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3 years ago

Write an expression that is equivalent to (3b+6) + 2

Mathematics

2 answers:

saw5 [17]3 years ago

8 0

You can just add the 2, and you have a new expression:
$(3b+6)+2 = 3b+8$

That's your answer!

cluponka [151]3 years ago

3 0

Since you're not multiplying, you can remove the parentheses.

3b+6+2

which gives you . ....

3b+8

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Show work please~

love history [14]

For every 1 cup of blue paint, $\frac{10}{4}$ cups of red paint are needed

For every 1 cup of red paint, $\frac{4}{10}$ cup of blue paint is needed

For every 4 cups of red paint, $\frac{16}{10}$ cups of blue paint are needed

<em><u>Solution:</u></em>

Given that, there are 3 1/3 red cups of paint for every 1 1/3 cups of blue paint

Therefore, ratio is

$Red : blue = 3\frac{1}{3} : 1\frac{1}{3}\\\\Red : blue = \frac{10}{3} : \frac{4}{3}$

<h3><u>For every 1 cup of blue paint, ___ cups of red paint are needed</u></h3>

Let "x" be the cups of red paint needed

Then we get,

$\frac{10}{3} : \frac{4}{3}\\\\x : 1$

This forms a proportion

$1 \times \frac{10}{3} = \frac{4}{3} \times x\\\\x = \frac{10}{4}$

Therefore, 10/4 cups of red are needed for 1 cup of blue

<h3><u>For every 1 cup of red paint, ___ cup of blue paint is needed</u></h3>

Let "x" be the cups of blue paint needed

Then, we get

$\frac{10}{3} : \frac{4}{3}\\\\1 : x$

This forms a proportion

$\frac{10}{3} \times x = \frac{4}{3} \times 1\\\\x = \frac{4}{10}$

Thus, 4/10 cups of blue are needed for 1 cup of red paint

<h3><u>For every 4 cups of red paint,___ cups of blue paint are needed</u></h3>

Let "x" be the cups of blue paint needed

Then, we get

$\frac{10}{3} : \frac{4}{3}\\\\4 : x$

This forms a proportion

$\frac{10}{3} \times x = \frac{4}{3} \times 4\\\\x = \frac{16}{10}$

Thus 16/10 cups of blue paint are needed for every 4 cups of red paint

5 0

3 years ago

Use the discriminant to determine the number and type of solutions the equation has.

White raven [17]

$x^2 + 8x + 12 = 0\\ \\a=1 , b= 8, c= 12 \\ \\ \Delta =b^2-4ac = 8^2 -4\cdot1\cdot12= 64-48= 16\\ \\\Delta > 0 \\ \\ Answer : \ C. \ \ two \ rational \ solutions$

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3 years ago

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3. A rumour is being spread in a community that the president is going to retire before the next election 2015. Initially 2 peop

Vera_Pavlovna [14]

Answer:

I'm not sure if that's what is meant cuz the text is a little ambiguous

Nevertheless, 62 people

Step-by-step explanation:

Amount = 2 + 4 + 8 + 16 + 32 =62 people

"Exponential Growth"

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3 years ago

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A particle moving in a planar force field has a position vector x that satisfies x'=Ax. The 2×2 matrix A has eigenvalues 4 and 2

andrey2020 [161]

Answer:

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

Step-by-step explanation:

Consider the provided matrix.

$v_1=\begin{bmatrix}-3\\1 \end{bmatrix}$

$v_2=\begin{bmatrix}-1\\1 \end{bmatrix}$

$\lambda_1=4, \lambda_2=2$

The general solution of the equation $x'=Ax$

$x(t)=c_1v_1e^{\lambda_1t}+c_2v_2e^{\lambda_2t}$

Substitute the respective values we get:

$x(t)=c_1\begin{bmatrix}-3\\1 \end{bmatrix}e^{4t}+c_2\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-3c_1e^{4t}-c_2e^{2t}\\c_1e^{4t}+c_2e^{2t} \end{bmatrix}$

Substitute initial condition $x(0)=\begin{bmatrix}-6\\1 \end{bmatrix}$

$\begin{bmatrix}-3c_1-c_2\\c_1+c_2 \end{bmatrix}=\begin{bmatrix}-6\\1 \end{bmatrix}$

Reduce matrix to reduced row echelon form.

$\begin{bmatrix} 1& 0 & \frac{5}{2}\\ 0& 1 & \frac{-3}{2}\end{bmatrix}$

Therefore, $c_1=2.5,c_2=1.5$

Thus, the general solution of the equation $x'=Ax$

$x(t)=2.5\begin{bmatrix}-3\\1\end{bmatrix}e^{4t}-1.5\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

6 0

3 years ago

10. Name the one example of Analog computer

BartSMP [9]

Answer:

example of Analog computer=

Operational amplifiers

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3 years ago

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