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netineya [11]
3 years ago
6

Jerry was making two different types of cookies. One recipe needed 3/4 cups of sugar and the other needed 2/3 cups of sugar. How

much sugar did he need to make both recipes.!!!
Mathematics
2 answers:
Bad White [126]3 years ago
6 0

u need to first find a common denominator which would be 12 cause 4 and 4 which are the denominators both go into 12 he would need 1and 5/12
inn [45]3 years ago
5 0
Both recipes would add up to 1 5/12 this is using the black widow way
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Beth is knitting mittens and gloves. Each pair must be processed on three machines. Each pair of mittens requires 2 minutes on M
anygoal [31]

Answer:

Two mittens and seven gloves  

Step-by-step explanation:

I presume you are asking how many mittens and how many gloves Beth should knit to produce the most profit.

Let x = the number of mittens and

Let y = the number of gloves

1. Summarize the information in a table

\begin{array}{cccc}&\textbf{Mittens}& \textbf{ Gloves} & \textbf{Minutes Available}\\\text{Machine A} & 2 & 4 & 32\\\text{Machine B} & 2 & 2 & 18\\\text{Machine C} & 4 & 1 & 24\\\text{Unit profit} & $8.00 & $10.00 & \\\end{array}

2. List the constraints

(a) Beth can't make a negative number of mittens, so

x ≥ 0.

(b) Neither can she make a negative number of gloves, so

y ≥ 0.

(c) The total number of minutes on Machine A cannot exceed 32, so

2x + 4y ≤ 32.

(d) The total number of minutes on Machine B cannot exceed 18, so

2x + 2y ≤ 18.

(e) The total number of minutes on Machine C cannot exceed 24, so

4x +   y ≤ 24.

3. Write an equation for the profit

P = 8.00x + 10.00y

4. Graph the constraints to identify the feasible region

See the figure below. The feasible region is the dark green area where all three regions overlap.

5. Determine the points of intersection between the constraints  

(i) Constraints (c) and (d)

\begin{array}{rcr}2x + 4y  & = & 32\\2x + 2y & = & 18\\2y & = & 14\\y & = & \mathbf{7}\\2x + 14 & = & 18\\2x & = &4\\x & = & \mathbf{2}\\\end{array}\\

The lines intersect at (2,7).

(ii) Constraints (c) and (e)

\begin{array}{rcl}2x + 4y  & = & 32\\4x + y & = & 24\\4x + 8y & = & 64\\7y & = & 40\\y & = & \mathbf{\dfrac{40}{7}}\\\\4x + \dfrac{40}{7} & = & 24\\\\4x & = &24 - \dfrac{40}{7}\\\\4x & = & \dfrac{128}{7}\\\\x & = & \mathbf{\dfrac{32}{7}}\\\\\end{array}\\

The lines intersect at (27/7,32/7).

(iii) Constraints (d) and (e)

\begin{array}{rcr}2x + 2y  & = & 18\\4x + y & = & 24\\4x + 4y & = & 36\\3y & = & 12\\y & = & \mathbf{4}\\4x +4 & = & 24\\4x & = &20\\x & = & \mathbf{5}\\\end{array}\\

The lines intersect at (5,4).

6. Determine the x- and y-intercepts of the feasible region

(i) x-intercept

\begin{array}{rcr}4x + y & = & 24\\4x + 0  & = & 24\\x & = & \mathbf{6}\\\end{array}

The x-intercept is at (6,0).

(ii) y-intercept

\begin{array}{rcr}2x + 4y & = &32\\2(0) + 4y & = &32\\4y & = & 32\\y & = & \mathbf{8}\\\end{array}

The y-intercept is at (0,8).

The five black dots are the vertices of the polygon that represents the feasible region.

7. Calculate the maximum profit

Calculate the profit at each of the vertices.

(i) At (0,0)

P = 8.00x + 10.00y = 8.00(0) + 10.00(0) = 0 + 0 = $0

(ii) At (2,7)

P =  8.00(2) + 10.00(7) = 16 + 70 = $86

(iii) At (5,4)

P =  8.00(5) + 10.00(4) = 40 + 40 = $80

(iv) At (6,0)

P =  8.00(6) + 10.00(0) = 48 + 0 = $48

The maximum profit occurs at (2,7)

Thus, Beth should knit two mittens and seven gloves.

 

7 0
3 years ago
Directions: Select all the correct answers.
Kay [80]
The correct answer is C and D .
4 0
3 years ago
Polygon ABCD will be dilated by a scale factor of 2.2 with the origin as the center of dilation, resulting in the image A′B′C′D′
Citrus2011 [14]

m = undefined, C′D′ = 13.2 units

4 0
3 years ago
If you place a 17 foot ladder against the top of a 8 foot building how many feet will the bottom of the ladder be from the botto
KatRina [158]
9 because if you subtract 17 from 8 you will get 9 I hope this works :)
7 0
3 years ago
Read 2 more answers
Help?
Rashid [163]
*Hint: When a figure is reflective about the y-axis, the rule would be (-x, y)

So as you can see, all the points of the figure changed from a negative x to a positive one but kept the same y value. And then after the translation up by 6 units, the final rule would be (-x, y + 6) and if you were to plug in the points, you would see they would end up as the image.

The answer to this question would be:

B.) Reflection about the y-axis followed by translation up by 6 units.
3 0
3 years ago
Read 2 more answers
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