Answer:
Scale factor:
Actual area:
Scale drawing area:
Ratio of areas:
Scale factor 2:
Scale factor :
Scale factor :
Observation: The ratio of the areas of the triangles is the square of the scale factor of the sides
Scale factor :
Step-by-step explanation:
The scale factor is
The actual area is
The scale drawing area is
Ratio of areas:
When the scale factor of the sides was 2, then the value of the ratio of the areas was 4.
When the scale factor of the sides was , then the value of the ratio of the areas was .
When the scale factor of the sides was , then the value of the ratio of the areas was .
Observation: The ratio of the areas of the triangles is the square of the scale factor of the sides.
If the scale factor is , then the ratio of the areas is , based on the observation.
Extra: Proof of observation.
Let the legs of the actual triangle be and . Then the legs of the scale triangle are and , with being the scale factor.
The area of the actual triangle is . The area of the scale triangle is .
The ratio of these areas is , as desired.
Answer:
[See Below]
Step-by-step explanation:
<h2>For Point Slope Form:</h2>
Point slope form is:
'm' is the slope
(x1, y1) is a coordinate point.
<h3>Slope:</h3>
Slope is rise over run.
We are given the points (-1,5) and (3,-3).
The slope of the line is -2.
I will use (-1,5) as the point:
<h2>For Slope Intercept:</h2>
Slope intercept is:
'm' - Slope
'b' - y-intercept
We can use the point slope equation to convert it into slope intercept form:
<h2>For Standard Form:</h2>
Standard form is
Using out slope intercept form equation:
This is an RTD question. Here is a table based on the given information:
up/down . . . .rate . . . .time . . . .distance
upstream . . . . r-4 . . . . T . . . . 7
downstream . . . . r+4 . . . . T . . . .15
Now, rate x time = distance, so
time = distance / rate.
solve each for T and we get
T = (7/(r-4))
T = (15/(r+4))
set the times equal and we get
7%2F%28r-4%29+=+15%2F%28r%2B4%29
cross multiply to get
7r+%2B+28+=+15r+-+60
subtract 7r to get
28+=+8r+-+60
add 60 to both sides to get
88+=+8r
divide by 8 to get
r+=+8
Answer:
The north - south distance across swan lake is 8 km
Step-by-step explanation:
<em>Look to the attached figure</em>
Kendra's house and the distances between it and the North tip, southern tip of swan lake formed a right Δ
∵ Kendra lives 10 Km from the northern tip of swan lake
- That means the length of the hypotenuse of the right Δ is 10
∴ The hypotenuse of the right Δ = 10
∵ Kendra lives 6 Km from the southern tip of swan lake
- That means the length of the horizontal leg of the right Δ is 6
∴ The horizontal leg = 6
- By using Pythagoras Theorem
∵ (hypotenuse)² = (H.leg)² + (V.leg)²
∴ (10)² = (6)² + (x)²
∴ 100 = 36 + x²
- Subtract 36 from both sides
∴ 64 = x²
- Take √ for both sides
∴ 8 = x
∴ The vertical leg of the right triangle = 8
∵ x represents the north-south distance across swan lake
∴ The north - south distance across swan lake is 8 km