For question 4, units,
For question 5, units.
Step-by-step explanation:
Step 1:
Since the given polygons are similar to each other, all the ratios of one polygon to the other will remain equal for all the values of the two similar polygons.
We take the ratio of the same sides of both polygons i.e. the ratio of the lengths or the ratio of the widths.
Step 2:
For question 4, the first rectangle has a length of 9 units while the width is 3 units.
For the second rectangle, the length is x as x is greater than the width in the first rectangle. The width is 6 units.
The ratio of the first rectangle to the second is;
So units.
Step 3:
The shapes in question 5 are made of a square and a triangle.
For the first shape, the side length is 6 units while the side of the triangle is 10 units.
For the second shape, the side length is 5 units while the side of the triangle is x units.
The ratio of the first shape to the second is;
So units.
The original price of the shirt is $25. In union city, there is a 3.2% discount. So, the discounted price of the shirt at union city is $24.20. In river city, there is a discount of 3% for the same shirt. So, the price of the shirt at river city is $24.25. Therefore, the shirt will cost $0.05 more in river city than in union city.
Answer:
the slpoe is 10,678 feet on mountrainerStep-by-step explanation:
23.994 miles is the radius of the circle. divide 1808.64 by pi and set it equal to x^2. then take the square root of both sides
Let the point_1 = p₁ = (1,4)
and point_2 = p₂ = (-2,1)
and Point_3 = p₃ = (x,y)
The line from point_1 to point_2 is L₁ and has slope = m₁
The line from point_1 to point_3 is L₂ and has slope = m₂
m₁ = Δy/Δx = (1-4)/(-2-1) = 1
m₂ = Δy/Δx = (y-4)/(x-1)
L₁⊥L₂ ⇒⇒⇒⇒ m₁ * m₂ = -1
∴ (y-4)/(x-1) = -1 ⇒⇒⇒ (y-4)= -(x-1)
(y-4) = (1-x) ⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒ equation (1)
The distance from point_1 to point_2 is d₁
The distance from point_1 to point_3 is d₂
d =
d₁ =
d₂ =
d₁ = d₂
∴
⇒⇒ eliminating the root
∴(-2-1)²+(1-4)² = (x-1)²+(y-4)²
(x-1)²+(y-4)² = 18
from equatoin (1) y-4 = 1-x
∴(x-1)²+(1-x)² = 18 ⇒⇒⇒⇒⇒ note: (1-x)² = (x-1)²
2 (x-1)² = 18
(x-1)² = 9
x-1 =
∴ x = 4 or x = -2
∴ y = 1 or y = 7
Point_3 = (4,1) or (-2,7)