What is the measure of angle x?

From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th

wel

Answer:

$\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}$

Step-by-step explanation:

The width of a square is its side length.

The width of a circle is its diameter.

Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.

Formulas

$\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}$

$\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}$

$\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}$

If the diameter is equal to the side length of the square, then:
$\implies \sf r=\dfrac{1}{2}s$

Therefore:

$\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}$

So the ratio of the area of the circle to the original square is:

$\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}$

Given:

side length (s) = 6 in
radius (r) = 6 ÷ 2 = 3 in

$\implies \sf \textsf{Area of square}=6^2=36\:in^2$

$\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)$

Ratio of circle to square:

$\implies \dfrac{28}{36}=\dfrac{7}{9}$

5 0

2 years ago

Factor completely: <img src="https://tex.z-dn.net/?f=3x%5E3%2B21x%5E2%2B36x" id="TexFormula1" title="3x^3+21x^2+36x" alt

guajiro [1.7K]

To factor, you can first treat it like a single bracket and find the common factor. In this case, the common factor is 3x, so you get
3x(x² + 7x + 12)
Now you can factor the bracket normally, by finding factors of 12 that add up to make 7. The factors would be 3 and 4, so the bracket becomes (x + 3)(x + 4).
This leaves your final answer as
3x(x + 3)(x + 4)

I hope this helps!

5 0

3 years ago

How would you do this question?

Katarina [22]

Answer:

plot the reflection by finding the corresponding points by pretending that y=x-6 is the x-axis, so like (4,-1), (0,-5), (0,-3)

Step-by-step explanation:

7 0

3 years ago

7. In the accompanying diagram of rhombus CDEF, diagonal FD is drawn and the

tatiyna

Answer:

m∠CFD is 70°

Step-by-step explanation:

In the rhombus

Diagonals bisect the vertex angles

Every two adjacent angles are supplementary (their sum 180°)

Let us solve the question

∵ CDEF is a rhombus

∵ ∠E and ∠F are adjacent angles

→ By using the second property above

∴ ∠E and ∠F are supplementary

∵ The sum of the measures of the supplementary angles is 180°

∴ m∠E + m∠F = 180°

∵ m∠E = 40°

∴ 40° + m∠F = 180°

→ Subtract 40 from both sides

∵ 40 - 40 + m∠F = 180 - 40

∴ m∠F = 140°

∵ FD is a diagonal of the rhombus

→ By using the first property above

∴ FD bisects ∠F

→ That means FD divides ∠F into 2 equal angles

∴ m∠CFD = m∠EFD = $\frac{1}{2}$ m∠F

∴ m∠CFD = $\frac{1}{2}$ (140°)

∴ m∠CFD = 70°

6 0

3 years ago

Louisa wants to buy an online movie subscription that is on sale for 15% off. She writes the expression c − 0.15c to represent t

Tpy6a [65]

Answer:

#UseSimplifiedExpression

Step-by-step explanation:

6 0

2 years ago