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3 years ago

How many solutions does the absolute value equation have? I x - 3 I + 2 = -2

Mathematics

1 answer:

choli [55]3 years ago

4 0

9514 1404 393

Answer:

the correct answer is marked

Step-by-step explanation:

When the graph of the left side of the equation does not intersect the graph of the right side of the equation, there are no solutions.

Additional comment

Even if you extend the domain to complex numbers, there are no solutions. The f(x) = |x| function always returns a positive real value, even for complex numbers.

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frez [133]

Answer:

Option 2

Step-by-step explanation:

1/4 is equal to .25 or 25/100

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small cubes with edge lengths of 1/4 inch will be packed into the right rectangular prism shown.( the base is 4 1/2, the width i

ss7ja [257]

General Idea:

We need to find the volume of the small cube given the side length of the small cube as 1/4 inch.

Also we need to find the volume of the right rectangular prism with the given dimension (the height is 4 1/2, the width is 5, and the length is 3 3/4).

To find the number of small cubes that are needed to completely fill the right rectangular prism, we need to divide volume of right rectangular prism by volume of each small cube.

Formula Used:

$Volume \; of \; Cube = a^3 \; \\\{where \; a \; is \; side \; length \; of \; cube\}\\\\Volume \; of \; Right \; Rectangular \; Prism=L \times W \times H\\\{Where \; L \; is \; Length, \; W \; is \; Width, \;and \; H \; is \; Height\}$

Applying the concept:

Volume of Small Cube:

$V_{cube}= (\frac{1}{4} )^3= \frac{1}{64} \; in^3\\\\V_{Prism}= 3 \frac{3}{4} \times 5 \times 4 \frac{1}{2} = \frac{15}{4} \times \frac{5}{1} \times \frac{9}{2} = \frac{675}{8} \\\\Number \; of \; small \; cubes= \frac{V_{Prism}}{V_{Cube}} = \frac{675}{8} \div \frac{1}{64} \\\\Flip \; the \; second \; fraction\; and \; multiply \; with \; the \; first \; fraction\\\\Number \; of \; small \; cubes \;= \frac{675}{8} \times \frac{64}{1} = 5400$

Conclusion:

The number of small cubes with side length as 1/4 inches that are needed to completely fill the right rectangular prism whose height is 4 1/2 inches, width is 5 inches, and length is 3 3/4 inches is 5400 

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3 years ago

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Solve and graph the inequality 6 + 3n ≤40

Kazeer [188]

6+3n≤40
Use inverse operations i.e.
4x+2<10
-2 -2
4x<8
4*x/4<8/4
x<2

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2 years ago

A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters

PilotLPTM [1.2K]

Answer:

e. 0.0072

Step-by-step explanation:

We are given that a bottling company uses a filling machine to fill plastic bottles with cola. And the contents vary according to a Normal distribution with Mean, μ = 298 ml and Standard deviation, σ = 3 ml .

Let Z = $\frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1) where, Xbar = mean contents of six randomly

selected bottles

n = sample size i.e. 6

So, Probability that the mean contents of six randomly selected bottles is less than 295 ml is given by, P(Xbar < 295)

P(Xbar < 295) = P( $\frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{295 - 298}{\frac{3}{\sqrt{6} } }$ ) = P(Z < -2.45) = P(Z > 2.45)

Now, using z% score table we find that P(Z > 2.45) = 0.00715 ≈ 0.0072 .

Therefore, option e is correct .

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3 years ago