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Gre4nikov [31]
3 years ago
6

If

Mathematics
1 answer:
Vitek1552 [10]3 years ago
8 0

Answer:

Given :

→x-y=12

→xy= 3²

=9

Equation formed:

{(x - y)}^{2}  =  {x}^{2}  +  {y}^{2}  - 2xy

Step by step explanation:

{(12)}^{2}  =  {x}^{2}  +  {y}^{2}  - 2 \times 9 \\  144   + 18 =  {x}^{2}  +  {y}^{2}  \\  = 162

hope it helped you:)

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ExtremeBDS [4]
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3 0
3 years ago
Find the x- and y-intercepts of the following equation:<br> 2x+3y=-24
Ilya [14]

Answer:

Algebra 

 Topics 

How do you find the intercepts of x2y−x2+4y=0?

Algebra  Graphs of Linear Equations and Functions  Intercepts by Substitution

2 Answers

Gió

Mar 24, 2015

For the intercepts you set alternately x=0 and y=0 in your function:

and graphically:

Answer link

Alan P.

Mar 24, 2015

On the X-axis y=0

So

x2y−x2+4y=0

becomes

x2(0)−x2+4(0)=0

→−x2=0

→x=0

On the Y-axis x=0

and the original equation

x2y−x2+4y=0

becomes

(0)2y−(0)2+4y=0

→y=0

The only intercept for the given equation occurs at (0,0)

Answer link

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What is the x and y Intercepts?

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How do you use the x and y intercepts to graph a linear equation?

How do you find the x and y intercept for y=2x+3?

How do you find the x intercept for y=2?

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4 0
2 years ago
The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont
BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)

and its cumulative distribution function (CDF) is

\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so  A∩B = B and  

\bf P(A | B) = P(B)P(B) = (P(B))^2

We have  

\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237

hence,

\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}

<em>Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection. </em>

This means that,

<em>Probability that at least one of them needs replacement at the first inspection =  </em>

\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021

5 0
3 years ago
An angle that measures 89 degrees is called?
mafiozo [28]
An acute angle is any angle that is below 90 degrees, so 89 degrees is an ancute angle
5 0
3 years ago
Find the exact value of the given expression.<br> sin(2cos^-1(5/13))
xeze [42]

Answer:

+120/169 or -120/169

Step-by-step explanation:

  • let cos^{-1}[\frac{5}{13}  ] = \alpha

where, alpha is some angle that satisfies the assumed condition.

  • so, cos\alpha= 5/13

[ taking cos to the other side  or applying cos on both sides]

  • now, substitute this in the given expression
  • sin(2cos^-1(5/13)) = sin(2\alpha )

as sin\beta =  + or -\sqrt{1-(cos\beta) ^{2}

[by general trigonometry formula: cos^{2}[\beta]  +sin^{2}[\beta]=1]

so if  cos\alpha= 5/13, we can get sin\alpha from the above formula as + or - 12/13

(because, after taking square root on both sides we keep + or -]

  • as, sin2\beta  = 2*sin[\beta ]*cos[\beta ]

[by general trigonometry formula]

  • here, now sin[2\alpha ]=2*(+or- 12/13)*5/13\\

so, the final value can be 120/169 or -120/169.

4 0
3 years ago
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