Answer:
MC = 4.5cm
Step-by-step explanation:
Question:
Let the isosceles triangle ABC with AB = AC = 3 cm. if the mediator of the sides AC intersects with the side BC in M and the perimeter of the triangle AMC = 12 cm. Calculate MC.
Solution:
Find attached the diagram used in solving the question.
Given:
∆ABC is an isosceles triangle (two sides and angles are equal)
AB = BC = 3cm
Perimeter of ∆AMC = 12cm
From the diagram, M cuts AC at the the middle.
AD = CD = AC/2 = 3/2
Perimeter of Right angled ∆AMD = AM + AD + MD
= 3/2 + AM +MD
Perimeter of Right angled ∆CMD =CM + CD + MD
= 3/2 + CM +MD
Right angled ∆AMD = Right angled ∆CMD
CM = AM
Therefore ∆AMC is an isosceles triangle
CM = AM (two sides of an isosceles triangle are equal)
Let CM = AM = x
Perimeter of ∆AMC = AM + CM + AC
12 = x + x + 3
12 = 2x + 3
2x = 12-3
2x = 9
x = 9/2 = 4.5
CM = AM = 4.5cm
MC = CM = 4.5cm
Answer:
Equation of the parabola: y = 3 - 7x^2
Step-by-step explanation:
The equation of the parabola with vertex (h,k) is y = a(x - h)^2 + k
Thus, the equation of this parabola is y = ax^2+3
To find a, use the fact that the parabola passes through the point (1,−4):
-4 = a(1)^2 +3
Solving this equation, we get that a = −7.
Thus, the equation of the parabola is y = 3 − 7x^2.
Answer:
50
Step-by-step explanation:
38% of x= 19
38/100 * x= 19
38x=19*100
x=1900/38
x=50
Three quarters, or 75% of an hour. An hour is 60 mins, so it can be expressed as 45/60, which simplifies into 3/4.
Answer:
option a
step-by-step explanation:
To rationalize the expresion we need to multiply and divide the expression by the conjugate of the denominator as follows
sqrt(9) / (sqrt(3) + sqrt(x)) = sqrt(9) ((sqrt(3) - sqrt(x)) / ((sqrt(3) + sqrt(x))(sqrt(3) - sqrt(x)))
3((sqrt(3) - sqrt(x)) / (3 - x)
So the result es option a:
(3sqrt(3) - 3sqrt(x)) / (3 - x)
