1. The perimeter of a rectangle is 30 inches. If its length is three times its width, find both

The measure of angle θ is 3pi/2 . The measure of its reference angle is /, and tan θ is .

Sphinxa [80]

Answer:

Reference angle: $\frac{\pi}{2}$

$tan(\theta)=tan(\frac{3\pi}{2})$ is not defined.

Step-by-step explanation:

The angle $\theta$ goes from the positive x-axis to the negative y-axis.

Therefore the reference angle can be calculated as following:

$\frac{3\pi}{2}-\pi=\frac{\pi}{2}$

We know that $tan(\theta)$ is:

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

If $\theta=\frac{3\pi}{2}$ then $cos(\frac{3\pi}{2})=0$ , therefore $tan(\frac{3\pi}{2})$ is not defined, because the division by 0 is not defined.

8 0

3 years ago

I need help to solve this

Svetach [21]

Sorry, don't even think i've learned this yet, maybe look up a video from khan academy?

5 0

3 years ago

Please only answer if you have a serious answer not just “do your work” I’m in 18 classes and my school won’t let me out of any

enyata [817]

9514 1404 393

Explanation:

1) 2x^2 -5x -3 = 0 . . . . standard form equation

To convert this to factored form, you can look for factors of the product (2)(-3) that have a sum of -5. It can help to start by listing the ways that -6 can be factored. Since we want the sum of factors to be negative, we want to have larger negative factors.

-6 = (1)(-6) = (2)(-3)

The sums of these factor pairs are -5 (what we want) and -1 (not relevant). We can call these factors p=1 and q=-6.

If a = 2 is the leading coefficient of our standard form quadratic, we want to use these factors in the form ...

(ax +p)(ax +q)/a . . . . . factored form of the quadratic

(2x +1)(2x +(-6))/2 . . . .fill in the values we know

(2x +1)(x -3) . . . . . . . factor 2 from the second binomial

So, the factored form of the quadratic equation is ...

(2x +1)(x -3) = 0 . . . . factored form equation

__

2) f(x) = x^2 +7x +10 . . . . standard form quadratic function

Using the thinking process described above, we are looking for factors of 10 that have a sum of 7. We know those are 2 and 5. So, the factored form of the function is ...

f(x) = (x +2)(x +5) . . . . . . factored form quadratic function

The leading coefficient is 1, so we have no further work to do.

Roots, x-intercepts, zeros

The graph attached below shows this function crosses the x-axis when x=-2 and x = -5. These values of x are variously called "roots", "x-intercepts", and "zeros" of the function. They are values for which the factors and the function are zero. (x+2=0 when x=-2, for example)

Solutions

Often, we are interested in solving the equation ...

f(x) = 0

For that equation, the solutions are the zeros or x-intercepts or roots. The graph attached also shows solutions for ...

f(x) = 4

Those solutions are x = -6 and x = -1. The function value is not zero for these values of x, so the roots, x-intercepts, or zeros are not solutions to this equation.

6 0

3 years ago

A dwarf sea horse swims 3/4 inch in a minute. how many minutes would it take a seahorse to swim 1/3 of a inch?

kiruha [24]

Answer:

0.25

Step-by-step explanation:

maybe this will work .

5 0

3 years ago

Juan drove his car on a vacation trip. His odometer Read 1460.3 when he began and 1830.2 at the end. If he used 20 gallons of ga

Aleonysh [2.5K]

Answer:

Juan got 18.50 miles per gallon.

Step-by-step explanation:

We are given the following in the question:

Odometer in the beginning of trip = 1460.3 miles

Odometer at the end of trip = 1830.2

Gallons of gas used for trip = 20 gallons

Distance of trip =

= Odometer at the end of trip - Odometer in the beginning of trip

$=1830.2-1460.3\\=369.9\text{ miles}$

Thus, the trip was of 369.9 miles.

Miles per gallon =

$=\dfrac{\text{Distance cover in trip}}{\text{Gallons of gas used}}\\\\=\dfrac{369.9}{20}\\\\=18.495\approx 18.50\text{ miles per gallon}$

Thus, Juan got 18.50 miles per gallon.

5 0

3 years ago