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kenny6666 [7]
2 years ago
13

The length of the minute hand is 150% of the length of the hour hand. In 1 hour, how much farther does the tip of the minute han

d move than the tip of the hour hand? Round to the nearest hundredth.
The length of the minute hand is 150% of the length of the hour hand.
Mathematics
1 answer:
tatiyna2 years ago
5 0

Answer:

17(pi)r/6

Step-by-step explanation:

Since neither hand length is known, you can have an answer in terms of one of the hands, but you cannot get just a number.

Let r = the length of the hour hand.

Then, the length of the minute hand is 150% of r = 1.5r.

The minute hand is the radius of the circle drawn by the tip of the minute hand. In 1 hour, the minute hand rotates one full revolution, so the tip of the minute hand moves the circumference of the circle drawn by the tip of the minute hand.

Now we find the circumference of the circle of the tip of the minute hand.

C = 2 * pi * r,

but the radius here is 1.5r, so we get

C_minute_hand =  2 * pi * (1.5)r

C_minute_hand = 3(pi)r

The hour hand rotates a full revolution in 12 hours, so it rotates 1/12 of a revolution in 1 hour. The radius is r.

C_hour_hand = 2 * pi * r * 1/12

C_hour_hand = (pi)r/6

The difference in how much each tip travels is

3(pi)r - (pi)r/6 = (pi)r(3 - 1/6) = 17(pi)r/6

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kkurt [141]

Answer:

20. x = 5, y = -2

21. x = 11, y = 12

22. x = 22, y = 11

23. x = 11, y = 10

Step-by-step explanation:

20. Opposite sides in the parallelogram are congruent, so

2y+18=3x-1\\ \\6x-3=17-5y

Solve this system of two equations:

\left\{\begin{array}{l}2y-3x=-19\\ \\6x+5y=20\end{array}\right.

Multiply the first equation by 2 and add two equations:

2(2y-3x)+6x+5y=2\cdot (-19)+20\\ \\4y-6x+6x+5y=-38+20\\ \\9y=-18\\ \\y=-2

Substitute it into the first equation:

2\cdot (-2)-3x=-19\\ \\-3x=-19+4\\ \\-3x=-15\\ \\x=5

21. Opposite angles in the parallelogram are congruent, so

11x+5=10y+6

Consecutive angles are supplementary, so

6x-y+11x+5=180^{\circ}

Solve this system of two equations:

\left\{\begin{array}{l}11x-10y=1\\ \\17x-y=175\end{array}\right.

From the second equation

y=17x-175

Substitute it into the first equation:

11x-10(17x-175)=1\\ \\11x-170x+1750=1\\ \\-159x=-1749\\ \\x=11\\ \\y=17\cdot 11-175=187-175=12

22. Opposite angles in the parallelogram are congruent, so

2x-5=3y-12

Consecutive angles are supplementary, so

2x-5+7y+x=180^{\circ}

Solve this system of two equations:

\left\{\begin{array}{l}2x-3y=-7\\ \\3x+7y=185\end{array}\right.

From the first equation

x=-3.5+1.5y

Substitute it into the second equation:

3(-3.5+1.5y)+7y=185\\ \\-10.5+4.5y+7y=185\\ \\-105+45y+70y=1,850\\ \\115y=1,850+105\\ \\115y=1,955\\ \\y=17\\ \\x=-3.5+1.5\cdot 17=22

23. Opposite sides in the parallelogram are congruent, so

2x+9=4y-9\\ \\3x-5=2y+8

Solve this system of two equations:

\left\{\begin{array}{l}2x-4y=-18\\ \\3x-2y=13\end{array}\right.

Multiply the second equation by 2 and subtract it from the first equation:

2x-4y-2(3x-2y)=-18-2\cdot 13\\ \\2x-4y-6x+4y=-18-26\\ \\-4x=-44\\ \\x=11

Substitute it into the first equation:

2\cdot 11-4y=-18\\ \\-4y=-18-22\\ \\-4y=-40\\ \\y=10

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3 years ago
What is GC? A.9 B.12 C.13 D.14
Kazeer [188]

Answer:

D

Step-by-step explanation:

For the median GC, the distance from the vertex to the centroid G is twice as long as the distance from the centroid to the midpoint, that is

GC = 2 GD = 2 × 7 = 14 → D

5 0
3 years ago
Is it necessary to have a common denominator when you multiply two fractions? Explain.
Softa [21]

It is not necessary to have a common denominator when you multiply two fractions

<h3>How to determine the true statement?</h3>

The statement is about the relationship between the denominator of fractions when they are multiplied

Take for instance, we have the following fractions

a/b and x/y

In the above fractions, we have

Numerator = a and x

Denominator = b and y

Where b and y do not have the same value

When they are multiplied, we have

Product  = ax/by

The denominators do not have the same value

And we were able to calculate the product

This means that the fraction denominator do not have to be common

Read more about fractions at

brainly.com/question/1622425

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7 0
1 year ago
Jessica was given the area and the length of the base of a triangle. A = 17.5 units, b = 5 units. She solved the formula for are
pychu [463]

Answer:

She messed up the equation, A= B x h, she changed it midway, and also, you need to add the one half to make the equation valid

Step-by-step explanation:

A=1/2 x b xh

17.5 = 1/2 x 5 x h

35=5h     (multiply both sides by 2 to get rid of one half)

35/5 = 5h/5

7=h

The height of the triangle is 7 units

Please mark me brainliest, it really helps!

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2 years ago
Last week, Mr. Thomas rode his bike 49 miles. This week, Mr. Thomas rode his bike 14 miles less than he did last week. Part A. M
soldi70 [24.7K]
Part A
49-14 = 35 
<span>35/7 = 5 </span>

Part B
5 miles each day

Part C
<span>49+35 = 84 </span>
<span>84+40 = 124, which is a good estimate and it is reasonable</span>
7 0
3 years ago
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