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sp2606 [1]
2 years ago
8

‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️‼️

Mathematics
2 answers:
SSSSS [86.1K]2 years ago
8 0
Answer:
A: 6:4
B: 9 cups of water
C: 3 cups of flour
rusak2 [61]2 years ago
8 0

Answers:

  • a) The ratio of water to flour is 3:2
  • b) 9 cups of water
  • c)  1 & 1/3 cups of flour

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

Work Shown:

Problem 1

6 cups water: 4 cups flour

(6/2) cups water: (4/2) cups flour

3 cups water: 2 cups flour

3:2 is the ratio of water to flour

In the second step, I divided both parts by the GCF 2 to reduce the ratio.

-------------------------

Problem 2

(3 cups water)/(2 cups flour) = (x cups water)/(6 cups flour)

3/2 = x/6

3*6 = 2*x ... cross multiply

18 = 2x

2x = 18

x = 18/2

x = 9

You'll need 9 cups of water

-------------------------

Problem 3

(3 cups water)/(2 cups flour) = (2 cups water)/(y cups flour)

3/2 = 2/y

3y = 2*2

3y = 4

y = 4/3

y = (3+1)/3

y = 3/3 + 1/3

y = 1 + 1/3

y = 1 & 1/3

You'll need 1 & 1/3 cups of flour

This value is a mixed number with the first "1" being the whole part, and the 1/3 being the fractional part.

This is saying you'll need 1 full cup of flour, plus an additional one-third cup of flour to go on top of that.

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y-x =2

Replace y in the second equation with the first one:

x^2 + 5x -3 - x = 2

Simplify by combining like terms:

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Subtract 2 from both sides:

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Fctor the polynomial:

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zloy xaker [14]

Part A: y=-\frac{5}{4} x+\frac{35}{2} is the equation of the line.

Part B: Anika worked 17.5 hours on day 0.

Part C: The setup time decreases with 1 hour and 15 min per day.

Explanation:

Part A: Let us find the equation of the line using the points (2,15) and (6,10)

The equation of the line is given by,

y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \cdot\left(x-x_{1}\right)

Substituting, we get,

y-15=\frac{10-15}{6-2} (x-2)

Simplifying, we have,

y-15=-\frac{5}{4} (x-2)

y-15=-\frac{5}{4} x+\frac{5}{2}

Subtracting both sides by 15, we get,

y=-\frac{5}{4} x+\frac{35}{2}

Hence, the equation of the line is y=-\frac{5}{4} x+\frac{35}{2}

Part B: To determine the number of hours Anika worked on day 0, let us substitute x = 0 in the equation of the line.

Thus, we get,

y=\frac{35}{2}\\y=17.5

Hence, Anika worked 17.5 hours on day 0.

Part C: The setup time decrease per day can be determined using the slope.

The formula for slope is given by

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

Substituting , we have,

m=\frac{10-15}{6-2}=-\frac{5}{4}

Converting the fraction into hours and minutes, we get,

-\frac{5}{4}\times60=-75 min

Since, 1 hour = 60 min

Subtracting 60 and 75 = 15 min

Thus, the setup time decreases with 1 hour and 15 min per day.

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