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2 years ago

7

You roll two number cubes. What is the probability of rolling double threes? The probability is

1 answer:

julsineya [31]2 years ago

6 0

Answer is 2/36 or 5.55...%

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(m+2)(m+3)=(m+2)(m-2) what is the answer please

Vika [28.1K]

$(m+2)(m+3)=(m+2)(m-2)\\\\m^2+3m+2m+6=m^2-4\\\\m^2-m^2+5m=-4-6\\\\5m=-10\ \ \ \ /:5\\\\m=-2$

5 0

3 years ago

Read 2 more answers

Help with 30 please. thanks.

Svet_ta [14]

Answer:

See Below.

Step-by-step explanation:

We have the equation:

$\displaystyle y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}$

And we want to show that:

$\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}$

Instead of differentiating directly, we can first square both sides:

$\displaystyle y^2 = 3e^{2x} -4x + 1$

We can find the first derivative through implicit differentiation:

$\displaystyle 2y \frac{dy}{dx} = 6e^{2x} -4$

Hence:

$\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}$

And we can find the second derivative by using the quotient rule:

$\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}$

Substitute:

$\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}$

Combine fractions:

$\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}$

Simplify:

$6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}$

Q.E.D.

6 0

2 years ago

Simplify the expression. 9r 3r2 – 5r 7

Ksenya-84 [330]

Your final answer is going to be 4r + 3r ^2 +7

7 0

2 years ago

Read 2 more answers

What is the slope of the line that passes through the points (1,7) and (-4,-8)?

Aleksandr [31]

Answer:

D. 3

Step-by-step explanation:

To find the slope of a line, we can use the equation y2-y1/x2-x1=m or slope.

All we can do now is insert the values of the points into the equation.

-8-7/-4-1=m

-15/-5=m

3=m

Thus, the slope is 3.

Hope this helps!

5 0

2 years ago

Read 2 more answers

The height of the plant is given by the equation h = 0.5d + 4. Rewrite this as a function rule where f(x) is the height, in cent

ad-work [718]

Answer:

Here's what I get

Step-by-step explanation:

h = 0.5d + 4

A function rule tells you how to convert an input value (x) into an output value (y).

Your function rule is

ƒ(x) = 0.5x + 4

An easy way to represent your function is to make a graph.

The easiest way to make a graph is to make a table containing some inputs and their corresponding outputs.

Here's a typical table.

$\begin{array}{cc}\textbf{x} &\textbf{y} \\0 & 4 \\2 & 5 \\4 & 6 \\6 & 7\\6 & 8 \\\end{array}$

The graph is like the one below.

4 0

2 years ago