Answer:
A. 5
Step-by-step explanation:
The triangle will be a right triangle when the side lengths satisfy the Pythagorean theorem: the sum of the squares of the legs is equal to the square of the hypotenuse.
(x +1)^2 +x^2 = (√61)^2
x^2 +2x +1 +x^2 = 61 . . . eliminate parentheses
2x^2 +2x = 60 . . . . . . .subtract 1, collect terms
x^2 +x -30 = 0 . . . . . divide by 2, subtract 30
(x +6)(x -5) = 0 . . . . factor the quadratic
x = -6 or +5
The solution is x = 5.
_____
Side lengths cannot be negative. Solution values are values of x that make the factors zero. x+6=0 when x=-6, for example.
Answer:
a = 
b = 12
c = 
Step-by-step explanation:
Since the triangles are right triangles with 60 and 45 degree angles, their side lengths follow special triangles.
A 45-45-90 right triangle has side lengths
.
A 30-60-90 right triangle has side lengths
.
Starting with the top triangle which has a 60 degree angle, its side length 6 corresponds to a side length of 1 in the special triangle. It is 6 times bigger so its remaining sides will be 6 times bigger too.
Side a corresponds to side length
. Therefore,
.
Side b corresponds to side length 2, b = 2*6 = 12.
The bottom triangle has a 45 degree angle, its side length b= 12 corresponds to
. This means
was multiplied by
. This means that side c is
.
<u>x₁ + x₂</u> <u>y</u>₁ + <u>y</u>₂<u>
</u> 2 = M 2 = M
<u>
x + 8</u> <u>y + -2</u><u>
</u> 2 = -4 2 =6
<u>multiply both sides by 2.
</u>x+8=-8 y - 2 = 12
<u>x = -16</u> <u>y = 14
</u>
Final Answer: (-16, 14)
Answer:
Marginal cost refers to the increase or decrease in the cost of producing one more unit or serving one more customer.
Step-by-step explanation:
Definition: Marginal cost is the additional cost incurred for the production of an additional unit of output. The formula is calculated by :
Marginal Cost = (Change in the total cost)/(Change in the product output)