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2 years ago

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What are the classifications of each system? Drag the answer into the box to match each system. {4x−2y=102x−y=5 {y=2x−3−2x+y=−5

{2x−5y=143x+4y=10

2 answers:

siniylev [52]2 years ago

7 0

The first one is. coincident
second. inconsistent
third. consistent independent

I just did this quiz (:

Ratling [72]2 years ago

4 0

we know that

If a system has exactly one solution, it is a consistent independent system.

If a system has an infinite number of solutions, it is a consistent dependent system .

If a system has no solution, it is said to be inconsistent

We're going to solve each system to determine its classification

<u>case A)</u>

$4x-2y=10$ ------> equation A

$2x-y=5$ ------> equation B

Multiply equation B by $2$ both sides

$2*(2x-y)=2*5$ -----> $4x-2y=10$

Equation A and equation B are the same line

Therefore

The system has an infinite number of solutions

The answer case A) is

The system is a consistent dependent system (coincident)

<u>case B)</u>

$y=2x-3$ ------> equation A

$-2x+y=-5$ ------> equation B

Isolate the variable y in the equation B

$y=2x-5$

Both lines are parallel lines, because has the same slope

Therefore

The system has no solution

the answer case B) is

The system is inconsistent

<u>case C)</u>

$2x-5y=14$ ------> equation A

$3x+4y=10$ ------> equation B

Multiply equation A by $4$ and equation B by $5$ both sides

$4*(2x-5y)=4*14$ -----> $8x-20y=56$

$5*(3x+4y)=5*10$ -----> $15x+20y=50$

Adds the equations

$8x-20y=56 \\15x+20y=50\\-------\\8x+15x=56+50 \\23x=106 \\x=4.61$

Find the value of y

$2*4.6-5y=14$

$y=-0.96$

therefore

The system has one solution

The answer case C) is

The system is a consistent independent system

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Harman [31]

<u>ANSWER</u>

$\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2}$

<u>EXPLANATION</u>

We want to find the cube root of

$- 729 {a}^{9} {b}^{6}$

We express this symbolically as:

$\sqrt[3]{- 729 {a}^{9} {b}^{6} }$

The expression under the radical called the radicand.

We need to express this radical in exponential form using the property,

${x}^{ \frac{m}{n} } = \sqrt[n]{ {x}^{m} }$

Applying this rule gives us:

$\sqrt[3]{- 729 {a}^{9} {b}^{6} } = ({- 729 {a}^{9} {b}^{6}})^{ \frac{1}{3} }$

$\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3} {a}^{9} {b}^{6}})^{ \frac{1}{3} }$

Recall that

$({a}^{m} )^{n} = {a}^{mn}$

We apply this rule on the RHS to get,

$\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3 \times { \frac{1}{3} } } {a}^{9 \times { \frac{1}{3} } } {b}^{6 \times { \frac{1}{3} } }})$

This simplifies to

$\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2}$

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nikdorinn [45]

Answer:

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Now. we know the slope of a straight line through the points ( $x_{1},y_{1}$ ) and ( $x_{2},y_{2}$ ) is given by $[\frac{y_{2} - y_{1} }{x_{2} - x_{1}} ]$ .

So, in our case ( $x_{1},y_{1}$ ) ≡ (-5,-10) and ( $x_{2},y_{2}$ ) ≡ (-1,5).

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If a hurricane was headed your way, would you evacuate? The headline of a press release states, "Thirty-four Percent of People o

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Answer:

The 98% confidence interval would be given by (0.326;0.354)

Step-by-step explanation:

1) Notation and definitions

$X=63$ number of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states

$n=6138$ random sample taken

$\hat p=0.34$ estimated proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states

$p$ true population proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

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2) Confidence interval

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 98% of confidence, our significance level would be given by $\alpha=1-0.98=0.02$ and $\alpha/2 =0.01$ . And the critical value would be given by:

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If we replace the values obtained we got:

$0.34 - 2.33\sqrt{\frac{0.34(1-0.34)}{6138}}=0.326$

$0.34 + 2.33\sqrt{\frac{0.34(1-0.34)}{6138}}=0.354$

The 98% confidence interval would be given by (0.326;0.354)

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