Answer:
<h2>a = 3</h2>
Step-by-step explanation:
The slope of a line given two points can be found by using the formula

From the question the slope is - 3
To find the value of a we have

Divide both sides by - 3

We have the final answer as
<h3>a = 3</h3>
Hope this helps you
Answer:
x = 4
Step-by-step explanation:
If you do not want to read the explanation go the the next part in bold
Ok so the shorter leg of the triangle is a radius of the circle. ( This is indicated by the point in the middle of the circle.) for the hypotenuse we are given one part of the length (2) The other part also happens to be a radius ( remember that a radius is a line that starts from the center of the triangle to any point of the circumference. ) Also remember that the radius is equal to 3. That being said the hypotenuse = 2+3 which equals 5.
This triangle then happens to be a right triangle. ( A triangle formed by a tangent line and a radius is a right triangle.) This means that we can use the Pythagorean theorem to solve for x.
Below here is where the work is shown
a² + b² = c². where a and b = legs and c = hypotenuse. We are given the hypotenuse (5) and a leg (3) So we plug in what we are given and solve for the missing information. 5² = 3² + b²
5² = 25
3² = 9
we would then have 25 = 9 + b²
Next we subtract 9 from each side
25 - 9 = 16
9 - 9 cancels out
Now we have 16 = b²
finally we want to get rid of the ²
To do so we take the square root of each side

we're left with b = 4 which means that x = 4
Answer:
∠B=60°
Step-by-step explanation:
In this right traingle, using angle B, you have the opposite side which is 6√102, and the adjacent side which is 6√34. Using SOHCAHTOA this invlolves TOA so tangent B = OPPOSITE/ADJACENT or tan B = 6√102/6√34. Simplifying gives tan B=√3. You can use your calculator to solve for B by taking the inverse tangent of √3 or you can use the known trig ratios from the unit circle if you have already learned that to find that angle B is 60°
Answer:
x = 78
Step-by-step explanation:
Look at Triangle DBH. Two of its angles are known. Let y = <DHB
47 + 31 + y = 180 All triangles have 180 degrees. Combine the left.
78 + y = 180 Subtract 78 from both sides.
78-78+y = 180-78 Combine
y = 102
Notice that y + x = 180 They form a straight line.
102 + x = 180 Subtract 102 from both sides.
x = 78
You should notice that x is an exterior angle. (I didn't at first).
Exterior angles are the sum of the two remote interior angles which in this case, are 31 + 47 = 78
Much shorter and much easier.