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2 years ago

Simplify completely ((x2-4x+4)/(x2+10x+25)) x ((x+5)/(x2+3x-10)) ...?

1 answer:

3 0

First of all you'll have to
Factor x^2-4x+4 = (x-2)^2
Factor x^2+10x+25 = (x+5)^2
Factor x^2+3x-10 = (x+5)(x-2)

So you'll have (x-2)^2/(x+5)^2 X (x+5)/(x+5)(x-2)
Then cancel the (x-2) and (x+5) on both sides

Thus getting the answer of x-2/(x+5)^2
or x-2/x+10+25

You might be interested in

In an isolated environment, a disease spreads at a rate proportional to the product of the infected and non-infected populations

eimsori [14]

Answer:

Expression: N = C·L·l(t)· T + 20

The initial value problem and solution are expressed as a first order differential equation.

Step-by-step explanation:

First, gather the information:

total population, N = 2 000

Proportionality constant, C = 0.0002

l(t) number of infected individuals = l(t)

healthy individuals = L

The equation is given as follows:

N = C·L·l(t)

However, there is a change with time, so the expression will be:

$\frac{dN}{dt}$ = C·L·l(t)

multiplying both sides by dt gives:

dN = C·L·l(t)

Integrating both sides gives:

$\int\limits^a_b {dN} \, dt$ = $\int\limits^a_b {CLl(t)} \, dt$

N = C·L·l(t)· T + K

initial conditions:

T= 0, N₀ = (0.01 ₓ 2 000) = 20

to find K, plug in the values:

N₀ = K

20 = K

At any time T, the expression will be:

N = C·L·l(t)· T + 20 Ans

8 0

3 years ago

A researcher was interested in seeing how many names a class of 38 students could remember after playing a name game After playi

Andreas93 [3]

Answer:

Proportion of the students recalled more than 15 names is 91.77%.

Step-by-step explanation:

We are given that a researcher was interested in seeing how many names a class of 38 students could remember after playing a name game After playing the name game, the students were asked to recall as many first names of fellow students as possible.

The mean number of names recalled was 19.41 with a standard deviation of 3.17.

Let X = number of names recalled

SO, X ~ N( $\mu = 19.41,\sigma^{2} = 3.17^{2}$ )

The z-score probability distribution is given by ;

Z = $\frac{X-\mu}{\sigma} } }$ ~ N(0,1)

where, $\mu$ = mean number of names recalled = 19.41

$\sigma$ = standard deviation = 3.17

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, proportion of the students recalled more than 15 names is given by = P(X > 15 names)

P(X > 15) = P( $\frac{X-\mu}{{\sigma} } }$ > $\frac{15-19.41}{3.17} }$ ) = P(Z > -1.39)

= P(Z < 1.39) = 0.9177 {using z table}

Therefore, proportion of the students recalled more than 15 names is 91.77%.

4 0

3 years ago

Find the x and y intercept of each line y=7x + 5

Zina [86]

Answer:

y intercept is 5. x intercept is 5/7

4 0

3 years ago

A realtor earns 1.25%commision on the price of any home she sells last month she sold two homes for a total of $750,000. How muc

TEA [102]

Answer: total amount of money in commission that the realtor earned is $9375

Step-by-step explanation:

The realtor earns 1.25% commission on the price of any home she sells.

Last month she sold two homes for a total of $750,000

It means that the amount of money in commission that the realtor earned last month would be

1.25/100 × 750 000 = 0.0125 × 750000 = $9375

4 0

3 years ago

Read 2 more answers

Write a conditional statement. Write the converse, inverse and contrapositive for your statement and determine the truth value o

photoshop1234 [79]

A conditional statement involves 2 propositions, p and q. The conditional statement, is a proposition which we write as: p⇒q,

and read "if p then q"

Let p be the proposition: Triangle ABC is a right triangle with m(C)=90°.

Let q be the proposition: The sides of triangle ABC are such that

$|AB|^2=|BC|^2+|AC|^2$ .

An example of a conditional statement is : p⇒q, that is:

if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that $|AB|^2=|BC|^2+|AC|^2$

This compound proposition (compound because we formed it using 2 other propositions) is true. So the truth value is True,

the converse, inverse and contrapositive of p⇒q are defined as follows:

converse: q⇒p
inverse: ¬p⇒¬q (if [not p] then [not q])
contrapositive: ¬q⇒¬p

Converse of our statement:

if The sides of triangle ABC are such that $|AB|^2=|BC|^2+|AC|^2$
then Triangle ABC is a right triangle with m(C)=90°

True

Inverse of the statement:

if Triangle ABC is not a right triangle with m(C) not =90° then The sides of triangle ABC are not such that $|AB|^2=|BC|^2+|AC|^2$

True

Contrapositive statement:

if The sides of triangle ABC are not such that $|AB|^2=|BC|^2+|AC|^2$ then Triangle ABC is not a right triangle with m(C)=90°

True

4 0

3 years ago