Answer:
x = 18√3
Step-by-step explanation:
From the picture attached,
In a right triangle,
Measure of one angle = 30°
Measure of adjacent side of the angle = 9 units
We have to find the measure of Hypotenuse from the given properties.
By cosine rule,
cos(30°) = 
Therefore, measure of Hypotenuse is 18√3 units.
Answer: x = 10========================================================
Explanation:
Check out the attached image. I've basically redrawn your image and added point D. This point is the intersection of the angle bisector and segment BC. The red angle (DAC) and the green angle (DAB) are congruent.
The reason why I added point D is to help with the angle bisector theorem. This theorem states that if we have a triangle ABC, and angle A is bisected (as the diagram shows), then we can set up the following proportion
AB/BD = AC/CD
Note how AB and BD are on the left side of point D, and they form the ratio AB/BD. Similarly, AC and CD are to the right of point D so they form the ratio AC/CD. These two ratios are equal by the angle bisector theorem.
---------------------
Let's plug in the given info and then isolate x
AB/BD = AC/CD
8/(x+4) = 12/(2x+1)
8(2x+1) = 12(x+4) ... cross multiply
8(2x)+8(1) = 12(x)+12(4) ... distribute
16x+8 = 12x+48
16x+8-8 = 12x+48-8 ... subtract 8 from both sides
16x = 12x+40
16x-12x = 12x+40-12x ... subtract 12x from both sides
4x = 40
4x/4 = 40/4 ... divide both sides by 4
x = 10---------------------
Check:
8/(x+4) = 12/(2x+1)
8/(10+4) = 12/(2*10+1) ... replace every x with 10
8/(10+4) = 12/(20+1)
8/14 = 12/21
4/7 = 4/7
Answer is confirmed
Answer:
3
Step-by-step explanation:
23=5x-4
Add 4 to both sides
27=9x
Divide 9 To both sides
27/9 9x/9
x=3
I'm pretty sure the answer would be
1/5 or .2
(that's the same answer in decimal and fraction form)
