Answer:
CBD is 120 degrees
Step-by-step explanation:
x=30
4x30+30+30=180
Answer:
1. x = 67.5
2. x = 2.5
3. x = 35.2
4. x = 2.0
5. x = 17.0
Step-by-step explanation:
Question 1
The proportion is set up in the form x/9 = 15/2. Multiply both sides by two to get rid of the two in the denominator on the right side. After doing so, multiply by 9 on both sides to get rid of the 9 in the denominator on the left:
2x/9 = 15
2x = 9(15)
Next solve for x:
2x = 135
x = 67.5
Question 2
The proportion is set up in the form 20/8.7 = 5.8/x. Multiply both sides by the second denominator, x, and then both sides by the first, 8.7. This will leave you with the work below:
20x/8.7 = 5.8
20x = 8.7(5.8)
Next, solve for x:
20x = 50.46
x = 2.523
Round to the nearest tenth:
x = 2.5
Question 3
The proportion is set up in the form 5/16 = 11/x. Multiply both sides by the second denominator, x, and then both sides by the first, 16. This will leave you with the work below:
5x/16 = 11
5x = 11(16)
Next, solve for x:
5x = 176
x = 35.2
Question 4
The proportion is set up in the form x/0.06 = 17/0.5. Multiply both sides by the second denominator, 0.5, and then both sides by the first, 0.06. This will leave you with the work below:
0.5x/0.06 = 17
0.5x = 17(0.06)
Next, solve for x:
0.5x = 1.02
x = 2.04
Round to the nearest tenth:
x = 2.0
Question 5
The proportion is set up in the form 29/x = 75/44. Multiply both sides by the second denominator, 44, and then both sides by the first, x. This will leave you with the work below:
29(44)/x = 75
29(44) = 75x
Next, solve for x:
1276 = 75x
x = 17.0133
Round to the nearest tenth:
x = 17.0
Answer:
Height of second tower = 17.32m
Step-by-step explanation:
I have attached a diagram depicting the question.
From the diagram, The first tower is depicted by side AEB and the second tower CD.
While d is the distance that separates the two towers and it's given as 15m.
Now, since the angle of depression of the second tower’s base is 60°, then for triangle BAC. Angle C = 60°.
Thus; using trigonometric ratios;
tan 60° = AB/AC.
This gives; AB = d*tan 60°
Similarly, for the triangle BED, BE = d*tan 30°
Since, AE = CD, thus ;
CD = AB − BE
CD = d (tan 60° − tan 30°)
CD = 15(1.7321 − 0.5774)
CD = 15 × 1.1547
CD ≈ 17.32 m.
So, height of second tower = 17.32 m
Answer:
295 minutes
Step-by-step explanation:
It is given that Speedy the Sloth drinks tea at a steady rate of 2/7 cups per hour.
Yesterday she drank 1 cup and today she drank 17/42 of a cup more than yesterday. This means today she drank 1 + 17/42 cups.
Time taken to drink 2/7 of a cup = 1 hour = 60 minutes
Time taken to drink 1 cup = 
minutes
Time taken to drink 1+17/42 cups = 
minutes
Since she drinks tea as long as she stay awakes. This means, she stayed awake for 295 minutes today.
