Ms. chen is getting a new tile floor for her workshop. Her workshop is 15ft long and 11ft wide.

The area of a room is 600 square feet. The length is (x + 5) feet and the width is (x + 4) feet. Find the dimensions of the room

tangare [24]

I'm going to assume that the room is a rectangle.

The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle.

You're given that the length, l = (x+5)ft and the width, w = (x+4)ft. You're also told that the area, A = 600 sq. ft. Plug these values into the equation for the area of a rectangle and FOIL to multiply the two factors:
$A = lw\\
600 = (x+5)(x+4)\\
600 = x^{2} + 9x + 20
$

Now subtract 600 from both sides to get a quadratic equation that's equal to zero. That way you can factor the quadratic to find the roots/solutions of your equation. One of the solutions is the value of x that you would use to find the dimensions of the room:
$600 = x^{2} + 9x + 20\\
x^{2} + 9x - 580 = 0\\
(x + 29)(x - 20) = 0\\
x + 29 = 0, \:\: x - 20 = 0\\
x = -29, x = 20$

Now you know that x could be -29 or 20. For dimensions, the value of x must give you a positive value for length and width. That means x can only be 20. Plugging x=20 into your equations for the length and width, you get:
Length = x + 5 = 20 + 5 = 25 ft.
Width = x + 4 = 20 + 4 = 24 ft.

The dimensions of your room are 25ft (length) by 24ft (width).

8 0

3 years ago

Read 2 more answers

2. Find the value of x for which l | | m.

joja [24]

2x-5=95 due to the alternate interior angles thm so you just add 5 to 95 to get 2x=100 then divide by 2 to get x=50!

7 0

3 years ago

If two matrices, A and B, are equal, which of the

alexandr402 [8]

If A and B are equal:

Matrix A must be a diagonal matrix: FALSE.

We only know that A and B are equal, so they can both be non-diagonal matrices. Here's a counterexample:

$A=B=\left[\begin{array}{cc}1&2\\4&5\\7&8\end{array}\right]$

Both matrices must be square: FALSE.

We only know that A and B are equal, so they can both be non-square matrices. The previous counterexample still works

Both matrices must be the same size: TRUE

If A and B are equal, they are literally the same matrix. So, in particular, they also share the size.

For any value of i, j; aij = bij: TRUE

Assuming that there was a small typo in the question, this is also true: two matrices are equal if the correspondent entries are the same.

8 0

3 years ago

Read 2 more answers

An athlete goes on a diet. He loses 3 pounds each month for 8 months. He lost a total of 24 pounds. If he wants to lose 30 pound

sukhopar [10]

If he wants to loose 30 points total, subtract what he lost already, 24, from 30. He needs to lose 6 more pounds.

5 0

3 years ago

The nature of a graph, which has an even degree and a positive leading coefficient will be

zaharov [31]

The nature of a graph, which has an even degree and a positive leading coefficient will be<u> up left, up right</u> position

<h3 /><h3>What is the nature of the graph of a quadratic equation?</h3>

The nature of the graphical representation of a quadratic equation with an even degree and a positive leading coefficient will give a parabola curve.

Given that we have a function f(x) = an even degree and a positive leading coefficient. i.e.

y = f(x) = 2x²+ 4

The domain of this function varies from -∞ < x < ∞ and the parabolic curve will be positioned on the upward left and upward right x-axis.

Learn more about the graph of a quadratic equation here:

brainly.com/question/9643976

#SPJ1

6 0

2 years ago