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ANEK [815]
3 years ago
7

What is the equation of the line that has a slope of 3 and passes through the point (1, -2)

Mathematics
1 answer:
Gnesinka [82]3 years ago
3 0

Answer:

. JUST LOAD

Step-by-step explanation:

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3∙(a+x), if a=8; x=−10
Oksi-84 [34.3K]
Your answer should be -6
6 0
3 years ago
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
I need help . not sure what the answer is
stich3 [128]

Answer:

2.21 i believe

Step-by-step explanation:

7 0
3 years ago
There are 10 marbles in a bag.
pickupchik [31]
The ratio would be 4:6 because 4 of the marbles are pink and 6 (the rest) are blue
7 0
3 years ago
Read 2 more answers
An isosceles triangle has base angles that each measure 42°. Which equation can be used to find z, the measure of the third angl
kicyunya [14]
The angles all add up to 180

42 + 42 + x = 180

84 + x = 180

x = 96

x = the third angle

6 0
3 years ago
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