Which proportion could be used to find the length of side b?

Mathematics

2 answers:

Svetradugi [14.3K]3 years ago

5 0

Answer: A for Apex.

Step-by-step explanation:

yan [13]3 years ago

3 0

Answer:

A) $\frac{\sin{23}}{6.2}=\frac{\sin{85}}{b}$

Step-by-step explanation:

In order to use the Law of Sines, we must have a known angle and the known side opposite it.

The only side measure we have is that of AB, which is 6.2. The angle opposite this is ∠C, which we do not have the measurement of.

We do have the measurement of ∠A and ∠B; we can use these to find the measure of ∠C. We know that the sum of the measures of the angles in a triangle is 180°; this means

m∠C = 180-(72+85) = 180-157 = 23°

This makes the first ratio in the Law of Sines

$\frac{\sin{23}}{6.2}$

We are trying to find the measure of b. This means we use the angle opposite b, ∠B; m∠B = 85°. This gives us the ratio

$\frac{\sin{85}}{b}$

Together, this gives us the proportion

$\frac{\sin{23}}{6.2}=\frac{\sin{85}}{b}$

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The length plus the width of a rectangle is 10. Let x represent the length. The equation for the area y of the

yuradex [85]

Answer:

length of rectangle = 5

width of rectangle = 5

Area of rectangle = 25

Step-by-step explanation:

Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:

$y=x\,(10-x)=10x-x^2$

Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.

Recall that the formula for the x of the vertex of a quadratic of the form :

$y=ax^2+bx+c$