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3 years ago

Mark rolls a fair dice 48 times. How many times would Mark expect to roll a one?

Mathematics

1 answer:

Free_Kalibri [48]3 years ago

3 0

Answer:

8 Times, Mark would expect to roll a one 'Eight times'

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Solve (x + 3)2 + (x + 3) – 2 = 0. Let u = Rewrite the equation in terms of u. (u2 + 3) + u – 2 = 0 u2 + u – 2 = 0 (u2 + 9) + u –

Verdich [7]

Answer:

The solutions of the original equation are x=-5 and x=-2

Step-by-step explanation:

we have

$(x+3)^2+(x+3)-2=0$

Let

$u=(x+3)$

Rewrite the equation

$(u)^2+(u)-2=0$

Complete the square

$u^2+u=2$

$u^2+u+1/4=2+1/4$

$u^2+u+1/4=9/4$

rewrite as perfect squares

$(u+1/2)^2=9/4$

square root both sides

$(u+1/2)=\pm\frac{3}{2}$

$u=(-1/2)\pm\frac{3}{2}$

$u=(-1/2)+\frac{3}{2}=1$

$u=(-1/2)-\frac{3}{2}=-2$

the solutions are

u=-2,u=1

Alternative Method

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

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

in this problem we have

$(u)^2+(u)-2=0$

$a=1\\b=1\\c=-2$

substitute in the formula

$u=\frac{-1\pm\sqrt{1^{2}-4(1)(-2)}} {2(1)}$

$u=\frac{-1\pm\sqrt{9}} {2}$

$u=\frac{-1\pm3} {2}$

$u=\frac{-1+3} {2}=1$

$u=\frac{-1-3} {2}=-2$

the solutions are

u=-2,u=1

Find the solutions of the original equation

For u=-2

$-2=(x+3)$ ----> $x=-2-3=-5$

For u=1

$1=(x+3)$ ----> $x=1-3=-2$

therefore

The solutions of the original equation are

x=-5 and x=-2

4 0

4 years ago

Read 2 more answers

Please help with these questions and show how u found them i will mark you brainliest

nata0808 [166]

Answer:

5(x+8)

5x+8x

5x+40

6q+2+3q+5

9q+7

8 0

3 years ago

Read 2 more answers

In a science test. Devi scores 16 marks more than Ali. lf

sergeinik [125]

Let the marks of Devi be x and Ali be y.

So, the equations:

2y = x and y + 16 = x

So,

2y = y + 16. [ because we know equals are equal to equals]

=> 2y - y = 16

=> y = 16

Check

Ali's marks are half of Devi's marks.

Devi's marks are 16 more than alis.

So, Devi's marks will be 16×2 = 32 and 32 is 16 greater than 16 (16+16=32).

3 0

3 years ago

(7-3)x(9-2)= what I am stuck help me

natka813 [3]

7-3=4
9-2=7
4x7=28
Use PEMDAS for order of operations, it will save your life
Parenthesis Exponents Multiply Divide Add Subtract
Multiply and Divide and Add and Subtract can be switched around with each other, but multiply and divide always happens before add and subtract. The reason you add first here is because it is in the parenthesis.

3 0

4 years ago

2(3x−5a)+9(2a−7b)+3(5a−2x)=0

alexdok [17]

Answer:

a=63b/23, b=23a/63

7 0

3 years ago