Help?!

What is the measure of angle A?

antoniya [11.8K]

Answer:

A = 19.47

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hypotenuse

sin A = 2/6

Take the inverse sin of each side

sin ^-1 ( sin A) = sin ^-1 (2/6)

A =19.47122063

To the nearest hundredth

A = 19.47

3 0

3 years ago

What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

telo118 [61]

Answer:

$f(x)=-\frac{1}{8}(x-3)^2+3$

Step-by-step explanation:

We want to find the equation of the parabola with a focus of $(3,1)$ and directrix $y=5$ .

Considering the directrix, the quadratic graph must open downwards.

The equation of this parabola is given by the formula,

$(x-h)^2=4p(y-k)$ , where $(h,k)$ is the vertex of the parabola.

The axis of this parabola meets the directrix at $(3,5)$ .

Since the vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix,

$h=\frac{3+3}{2}=3$ and $k=\frac{5+1}{2}=3$ .

The equation of the parabola now becomes,

$(x-3)^2=4p(y-3)$ .

Also $|p|$ is the distance between the vertex and the directrix.

$|p|=2$

This implies that $p=-2\:or\:2$ .

Since the parabola turns downwards,

$p=-2$ .

Our equation now becomes,

$(x-3)^2=4(-2)(y-3)$ .

$(x-3)^2=-8(y-3)$ .

We make y the subject to get,

$y=-\frac{1}{8}(x-3)^2+3)$ .

This is the same as

$f(x)=-\frac{1}{8}(x-3)^2+3)$ .

4 0

3 years ago

Principal=$100 rate=5% years=3 what is the interest?

hammer [34]

Answer:

Interest would be $15 every 3 years

Step-by-step explanation:

Interest = Principal x Rate x Time

Interest = 100 x 5% x 3

Interest = 5 x 3

Interest = 15

6 0

3 years ago

A microscope can magnify the object it is looking at 10×4 times. How many times is that? (MCC.8.EE.3) A. 40,000 times B. 40 time

damaskus [11]

Answer:

10×4 = 40

10^4 = 10,000

Step-by-step explanation:

10^4 is another way to write 10⁴ = 10·10·10·10 = 10,000.

Essentially, the exponent tells you how many places to the right of the leading digit the decimal point lies (here, the number of zeros in the number).

_____

Comment on the answer choice

The appropriate answer depends on what you mean by your problem statement. Some microscopes magnify 40 times; others magnify 10,000 times, so we cannot tell the appropriate answer using our knowledge of microscopes.

3 0

3 years ago

35 POINTS AVAILABLE

aliina [53]

Answer:

Part 1) The length of each side of square AQUA is $3.54\ cm$