An architect is designing square windows with an area of(x2 + 16x +64) ft?. The dimensions of the

Mathematics

2 answers:

GrogVix [38]2 years ago

7 0

Answer:

A) The dimensions are (x+10) by (x+10).

B) The perimeter is given by 4x+40.

C) The perimeter when x is 4 is 56.

Step-by-step explanation:

I filled two notebook papers to solve this

Darina [25.2K]2 years ago

6 0

A) The dimensions are (x+10) by (x+10).

B) The perimeter is given by 4x+40.

C) The perimeter when x is 4 is 56.

The quadratic can be factored by finding factors of c, the constant, that sum to b, the coefficient of x. Our c is 100 and our b is 20; we want factors of 100 that sum to 20. 10*10=100 and 10+10=20, so those are what we need. This gives us (x+10)(x+10 for the factored form.

Since the dimensions are all (x+10), and there are 4 sides, the perimeter is given by 4(x+10). Using the distributive property we have 4*x+4*10=4x+40.

To find the perimeter when x=4, substitute 4 into our perimeter expression:

4*4+40=16+40=56.

You might be interested in

Erika pours 6 cups of milk into 8 glasses. Each glass has the same amount of milk. How many cups of milk are in each glass?

MrMuchimi

Answer:

each glass will have 0.75 of a cup or 3/4 of a cup * 0.75 and 3/4 is the same*

7 0

3 years ago

The formula for the area of a circle is A = πr^2. Which equation shows the formula in terms of r?

Julli [10]

$A=\pi r^2\\\\\pi r^2=A\ \ \ |\text{divide both sides by}\ \pi\\\\r^2=\dfrac{A}{\pi}\ \ \ \ |\text{square root both sides}\\\\r=\sqrt{\dfrac{A}{\pi}}$

6 0

3 years ago

If T: (x, y) → (x + 6, y + 4), then T-1: (x,y) → _____.

alexgriva [62]

T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

$\left[\begin{array}{ccc}7&6\\4&5\end{array}\right]$

The inverse of the matrix is

$\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]$

So, the Inverse Transformation is given by

$T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})$