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notsponge [240]
2 years ago
15

An art teacher has a total of 7/8 pound of clay.The teacher puts 1/16 pound of clay at each workstation. The teacher sets up an

equal number of workstations in each of 2 classrooms. How many workstations does the teacher set up in each of the classrooms? Show your work
Mathematics
1 answer:
Pie2 years ago
7 0

Answer:

The teacher establishes 7 work stations in each of the classrooms.

Step-by-step explanation:

Each work station has 1/16 pounds of clay.

There are two classrooms with the same number of workstations.

The total amount of clay is 7/8

Then, we look for a number of work stations per classroom x, which multiplied by the number of classrooms (2) and multiplied by the amount of clay per work station (1/16) is equal 7/8.

Then we propose the following equation

\frac{1}{16}(2x) =\frac{7}{8}\\\\ \frac{2}{16}x = \frac{7}{8}\\\\ x = \frac{16 * 7}{8 * 2}\\\\ x = 7

The teacher establishes 7 work stations in each of the classrooms.

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Romashka-Z-Leto [24]

Answer:

x = -3

Step-by-step explanation:

3(x - 6)= -2 + 5(2x + 1)

= 3x - 18 = -2 + 10x + 5

= -18 = -2 + 7x + 5

= -18 = 7x + 3

= -21 = 7x

= -3 = x

= x = -3

5 0
2 years ago
Which equation is the inverse of y = 9x2 - 4?
m_a_m_a [10]

Answer:

The inverse will be:

y' = \frac{\sqrt{x+4}}{3}

Step-by-step explanation:

In order to find the inverse of the equation, we do a variable change, since we are finding the inverse, :

f(x)  = 9x^{2} - 4

y = 9x^{2} - 4

x = 9y' ^{2} - 4

Now solve for y'.

First add 4 in both sides of the equation and change to the left y'.

x + 4= 9y'^{2} - 4+4

9y'^{2} = x + 4

Second divide by 9

9y'^{2}/9 = (x + 4)/9

y'^{2} = (x + 4)/9

Now you will have to clear y, with the square root.

[tex]y'^{\frac{2}{2}} = \sqrt{x + 4}  / \sqrt{9}[/tex] =

Simplifying terms

y' = \frac{\sqrt{x+4}}{3}

f^{-1}(x)  = \frac{\sqrt{x+4}}{3}

You can check the answer by doing the evaluation of the following equation:

(f o f^{-1} ) (x)

substitute the equation for y' or inverse function f^{-1}

f(\frac{\sqrt{x+4} }{3})

Now substitue the value into f(x)

You will have

= 9(\frac{\sqrt{x+4} }{3}} )^{2}  - 4\\\\Solving\\\\9(\frac{{x+4} }{9}} )  - 4

=x

5 0
3 years ago
1. A card is picked at random from a pack of 52 playing cards. The probability that it is a 6 is?
salantis [7]

Answer:

1.) A - 5/52

2.) B - 4/9

3 0
2 years ago
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Answer:

Option "d" might be 11/13

Step-by-step explanation:

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Remove this 8 cards from 52 cards which gives

=>44

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2 years ago
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