Answer:
x = 3
Step-by-step explanation:
Angle S and Angle T are consecutive interior angles. Therefore, we know that T + S = 180°.
First, we need to solve for T, and since angles S and T are consecutive interior angles, we know that T + S = 180°. If we reorganize the equation to include the things we know (S = 105°), then we get 180° - 105° = 75°. So T is 75°.
Now, we use T = 75° and the information given to us in the picture to set up an equation. 75 = 24x + 3. Now, we can find x by isolating it. Do this by:
1) Subtracting 3 from both sides to give you 72 = 24x. We do this to get rid of the 3 from the "x side", but we must also do it to the other to keep the equation true. This moves the 3 from the "x side" to the other since we're trying to isolate x.
2) Divide 24 by both sides to get 3 = x. We use the same logic as we did for 3, except this time we divide since that's the opposite of multiplying.
In conclusion, x = 3.
Answer:
(x, y) = (4, -3)
Step-by-step explanation:
Relative to straight east with angles measured CCW, the vector is ...
5∠-36.9° = 5(cos(-36.9°), sin(-36.9°)) = 5(0.8, -0.6) = (4, -3)
Answer:
First, plot the y-intercept. The y-intercept is 1, so plot the point (0,1).
Then go up 2 points and to the right 3 points and plot a point there. (3,3)
We go to the right because the slope is positive.
Draw a line through the two points.
Step-by-step explanation:
y = mx+b
m = slope
b = y-intercept
Answer:
They are not independent
Step-by-step explanation:
Given
E = Occurrence of 1 on first die
F = Sum of the uppermost occurrence in both die is 5
Required
Are E and F independent
First, we need to list the sample space of a roll of a die

Next, we list out the sample space of F


In (1): the sample space of E is:

So:


In (2): the sample space of F is:

So:



For E and F to be independent:

Substitute values for P(E) and P(F)
This gives:


However, the actual value of P(E and F) is 0.
This is so because
and
have 0 common elements:
So:

Compare
and
.
These values are not equal.
Hence: the two events are not independent
First, let's add 30 to both sides:
4x - 30 +30 ≥ -3x + 12+30
4x ≥ -3x + 42
Now, let's add 3x to both sides
4x +3x ≥ -3x+3x + 42
7x ≥ 42
Let's divide both by 7:
x ≥ 6