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3 years ago

If x2 - y2 = 12 and x - y = 4, what is the value

Mathematics

1 answer:

ira [324]3 years ago

6 0

Step-by-step explanation:

x²-y²=12

(x-y)(x+y)=12

but x-y=4

4(x+y)=12

x+y=12/4

x+y=3

lets make x the subject of the formula

x=3-y

since x-y=4

(3-y)-y=4

3-y-y=4

-2y=1

y=-1/2

then x=3-y

x=3-(-1/2)

x=(6--1)/2

x=7/2

therefore; x²+2xy+y

=(7/2)²+2×7/2×-1/2+(-1/2)

=49/4-7/2-1/2

=(49-14-2)/4

=33/4

=8.25

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PLEASE PLEASE PLEASE HELP!!

irga5000 [103]

9 a
------ = -----
a 5

a^2 = 45

a = 3<span>√5
</span>
4 b
------ = -----
b 5

b^2 = 20

b = 2√5

answer:

a = 3√5
b = 2√5

hope it helps

7 0

2 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:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.28$

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.

5 0

3 years ago

2x squared + 9x=-5 i need to solve for x

In-s [12.5K]

$2x^2+ 9x=-5 \\ \\2x^2 + 9x+5 =0 \\\\a=2, \ \ b=9 , \ \ c=5 \\\\\Delta =b^2-4ac = 9^2 -4\cdot 2\cdot 5 = 81-40=41 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-9-\sqrt{41}}{2\cdot 2 }=\frac{-9-\sqrt{41}}{ 4 }\\\\ x_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{-9+\sqrt{41}}{2\cdot 2 }=\frac{-9+\sqrt{41}}{4 }$