the focus and directrix will both be shifted down 3 units
Answer:
Step-by-step explanation:
The <u>width</u> of a square is its <u>side length</u>.
The <u>width</u> of a circle is its <u>diameter</u>.
Therefore, the largest possible circle that can be cut out from a square is a circle whose <u>diameter</u> is <u>equal in length</u> to the <u>side length</u> of the square.
<u>Formulas</u>
If the diameter is equal to the side length of the square, then:
Therefore:
So the ratio of the area of the circle to the original square is:
Given:
- side length (s) = 6 in
- radius (r) = 6 ÷ 2 = 3 in
Ratio of circle to square:
Answer:
It is a perfect square. Explanation below.
Explanation:
Perfect squares are of the form
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
. In polynomials of x, the a-term is always x.(
(
x
+
c
)
2
=
x
2
+
2
c
x
+
c
2
)
x
2
+
8
x
+
16
is the given trinomial. Notice that the first term and the constant are both perfect squares:
x
2
is the square of x and 16 is the square of 4.
So we find that the first and last terms correspond to our expansion. Now we must check if the middle term,
8
x
is of the form
2
c
x
.
The middle term is twice the constant times x, so it is
2
×
4
×
x
=
8
x
.
Okay, we found out that the trinomial is of the form
(
x
+
c
)
2
, where
x
=
x
and
c
=
4
.
Let us rewrite it as
x
2
+
8
x
+
16
=
(
x
+
4
)
2
. Now we can say it is a perfect square, as it is the square of
(
x
+
4
)
.
Answer:
q=-5
Step-by-step explanation:
6+q=1
Isolate the variable by subtracting 6 from both sides of the equation
q=1-6
q=-5
Answer: I believe the area of this shape is 40
Step-by-step explanation:The formula for the surface area of a prism is obtained by taking the sum of (twice the base area) and (the lateral surface area of the prism). The surface area of a prism is given as S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.
