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3 years ago

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

Mathematics

2 answers:

Bad White [126]3 years ago

8 0

Answer:

The final answers are x = 1 OR x = -3.

Step-by-step explanation:

Given the equation is x^2 -3 = -2x

Rewriting it in quadratic form as:- x^2 +2x -3 = 0.

a = 1, b = 2, c = -3.

Using Quadratic formula as follows:- x = ( -b ± √(b² -4ac) ) / (2a)

x = ( -2 ± √(4 -4*1*-3) ) / (2*1)

x = ( -2 ± √(4 +12) ) / (2)

x = ( -2 ± √(16) ) / (2)

x = ( -2 ± 4 ) / (2)

x = (-2+4) / (2) OR x = (-2-4) / (2)

x = 2/2 OR x = -6/2

x = 1 OR x = -3

Hence, final answers are x = 1 OR x = -3.

butalik [34]3 years ago

8 0

Answer:

x=1 or x=-3

Step-by-step explanation:

Given equation is:

x²-3=-2x

We have to find the value of x.

x²-3=-2x

Adding 2x to both sides of above equation,we get

x²-3+2x=-2x+2x

x²+2x-3=0 eq(1)

ax²+bx+c=0 is general form of quadratic equation.

x= (-b±√b²-4ac)/2a is quadratic formula to find the value of x.

Comparing eq(1) with general quadratic equation,we get

a=1 b=2 and c=-3

Putting above values in quadratic formula,we get

x= (-2±√2²-4(1)(-3))/2(1)

x=(-2±√4+12)/2

x=(-2±√16)/2

x=(-2±4)/2

x=-2+4/2 or x=-2-4/2

x=2/2 or x=-6/2

x=1 or x=-3 is solution of given equation.

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Factor -7x^3+21x^2+3x-9 by grouping. what is the resulting expression?

Daniel [21]

Answer:

c) (3-7x^2)(x-3)

Step-by-step explanation:

-7x^3+21x^2+3x-9

Factor out a -7x^2 from the first two terms and a 3 from the last two terms

-7x^2 (x -3) +3(x-3)

Now factor out (x-3)

(x-3) (-7x^2+3)

Rearranging)

(x-3) (3-7x^2)

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3 years ago

What expression is equivalent to 32

Alekssandra [29.7K]

Answer:

8x=32

Step-by-step explanation:

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3 years ago

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gladu [14]

Answer:

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Step-by-step explanation:

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3 years ago

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P(X< ) 1-P(X> ) A softball pitcher has a 0.626 probability of throwing a strike for each curve ball pitch. If the softball

Mashutka [201]

Answer:

19.49% probability that no more than 16 of them are strikes

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 30, p = 0.626$

$\mu = E(X) = np = 30*0.626 = 18.78$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.626*0.374} = 2.65$

What is the probability that no more than 16 of them are strikes?

Using continuity correction, this is $P(X \leq 16 + 0.5) = P(X \leq 16.5)$ , which is the pvalue of Z when X = 16.5. So

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

$Z = \frac{16.5 - 18.78}{2.65}$

$Z = -0.86$

$Z = -0.86$ has a pvalue of 0.1949

19.49% probability that no more than 16 of them are strikes

7 0

3 years ago

THANK YOU , PLEASE INCLUDE EXPLANATION

frosja888 [35]

Remark

This will be a little late, but I'll answer it anyway. The more you see of the sine law, the clearer it will be.

Step One

Set up the sine Law.

$\dfrac{Sin(x)}{12}=\dfrac{sin(75)}{22}$

Step Two

Substitute values

Sin(x) = ??

sin(75) = 0.9659

$\dfrac{Sin(x)}{12}=\dfrac{0.9659}{22}$

Step Three

Cross multiply and Solve

22* Sin(x) = 12 * 0.9659

22* Sin(x) = 11.591 divide by 22

sin(x) = 11.591 / 22

sin(x) = 0.5269

Step Four

You have to know how to use the inverse of an angle to get the answer. I do it as my calculator would do it. If it doesn't work with yours, let me know.

x = sin^-1(0.5269)

2nd F

Sin^-1

(

0.5269

)

You should get 31.79 degrees.

5 0

3 years ago