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3 years ago

What is the value of the rational expression 2x^2+5x+9/x^2+2x-1 when x=-2

Mathematics

2 answers:

anygoal [31]3 years ago

6 0

Answer: -7

Step-by-step explanation:

Sergio039 [100]3 years ago

5 0

Answer:

The value of the Rational expression when $x=-2$ is: $-7$

Step-by-step explanation:

For this exercise is important to remember:

When a negative number is raised to an even power, the result will be positive.
The multiplication of signs:

$(+)(+)=+\\(-)(-)=+\\(-)(+)=-$

Then, given the following Rational expression:

$\frac{2x^2+5x+9}{x^2+2x-1}$

You need to follow these steps in order to find its value when $x=-2$ :

1. Substitute the given value of "x" ( $x=2$ ) into the expression:

$\frac{2(-2)^2+5(-2)+9}{(-2)^2+2(-2)-1}$

2. Evaluate and simplify:

$\frac{2(4)+5(-2)+9}{4+2(-2)-1}=\frac{8-10+9}{4-4-1}=\frac{7}{-1}=-7$

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Spila Motors Inc. earned income of $69,000 from its operating activities for a specified period. During the same period, it sold

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The right answer is Option C.

Step-by-step explanation:

Income = $69000

Gain = $3000

Total earned= Income + Gain

$Total = 69000+3000=\$72000$

Expenses on operating activities = $33000

Expenses on non operating activities = $8000

Total expenses = 33000+8000 = $41000

Profit = Total earned - Total expenses

$Net\ profit=72000-41000=\$31000$

The net profit made by Spila was $31000.

The right answer is Option C.

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2 years ago

Out of 1,000 students, 80 were asked by random sampling what color they would prefer for their first car. Their responses are sh

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Answer: First off, what answer are you looking for? it's hard for me to answer something without specification.

Step-by-step explanation:

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2 years ago

Read 2 more answers

Please help with this

Dafna1 [17]

Answer:

Step-by-step explanation:

● first one:

The diagonals of a rhombus are perpendicular to each others wich means that they form four right angles.

STP is one of them so this statement is true.

● second one:

If ST and PT were equal this would be a square not a rhombus.

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If SPQ was a right angle, this woukd be a square.

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3 years ago

It is known that the life of a particular auto transmission follows a normal distribution with mean 72,000 miles and standard de

scoray [572]

Answer:

a) $P(X$

$P(z$

b) $P(X>65000)=P(\frac{X-\mu}{\sigma}>\frac{65000-\mu}{\sigma})=P(Z>\frac{65000-72000}{12000})=P(z>-0.583)$

$P(z>-0.583)=1-P(Z$

c) $P(X>100000)=P(\frac{X-\mu}{\sigma}>\frac{100000-\mu}{\sigma})=P(Z>\frac{100000-72000}{12000})=P(z>2.33)$

$P(z>2.33)=1-P(Z$

Sicne this probability just represent 1% of the data we can consider this value as unusual.

d) $z=1.28$

And if we solve for a we got

$a=72000 +1.28*12000=87360$

So the value of height that separates the bottom 90% of data from the top 10% is 87360.

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the life of a particular auto transmission of a population, and for this case we know the distribution for X is given by:

$X \sim N(72000,12000)$

Where $\mu=72000$ and $\sigma=12000$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using excel or the normal standard table and we got:

$P(z$

Part b

$P(X>65000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>65000)=P(\frac{X-\mu}{\sigma}>\frac{65000-\mu}{\sigma})=P(Z>\frac{65000-72000}{12000})=P(z>-0.583)$

And we can find this probability using the complement rule and excel or the normal standard table and we got:

$P(z>-0.583)=1-P(Z$

Part c

$P(X>100000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>100000)=P(\frac{X-\mu}{\sigma}>\frac{100000-\mu}{\sigma})=P(Z>\frac{100000-72000}{12000})=P(z>2.33)$

And we can find this probability using the complement rule and excel or the normal standard table and we got:

$P(z>2.33)=1-P(Z$

Sicne this probability just represent 1% of the data we can consider this value as unusual.

Part d

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.1$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

$P(X$