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olga nikolaevna
7 days ago
9

Point Q is the centroid of △ABC. QE = _____

Mathematics
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In the diagram, DG = 15, GF = 5, EH = 12, and DE = 8. To prove that △DFE ~ △GFH by the SSS similarity theorem using the informat
lawyer [12517]

Answer: C) HF measures 4 units and GH is 2 units.

Step-by-step explanation:

The SSS similarity theorem asserts that triangles are similar if the lengths of their corresponding sides are in proportion.

For triangles ΔDFE and ΔGFH:

DG equals 15, GF is 5, EH equals 12, and DE is 8.

To demonstrate the similarity of ΔDFE and ΔGFH according to the SSS similarity theorem, we require:

\frac{DF}{GF}=\frac{FE}{FH}=\frac{DE}{GH}\\\\\Rightarrow\frac{DG+GF}{GF}=\frac{FH+EH}{FH}=\frac{DE}{GH}\\\\\Rightarrow\frac{5+15}{5}=\frac{12+HF}{FH}=\frac{8}{GH}\\\\\Rightarrow\frac{20}{5}=\frac{12+HF}{FH}\ and\ \frac{20}{5}=\frac{8}{GH}\\\\\Rightarrrow4HF=12+HF\ and\ GH=\frac{8}{4}\\\\\Rightarrow3HF=12\ and\ GH=2\\\\\Rightarrow HF=4\ and\ GH=2

Thus, to confirm that △DFE is similar to △GFH utilizing the SSS similarity theorem and the data from the diagram, it is essential to establish that HF measures 4 units and GH measures 2 units.

5 0
2 months ago
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A Medical company tested a new drug on 100 people for possible side effects. This table shows the results...
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p(side effects|child) = 0.44 p(side effects|adult) = 0.14 Conclusion: children are significantly more likely to experience side effects compared to adults. Step-by-step explanation: I just completed it on apex. Good luck!
8 0
1 month ago
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Ms. Gallegos burns 236 calories riding her bike each hour. She wants to burn more than 590 calories riding her bike at the same
Svet_ta [12734]

Response:

354

Detailed explanation:

5 0
2 months ago
The average length of time that three lawn-service mowers operate on a given day is 930 minutes. None of the mowers operates for
AnnZ [12381]

Answer:

The answer is A. 990.

Step-by-step explanation:

To determine the maximum duration that any of the mowers can run.

The three lawn-service mowers have an average operating time of 930 minutes.

Thus, the overall duration for the three lawn mowers is 930\times 30=2790\ minutes.

The shortest time any mower runs is 900 minutes.

To find the longest operating time of any mower:

Let x represent the maximum operating time for any of the mowers.

Since any of the mowers works the longest time.

Consequently, the remaining two mowers operate at the minimum time.

Based on the question:

x+900+900=2790

x+1800=2790

After subtracting 1800 from both sides:

x=2790-1800

x=990.

Thus, the maximum potential operating time for any mower is 990 minutes.

Consequently, the answer is A. 990.

3 0
3 months ago
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