Use 10 for m. Then find the value of the expression 3.5m.
2 answers:
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Answer:
The length of AE is 20 units.
Step-by-step explanation:
Given two segments AD and BC intersect at point E to form two triangles ABE and DCE. Side AB is parallel to side DC. A E is labeled 2x+10. ED is labeled x+3. AB is 10 units long and DC is 4 units long.
we have to find the length of AE
AB||CD ⇒ ∠EAB=∠EDC and ∠EBA=∠ECD
In ΔABE and ΔDCE
∠EAB=∠EDC (∵Alternate angles)
∠EBA=∠ECD (∵Alternate angles)
By AA similarity, ΔABE ≈ ΔDCE
therefore,
⇒
⇒
⇒
Hence, AE=2x+10=2(5)+10=20 units
The length of AE is 20 units.
Answer:
14 pounds
Step-by-step explanation:
The given equations can be solved for y by substituting for x. The first equation is convenient for writing x in terms of y.
<h3>Solution</h3>x = 20 -y . . . . . . . subtract y from the first equation
7(20 -y) +5.5y = 119 . . . . . substitute for x in the second equation
140 -1.5y = 119 . . . . . . . . simplify
21 = 1.5y . . . . . . . . . . . add 1.5y -119 to both sides
14 = y . . . . . . . . . . . .divide by 1.5
14 pounds of soy nuts should be used in the mixture.
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<em>Additional comment</em>
There are many ways to solve a system of two linear equations. The attachments shows a matrix solution using a suitable calculator. It tells us that x=6 and y=14, as we found above.
