Question

the lengths of the side of a rectangular window have the ratio 1.7 to 1 the area of the window is 2,720 sqaure inches what are dimensions of the window

Answer 1

| Quadratic Functions and Equations |

(Note) This includes all except the last (17th question). For this, I would recommend you doing it on your own. Bare in mind that some questions may vary depending on the user. However, this is confirmed as of 12.6.22.

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1. The graph of
`y=x^2` is shown below.

Which of the following could be the graph of
`y=x^2-2` ?

• Graph A.

2. Which equation could be solved using the graph above?

• A)
  `x^2+4x+3=0`

3. What is the solution to the following equation?

`2x^2-3x+2=0`

• B)
  `x=(3-+i√(7) )/(4)`

4. What are the zeros of
`y=x^2+2x-8`?

• A)
  `-4,2`

5. How many real solutions does the function shown on the graph have?

• A) No Real Solutions

6. A football is kicked into the air from an initial height of 4 feet. The height, in feet, of the football about the ground is given by
`s(t)=-16t^2+50t+4`, where t is time, in seconds, and
`t\geq 0`. At what time will the football be 25 feet above the ground?

• D) 0.5 seconds or 2.625 seconds

7. The lengths of the sides of a rectangular window have the ration 1.7 to 1. The area of the window is 2,700 square inches. What are the dimensions of the window?

• D) 40 inches by 68 inches

8. What is the solution to the following equation?

`x^2-10x+24=0`

• C)
  `x=4` or
  `x=6`

9. David makes and sells chairs. The functions
`p(x)=-10x^2+100x-210,` graph below, indicates how much profit he makes in a month if he sells the chairs for 10 - x dollars each. What should David charge per chair to make the maximum profit, and what is the maximum profit he can make in a month?

• A) $40 at $5 per chair

10. Use graphing to find the solutions to the system of equations.

`\left \{ {{x^2-y=4} \atop {2x+y=-1}} \right.`

• Graph B

11. Which of the following are the most likely factors of the function graphed above?

• D)
  `(x+2)(x-3)`

12. Suppose a parabola has an axis of symmetry at x = -5, a maximum height of 9, and passes through the point (-7,1). Write the equation of the parabola in vertex form.

• D)
  `y=-2(x+5)^2+9`

13. Any number in the form of
`a-+bi,` where a and b are real numbers- and
`b\\eq 0` is considered a pure imaginary number.

• False

14. The minimum value of a function is the smallest y-value of the function.

• True

15.
`i^2=√(-1)`

• False

16. Complex numbers can be graphed on the real xy coordinate plane.

• False

17. DIY Essay

Good luck!

Answer 2

`Lenght: 68\ in\\\\Width: 40\ in`

Explanation:

The formula for calculate the area of a rectangle is:

`A=lw`

Where "l" is the lenght and "w" is the width.

You know that the ratio of the sides of the rectangular window is:

`1.7:1`

Then, let be
`x` the width (in inches) of the rectangular window and
`1.7x` the lenght (in inches) of the rectangular window.

Knowing that the area of the window is 2,720 square inches, you can know that:

`(1.7x)(x)=2,720`

Now you must solve for "x" in order to find the width:

`(1.7x)(x)=2,720\\\\1.7x^2=\\\\x=\sqrt{(2,720)/(1.7) }\\\\x=40`

Finally, the lenght is:

`1.7x=1.7(40)=68`