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solmaris [256]
3 years ago
9

Raphael graphed the functions g(x) = x + 2 and f(x) = x – 1. How many units below the y-intercept of g(x) is the y-intercept of

f(x)?

Mathematics
2 answers:
pantera1 [17]3 years ago
8 0

Answer:

The distance between y-intercepts of f(x) and g(x) = 3 units

Step-by-step explanation:

For better understanding of the solution, see the plotted graph which is attached below :

f(x) = x - 1

g(x) = x + 2

Now, to find the distance between the y - intercepts of f(x) and g(x), First find the y-intercepts of both the given functions

y-intercepts of f(x) = x - 1

At y-intercept the x-coordinate = 0

⇒ y = 0 - 1

⇒ y = -1

y-intercepts of g(x) = x + 2

At y-intercept the x-coordinate = 0

⇒ y = 0 + 2

⇒ y = 2

Now, distance between the two intercepts = 2 - (-1)

                                                                        = 2 + 1

                                                                        = 3

Hence, the distance between y-intercepts of f(x) and g(x) = 3 units

muminat3 years ago
3 0
These functions are in the form y=mx+b
Therefore, we know that in g(x) = x+2, the y-intercept is 2. 
For f(x) = x-1, the y-intercept is -1. 
Now find the difference between them. 
2-(-1)= 3
The y-intercept for f(x) is 3 units below g(x)
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DENIUS [597]

9514 1404 393

Answer:

  • 52°: angles 4, 13, 18
  • 128°: angles 1, 3, 14, 17
  • 44°: angles 5, 12, 15
  • 136°: angles 2, 6, 11, 16
  • 84°: angles 7, 10
  • 96°: angles 8, 9

Step-by-step explanation:

Where a transversal (t or u) crosses parallel lines (m and n), there are four angles formed at each intersection. Corresponding and vertical angles are congruent.

Angles in a linear pair are always supplementary. Of course, the angles interior to a triangle always total 180°. These facts let you find the relationships of all the angles in the figure.

Angle 13 corresponds to the given angle 52°, so has the same measure. Angles 4 and 18 are vertical angles with respect to those, so also have the same measure. Angles 1 and 3, 14 and 17 are supplementary to the ones just named, so all have measure 128°.

In the same way, angles on the other side of the figure can be found from the one marked 44°. Angles 5, 12, and 15 also have that measure; and angles 2, 6, 11, and 16 are supplementary, 136°. Angles 7 and 10 finish the triangle interior so that its sum is 180°. That means they are 180° -52° -44° = 84°. Of course, angles 8 and 9 are the supplement of that value, 96°.

In summary:

  • 52°: angles 4, 13, 18
  • 128°: angles 1, 3, 14, 17
  • 44°: angles 5, 12, 15
  • 136°: angles 2, 6, 11, 16
  • 84°: angles 7, 10
  • 96°: angles 8, 9
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3 years ago
Consider the sequence 3, 6, 12, 24, 48, .... (a) Write a recursive rule to represent the sequence. (b) Write an explicit rule to
saveliy_v [14]

Answer:

  a. a[1] = 3; a[n] = 2a[n-1]

  b. a[n] = 3·2^(n-1)

  c. a[15] = 49,152

Step-by-step explanation:

Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.

The first term is 3, and the common ratio is 2.

<h3>(a)</h3>

The recursive rule is ...

  a[1] = 3

  a[n] = 2×a[n-1]

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<h3>(b)</h3>

The explicit rule is ...

  a[n] = a[1]×r^(n-1)

  a[n] = 3×2^(n-1)

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<h3>(c)</h3>

The 15th term is ...

  a[15] = 3×2^(15-1) = 3×2^14

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Answer:

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x = (41285 * 11.2)/50

x = 9247.84

the number of women is 9247.84 or if we round it since we can not have 0.84 of a woman employee, is it 9248.

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