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2 years ago

When a die is rolled what is the probability of rolling a 2 or a 5?

Mathematics

2 answers:

Travka [436]2 years ago

4 0

$\dfrac{1}{6}+\dfrac{1}{6}=\dfrac{2}{6}=\dfrac{1}{3}$

Elis [28]2 years ago

4 0

1/3 because there is a 1/6 chance of getting any number. So 1/6 + 1/6 = 2/6 which is simplified to 1/3

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Solve for x:a(a²+b²)x²+b²x-a

m_a_m_a [10]

Answer:

x = a/(a² + b²) or x = -1/a

Step-by-step explanation:

a(a²+ b²)x² + b²x - a =0

Use the quadratic equation formula:

$x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} =\dfrac{-b\pm\sqrt{D}}{2a}$

1. Evaluate the discriminant D

D = b² - 4ac = b⁴ - 4a(a² + b²)(-a) = b⁴ + 4a⁴ + 4a²b² = (b² + 2a²)²

2. Solve for x

$\begin{array}{rcl}x & = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-b^{2}\pm\sqrt{(b^{2}+2a^{2})^{2}}}{2a(a^{2} + b^{2})}\\\\ & = & \dfrac{-b^{2}\pm(b^{2}+ 2a^{2})}{2a(a^{2} + b^{2})}\\\\x = \dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}\\\\x =\dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\\end{array}$

$\begin{array}{rcl}x = \large \boxed{\mathbf{\dfrac{a}{a^{2} + b^{2}}}}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2b^{2}- 2a^{2}}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2(a^{2}+ b^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\large \boxed{\mathbf{-\dfrac{1}{a}}}\\\\\end{array}$

5 0

3 years ago

4. A boat sails east for 35 miles and then turns to sail 10 miles south. What is the distance of the boat from its ending point

Elden [556K]

Answer:

36.4mi

Step-by-step explanation:

The boat sailed two legs of a right-angled triangle.

The distance from the starting point is the hypotenuse of the triangle.

d = √(35² + 10²)

= √(1225 + 100)

= √1325

= 36.4 mi

5 0

2 years ago

Help Please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Kamila [148]

Answer:

x = 80°

Step-by-step explanation:

Angle on a straight line = 180°

(x + 40)° + (x - 20)° = 180°

x + 40° + x - 20° = 180°

2x + 20° = 180°

2x = 180° - 20°

2x = 160°

x = 160°/2

x = 80°

Check:

(x + 40)° + (x - 20)° = 180°

(80° + 40°) + (80° - 20°) = 180°

120° + 60° = 180°

180° = 180°

3 0

2 years ago

The product of two consecutive even numbers is 224. What are these two numbers?

Stells [14]

Answer:

14 and 16

Step-by-step explanation:

They are the ONLY consecutive even numbers

And also

x and (x+2)

x(x+2)=224 ( product of a number and the consecutive of that number)

x ²+ 2x-224=0

(x+16)(x-14) =0

x=-16 or 14

In this case 14 and (14+2) 14 and 16

The integers are either 14 and 16 or -14 and -16.

4 0

2 years ago

What has been your biggest learning for this year?

Elena-2011 [213]

Answer: my biggest learning is for this year is how bill of rights works

Step-by-step explanation:

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2 years ago