Find the axis of symmetry for the equation in vertex form. y=(x+2)^2+1

B2+10b+25/b29-9 . B+3/B+5

SCORPION-xisa [38]

b4 + b3 - 45b2 - 27b + 25 ————————————————————————— b2

7 0

3 years ago

Read 2 more answers

X+y+z =4

cestrela7 [59]

Akar akar persamaan kuadrat 2x² - 3x -1 = 0 adalah x1 dan x2. Persamaan kuadrat baru yang akar akarnya satu lebih kecil dari dua kali akar akar persamaan kuadrat di atas adalah ........A.x² - x - 4 = 0B.x² + 5x - 4 = 0C.x² - x + 4 = 0D.x² + x + 4 = 0E.x² - 5x - 4 = 0Jawaban : A
Penyelesaian :
Akar-akar persamaan lama : x1 dan x2

Akar-akar persamaan baru : xA dan xB
 xA = 2x1 - 1
 xB = 2x2 - 1
 xA + xB = (2x1 - 1) + (2x2 - 1)
 = 2 (x1 + x2) - 2
 = 2 () - 2
 = 3 - 2
 xA + xB = 1

 xA . xB = (2x1 - 1) (2x2 - 1)
 = 4 x1.x2 - 2(x1 + x2) + 1
 = 4.(-) - 2() + 1
 = -2 - 3 + 1
 xA . xB = -4

Jadi persamaan kuadrat baru : x² - (xA + xB)x + xA . xB = 0
 x² - x - 4 = 0

4 0

3 years ago

The area of a circular oil slick on the surface of the sea is increasing at a rate of [150m^2/s] how fast is the radius changing

Akimi4 [234]

Answer with Step-by-step explanation:

We are given that

$\frac{dA}{dt}=150m^2/s$

a.Radius =25 m

We have to find rate of change of radius.

We know that

Area of circle, $A=\pi r^2$

Differentiate w.r.t time

$\frac{dA}{dt}=2\pi r\frac{dr}{dt}$

Substitute the values then we get

$150=2\pi (25)\frac{dr}{dt}$

$\frac{dr}{dt}=\frac{150}{50\pi}=\frac{3}{\pi} m/s$

$\frac{dr}{dt}=\frac{3}{\pi} m/s$

b.A= $1000m^2$

Substitute the values then we get

$1000=\pi r^2$

$\pi=3.14$

$r^2=\frac{1000}{3.14}$

$r=\sqrt{\frac{1000}{3.14}}=17.8m$

$\frac{dA}{dr}=2\pi r\frac{dr}{dt}$

Substitute the values then we get

$150=2\pi(17.8)\frac{dr}{dt}$

$\frac{dr}{dt}=\frac{150}{2\pi(17.8)}=\frac{150}{35.6\pi}$ m/s

$\frac{dr}{dt}=\frac{75}{17.8\pi}$ m/s

4 0

3 years ago

About 1/4 of all adults in the United States have type O+ blood. If three randomly selected adults donate blood, find the probab

valina [46]

Answer:

a) 0.0156

b) 0.4219

c) 0.1406

Step-by-step explanation:

We are given the following information:

We treat adult having type O+ blood as a success.

P(Adult have type O+ blood) = 0.25

Then the number of adults follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 3

a) All three are type O+

$P(x =3)\\= \binom{3}{3}(0.25)^3(1-0.25)^0\\= 0.0156$

b) None of them is type O+

$P(x =0)\\= \binom{3}{0}(0.25)^0(1-0.25)^3\\= 0.4219$

c) Two out of the three are type O

$P(x =2)\\= \binom{3}{2}(0.25)^2(1-0.25)^1\\= 0.1406$

6 0

3 years ago

Please help me solve these are quadratic equations: I

julia-pushkina [17]

Answer:

$\boxed {\boxed {\sf a= 3, b=7, c=2}}$

$\boxed {\boxed {\sf Y-intercept = c }}$

$\boxed {\boxed {\sf Minimum}}$

Step-by-step explanation:

a. a, b, c

Quadratic equations in standard form are written as:

$f(x)= ax^2+bx+c$

The exponents are listed from greatest to least. The quadratic is already in this form, so match up the variables and values in the equation.

$f(x)= 3x^2+7x+2$

$a=3 \\b=7 \\c=2$

b. Y-intercept

The y-intercept for a quadratic is c.

You can also substitute 0 in for x, because the y-intercept occurs when the quadratic crosses the y-axis (at x=0).

$f(0)= 3(0)^2+7(0)+2$

$f(0)=3(0)+7(0)+2\\f(0)= 0+0+2\\f(0)=2$

We know that c=2, so the y-intercept is c.

c. Maximum/minimum

The entire quadratic is positive, so the quadratic opens up and has a minimum.

8 0

3 years ago