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2 years ago

The scale factor to dilate Triangle ABC to Triangle DEF is _.

Mathematics

1 answer:

zaharov [31]2 years ago

3 0

1/2

If ABC ~ DEF then 12/6, 16/8, and 18/9 would equal 2
BUT since we are going from a large triangle to a small triangle, our answer needs to be less then one, making our answer 1/2

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Sally is training for a marathon. She goes for a run every Tuesday and

nikdorinn [45]

Speed = distance / time

Tuesday: speed = 2.4km / 18 minutes = 0.13 km per minute

Friday: speed = 1.8 km / 12 minutes = 0.15 km per minute

0.15 is larger than 0.13 so she ran faster on Friday.

3 0

2 years ago

Read 2 more answers

How to find the central angle of a regular polygon

Annette [7]

Answer:

I hope this helps

Step-by-step explanation:

Central angle of a regular polygon:

The central angle of a polygon is the angle made at the center of a polygon by any two adjacent vertices as shown in the figure below.

In the above figure, the angles a, b, c, d, e and f are the central angles of the hexagon. There are 6 central angles in a hexagon. The number of central angles in a polygon is always equal to the number of sides of the polygon.

As you can see in the figure above, all the central angles of the polygon together will always form a complete circle. Hence the central angles add up to 360° in all polygons. Since a regular polygon has all equal sides, the central angles in a regular polygon are also equal.

So to find the measure of the central angles of a regular polygon follow the steps below:

First identify the number of sides ‘n’.

Then divide 360° by n.

For example: say you need to find the central angle of a regular pentagon.

First identify the number of sides ‘n’: here n = 5

Then divide 360° by n: 360° ÷ 5 = 72°.

Conversely, you can also find the number of sides of a regular polygon, when the central angle is given, by dividing 360 by the central angle.

Note: In the case of an irregular polygon, since there is no clear center for an irregular polygon, it has no central angle.

3 0

3 years ago

James has a piece of construction paper with a length of 9/10 feet and a width of 2/3 feet.

creativ13 [48]

Area = length x width

When you multiply fractions, multiply top number by top number and bottom number by bottom number:

9/10 x 2/3 = (9 x 2) / (10 x 3) = 18/30 this can be reduced by dividing both numbers by 6:

18/30 reduces to 3/5

Answer: 3/5 square feet

7 0

2 years ago

Read 2 more answers

We are standing on the top of a 1680 ft tall building and throw a small object upwards. At every second, we measure the distance

MAVERICK [17]

Answer:

a) The height of the small object 3 seconds after being launched is 2304 feet.

b) The small object ascends 128 feet between 5 seconds and 7 seconds.

c) The object will take 6 and 10 seconds after launch to reach a height of 2640 feet.

d) The object will take 21 seconds to hit the ground.

Step-by-step explanation:

The correct formula for the height of the small object is:

$h(t) = -16\cdot t^{2}+256\cdot t+1680$ (1)

Where:

$h$ - Height above the ground, measured in feet.

$t$ - Time, measured in seconds.

a) The height of the small object at given time is found by evaluating the function:

$h(3\,s)= -16\cdot (3\,s)^{2}+256\cdot (3\,s)+1680$

$h(3\,s) = 2304\,ft$

The height of the small object 3 seconds after being launched is 2304 feet.

b) First, we evaluate the function at $t = 5\,s$ and $t = 7\,s$ :

$h(5\,s)= -16\cdot (5\,s)^{2}+256\cdot (5\,s)+1680$

$h(5\,s) = 2560\,s$

$h(7\,s)= -16\cdot (7\,s)^{2}+256\cdot (7\,s)+1680$

$h(7\,s) = 2688\,s$

We notice that the small object ascends in the given interval.

$\Delta h = h(7\,s)-h(5\,s)$

$\Delta h = 128\,ft$

The small object ascends 128 feet between 5 seconds and 7 seconds.

c) If we know that $h = 2640\,ft$ , then (1) is reduced into this second-order polynomial:

$-16\cdot t^{2}+256\cdot t-960=0$ (2)

All roots of the resulting equation come from the Quadratic Formula:

$t_{1} = 10\,s$ and $t_{2}= 6\,s$

The object will take 6 and 10 seconds after launch to reach a height of 2640 feet.

d) If we know that $h = 0\,ft$ , then (1) is reduced into this second-order polynomial:

$-16\cdot t^{2}+256\cdot t +1680 = 0$ (3)

All roots of the resulting equation come from the Quadratic Formula:

$t_{1} = 21\,s$ and $t_{2} = -5\,s$

Just the first root offers a solution that is physically reasonable.

The object will take 21 seconds to hit the ground.

8 0

2 years ago

What is the area of the rhombus (figure only show one part of the diagonals)

Tomtit [17]

Answer:

60 cm^2 (dark blue)

Step-by-step explanation:

Since a rhombus's diagonal bisect each other, the diagonal's full length is 10 and 12. From there the area is 10*12 / 2 which is 60

5 0

3 years ago