Answer:
x = 35°
Step-by-step explanation:
The question is as following
cos x = sin(20 + x)° and 0° < x < 90° , find X?
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cos x = sin(20 + x)°
sin and cos are co-functions,
which means that: cos x = cos [90 - (20 + x)]
∴ x = 70 - x
∴ 2x = 70
∴ x = 35°
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Note: cos θ = sin ( 90 - θ )
Answer:
The slope of a line that includes the points (4, -2) and (5, 0) is 2
Step-by-step explanation:
You know that the formula y - y1 = m(x - x1) is the point-slope form of the equation of a line where m is the slope of a line.
The line must include the points (4, -2) and (5, 0). So, being:
- (x,y)= (4,-2)
- (x1,y1)= (5, 0)
and replacing in the point-slope form of the equation of a line:
-2-0=m(4-5)
You solve the equation for m and get:
-2=m*(-1)

m=2
<u><em>The slope of a line that includes the points (4, -2) and (5, 0) is 2</em></u>
Remember how the tangent function is defined as

Now where exactly are the vertical assymptotes? Well, where cosx = 0, because anything over 0 is undefined, and where a value is undefined, you are required to draw a vertical assymptote.
Now where exactly are the x interecepts? Well, where sinx = 0, because remember, an x-intercept is where y = 0, or where it crosses the x-axis, meaning where the tangent function is equal to 0.
So the x-intercepts are at where sinx = 0.
There are many ways to check if the point (1,3) is a solution to the linear equation
.
Let us check it by expressing y in terms of x.
The given expression is 5x-9y=32. If we add -5x to both sides we will get:

Multiplying both sides by -1 we will get:

In order to isolate y, we will divide both sides by 9 to get:

Now let us plug in the given value of x=1 from the point (1,3). This should give us y=3. Let us see if we get y=3 when we plug x=1 in the above equation.


Thus, we see that when x=1, y=-3 and that
and hence we conclude that the point (1,3) is not a solution to the original given linear equation 5x-9y=32.
For a better understanding of the explanation given here a graph has been attached. As can be seen from the graph, (1,3) does not lie on the straight line that represents 5x-9y=32, but (1,-3) does lie on it as we had just found out.
Answer:
18
Step-by-step explanation:
1/3 * 18 = 6 or 6/(1/3) = 18 or 6 * 3 =18