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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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<h3>Answer:  0.6</h3>

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

Work Shown:

sin(angle) = opposite/hypotenuse

sin(T) = VU/VT

sin(T) = 3/5

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6 0
2 years ago
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first combine like terms so 2n + 7n which is 9n


so 9n + 7 = 13 + 3n + 8n


then combine on other side so 9n + 7 = 13 + 11n

then subtract 7 to 13 so 6

sp 9n + 6 = 11n

then subtract 9 to the other side so 2n


6 = 2n then divide all by 2

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3 0
3 years ago
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What is an equation of the line that passes through the points (0, -4) and (-4, 6)?
victus00 [196]

Answer: y=-5/2x-4

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Hope this helps you out! ☺

5 0
3 years ago
Tickets to the zoo cost $14 for adults and $10 for children. A group of 12 people went to the zoo, and the tickets cost $140. Th
hjlf
 x is the number of adults and y is the number of children.
   x + y = 12
<span>14x + 10y = 140
lets multiply the first equation by -10 and then add it to the second equation:
-10x - 10y = -120
</span>14x + 10y = <span>140
</span>-----------------------
4x + 0 = 20
x = 20/4
x = 5
then substitute in the original equation:
x + y = <span>12
</span>5 + y = <span>12
</span>y = 12 - 5
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8 0
3 years ago
Can anybody help me please I'm stuck with this question.
tekilochka [14]

Answer: 18 units

Step-by-step explanation:since its is a horizontal line x2 - x1

7 -1 = 6

line 2:

since this is a vertical line y2 - y1

7 - 3 = 4

line 3:

since this is a horizontal line x2 - x1

7 - 4 = 3

line 4:

for this we need to use the distance formula which allows us to find the distance making a third point to form a right angle triangle

point 1: (1,3)

point 2: (4,7)

point 3 (new point) : (4,3)

now we can apply the pythogorean thereum (C squared = B squared + A squared) with the following lines.

line 1: (1,3) - (4,7)

line 2: (1,3) - (4,3)

line 3: (4,3) - (4,7)

line 1 squared = line2 squared + line 3 squared

calculate length of line 2 and 3

line 1 squared = (4 - 1) squared + (7 - 3) squared

line 1 squared = 3 squared + 4 squared

line 1 squared = 9 + 16

line 1 squared = 25

root both sides

line 1 = 5

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