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mezya [45]
2 years ago
9

Giovanni has been hired by a local clothing accessory store to make decorative belts that have green and blue beads carefully gl

ued on them. these belts are meant for a waist size of around 28inches. each bead (green or blue) is about 1 cm wide, and Giovanni has been told to put anywhere between 70 and 74 total beats on each belt (this makes a belt with 70 to 74 cm of Beads which is 27.5 to 29.1 inches.) the store once these beads to consist of mostly green beads but also wants to have a noticeable amount of blue beads, in fact, the store has specified that the ratio of green beads to Blue beads must be at least 1: 4 and at most 1: 6
Write a system of inequalities to model this scenario.
Mathematics
1 answer:
Len [333]2 years ago
6 0

The system of inequalities that model the number and types green (g)

and blue (b) beads in a belt are as follows;

  • <u>70 < g + b < 74</u>
  • <u>10 < g < 14</u>
  • <u>56 < b < 63</u>
  • \underline{\dfrac{1}{4} \leq \dfrac{b}{g} \leq \dfrac{1}{6}}

<h3>How can s system of inequalities be written?</h3>

The waist size for the belt = ±28 inches

The <em>x</em> represent the number of beads on each belt, we have;

Number of beads per belt 70 < x < 74

Minimum ratio of blue to green beads = 1 : 4

Maximum ratio of blue to green beads = 1 : 6

Therefore;

Minimum number of blue beads = \frac{70}{1 + 6} = 10

Maximum number of blue beads = \frac{74}{1 + 4} ≈ 14

The number of blue beads, <em>b</em>, in a belt is therefore;

  • <u>10 < g < 14</u>

<u />

Minimum number of green beads = \frac{4}{1 + 4} × 70 = 56

Maximum number of green beads = \frac{6}{1 + 6} × 74 ≈ 63

The number of green beads, <em>g</em>, in a belt is therefore;

  • <u>56 < b < 63</u>

The sum of the beads on each belt = g + b = x

Therefore;

<u />

  • <u>70 < g + b < 74</u>

From the given maximum and minimum ratios, we have;

  • \underline{\dfrac{1}{4} \leq \dfrac{b}{g} \leq \dfrac{1}{6}}

Learn more about inequalities here:

brainly.com/question/371134

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Wewaii [24]

Answer:

No real solutions;

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Step-by-step explanation:

The easiest method to solve an algebraic equation is to use inverse operations. This applies to the given equation;

(2x-3)^2=-4\\

- Take the square root of both sides

\sqrt{}                

==================================================================

As one can see, the right side is a negative number. However, one cannot take the square root of a negative number and get a real result. Therefore, one must use imaginary numbers. Remember, the imaginary unit (i) represents (\sqrt{-1}).

==================================================================

2x-3=2i

- Add (3) to undo the (-3)

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2x=2i+3

- Divide by (2) to remove the coefficient of (2x)

÷2           ÷

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Answer:

See below.

Step-by-step explanation:

The y-intercept is the point where the line passes the y-axis. In this instance, that is at the point (0, 3).

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