In <span>equilateral triangle all sides are equal =x,
from right triangle that is formed by </span>apothem , height 7*3= 21
hypotenuse /opposite leg = sin angle,
hypotenuse is a side of triangle =x, opposite leg is apotheme =21,
angle in equilateral triangle =60⁰
21/x= sin 60, x*sin60=21, x=21/sin60, x=21/(√3/2), x=42/√3
Area of triangle =1/2 x*x*sin angle
Area of triangle =1/2 *42/√3*42/√3*sin 60=1/2*(42²/3)*(√3/2) ≈ 255 cm²
this is just second way to do this problem, that I did at first (either way is correct)
<span> apothem divides one side by half,
so we get small right triangle with sides x hypotenuse, x/2 is one leg , and 21 is another leg
</span>by Pythagorean theorem
x²=(x/2)² +21²
x²-x²/4=441
3x²/4=441
3x²=441*4=1764
x²=1764/3
x=42/√3
Area of triangle =1/2*base *height =1/2*42/√3 *21≈255 cm²
The name of the answer of a division is quotient .
Answer:
a. x - cd = 0
b. d = 1 / 2
Step-by-step explanation:
d = 2
c = 7
a.
c is inversely proportional to d,
c ∝ 1 / d
This inversely proportional need to be removed by using a variation / variable.
Let the variable be " x ".
c = x / d
Multiply d on both sides,
cd = x
x = cd
Subtract cd on both sides,
x - cd = 0
Hence, the equation is " x - cd = 0 ".
b.
By using the equation,
x - cd = 0
Add cd on both sides,
x = cd
c = 17, d = 2
x = 17 * 2
x = 34
To find d, when c = 68.
x = cd
34 = 68 * d
Divide 68 on both sides,
34 / 68 = d
1 / 2 = d
d = 1 / 2
f(x) = 2x^2 - 4x - 3; opens up; vertex: (1, -5); y-intercept: (0, -3)
g(x) = -x^2 + x + 1; opens down; vertex: (0.5, 1.25); y-intercept: (0, 1)
h(x) = -2x^2 + 3x - 1; opens down; vertex: (0.75, 0.125); y-intercept: (0, -1)
m(x) = x^2 - 9; opens up; vertex: (0, -9); y-intercept: (0, -9)
n(x) = -3x^2 + 7; opens down; vertex: (0, 7); y-intercept: (0, 7)
I have attached an image of the functions and their graphs.
Hope this helps!