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docker41 [41]
2 years ago
7

A store sells toys in bulk. It sells wooden blocks for $5 a pound and plastic bricks for $10

Mathematics
1 answer:
Veseljchak [2.6K]2 years ago
5 0

9514 1404 393

Answer:

  • 6 # plastic bricks
  • 4 # wooden blocks

Step-by-step explanation:

Let p represent the number of pounds of plastic bricks in the mix. Then the number of pounds of wooden blocks is (10-p), and the total cost is ...

  10p +5(10-p) = 80

  5p = 30 . . . . . . . . . subtract 50

  p = 6 . . . . divide by 5; there are 6 pounds of plastic bricks in the mix

4 pounds of wooden blocks and 6 pounds of plastic bricks should be used to make a 10-lb mix worth $80.

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3 years ago
How do I find the equation of the perpendicular bisector between (-2,5) and (2,-1)?
Arturiano [62]

Answer:

y =  \frac{2}{3} x + 2

Step-by-step explanation:

Start by finding the slope of the given line.

\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }

Slope of given line

=  \frac{5 - ( - 1)}{ - 2 - 2}

=  \frac{5 + 1}{ - 4}

=  \frac{6}{ - 4}

=  -  \frac{3}{2}

A perpendicular bisector cuts through the line at its midpoint perpendicularly.

The product of the slopes of two perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

-  \frac{3}{2} m =  - 1

m =  - 1 \div ( -  \frac{3}{2} )

m =  - 1 \times ( -  \frac{2}{3} )

m =  \frac{2}{3}

y =  \frac{2}{3}x  + c, where c is the y-intercept.

To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.

\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1  + y_2}{2} )}

Midpoint of given line

=  ( \frac{ - 2+ 2}{2} , \frac{5 - 1}{2} )

=( \frac{0}{2} , \frac{4}{2} )

= (0, 2)

y =  \frac{2}{3} x + c

When x= 0, y= 2,

2= ⅔(0) +c

2= 0 +c

c= 2

Thus, the equation of the perpendicular bisector is y =  \frac{2}{3} x + 2.

7 0
2 years ago
Please help me. I don’t understand this at all...
mylen [45]
Problem 1

With limits, you are looking to see what happens when x gets closer to some value. For example, as x gets closer to x = 2 (from the left and right side), then y is getting closer and closer to y = 1/2. Therefore the limiting value is 1/2

Another example: as x gets closer to x = 4 from the right hand side, the y value gets closer to y = 4. This y value is different if you approach x = 0 from the left side (y would approach y = 1/2)

Use examples like this and you'll get the results you see in "figure 1"

For any function values, you'll look for actual points on the graph. A point does not exist if there is an open circle. There is an open circle at x = 2 for instance, so that's why f(2) = UND. On the other hand, f(0) is defined and it is equal to 4 as the point (0,4) is on the function curve.

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

Problem 2

This is basically an extension of problem 1. The same idea applies. See "figure 2" (in the attached images) for the answers. 

6 0
3 years ago
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