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2 years ago

X^2+10x-7 / x^2+10x+25=0 how do i solve for x?

Mathematics

2 answers:

liq [111]2 years ago

4 0

Factorize both the numerator and denominator then equate to zero ...you'll get X

Verizon [17]2 years ago

3 0

You just have to solve the next equation:
x²+10x-7=0
Because, if the numerator is equal to "0", then the next expression
(x²+10x-7) /( x²+10x+25)=0

Therefore:
x²+10x-7=0
x=[-10⁺₋√(100+28)]/2=(-10⁺₋√128)/2=(-10⁺₋8√2)/2=-5⁺₋4√2
We have two possible solutions:

x₁=-5-4√2
x₂=-5+4√2

Now, we have to check these possible solutions.
Remember the denominator cannot be equal to "0".

if x=-5-4√2

[(-5-4√2)²+10(-5-4√2)-7] / [(-5-4√2)²+10(-5-4√2)+25]=0/32=0

Therefore: x=-5-4√2 is a solution.

if x=-5+4√2

[(-5+4√2)²+10(-5+4√2)-7] / [(-5+4√2)²+10(-5+4√2)+25]=0/32=0

Therefore: x=-5+4√√2 is a solution.

Answer: we have two solutions for x:
x₁=-5-4√2
x₂=-5+4√2

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It has a time to failure distribution which is normal with a mean of 35,000 vehicle miles and a standard deviation of 7,000 vehi

Triss [41]

Answer:

The designed life should be of 21,840 vehicle miles.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 35,000 vehicle miles and a standard deviation of 7,000 vehicle miles.

This means that $\mu = 35000, \sigma = 7000$

Find its designed life if a .97 reliability is desired.

The designed life should be the 100 - 97 = 3rd percentile(we want only 3% of the vehicles to fail within this time), which is X when Z has a p-value of 0.03, so X when Z = -1.88.

$Z = \frac{X - \mu}{\sigma}$

$-1.88 = \frac{X - 35000}{7000}$

$X - 35000 = -1.88*7000$

$X = 21840$

The designed life should be of 21,840 vehicle miles.

3 0

2 years ago

Find an n^th degree polynomial with real coefficients satisfying the given conditions. n = 3; -2 and 2 i are zeros; f(-1) = 15.

Ira Lisetskai [31]

So, n = 3, is a 3rd degree polynomial, roots are -2 and 2i

well 2i is a complex root, or imaginary, and complex root never come all by their lonesome, their sister is always with them, the conjugate, so if 0+2i is there, 0-2i is there too

so, the roots are -2, 2i, -2i

now... $\bf \begin{cases}
x=-2\implies x+2=0\implies &(x+2)=0\\
x=2i\implies x-2i=0\implies &(x-2i)=0\\
x=-2i\implies x+2i=0\implies &(x+2i)=0
\end{cases}
\\\\\\
(x+2)\underline{(x-2i)(x+2i)}=0\\\\
-----------------------------\\\\
\textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
(x+2)[x^2-(2i)^2]=0\implies (x+2)[x^2-(2^2i^2)]=0
\\\\\\
(x+2)[x^2-(4\cdot -1)]=0\implies (x+2)(x^2+4)=0
\\\\\\
x^3+2x^2+4x+8=0$

now, if we check f(-1), we end up with 5, not 15
hmmm

so, how to turn our 5 to 15? well, 3*5, thus

$\bf 3(x^3+2x^2+4x+8)=f(x)\implies 3(5)=f(-1)\implies 15=f(-1)$

usually, when we get the roots, or zeros, if any common factor that is a constant is about, they get in a division with 0 and get tossed, and aren't part of the roots, thus, we can simply add one, in this case, the common factor of 3, to make the 5 turn to 15

6 0

3 years ago

What is the missing number in 12,24,72,288

Ronch [10]

12*2=24
24*3=72
72*4=288
n*(x+1)
288*(4+1)
288*5=1440

5 0

3 years ago

Help!!!!! Please!!!

miss Akunina [59]

The equation for line E is x = 8.
This is because the line intersects the x-axis at the point (8,0)

5 0

3 years ago