trinomial is $x^{2} +11x+28$

Part c) The area of the second rectangle is 54 in^2

Part d) see the explanation

Step-by-step explanation:

The complete question in the attached figure N 1

Part a) If the original square is shown below with side lengths marked with x, label the second diagram to represent the new rectangle constructed by increasing the sides as described above

we know that

The dimensions of the new rectangle will be

$Length=(x+4)\ in$

$width=(x+7)\ in$

The diagram of the new rectangle in the attached figure N 2

Part b) Label each portion of the second diagram with their areas in terms of x (when applicable) State the product of (x+4) and (x+7) as a trinomial

The diagram of the new rectangle with their areas in the attached figure N 3

we have that

To find out the area of each portion, multiply its length by its width

$A1=(x)(x)=x^{2}\ in^2$

$A2=(4)(x)=4x\ in^2$

$A3=(x)(7)=7x\ in^2$

$A4=(4)(7)=28\ in^2$

The total area of the second rectangle is the sum of the four areas

$A=A1+A2+A3+A4$

State the product of (x+4) and (x+7) as a trinomial

$(x+4)(x+7)=x^{2}+7x+4x+28=x^{2} +11x+28$

Part c) If the original square had a side length of x = 2 inches, then what is the area of the second rectangle?

we know that

The area of the second rectangle is equal to

$A=A1+A2+A3+A4$

For x=2 in

substitute the value of x in the area of each portion

$A1=(2)(2)=4\ in^2$

$A2=(4)(2)=8\ in^2$

$A3=(2)(7)=14\ in^2$

$A4=(4)(7)=28\ in^2$

$A=4+8+14+28$

$A=54\ in^2$

Part d) Verify that the trinomial you found in Part b) has the same value as Part c) for x=2 in

We have that

The trinomial is

$A(x)=x^{2} +11x+28$

For x=2 in

substitute and solve for A(x)

$A(2)=2^{2} +11(2)+28$

$A(2)=4 +22+28$

$A(2)=54\ in^2$ ----> verified

therefore

The trinomial represent the total area of the second rectangle

7 0

3 years ago

Lauren is given a 12% pay rise. Her new salary is £24,080

svet-max [94.6K]

Answer:

21,500

Step-by-step explanation:

3 0

3 years ago

Is the number a rational number? Help me out please!

krek1111 [17]

Answer:

first answer

Step-by-step explanation:

Hi, this is correct because repeating decimals are rational numbers.

Rational numbers can be written by a fraction of integers.

If there is a pattern, it means that this is the division of two integers.

hope this helps

8 0

2 years ago

Read 2 more answers

The pharmacist uses 67mg, 100g and 0.6 kg of drug to compound 3 separate precription. how much total drug did the pharmacist use

FromTheMoon [43]

Answer: 700.067 g

Step-by-step explanation:

Given : The pharmacist uses 67mg, 100g and 0.6 kg of drug to compound 3 separate prescription.

We know that 1 gram= 1000 milligram

and 1 kilogram = 1000 grams

Then, By UNITARY METHOD, $\text{1 mg}=\dfrac{1}{1000}\text{ gram}$

Now, We convert each amount of drug into grams as ,

$67\ mg=67\times\dfrac{1}{1000}\ g\\\\=0.067\text{ g}$

AND

$0.6\ kg=0.6\times100=60\text{ g}$

Now, the total drug used by Pharmacist (in grams) = $0.067+100+600=700.067\ g$

Hence, Pharmacist used 700.067 g of total drug.

8 0

2 years ago

If the area of a rectangle is 162 square meters, what is the length of the base

Contact [7]

Answer:

If the long side is down then the length of the base is 81 sq.m.

If the short side is down then the length of the base is 20.25 sq.m.

Step-by-step explanation:

162/4 is 40.5 that means if this were a square it would be 40.5 sq.m. On each side, if the base is longer you multiply 40.5 by 2 (or whatever youre supposed to honestl) and if the base is shorter you divide by 2 (or whatever you were supposed to)

7 0

3 years ago