Answer:
<h3>
f(x) = 6(x - 2)² + 3</h3>
Step-by-step explanation:
f(x) = a(x - h)² + k - vertex form of the equation of the parabola with vertex (h, k)
"the parabola opens upward" means: a>0
"the parabola has x = 2 as an axis of symmetry" means: h = 2
so f(x) = a(x - 2)² + k
"the parabola contains the point (1, 9)" means:
9 = a(1 - 2)² + k
9 = a(-1)² + k
9 = a + k
k = 9 - a
"the parabola contains the point (4, 27)" means:
27 = a(4 - 2)² + k
so:
27 = a(2)² + 9 - a
27 = 4a + 9 - a
3a = 18
a = 6
and k = 9 - 6 = 3
Therefore the vertex form for this parabola is:
<u> f(x) = 6(x - 2)² + 3</u>
Answer:
A. x = (20√3)/3, y = (40√3)/3
Step-by-step explanation:
The ratios of the side lengths of a 30°-60°-90° right triangle are (shortest to longest) ...
1 : √3 : 2
In this triangle, they are ...
x : 20 : y
Multiplying the first ratio by (20√3)/3, we get ...
x : 20 : y = (20√3)/3 : 20 : (40√3)/3
Then the values of the variables are x = (20√3)/3, y = (40√3)/3.
_____
The above side length ratios correspond to sin(60°) = cos(30°) = (√3)/2, cos(60°) = sin(30°) = 1/2. These are values you might have memorized.
Answer:
4 nickels
Step-by-step explanation:
The sides and angles of a triangle can be determined using trigonometry ratios
The values of x, y and z are , and
<h3>How to determine the missing values of the triangle</h3>
The upper triangle is a right triangle with an angle measure of 45 degrees.
So, the value of x is:
Next, we calculate the hypotenuse (h) of the lower triangle using:
So, we have:
Take the square roots of both sides
The value of y is then calculated using the following sine ratio
Make y the subject
Evaluate
The value of z is then calculated using the following cosine ratio
Make z the subject
Evaluate
Hence, the values of x, y and z are , and
Read more about right triangles at:
brainly.com/question/14628284
Well if you split 1/4 in half then that will give 1/8. You must also split 0.25 in half which gives 0.125
Now you can multiply that by 5 which gives 5/8. But also the fraction
Now we know that 5/8 = 0.625