If Lin runs for 24 minutes at the same rate, how many laps does she run?

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

What is the height of the tree show all work

poizon [28]

Answer:

x=32.91

Step-by-step explanation:

Given: Triangle

Find: x

_______

Tan(35°)=x/47

x=tan(35)×47

x=0.7×47

x=32.91

Hope it helps!

3 0

2 years ago

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Please help number 42

Ratling [72]

Answer:

All I know

Step-by-step explanation:All I know is that you have to distribute the top so 5{2k - 3} so that would be 10k-15 and then -3{k+4} would be -3k -12 hopefully this helps you out a littble bit so the top completely is 7k-27

7 0

3 years ago

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100 200 300 400 500 600 700 Quantity Supplied nstructions: Refer to the graph and answer the questions below

mash [69]

Answer:

a. 400

b. 4$

Step-by-step explanation:

2$ equals 0 Quantity

3$ equals 100 Quantity

4$ equals 200 Quantity

We can see that starting from 2$, a dollar will increase the Quantity by 100

7 0

1 year ago

The measured weights of 1,000 men in a certain village follow a normal distribution with a mean of 150 pounds and a standard dev

Hitman42 [59]

Z = (X-Mean)/SD
z1 = (165 - 150)/15 = +1 
z2 = (135 - 150)/15 = - 1 
According to the Empirical Rule 68-95-99.7 
Mean +/- 1SD covers 68% of the values 
100% - 68% = 32% 
The remaining 32% is equally distributed below z = - 1 and z = +1 
32%/2 = 16%

Therefore,

a) Number of men weighing more than 165 pounds = 16% of 1000 = 160 
b) Number of men weighing less than 135 pounds = 16% of 1000 = 160

3 0

3 years ago

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