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2 years ago

Use the space provided in each box to solve the equation. Use the opposite operation to solve the equation.

Mathematics

1 answer:

swat322 years ago

3 0

Answer:

(1): -11 (6): -9 (11): 80 (16): 75

(2): 18 (7): -6 (12): -17 (17): 27

(3): 4 (8): 12 (13): 39 (18): -13

(4): -5 (9): 22 (14): -24 (19): 100

(5): 24 (10): 46 (15): -65 (20) -30

Step-by-step explanation:

Please provide more points next time, this took long.

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What is the inverse of the function y= x^2-12

aalyn [17]

Answer:

$y=\sqrt{x+12}$

Step-by-step explanation:

To find the inverse of a function, what I like to do is to switch the places of x and y, and then try to isolate y again like so:

$x=y^2-12$

$x+12=y^2$

$y=\sqrt{x+12}$

Hope this helps!

7 0

4 years ago

A machine at a bottling company fills water bottles. the number of bottles filled is proportional to the amount of time the mach

Whitepunk [10]

In the table shown below:

Let N be the number of bottles filled,

Let T be the time in hours.

Given that the number of bottles filled is proportional to the amount of time the machine runs, we have

$\begin{gathered} N\propto T \\ \text{Introducing a proportionality constant, we have } \\ N\text{ = kT} \\ \Rightarrow k\text{ = }\frac{N}{T} \\ \end{gathered}$

Let's evaluate the value of k for each day.

Thus, on monday,

$\begin{gathered} N\text{ = 9900} \\ T\text{ = 5.5} \\ \text{thus,} \\ k\text{ = }\frac{9900}{5.5} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Tuesday:

$\begin{gathered} N\text{ = }11160 \\ T\text{ = }6.2 \\ \text{thus,} \\ k\text{ = }\frac{11160}{6.2} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Wednesday:

$\begin{gathered} N\text{ = }12330 \\ T\text{ = }6.25 \\ \text{thus,} \\ k\text{ = }\frac{12330}{6.25} \\ \Rightarrow k\text{ = 1972.8} \end{gathered}$

Thursday:

$\begin{gathered} N\text{ = }10440 \\ T\text{ = }5.80 \\ \text{thus,} \\ k\text{ = }\frac{10440}{5.8} \\ \Rightarrow k=1800 \end{gathered}$

It is observed that all exept wednesday have the same value of k.

Thus, the amount of time required for the number of bottles filled on wednesday is evaluated as

$\begin{gathered} N\text{ = }12330 \\ k\text{ = 1800} \\ T\text{ = ?} \\ \text{but} \\ k\text{ = }\frac{N}{T} \\ 1800\text{ = }\frac{12330}{T} \\ \Rightarrow T\text{ = }\frac{\text{12330}}{1800} \\ T\text{ = 6.85} \end{gathered}$

Hence, the incorrect day is Wednesday. The amount of time for that many bottles should be 6.85 hours.