Answer:
The value of Y is 24 km and distance from A to C to B is AC+Y=18+24=42 km
Step-by-step explanation:
Given that A highway between points A and B has been closed for repairs. An alternative route between there two locations is to travel between A and C and then from C to B. we have to find the value of Y and the total distance from A to C to B. Let AB=Z
In ΔBCD and ΔABD
∠BCD=∠ABD (∵each 90°)
∠D=∠D (∵common)
By AA similarity, ΔBCD~ΔABD
∴ their corresponding sides are proportional

Comparing last two terms, we get

⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
Hence, the roots are X=32, -50
X=-50 not possible as distance can never negative.
Hence, X=32 km
By applying Pythagoras theorem in ΔBCD we get


⇒ 
⇒ 
Hence, the value of Y is 24 km and the distance from A to C to B is AC+Y=18+24=42 km
Answer: c
Explanation: this is because the end behavior approaches negative infinity on the left side and positive infinity on the right side.
The two triangles are congruent through AA (angle-angle proportionality theorem) therefore all the sides are congruent to each other.
In this case:
2y = 5y - 7
2y - 5y = -7
-3y = -7
y = -7/-3
y = 7/3
Answer:
- Trapezoid with the area 16.5 unit²
Step-by-step explanation:
Plotted the given points to find out the figure is trapezoid.
<u>Area formula for trapezoid:</u>
<u>The length of the bases:</u>
- b₁ = DE = 3 - (-1) = 4
- b₂ = FG = 4 - (-3) = 7
<u>h is the horizontal distance between the bases:</u>
<u>The area is:</u>
- A = 1/2(4 + 7)(3) = 16.5 unit²