Answer:
<u>The circumcenter is (-1 , -6.5)</u>
Step-by-step explanation:
the circumcenter is the point where the perpendicular bisectors of a triangle intersects.
See the attached figure
A(-6, - 8), B(4. – 5), C(-6,-5).
As shown at the graph ΔABC is aright triangle at C
The perpendicular bisector of AC is the line y =-6.5
The perpendicular bisector of BC is the line x = -1
The intersection between y =-6.5 and x = -1 will be the point (-1,-6.5)
<u>So, The circumcenter is (-1 , -6.5)</u>
<u>Another solution:</u>
As the graph represents a right triangle.
The circumcenter of a right triangle lies exactly at the midpoint of the hypotenuse
The hypotenuse is the line segment AB
The midpoint of AB = (A + B)/2 = [(-6, - 8) +(4. – 5)]/2 = (-2,-13)/2 = (-1 , -6.5)
So, <u>The circumcenter is (-1 , -6.5)</u>
Answer:
Sandwich sells for $4.76 .
Step-by-step explanation:
As given
It costs $2.80 to make a sandwich at the local deli shop.
To make a profit, the deli sells it at a price that is 170% of the cost.
170% is written in the decimal form
= 1.7
Thus
Sandwich selling cost = 1.7 × Cost of making
Put all the values in the above
Sandwich selling cost = 1.7 × $ 2.80
= $4.76
Therefore the Sandwich sells for $4.76 .
Answer:
The length of the hypotenuse is 2 square root of 13 ⇒ c
Step-by-step explanation:
The rule of the area of the right triangle is A = × leg1 × leg2, where
leg1 and leg2 are the sides of the right angle
∵ The area of a right triangle is 12 in²
∵ The ratio of the length of its legs is 2: 3
→ Let leg1 = 2x and leg2 = 3x
∵ leg1 = 2x and leg2 = 3x
→ Substitute them in the rule of the area above
∴ 12 = × 2x × 3x
∵ 2x × 3x = 6x²
∴ 12 = × 6x²
∴ 12 = 3x²
→ Divide both sides by 3 to find x²
∴ 4 = x²
→ Take √ for both sides
∴ x = 2
→ Substitute x in the expressions of leg1 and leg2 to find them
∴ leg1 = 2(2) = 4 inches
∴ leg2 = 3(2) = 6 inches
∵ hypotenuse =
∴ hypotenuse =
∵ The simplest form of = 2
∴ The length of the hypotenuse = 2 inches
