Answer:
Step-by-step explanation:
<u>Given line:</u>
<u>Convert the equation into slope-intercept form:</u>
- x - 4y = 20
- 4y = x - 20
- y = 1/4x - 5
It has a slope of 1/4.
Parallel lines have equal slopes.
<u>Find the parallel line lines that passes through the point (2, - 5):</u>
<u>Substitute x and y values to work out the value of b:</u>
- - 5 = 1/4*2 + b
- - 5 = 1/2 + b
- b = - 5 - 1/2
- b = - 11/2
<u>The line is:</u>
<u>Covert this into standard form:</u>
- y = 1/4x - 11/2
- 4y = x - 22
- x - 4y = 22
| u | = √(2² + (-1²)) = √5
| v | = √ ( 1² + (-8)² = √65
cos (u,v) = ( u * v ) / (| u | * | v |) =
(2 * 1 + ( -1 ) * ( - 8 )) / √5 √ 65 = (2 + 8) / √5 √65 = 10 / (√5 √ 65 )
The length of a larger diagonal:
d 1² = | u |² + 2 |u| |v| + | v |² = 5 + (2 √5 √65 * 10 / √5 √65 )+65
d 1² = 70 + 20 = 90
d 1 = √ 90 = 3√10
d 2² = 70 - 20 = 50
d 2 = √50 = 5√2
Answer:
The lengths of the diagonals are: 3√10 and 5√2 .
Given:
It is given that,
PQ ⊥ PS and
∠QPR = 7x-9
∠RPS = 4x+22
To find the value of ∠QPR.
Formula
As per the given problem PR lies between PQ and PS,
So,
∠QPR+∠RPS = 90°
Now,
Putting the values of ∠RPS and ∠QPR we get,
or, 
or, 
or, 
or, 
Substituting the value of in ∠QPR we get,
∠QPR = 
or, ∠QPR = 
Hence,
The value of ∠QPR is 40°.
Step-by-step explanation:
d=20
r=10
π=3
If you really want to figure this out you make an equation to solve for the time
let's let
x = time from Elena to Jada and
x = time from Jada to Elena
12 then the equation
12 = 5x +3x
would help figuring out their distance say for one of them
12 = x(5+3)
12/8 = x
1.5 = x
1. 5 hours they will meet up
