Answer:
P(5, 1)
Step-by-step explanation:
Segment AB is to be partitioned in a ratio of 5:3. That means the ratio of the lengths of AP to PB is 5:3. We need to find the ratio of the lengths of AP to AB.
AP/PB = 5/3
By algebra:
PB/AP = 3/5
By a rule of proportions:
(PB + AP)/AP = (3 + 5)/5
PB + AP = AP + PB = AB
AB/AP = 8/5
AP/AB = 5/8
The first part of the segment is 5/8 of the length of the segment, and the second part of the segment has length of 3/8 of the length of segment AB.
Point P is located 5/8 of the distance from point A to point B. The x-coordinate of point P is 5/8 of the difference in x-coordinates added to the x-coordinate of point A. The y-coordinate of point P is 5/8 of the difference in y-coordinates added to the y-coordinate of point A.
x-coordinate:
difference in coordinates: |14 - (-10)| = |14 + 10| = 24
5/8 of 24 = 5/8 * 24 = 15
Add 15 to the x-coordinate of point A: -10 + 15 = 5
x-coordinate of point P: 5
y-coordinate:
difference in coordinates: |4 - (-4)| = |4 + 4| = 8
5/8 of 8 = 5/8 * 8 = 5
Add 5 to the y-coordinate of point A: -4 + 5 = 1
y-coordinate of point P: 1
Answer: P(5, 1)
<h2>Solution (1) :</h2>
∠<em>y</em><em> </em>and ∠<em>x</em> are alternate interior angles . Both of these angles will be equal in measure when on two parallel lines with a transversal .
<h2>Solution (2) :</h2>
∠y and ∠x are alternate interior angles . Both of these angles will have an equal angle measure when they lie on two parallel lines with a transversal .
<h2>Solution (3) :</h2>
∠y and ∠x vertically opposite angles . Both of these angles will be equal in measure when on two parallel lines with a transversal .
<h2>Solution (4) :</h2>
∠y and ∠x are adjacent angles as well as a linear pair . These angles will sum up to form 180° .
Answer:
$60
Step-by-step explanation:
the ratio is 100:60 or 5/3
if second place pays 36, to find out how much first place pays, multiply 36 by 5/3
36 * 5/3 = 60
Answer:
25
+ 30z³ + 29z² + 12z + 4
Step-by-step explanation:
(5z² + 3z + 2)²
= (5z² + 3z + 2)(5z² + 3z + 2)
Each term in the second factor is multiplied by each term in the first factor, that is
5z²(5z² + 3z + 2) + 3z(5z² + 3z + 2) + 2(5z² + 3z + 2) ← distribute parenthesis
= 25 + 15z³ + 10z² + 15z³ + 9z² + 6z + 10z² + 6z + 4 ← collect like terms
= 25 + 30z³ + 29z² + 12z + 4
To find a circumference of a circle you have to use this expression: C = d<span>π. d stands for the diameter, so let's find that first.
To find the diameter multiply the radius by 2.
2.5 x 2 = 5
Let's rewrite our equation now. C = 5 </span>· π
<span>15.71 = </span>5 · π
The answer is 15.71
