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Andrew [12]
3 years ago
10

Solve each system of linear equations albebraically

Mathematics
1 answer:
ANEK [815]3 years ago
5 0

Step-by-step explanation:

1.\\\left\{\begin{array}{ccc}y=3x&(1)\\2y=6x&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\2(3x)=6x\\6x=6x\qquad\text{subtract}\ 6x\ \text{from both sides}\\6x-6x=6x-6x\\0=0\qquad\text{TRUE}\\\\Answer:\ \text{Infinitely many solutions}\\\\\left\{\begin{array}{ccc}y=3x\\x\in\mathbb{R}\end{array}\right

2.\\\left\{\begin{array}{ccc}y=2x+5&(1)\\y-2x=1&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\(2x+5)-2x=1\\2x+5-2x=1\qquad\text{combine like terms}\\(2x-2x)+5=1\\5=-1\qquad\text{FALSE}\\\\Answer:\ \text{No solution.}

3.\\\left\{\begin{array}{ccc}3x-2y=9\\-6x+4y=1&\text{divide both sides by 2}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3x-2y=9\\-3x+2y=0.5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad0=9.5\qquad\text{FALSE}\\\\Answer:\ \text{No solution.}

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My car gets 27 miles per gallon, and gasoline costs $2.50 per gallon. If we consider only the cost of gasoline, how much does it
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Answer:

$71.50

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If f(x)=2x-1, find f(a+h)<br> A.) a+h-1<br> B.) 2a+h-1<br> C.) 2a+2h-2<br> D.) 2a+2h-1
nadezda [96]
Since f(x) = 2x - 1, all you need is to replace x with (a+h)

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anyanavicka [17]

Step-by-step explanation:

Part A

A) The denominator is 665, so this is a terminating decimal.

B) 11/99 = 1/9 = 0.1111...

C) 256/999 = 0.256256256...

D) 25/909 = 275/9999 = 0.027502750275...

B has 1 repeating digit, C has 3 repeating digits, and D has 4 repeating digits.  So the correct answer is C.

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6 0
3 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.

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1 year ago
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