Answer:
x=75
Step-by-step explanation:
We can use proportions to solve this problem. Put the side of the small triangle over the side of the large triangle.
42 50
------ = ----------
42+63 50+x
42 50
------ = ----------
105 50+x
Using cross products
42(50+x) = 50*(105)
2100+42x = 5250
Subtract 2100 from each side
2100-2100+42x = 5250-2100
42x =3150
Divide by 42
42x/42 = 3150/42
x = 75
Answer:
<em>The base is 24 cm long.</em>
Step-by-step explanation:
<u>Equations</u>
Let's call
b= base of the triangle
h=height of the triangle
The base is 9 cm longer than the height, thus:
b = h + 9
The area of the triangle is:


And its value is 180:

Multiplying by 2:

Operating:

Factoring:

The only valid positive solution is:
h = 15 cm
And b = h + 9 = 24
b = 24 cm
The base is 24 cm long.
The equation of the parabola is:

---------------------------
The <em>equation </em>of a parabola of vertex (h,k) and focus (0,f) is given by:

- Vertex at the origin means that
. - Focus (0,6) means that

Thus, the equation of the parabola is:



A similar problem is given at brainly.com/question/15165354
Answer:

Step-by-step explanation:
Given the expression 
According to the law of logarithm;
loga + log b = log(ab) and log a - log b = log(a/b)
The given expression becomes;
