Points A, B, C, and D lie on circle M. Line segment BD is a diameter. The measure of arc CD equals the measure of arc DA.

What is the value of h(2)?<br> 0-2<br> 0-1<br> O 0<br> O 3

11111nata11111 [884]

Answer:

-16

Step-by-step explanation:

3 0

3 years ago

Two airplanes are flying in the air at the same height: airplane A is flying east at 250 mi/h and airplane B is flying north at

just olya [345]

Answer:

decreasing at 390 miles per hour

Step-by-step explanation:

Airplane A's distance in miles to the airport can be written as ...

a = 30 -250t . . . . . where t is in hours

Likewise, airplane B's distance to the airport can be written as ...

b = 40 -300t

The distance (d) between the airplanes can be found using the Pythagorean theorem:

d^2 = a^2 + b^2

Differentiating with respect to time, we have ...

2d·d' = 2a·a' +2b·b'

d' = (a·a' +b·b')/d

__

To find a numerical value of this, we need to find the values of its variables at t=0.

a = 30 -250·0 = 30

a' = -250

b = 40 -300·0 = 40

b' = -300

d = √(a²+b²) = √(900+1600) = 50

Then ...

d' = (30(-250) +40(-300))/50 = -19500/50 = -390

The distance between the airplanes is decreasing at 390 miles per hour.

3 0

3 years ago

According to the Complex Conjugate Root Theorem, if a+bi is a root of a quadratic equation, then __blank__ is also a root of the

Trava [24]

Answer:

a-bi

Step-by-step explanation:

If a quadratic equation lx^2+mx+n=0 has one imaginary root as a+bi then the other root is the conjugate of a+bi = a-bi

Because we have l, m and n are real numbers and they are the coefficients.

Sum of roots = a+bi + second root = -m/l

When -m/l is real because the ratio of two real numbers, left side also has to be real.

Since bi is one imaginary term already there other root should have -bi in it so that the sum becomes real.

i.e. other root will be of the form c-bi for some real c.

Now product of roots = (a+bi)(c-bi) = n/l

Since right side is real, left side also must be real.

i.e.imaginary part =0

bi(a-c) =0

Or a =c

i.e. other root c-bi = a-bi

Hence proved.

3 0

3 years ago

Given the following functions f(x) and g(x), solve (f + g)(5) and select the correct answer below: f(x)=2x^2-10 g(x)=x+9

steposvetlana [31]

Answer:

$\large\boxed{(f+g)(5)=54}$

Step-by-step explanation:

$f(x)=2x^2-10,\ g(x)=x+9\\\\(f+g)(x)=f(x)+g(x)\\\\\text{Substitute:}\\\\(f+g)(x)=(2x^2-10)+(x+9)=2x^2-10+x+9=2x^2+x+(-10+9)\\\\(f+g)(x)=2x^2+x-1\\\\(f+g)(x)(5)\to\text{put x = 5 to the equation of the function:}\\\\(f+g)(5)=2(5^2)+5-1=2(25)+5-1=50+5-1=54$

8 0

3 years ago

On any given day, the probability that a large local river is polluted by carbon tetrachloride is 0.12. Each day, a test is cond

babymother [125]

Answer:

a) 0.2416

b) 0.4172

c) 0.0253

Step-by-step explanation:

Since the result of the test should be independent of the time , then the that the test number of times that test proves correct is independent of the days the river is correct .

denoting event a A=the test proves correct and B=the river is polluted

a) the test indicates pollution when

- the river is polluted and the test is correct

- the river is not polluted and the test fails

then

P(test indicates pollution)= P(A)*P(B)+ (1-P(A))*(1-P(B)) = 0.12*0.84+0.88*0.16 = 0.2416

b) according to Bayes

P(A∩B)= P(A/B)*P(B) → P(A/B)=P(A∩B)/P(B)

then

P(pollution exists/test indicates pollution)=P(A∩B)/P(B) = 0.84*0.12 / 0.2416 = 0.4172

c) since

P(test indicates no pollution)= P(A)*(1-P(B))+ (1-P(A))*P(B) = 0.84*0.88+ 0.16*0.12 = 0.7584

the rate of false positives is

P(river is polluted/test indicates no pollution) = 0.12*0.16 / 0.7584 = 0.0253

4 0

3 years ago