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:
Explanation:
Translate every verbal statement into an algebraic statement,
<u>1. Keith has $500 in a savings account at the beginning of the summer.</u>
<u>2. He wants to have at least $200 in the account by the end of summer. </u>
<u />
<u>3. He withdraws $25 a week for his cell phone bill.</u>
<u />
- Call w the number of weeks
<u>4. Write an inequality that represents Keith's situation.</u>
- Create your model: Final amount = Initial amount - withdrawals ≥ 500
With that inequality you can calculate how many week will pass before his account has less than the amount he wants to have in the account by the end of summer:
That represents that he can afford spending $ 25 a week during 12 weeks to have at least $ 200 in the account.
No matter what number you substitute for the variable, the simplification will result is a false statement.
Answer: 1111/ 1111/ 1111/ 1111/ 1111
Step-by-step explanation:
Answer:
Step-by-step explanation:
Add the 3/4 to cross it out on the left side and whatever you do to one side you do to the other side. so you add 3/4 or .75 on to 10 to get 10.75.
k-3/4=10
k=10.75
Subtract the 5/7 from the Z and subract it from -3 to get, -3.71.
Z+5/7=-3
Z=3.71
Subtract 9 from the left side and subtract 9 from the right side.
9+t/12=-3
t/12=-12
Then you would multiply by 12 from the left side and multiply by 12 from the right side.
t/12=-12
t=-144