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KonstantinChe [14]
3 years ago
7

at the local baseball diamond,the distance from home base to second base is 100 feet. Determine the distance from home base to f

irst base.
Mathematics
1 answer:
Archy [21]3 years ago
8 0

Answer:

  70.7 ft

Step-by-step explanation:

The triangle formed by home plate, first base, and second base is an isosceles right triangle with hypotenuse 100 ft. Then the side length (base-line distance between bases) is (100 ft)/√2 ≈ 70.7 ft.

___

For an isosceles right triangle with side lengths 1, the hypotenuse can be found from the Pythagorean theorem to be ...

  hypotenuse = √(side² + side²) = √(1²+1²) = √2

Then the diamond distances satisfy the proportion ...

  hypotenuse/side = 100 ft/(base distance) = √2/1

or ...

  base distance = (100 ft)/√2 ≈ 70.71068 ft

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A cable provider wants to contact customers in a particular telephone exchange to see how satisfied they are with the new digita
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Answer:

  a) uniform

  b) 1/2

  c) 1/1000

Step-by-step explanation:

a) "numbers with equal​ probability" have a uniform distribution.

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b) Even numbers make up 1/2 of all numbers.

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c) There are ten such numbers in the range, so the probability is ...

  10/10000 = 1/1000

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3 years ago
True of false? the slope of thia equation is zero <br>y=x+5<br>​
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false

Step-by-step explanation:

no solution

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Find the amount A accumulated after investing a principle P= $2,000 for t= 8 years at an interest rate r= 6%
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I=prt

(2000)(.06)(8)

=960
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3 years ago
7. What is the value of x to the nearest foot? *
Katena32 [7]
The answer is 6713 ft
3 0
2 years ago
Please I really need help
ohaa [14]

9514 1404 393

Answer:

  • scale factor: 3
  • rule: (x, y) ⇒ (3x +15, 3y -24)
  • center: (-7.5, 12)

Step-by-step explanation:

The scale factor can be found by comparing the length of CB to the length of RQ.

  B-C = (-2, 8) -(-4, 9) = (2, -1)

  Q-R = (9, 0) -(3, 3) = (6, -3)

The length of RQ is clearly 3 times the length of CB, so the scale factor (k) is ...

  ratio of corresponding differences = 6/2 = -3/-1 = 3 . . . . . scale factor

__

We know that for dilation about a point O, the distance from O is multiplied by the scale factor. For dilation of point B to point Q, this means ...

  k(B -O) = (Q -O)

Solving for Q, we get ...

  Q = kB -kO +O . . . . this is what our dilation rule will look like.

The quantity O-kO can be found by subtracting kB:

  Q -kB = O -kO = O(1 -k)

This is what we need for our dilation rule.

  Q -kB = (9, 0) -3(-2, 8) = (9+6, 0-24) = (15, -24)

So, our dilation rule is ...

  (x, y) ⇒ k(x, y) +(15, -24)

  (x, y) ⇒ (3x +15, 3y -24) . . . . . dilation rule

__

The center of dilation can be found from ...

  (Q -kB)/(1 -k) = O

  O = (15, -24)/(1 -3) = (-7.5, 12)

The center of dilation is (-7.5, 12).

_____

<em>Additional comments</em>

On the graph, the center of dilation can be found by drawing a line through a point and its image. (Points are always dilated along a line through the center of dilation.) The intersection of two such lines is the center of dilation.

On this graph, the center is just above the top edge of the chart, at point (-7.5, 12). You can see this if you carefully draw lines BQ and AP.

You usually have coordinates for two original points and two image points, so finding the scale factor the way we did is not difficult. If you just have one point on the original and the image, the scale factor is found by finding their distances from the center of dilation. Each image point is k times as far as each original point from that center.

7 0
2 years ago
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