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umka21 [38]
4 years ago
14

A manufacturing plant can produce 150 shoes or 100 sandals per hour. Let a represent the hours spent producing shoes and p repre

sent the hours spent producing sandals. What is the constraint equation if the plant can only produce foot ware for 30 hours a day?
150a + 100p = 30
150p + 100a = 30
50a = 30
a + p = 30
Mathematics
1 answer:
Ksju [112]4 years ago
5 0
If "a" and "p" equal hours.

a + p = 30 would be the correct choice.
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A system of equations is shown below. Which of the following statements describes the graph of this system of equations in the (
ollegr [7]

The given system of equations represent a single line with positive slope. So option C is correct.

<u>SOLUTION: </u>

Given system of equations are

\begin{array}{l}{3 y-5 x=15 \rightarrow(1)} \\\\ {6 y-10 x=30 \rightarrow(2)}\end{array}

Now, if we observe, (1) \times 2 \rightarrow(2) multiplying the 1^{st} equation with 2 results in 2^{nd} equation.

which means the two line equations represents the same line.

Now, let us find the slope of line, \text { slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-3}{-5}=\frac{3}{5}=\text { positive slope }

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4 years ago
A coordinate grid is placed over a map. City A is located at (- 3, 2) , and City B is located at (4, 8) . If City C is at the mi
Andreyy89

Answer:

City A is the closest

Step-by-step explanation:

Given

City A = (-3,2)

City B = (4,8)

First, we calculate the coordinates of City C

If City C is located at the midpoint between A and B, then it's coordinates is

(x1 + x2)/2 , (y1 + y2)/2

where

x1 = x coordinate of City A = -3

x2 = x coordinate of City B = 4

y1 = y coordinate of City A = -2

y2 = y coordinate of City B = 8

So, the coordinates of City C = (-3+4)/2 , (-2+8)/2

City C = (½,6/2)

City C = (½,3)

We then calculate the distance between City C and City A

And

We also calculate the distance between City C and City B

Then we compare both results

Formulation for distance = √(x2-x1)² + (y2-y1)²

For City C and City A

City A coordinatates = (x1,y1) = (-3,2)

City C coordinates = (x2,y2) = (½,3)

Distance between A and C = √(½-(-3))² + (3-2)² -------- Simplify the bracket

Distance = √(½+3)² + (1)² ---------- Solve the fraction

Distance = √(7/2)² + (1)² ------------ Open all brackets

Distance = √49/4 + 1

Distance = √53/4

Distance = 7.280109889280518/2

Distance = 3.640054944640259

Distance between City A and C = 3.64 (approximated)

For City C and City B

City B coordinatates = (x1,y1) = (4,8)

City C coordinates = (x2,y2) = (½,3)

Distance between B and C = √(½-(-3))² + (8-4)² -------- Simplify the bracket

Distance = √(½+3)² + (4)² ---------- Solve the fraction

Distance = √(7/2)² + (4)² ------------ Open all brackets

Distance = √49/4 + 16

Distance = √113/4

Distance = 10.63014581273464/2

Distance = 5.315072906367324

Distance between City B and C = 5.32 (approximated)

Comparing the results (3.64) and (5.32),

We conclude that City C is closer to City A than City B

7 0
3 years ago
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