The decimal 0.4444 is an example of what kind of number

Write the quadratic equation whose roots are six and -2 and who’s leading coefficient is 3 use the letter X to represent the var

Artist 52 [7]

Answer:

$3X^{2} - 12X - 36 = 0$

Step-by-step explanation:

6 and - 2 are the only two solutions to the required quadratic equation.

So, if the variable is represented by X then (X - 6) and (X + 2) will be the only two factors of the polynomial function.

Therefore, the equation is

(X - 6)(X + 2) = 0

⇒ $X^{2} - 4X - 12 = 0$

If the leading coefficient of the equation is 3 then we can write the equation as $3X^{2} - 12X - 36 = 0$ (Answer)

6 0

3 years ago

Sam's closet contains blue and green shirts. He has eight blue shirts, and seven green shirts. Five of the blue shirts have stri

Bas_tet [7]

Answer: The answer is 80%.

Step-by-step explanation: Let us define the following events.

B = the event that the shirt is blue,

G = the event that the shirt is green

and

S = the event that the shirt is striped.

So, n(B) = 8, n(G) = 7, n(B and S) = 5, n(G and S) = 4.

n(S) = 5 + 4 = 9.

We have

$n(B\cup S)=n(B)+n(S)-n(B\cap S)=8+9-5=12.$

Therefore, the required probability is

$p=\dfrac{n(B\cup S)}{8+7}=\dfrac{12}{15}=\dfrac{4}{5}=0.8=80\%.$

Thus, the answer is 80%.

3 0

2 years ago

What is the solution to this system of equations?

Maurinko [17]

Answer:

(x, y) = (5, -2)

Step-by-step explanation:

A graphing calculator provides a quick and easy way to find the solution.

_____

There are several other ways to solve these equations. Or you can estimate where the answer might be using logic like this:

The intercepts of the first equation are ...

x-intercept = 26/4 = 6 1/2
y-intercept = -26/3 = -8 2/3

So the graph of it will form a triangle with the axes in the 4th quadrant.

The intercepts of the second equation are ...

x-intercept = 11/3 = 3 2/3
y-intercept = 11/2 = 5 1/2

So the graph of it will form a triangle with the axes in the 1st quadrant. The x-intercept of this one is less than the x-intercept of the first equation, so the two lines must cross in the 4th quadrant.

The only 4th-quadrant answer choice is (5, -2).

3 0

3 years ago

Find the distance between the complex numbers. z1 = 9 - 9i z2 = 10 - 9i

steposvetlana [31]

Answer:

The distance between the two given complex numbers = 9

Step-by-step explanation:

Explanation:-

Step(i):-

Given Z₁ = 9 - 9 i and Z₂ = 10 -9 i

Let A and B represent complex numbers Z₁ and Z₂ respectively on the argand plane

⇒ A = Z₁ = x₁ +i y₁ = 9 - 9 i and

B = Z₂ = x₂+ i y₂ = 10 -9 i

Let (x₁ , y₁) = ( 9, -9)

(x₂, y₂) = (10, -9)

Step(ii):-

The distance between the two points are

A B = $\sqrt{(x_{2} - x_{1})^{2}+(y_{2} - y_{1})^{2} }$

A B = $\sqrt{(10 - 1)^{2}+(-9 - (-9))^{2} }$

AB = $\sqrt{(9)^{2} +(-9+9)^{2} }$

AB = √81 = 9

Conclusion:-

The distance between the two given complex numbers = 9

3 0

2 years ago

An airplane climbs at an angle of 13 with the ground . What is the distance it has traveled when it has attained an altitude of

nevsk [136]

The distance traveled is the hypotenuse of the right triangle formed with the ground.

sinα=400/d

d=400/sinα, we are told α=13° so

d=400/sin13 ft

d≈1778ft (to nearest whole foot)

6 0

3 years ago