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Rus_ich [418]
3 years ago
7

A+3a-4(9-a) what is the answer please

Mathematics
2 answers:
oksano4ka [1.4K]3 years ago
8 0

Answer:

a + 3a - 4(9 - a) \\ 4a - 36 + 4a \\ collecting \: like \: terms \:  \\ 4a +4a - 36 \\ 8a - 36

Step-by-step explanation:

please mark me brainliest

Juli2301 [7.4K]3 years ago
5 0

Step-by-step explanation:

=3a+a-36+4a

=4a+4a-36

=8a-36

=4(2a-9)

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Find the estimated monthly payment for the following simple interest loan. Round your answer to the nearest dollar.
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Answer:

$184

Step-by-step explanation:

I looked at an APR calculator

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3 years ago
Determine whether the quadrilateral is a parallelogram justify your answer.
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Step-by-step explanation:

Yes, it is a parallelogram because the opposite angles are congruent

Option C

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3 years ago
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Consider the following differential equation. x^2y' + xy = 3 (a) Show that every member of the family of functions y = (3ln(x) +
Veronika [31]

Answer:

Verified

y(x) = \frac{3Ln(x) + 3}{x}

y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{x}

Step-by-step explanation:

Question:-

- We are given the following non-homogeneous ODE as follows:

                           x^2y' +xy = 3

- A general solution to the above ODE is also given as:

                          y = \frac{3Ln(x) + C  }{x}

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.

Solution:-

- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

                          y' = \frac{\frac{d}{dx}( 3Ln(x) + C ) . x - ( 3Ln(x) + C ) . \frac{d}{dx} (x)  }{x^2} \\\\y' = \frac{\frac{3}{x}.x - ( 3Ln(x) + C ).(1)}{x^2} \\\\y' = - \frac{3Ln(x) + C - 3}{x^2}

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

                          -\frac{3Ln(x) + C - 3}{x^2}.x^2 + \frac{3Ln(x) + C}{x}.x = 3\\\\-3Ln(x) - C + 3 + 3Ln(x) + C= 3\\\\3 = 3

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.

- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

                         y( 1 ) = \frac{3Ln(1) + C }{1} = 3\\\\0 + C = 3, C = 3

- Therefore, the complete solution to the given ODE can be expressed as:

                        y ( x ) = \frac{3Ln(x) + 3 }{x}

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

                         y(3) = \frac{3Ln(3) + C}{3} = 1\\\\y(3) = 3Ln(3) + C = 3\\\\C = 3 - 3Ln(3)

- Therefore, the complete solution to the given ODE can be expressed as:

                        y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{y}

                           

Download docx
6 0
3 years ago
You have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 100 dollars gi
Flauer [41]

Answer: 75 < x < 125.

Step-by-step explanation:

Let x be the amount of money in your wallet.  

The phrase "100 dollars give or take 25" means wallet can have money between (100-25) dollars and (100+25) dollars.

i.e. 100-25 < x < 100+25

⇒ 75 < x < 125.

That means the amount of money in your wallet lies between 75 dollars and 125 dollars.

Hence, the inequality to describe the amount of money in your wallet is 75 < x < 125.

6 0
3 years ago
a machine made 2 2/6 pencils in 3 3/4 minutes. how many pencils would the machine have made after/minute
erma4kov [3.2K]

<em><u>Question:</u></em>

A machine made 2 2/6 pencils in 3 3/4 minutes. How many pencils would the machine have made after 9 minutes?

<em><u>Answer:</u></em>

\frac{504}{90}\ or\ 5.6 pencils is made after 9 minutes

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

Given that,

A machine made 2 2/6 pencils in 3 3/4 minutes

Which means,

2\frac{2}{6} = \frac{14}{6}

3\frac{3}{4} = \frac{15}{4}

Let "x" be the number of pencils made in 9 minutes

Therefore,

\frac{14}{6}\ pencils = \frac{15}{4}\ minutes\\\\x\ pencil = 9\ minutes

This forms a proportion and we can solve by cross multiplying

\frac{14}{6} \times 9 = \frac{15}{4} \times x\\\\x = \frac{14}{6} \times 9 \times \frac{4}{15}\\\\x = \frac{504}{90}\\\\x = 5.6

Thus, \frac{504}{90}\ or\ 5.6 pencils is made after 9 minutes

7 0
3 years ago
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