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Yuki888 [10]
3 years ago
5

3 cm

Mathematics
1 answer:
Roman55 [17]3 years ago
5 0

The surface area of given figure = 3×Area of rectangle + 2×area of triangle base.

Surface area = 3×6×3+2×15.6

Surface area = 85.2 cm²

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Which expression is equivalent to (2 + 6i)(5 + 2i)?
skelet666 [1.2K]

Answer:

c. -2 + 34i

Step-by-step explanation:

(2 + 6i)(5 + 2i)

c. -2 + 34i

4 0
2 years ago
A motorboat is capable of traveling at a speed of 14 miles per hour in still water. On a particular day, it took 15 minutes long
Anon25 [30]

By solving a system of equations we will find that the rate of current in the stream is S = 2 mi/h.

When the motorboat travels downstream, the total velocity will be the velocity of the motorboat in still water plus the velocity of the stream, while if the motorboat travels upstream, we have the velocity of the stream subtracted.

So upstream the speed is:

(14 mi/h - S)

Downstream the speed is:

(14 mi/h + S)

Where S is the rate of current in the stream.

We know that downstream it takes 15 minutes more to travel 12 miles, then we can write the system of equations:

(14 mi/h + S)*T = 12 mi

(14 mi/h - S)*(T - 15 min) = 12 mi

To solve this, we need to isolate one of the variables in one of the equations, I will isolate T in the first one:

T = (12 mi)/(14 mi/h + S)

Replacing that in the other equation we will get:

(14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi

Now we can solve this for S. Now we can multiply both sides by (14 mi/h + S).

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 15 min) = 12 mi*(14 mi/h + S)

Also notice that the speeds are in hours, so we can rewrite:

- 15 min = -0.25 h

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 0.25 h) = 12 mi*(14 mi/h + S)

168 mi^2/h - 12mi*S  + 49mi^2/h + 0.25h*S^2 = 168mi^2/h + 12mi*S

- 12mi*S  + 49mi^2/h - 0.25h*S^2 = 12mi*S

-24mi*S -  0.25h*S^2  + 49mi^2/h = 0

This is a quadratic equation, the solutions are:

S = \frac{24mi \pm \sqrt{(-24mi)^2 - 4*(49mi^2/h)*(-0.25h)}  }{2*-0.25h} \\\\S =  \frac{24mi \pm 25 mi  }{-0.5h}

We only take the positive solution, so we get:

S = (24 mi - 25 mi)/(-0.5 mi) = 2 mi/h

The rate of current in the stream is 2 mi/h.

If you want to learn more, you can read:

4 0
2 years ago
Do I add multiply, add, subtract ? I need help!
bazaltina [42]

Answer:

x=35

Step-by-step explanation:

you are going to want to subtract. the best thing about triangle angles is that they all add to equal 180º no matter what. so what you can do is subtract the given angles from 180. so 180-80-65. which gives us 35.

Hope this helps!

5 0
2 years ago
Read 2 more answers
Describe how you can find a co-terminal angle in radians
lyudmila [28]

Answer:

If the initial angle is given in the form or radians, add or subtract 2π instead of 360°. radians. Adding 2π to the original angle yields the positive coterminal angle. By subtracting 2π from the original angle, the negative coterminal angle has been found.

Step-by-step explanation:

5 0
2 years ago
Is 7/10 greater than 5/8
wariber [46]
Yes

7/10=.70
5/8=0.625
4 0
3 years ago
Read 2 more answers
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