Answer:
45
Step-by-step explanation:
The known side is 3 times the length of the smaller figure. To make sure the figures remain similar, you must also multiply the longer side of the smaller figure(15) by 3. This will give you 45.
<em>Change 1 1/2 into improper faction</em>
1 1/2 = 3/2
<em>Change 3/2 to quarters</em>
3/2 = 6/4
1 measure cups = 1/4 cup
<em>To get 6/4 cups </em>
6/4 ÷ 1/4 = 6/4 x 4/1 = 6
He needs to fill in 6 times
Answer:

Step-by-step explanation:
<u>Solution 1:</u>
Recall that in an isosceles triangle, the two angles adjacent to the congruent sides are equal. Since the sum of interior angles in a triangle add up to
, we set up the following equation:
.
Solving, we get:
.
<u>Solution 2:</u>
The Law of Sines states:
, for any triangle.
We can use this to set up a proportion with the information given:
.
Solving, we get:
.
Answer:
(x - 1)² + (y - 4)² = 25
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (1, 4), so
(x - 1)² + (y - 4)² = r²
The radius is the distance from the centre to a point on the circle
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (4, 8)
r = 
=
=
=
= 5
Hence
(x - 1)² + (y - 4)² = 5², that is
(x - 1)² + (y - 4)² = 25 ← equation of circle