Identify the correct explanation for why the triangles are similar. Then find OP and MN.
Options:
A. ∠M≅∠N. Since OP¯¯¯¯¯∥MN¯¯¯¯¯¯¯, ∠LOP≅∠LMN by the Alt. Int. ∠s Thm. Therefore, △LOP∼△LMNby AA∼. OP=8 and MN=4.
B. ∠L≅∠L by the Reflex Prop. of ≅. Since OP¯¯¯¯¯∥MN¯¯¯¯¯¯¯, ∠LOP≅∠LMN by the Corr. ∠s Post. Therefore, △LOP∼△LMNby AA∼. OP=2 and MN=6.
C. ∠L≅∠L by the Reflex Prop. of ≅. Since OP¯¯¯¯¯∥MN¯¯¯¯¯¯¯, ∠LOP≅∠LMN by the Corr. ∠s Post. Therefore, △LOP∼△LMNby AA∼. OP=4 and MN=8.
D. ∠M≅∠N. Since OP¯¯¯¯¯∥MN¯¯¯¯¯¯¯, ∠LOP≅∠LMN by the Alt. Int. ∠s Thm. Therefore, △LOP∼△LMNby AA∼. OP=2 and MN=6.
Answers
Answer:
The correct explanation is option B;
B. ∠L ≅ ∠L By Reflexive Prop. ≅.
Since [tex]\overline {OP}[/tex] ║ [tex]\overline {MN}[/tex], ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6
Step-by-step explanation:
The given parameters are;
[tex]\overline {LP}[/tex] = 5
[tex]\overline {NP}[/tex] = 10
[tex]\overline {LN}[/tex] = [tex]\overline {LP}[/tex] + [tex]\overline {NP}[/tex] = 15
[tex]\overline {OP}[/tex] = x - 3
[tex]\overline {MN}[/tex] = x + 1
A two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
∠L ≅ ∠L [tex]{}[/tex] By Reflexive property of congruency
[tex]\overline {OP}[/tex] ║ [tex]\overline {MN}[/tex] [tex]{}[/tex] Given
∠LOP ≅ ∠LMN [tex]{}[/tex] By the Corresponding angles Postulate
Therefore
ΔLOP ~ ΔLMN [tex]{}[/tex] By AA similarity Postulate
Where we have that ΔLOP and ΔLMN, we get;
[tex]\overline {OP}[/tex]/[tex]\overline {MN}[/tex] = [tex]\overline {LP}[/tex]/[tex]\overline {LN}[/tex] = 5/15 = 1/3
∴ (x - 3)/(x + 1) = 1/3
3·(x - 3) = 1·(x + 1)
3·x - 9 = x + 1
3·x - x = 1 + 9 = 10
2·x = 10
x = 10/2 = 5
x = 5
[tex]\overline {OP}[/tex] = (x - 3) = 5 - 3 = 2
[tex]\overline {OP}[/tex] = 2
[tex]\overline {MN}[/tex] = x + 1 = 5 + 1 = 6
[tex]\overline {MN}[/tex] = 6
Therefore, the correct option is ∠L ≅ ∠L By Reflexive Prop. ≅.
Since [tex]\overline {OP}[/tex] ║ [tex]\overline {MN}[/tex], ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6.
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move it 1 place to the right
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Two places to the right.
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Step-by-step explanation:
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Answers
Answer:
Step-by-step explanation:
10% of 10.40=1.04
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Calculate the amount of money she receives after tax each month.
Answers
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Answers
Answer:
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Answers
Answer:
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This is not a web answer i answered myself took me some time!
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WILL GIVE BRAINLIEST AND 20 POINTS!
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yd2
Answers
Answer:
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Answer:
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Answer:
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Answers
Answer:
E. If the radius of the cone is 2 inches, the volume of the cone is 25 cubic inches.
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Step-by-step explanation:
The true statement regarding the cones should be
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There are
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6 pens in each pack of green pens
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A total of 212 pens were sold.
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Answers
Answer:
The number of green pens sold are 96 green pens
Step-by-step explanation:
The given parameters for the packs of pens sold by the shop are;
The number of pens in each pack of black pens = 2 pens
The number of pens in each pack of red pens = 5 pens
The number of pens in each pack of green pens = 6 pens
The ratio of number of packs of pens sold Black : Red : Green = 7 : 3 : 4
The total number of pens sold = 212
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Similarly, we have;
The fraction of the packs the pens sold that are green pens = 4/14 = 2/7
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x/2 × 2 + 3·x/14 × 5 + 2·x/7 × 6 = 212
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3·x/14 × 5 = The number of red pens sold
2·x/7 × 6 = The number of green pens sold
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learning task 4 answer the following show your solution using decimal and proportion methods
1. in survey the barangay had a certain number of families and 60% of them are identified and belong to the poor or marginalized sector if the total families is 150 how many families are belong to the poor sector?
2. lola remedios went to groceries to buy her daily needs if the total amount of her groceries is P 2,500.00 what would be the new amount if the store granted her 20% senior citizens discounts?
3. a passenger bus can accommodate 60 sits. During pandemic they reduce their accommodation to 50%. what is the actual sits can accommodate by the passengers?
Answers
Answer:
1. 90 families
2. P 500
3. 30 sits
Step-by-step explanation:
The computation is shown below:
1. The number of families belong to the poor sector is
= 150 ×60%
= 90 families
2. The new amount is
= P 2,500 × 0.20
= P 500
3. The actual sits accommodated by the passengers is
= 60 sits ×50%
= 30 sits
Which of the following lists the missing reasons in the respective order?
Alternate Interior Angle Theorem, ASA, CPCTC
Vertical Angle Theorem, ASA, CPCTC
Linear Pair Postulate, SSS, CPCTC
Reflexive Property, CPCTC, AAS
Answers
Answer:Vertical Angle Theorem, ASA, CPCTC
Step-by-step explanation: It's definitely a vertical Angle .
Corey spent $17.00, inculding sales tax, on 2 sanwiches cost $5.25 each and the total sales tax was $0.92. What was the cost of each drink.
Answers
Answer:
Well to start you already know the sandwich cost 5.25 and the total sales tax .92.
To find the cost of each drink
5.25 x 2= 10.50
10.50+.92=11.42
17.00-11.42= 5.58
5.58/3= 1.86
So the cost per Drink is $1.86
Step-by-step explanation:
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Answer:
30 times
Step-by-step explanation
Answer:
30
Step-by-step explanation:
Which expression is equivalent to -3(m + 5)?
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B: -3m + 5.
C: -3m - 15.
D: - 15m.
Answers
the answer is -3m - 15 .
hope it helps you
