Question 1 (1 point)

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

Wesley makes spherical fish tanks with a diameter of 30. A customer requests a smaller tank with half the volume of the tank tha

grandymaker [24]

Answer:

23.8

Step-by-step explanation:

V = 4/3 π r³

V = 4/3 π (15)³

V = 4500 π

V = 4/3 π r³

4500 π / 2 = 4/3 π r³

1687.5 = r³

r ≈ 11.9

d ≈ 23.8

5 0

3 years ago

Which of the following World Record times from Track and Field is least

Gre4nikov [31]

I think the answer is B. Or A.

3 0

2 years ago

Read 2 more answers

You decide that you want to purchase a Tesla SUV. You borrow \$95,000 for the purchase. You agree to repay the loan by paying eq

liraira [26]

Using compound interest and a graphing calculator, it is found that it will take about 15 years for the loan to be paid off.

<h3>What is compound interest?</h3>

The amount of money earned, in compound interest, after t years, is given by:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

In which:

A(t) is the amount of money after t years.

P is the principal(the initial sum of money).

r is the interest rate(as a decimal value).

n is the number of times that interest is compounded per year.

For this problem, the parameters are given as follows:

A(0) = 95000, r = 0.06, n = 12.

Hence the value of the loan after t years is:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

$A(t) = 95000\left(1 + \frac{0.06}{12}\right)^{12t}$

$A(t) = 95000(1.005)^{12t}$

You have monthly payments of $1,200, hence the amount paid after t years is:

P(t) = 12 x 1,200t = 14400t

Then we have to solve for:

A(t) = P(t)

$14400t = 95000(1.005)^{12t}$

Which is solved in the graph below, meaning that it will take about 15 years for the loan to be paid off.

More can be learned about compound interest at brainly.com/question/25781328

#SPJ1

5 0

1 year ago

Need help with this math problem

musickatia [10]

Make sure you match up your negative and positive so that you can get a good coordinate and pattern

6 0

3 years ago