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2 years ago

What substitution should be used to rewrite 4x12 – 5x6 – 14 = 0 as a quadratic equation? u = x2 u = x3 u = x6 u = x12

Mathematics

2 answers:

VLD [36.1K]2 years ago

8 0

Answer: $u=x^6$

Explanation:

A quadratic equation is an equation written in the form

$au^2 + bu + c=0$ (1)

where a,b,c are coefficients and where u is the variable.

Our original equation is:

$4x^{12} - 5x^6 -14=0$

If we make the substitution $u=x^6$ , we obtain

$4u^2 -5u-14 =0$

Which corresponds to eq.(1), with coefficients a=4, b=-5, c=-14.

Arada [10]2 years ago

5 0

Sent a picture of the solution to the problem (s).

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Two plane mirrors intersect at right angles. a laser beam strikes the first of them at a point 11.5 cm from their point of inter

vivado [14]

The angle measured from the normal to the mirror will be
.. arctan(14/11.5) ≈ 50.6°

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1 year ago

Compare the functions shown below: f(x) = 4x + 5 g(x) tangent function with y intercept at 0, 2 h(x) = 3 sin(2x + π) − 2 Which f

KATRIN_1 [288]

The y-intercept of the graph of a function is the value of f(0) for any function f.
That is, it is the y-value in the pair (0, y)

The y-intercept of <span>f(x) = 4x + 5 is f(0)=4*0+5=5

The y-intercept of (0, 2) is 2.

The y-intercept of </span>h(x) = 3 sin(2x + π) − 2 is:

h(0) = 3 sin(2*0 + π) − 2=3 sin(π) − 2=3*0-2=-2

<span>Answer: The function f has the greatest y-intercept.

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7 0

2 years ago

The factory quality control department discovers that the conditional probability of making a manufacturing mistake in its preci

Anni [7]

Answer:

The probability that a defective ball bearing was manufactured on a Friday = 0.375

Step-by-step explanation:

Let the event of making a mistake = M

The event of making a precision ball bearing production on Monday = Mo

The event of making a precision ball bearing production on Tuesday = T

The event of making a precision ball bearing production on Wednesday = W

The event of making a precision ball bearing production on Thursday = Th

The event of making a precision ball bearing production on Friday = F

the conditional probability of making a manufacturing mistake in its precision ball bearing production is 4% on Tuesday, P(M|T) = 4% = 0.04

4% on Wednesday, P(M|W) = 0.04

4% on Thursday, P(M|Th) = 0.04

8% on Monday, P(M|Mo) = 0.08

and 12% on Friday = P(M|F) = 0.12

The Company manufactures an equal amount of ball bearings (20 %) on each weekday, Hence, the probability that a random precision ball bearing was made on a particular day of the week, is mostly the same for all the five working days.

P(Mo) = 0.20

P(T) = 0.20

P(W) = 0.20

P(Th) = 0.20

P(F) 0.20

The probability that a defective ball bearing was manufactured on a Friday = P(F|M)

P(F|M) = P(F n M) ÷ P(M)

P(F n M) = P(M n F)

P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)

We can obtain each of these probabilities by using the expression for conditional probability.

P(Mo n M) = P(M|Mo) × P(Mo) = 0.08 × 0.20 = 0.016

P(T n M) = P(M|T) × P(T) = 0.04 × 0.20 = 0.008

P(W n M) = P(M|W) × P(W) = 0.04 × 0.20 = 0.008

P(Th n M) = P(M|Th) × P(Th) = 0.04 × 0.20 = 0.008

P(F n M) = P(M|F) × P(F) = 0.12 × 0.20 = 0.024

P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)

P(M) = 0.016 + 0.008 + 0.008 + 0 008 + 0.024 = 0.064

P(F|M) = P(F n M) ÷ P(M)

P(F n M) = P(M n F) = 0.024

P(M) = 0.064

P(F|M) = P(F n M) ÷ P(M) = (0.024/0.064) = 0.375

Hope this Helps!

4 0

1 year ago

People are arriving at a party one at a time. While waiting for more people to arrive they entertain themselves by comparing the

Marina CMI [18]

Answer:

=(k−1)*P(X>k−1) or (k−1)365k(365k−1)(k−1)!

Step-by-step explanation:

First of all, we need to find PMF

Let X = k represent the case in which there is no birthday match within (k-1) people

However, there is a birthday match when kth person arrives

Hence, there is 365^k possibilities in birthday arrangements

Supposing (k-1) dates are placed on specific days in a year

Pick one of k-1 of them & make it the date of the kth person that arrives, then:

The CDF is P(X≤k)=(1−(365k)k)/!365k, so the can obtain the PMF by

P(X=k) =P (X≤k) − P(X≤k−1)=(1−(365k)k!/365^k)−(1−(365k−1)(k−1)!/365^(k−1))=

(k−1)/365^k * (365k−1) * (k−1)!

=(k−1)*(1−P(X≤k−1))

=(k−1)*P(X>k−1)

6 0

2 years ago

Luke has 1/5 of a package of dried apricots. He divides the dried apricots equally into 4 small bags. Luke gives one of the bags

Ivahew [28]

Answer:

3/80

Step-by-step explanation:

If one fifth of apricots are split into 4 parts, each bag has 1/5 * 1/4 of the original apricots

1/5 * 1/4 = 1/20

Luke keeps 3/4 of those so that's

3/4 * 1/20 = 3/80

7 0

1 year ago