The missing figure is attached down
Answer:
The measure of EC is 1 foot
Step-by-step explanation:
Let us revise the cases of similarity
- AAA similarity : two triangles are similar if all three angles in the first triangle equal the corresponding angle in the second triangle
- AA similarity : If two angles of one triangle are equal to the corresponding angles of the other triangle, then the two triangles are similar.
- SSS similarity : If the corresponding sides of the two triangles are proportional, then the two triangles are similar.
- SAS similarity : In two triangles, if two sets of corresponding sides are proportional and the included angles are equal then the two triangles are similar.
From the attached figure
∵ DE // BC
∴ ∠ADE ≅ ABC ⇒ corresponding angles
∴ ∠AED ≅ ACB ⇒ corresponding angles
In Δs ADE and ABC
∵ ∠ADE ≅ ABC ⇒ proved
∵ ∠AED ≅ ACB ⇒ proved
∵ ∠A is a common angle in the two triangles
∴ Δ ADE is similar to triangle ABC by AAA postulate
From the results of similarity the corresponding sides of the triangles are proportion
∴ 
∵ AD = 8 feet
∵ DB = 2 feet
∴ AB = AD + DB
∴ AB = 8 + 2 = 10 feet
∵ AE = 4 feet
By using the proportion statement above 
∴ 
By using cross multiplication
∴ 8 × AC = 10 × 4
∴ 8 AC = 40
Divide both sides by 8
∴ AC = 5 feet
∵ AC = AE + EC
∴ 5 = 4 + EC
Subtract 4 from both sides
∴ 1 = EC
∴ The measure of EC is 1 foot
Answer:
infinite solutions
Step-by-step explanation:
Answer:
A. x = -7, B. x = -8, C. x = 9, D. x = 2, E. x = -3
Step-by-step explanation:
A. 4x= -28
Divide both sides by 4.
=
. x= -7
B. x- -6= -2 -> x+6= -2
Subtraction 6 to both sides.
x- +6-6= -2-6, x= -8
C. -x+= -9 -> x= 9
D. -3x+7=1
Subtraction 7 to both sides.
-3x+7-7 =1-7 , -3x=-6
Divide both sides by -3.
=
, x= 2
E. 25x+-11= -86 -> 25x-11= -86
Add 11 to both sides.
25x-11+11= -86+11, 25x= -75
Divide both sides by 25.
=
, x= -3
2. 2x+9= -15
Subtraction 9 to both sides.
2x+9-9= -15-9, 2x= -24
Divide both sides by 2.
=
, x= 12
I don't think there's an answer.
I hope it helps you!
Answer:
50,66.7,80
Step-by-step explanation:
100/2= 50
200/3=66.7
400/5=80
Answer:
Second choice
and the last 2 choices
Step-by-step explanation:
32m/16m=2 and our constant is 3 not 2 so not choice A
4m^2/2m=2m so possible 6m/2m=3 so choice B
4m/2m=2 and our constant is 3 not 2 so not choice C
10m/5m=2 same reason as A and C
10m^2/5m=2m possible...15m/5m=3 so choice E
32m^2/16m=2m and 48m/16m=3 so this last choice too