Answer:
1) b and m
2) m∠8=m∠6
3) 160°
4)x=60°
Step-by-step explanation:
1) all straight lines sum to 180°
subtract the angles given from 180°
the other angle for b is 25°, while the other angle for m is 155°
so we can see that the angles for both lines are the same, hence they are parallel.
2) ∠8 should be the same as ∠6, ∠10 should be the same as ∠3, ∠7 same as ∠5 and ∠9 same as ∠4
in the options we are only given '∠8 should be the same as ∠6' as the correct answer, so we take that.
3) from the image we can see that both horizontal lines are parallel to each other, so both angles on the lines should be same, so ∠CET would be (2x-16)°
(2x-16)°+(7x+20)°=180°
we get x=20(nearest whole number)
∠CED=7x+20=7(20)+20=160°
4) since we need to show that they are parallel,
(2x+30)°=(4x-90)°
2x-4x=-90-30
-2x=-120
x=60
we then plug the x value into the two equations, in which we get 150° for both the angles [2(60)+30=4(60)-90] ⇒ (150=150)
I hope u understand it the way I put it.
Answer:
50.4 km (Answer B)
Step-by-step explanation:
From this information, we are able to create a proportion, 2cm/21km= 4.8cm/x km (x representing the actual distance). After cross-multiplying and simplifying, you get an answer of 50.4km. Hope this helps!
Answer:
60 ships.
Step-by-step explanation:
Let the total number of ships in the naval fleet be represented by x
One-third of the fleet was captured = 1/3x
One-sixth was sunk = 1/6x
Two ships were destroyed by fire = 2
Let surviving ships be represented by y
One-seventh of the surviving ships were lost in a storm after the battle = 1/7y
Finally, the twenty-four remaining ships sailed home
The 24 remaining ships that sailed home =
y - 1/7y = 6/7y of the surviving fleet sailed home.
Hence
24 = 6/7y
24 = 6y/7
24 × 7/ 6
y = 168/6
y = 28
Therefore, total number of ships that survived is 28.
Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4
Total number of ships in the fleet(x) =
x = 1/3x + 1/6x + 2 + 28
Collect like terms
x - (1/3x + 1/6x) = 30
x - (1/2x) = 30
1/2x = 30
x = 30 ÷ 1/2
x = 30 × 2
x = 60
Therefore, ships that were in the fleet before the engagement were 60 ships.
Answer:B
Step-by-step explanation:
4E and LA are right angles; therefore, these angles are congruent since all right
angles are congruent. Is - 15 over 5 and 12 over 4shows the corresponding sides are proportional;
therefore, ABC ~ AEDC by the SSS Similarity Postulate.
2. 4/6 , 6/9
3. 2/4 , 3/6
4. 8/10 , 12/15
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