The diagram represents two statements: p and q

Marianna [84]

Look at the rectangle. The bottom side measures 8 miles, so the top side also measures 8 miles.

Now look at the upper right triangle. For the angle of 32 deg, the top side of the triangle is the adjacent leg of the triangle. The air distance, marked x, is the hypotenuse of the triangle.

The trig ratio that relates the adjacent leg and the hypotenuse is the cosine.

$\cos \theta = \dfrac{adj}{hyp}$

$\cos 32^\circ = \dfrac{8~miles}{x}$

$x = \dfrac{8~miles}{\cos 32^\circ}$

$x = 9.4 ~miles$

6 0

3 years ago

Select all the expressions that give the area of the figure in square units.

vodomira [7]

Where? Are the expressions?

8 0

4 years ago

2/3(9 + x)= -5( 4 - x)

MrRa [10]

Answer is 6!
Explanation ; Step by step

5 0

3 years ago

Given two sets of polar coordinates that could be used to play the given point

topjm [15]

Answer: a. (2.5, 300°) and (-2.5, 120°)

b. (4, 270°) and (-4, 90°)

<u>Step-by-step explanation:</u>

Polar coordinates are written as (r, θ) where

r is the radius
θ is the angle

In the first graph, the radius is 2.5 and the angle is 300° --> (2.5, 300°)

You can also list the radius as -2.5 at angle 120° --> (-2.5, 120°)

↓

(300 - 180)

In the second graph, the radius is 4 and the angle is 270° --> (4, 270°)

You can also list the radius as -4 at angle 90° --> (-4, 90°)

↓

(270 - 180)

5 0

3 years ago

(3 points) Determine whether each of these functions f : {a, b, c, d} → {a, b, c, d} is one-to-one and whether each of these fun

finlep [7]

Answer:

Step-by-step explanation:

Recall the following. Given a function f we say that

f is one to one if for x,y in the domain of f and f(x)=f(y) then x=y.

This means that there are no different elements in the domain of the function that are linked to the same value.

f is onto if for every y in the codomain of f, then there is an element x in the domain of f such that f(x) = y. That is, given an element y in the codomain of f, there exists and element in the domain that is linked to y.

a)

f(a) =b, f(b)=a, f(c) = c, f(d) = d. Note that this function links each element in {a,b,c,d} to different elements in {a,b,c,d}, so it is a one to one function. Since for every element x in {a,b,c,d} there is an element y in {a,b,c,d} such that f(y) = x, then this function is also onto.

b)

f(a)=b, f(b) = b, f(c) = d, f(d) = c. Note that the elements a,b are linked both to b, so this function fails to be one-to-one. Also, note that the element a has no element x in {a,b,c,d} such that f(x) = a, so this function fails to be onto.

c)

f(a) = d, f(b) = b, f(c) = c, f(d) = d.

As in b), since a and d are linked to d, then this function is not one to one. Also, since the element a has no element x in {a,b,c,d} such that f(x) = a, then it also fails to be onto.

8 0

3 years ago