Answer:
5.7
Step-by-step explanation:
The altitude divides right triangle ABC into similar right triangles ADB and BDC. The ratios of short leg to long leg will be proportional in these similar triangles, so you have ...
AD/BD = BD/CD
Cross multiplying gives ...
AD·CD = BD²
(x+3)(2x+3) = 5²
2x² +9x = 16 . . . . . perform the multiplication, subtract 9
2(x² +4.5x) = 16
2(x² +4.5x +2.25²) = 16 +2(2.25²) . . . . . add 2(2.25²) to complete the square
2(x +2.25)² = 26.125 . . . . . write as a square
x +2.25 = √13.0625 . . . . . .divide by 2, take the positive square root
x = -2.25 +√13.0625 . . . . subtract 2.25 to find x
We want the value of CD, so ...
CD = 2x +3 = 2(-2.25 +√13.0625) +3
CD = -1.5 +2√13.0625 ≈ 5.7284
The length of CD is about 5.7 units.
In order for two lines to be perpendicular, their slopes must multiply together to equal to negative one
So we do negative one divided by 2/5 to get the slope of the red line
Which is -5/2
To check, we do 2/5 multiplied by -5/2 which equals to -1 so our answer is correct
Answer:
paul will spend 33
Step-by-step explanation:
66-43
Answer:
Step-by-step explanation:
here you go mate
step 1
x-6 = 5(x + 2) equation/Question
step 2
x-6 = 5(x + 2) simplify
x+(-)6=5x+10
x-6=5x+10
step 3
x-6=5x+10 subtract 5x
-4x-6=10
step 4
-4x-6=10 add 6
-4x=16
step 5
answer
x=-4
<u><em>Answer:</em></u>
Exact volume = 294π in³
Approximate volume = 923.6 in³
<u><em>Explanation:</em></u>
<u>The volume of a cylinder can be calculated using the following rule:</u>
volume = πr²h
where r is the radius and h is the height of the cylinder
<u>In the given cylinder:</u>
radius = r = 7 in
height = h = 6 in
<u>Substitute with the givens in the formula to get the volume:</u>
Volume of cylinder = πr²h = π(7)²(6) = 294π in³ ≈ 923.6 in³ to the nearest tenth
Hope this helps :)
